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44

Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

Dec 07, 2014

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Now Ex-IB Examiner's Online or face to face Help: +91 9911918255 or +91 9716570693 Email: [email protected] Website: http://www.topclassibtutors.com/ Online Help/Tuition all over the world; Mail us or call us for any queries:

MATHEMATICS
Higher Level
The portfolio – IA tasks
For use in 2012 and 2013
SHADOW FUNCTIONS HL TYPE I

While real zeros of polynomial functions may be easily read off the graph of the
polynomial, the same is not true for complex zeros. In this task, you will investigate the
method of shadow functions and their generators, which helps identify the real and
imaginary components of complex zeros from key points along the x-axis.
Part A (Quadratic Polynomials)
Consider the quadratic function 2 2
Write down the coordinates of the vertex.
Show that 1 y has zeros, where.

_ How can the findings with quadratics and cubics be applied to quartics?
PATTERNS FROM COMPLEX NUMBERS HL TYPE I
To the student: The work that you produce to address the questions in this task should be a report
that can stand on its own. It is best to avoid copying the questions in the task to adopt a “question
and answer” format.

THE DICE GAME HL Type II
To the student: The work that you produce to address the questions in this task should be a report
that can stand on its own. It is best to avoid copying the questions in the task to adopt a “question
and answer” format.
The aim of this task is to create a dice game in a casino and model this using
probability. It is important to examine how best to run the game from both the
perspective of a player and the casino. In doing so analyse the game to consider the
optimal payments by the player and payouts by the casino.
_ Consider a game with two players, Ann and Bob. Ann has a red die and Bob a white die.

_ Now consider other models for the game including cases such as where the player or the
bank rolls their dice multiple times, or where multiple players are involved in the game.
FILLING UP THE PETROL TANK HL Type II
To the student: The work that you produce to address the questions in this task should be a report
that can stand on its own. It is best to avoid copying the questions in the task to adopt a “question
and answer” format.
In this task, you will develop a mathematical model that helps motorists decide which of
the following two options is more economical.
Option 1: to buy petrol from a station on their normal route at a relatively higher price.
Option 2: to drive an extra distance out of their normal route to buy cheaper petrol.
Consider a situation in which two motorists, Arwa and Bao, share the same driving route but own
different sized vehicles. Arwa fills up her vehicle’s tank at a station along her normal route for
US$ 1 p per litre. On the other hand, Bao drives an extra d kilometres out of his normal route to fill
up his vehicle’s tank for US$ p2 per litre where p2 _ p1 .
Please feel free to contact us for help in ib dp hl sl mat
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Page 1: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

Now Ex-IB Examiners Online or face to face Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website httpwwwtopclassibtutorscom Online HelpTuition all over the world Mail us or call us for any queries

Face to face help all over Delhi Gurgaon Noida Mumbai Bangalore Hyderabad Kolkata Jaipur Ahmedabad Vadodara Pune etc

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Aali Isa Town Sitra Budaiya Jidhafs Al-Malikiyah Adliya Bahrain Doha Ar Rayyān Umm Şalāl Muḩammad Al Wakrah Al Khawr Ash Shaḩānīyah Dukhān Al Wukayr Ar Ruays Umm Bāb Qatar as-Salimiyah Jalib as-Suyuh Kuwait City Istanbul Ankara Izmir Bursa Adana Gaziantep Konya Antalya Mersin Kayseri Eskisehir Urfa Malatya Erzurum Samsun Turkey Cairo Alexandria Sharm el Sheikh Hurghada Marina Bur (Port) Said Ismailia Aswan Giza Luxor Egypt Baghdad Mosul Basrah Iraq Sanaa Aden Hodiedah Taiz Mukalla Yemen Aleppo Damascus Jaramana Duma Idlib Tartus Manbij Salamiyah Abu Kamal Jablah Darayya Nawa Baniyas Masyaf Qatana Syria Jerusalem West Jerusalem Haifa Tel Aviv Ashdod Rishon LeẔiyyon Petah Tikva Beersheba Netanya HE olon Israel Zarga Irbid Ramtha Aqaba Madaba Salt Karak Jerash Amman Jordan Aanjar Baalbeck Beiteddine Byblos The Cedars Eshmoun Sidon Tripoli Tyre Zahle Lebanon Gaza Jerusalem (PAL) Hebron Jabaliyah Nablus Rafah Ramallah Jericho Al Bireh Khan Yunus Bethlehem Tulkarm Jenin Palestinian territories Pakistan Islamabad Karachi Lahore Larnaca Lemesos Gazimagusa Nicosia Paphos Girne Guzelyurt Aradippou Paralimni Lefka Geri Ypsonas Livadia Dromolaxia Dipkarpaz Cyprus Canberra Melbourne Brisbane Adelaide Hobart Perth Darwin Cairns Central Coast Gold Coast Northern Territory Sunshine Coast Tasmania Townsville Wollongong Alice Spring Australia Argentina Buenos Aries Cordoba La Plata May del Plata Mendoza Rosario San Miguel de Tucuman San Carlos de Bariloche Bangladesh Dhaka Chittagong Somapuri Vihara Belgium Brussels Brugge Antwerp and Ghent Brazil Brasilia Rio de Janeiro Manaus Salvador Recife China Macao Shenyang QINGHUANGDAO SHENZHEN CHANGCHUN LHASA

KUNMING SANYA HARBIN TIANJIN URUMQI CHENGDU CHONGQING GUANGZHOU QINGDAO NANJING HANGZHOU XIAN Denmark Copenhagen Arhus Odense Aalborg Esbjerg Greece Athens Peloponnese Cyclades Crete Hungary Budapest Peacutecs Szeged Sopron Debrecen Indonesia Jakarta Makassar Medan Banda Aceh Surabaya Bandung Denpasar Ireland Dublin Cork Limerick Kilkenny Galway Waterford Wexford Sligo Kenmare Tralee Italy Rome Venice Florence Milan Naples Verona Turin Bologna Perugia Genova Japan Tokyo Yokohama Osaka Nagoya Sapporo Kobe Kyoto Fukuoka Kawasaki Saitama Hiroshima Sendai Kitakyushu Malaysia Kuala Lumpur Johor Bahru Ipoh Kuching Kuala Terengganu Kuantan Kota Bahru Seremban Georgetown Kota Kinabalu Sandakan Taiping Kajang-Sungai Chua Alor Setar Sibu Tawau Kluang Sungai Petani Miri Melaka Bandar Penggaram Mexico Mexico City Guadalajara Ecatepec Nezahualcoyotl Puebla Monterrey Tijuana Ciudad Juaacuterez Leon Zapopan Guadalupe Quereacutetaro Cuernavaca Tampico Veracruz Naucalpan Toluca Morelia Aguascalientes Netherlands Amsterdam Rotterdam Utrecht Den Haag(The Haugue) Eindhoven Tilburg Groningen Nijmegen Leiden Zwolle Venlo New Zealnd Auckland Hamilton Nelson Dunedin Napier Rotorua Taupo Tauranga Blenheim Invercargill Kaikoura Peru Lima (and Callao) Arequipa Trujillo Chiclayo Piura Iquitos Cusco Chimbote Huancayo Tacna Philippines Manila Cebu Baguio Boracay Palawan Albay Davao Zamboanga General Santos City Poland Cracow Gdansk Poznan Szczecin Warsaw

Wroclaw Poznari Tricity Russia Moscow Saint Petersburg Kazan Yekaterinburg Volgograd Irkutsk Vladivostok Nizhny Novgorod Saudi Arabia Abha Dhahran Jubail Qatif Al-Ahsa Hail Madinah Riyadh Al-khobar Jeddah Makkah Tabouk Baha Jizan Najran Taif Dammam Jouf Qassem Yanbu Singapore Bedok Seletar Woodlands Toa Payoh Ang Mo Kio Choa Chu Kang Tampines South Africa Alberton Benoni Cape Town Carltonville Durban East London Johannesburg Kimberley Klerksdorp Krugersdorp Mhluzi Midrand Msunduzi Newcastle Paarl Pretoria Soweto Port Elizabeth Spain Madrid Barcelona Valencia Sevilla Saragoza Malaga Zaragoza Murcia Palma de Mallorca Las Palmas Bilbao Switzerland Geneva Zuumlrich Bern Lausanne Base Luzern Thailand Phuket Chiang Rai Khon Kaen Chiang Mai Lampang Pak Kret Hat Yai Phitsanulok Trang Udon Thani Yala Samut Prakan Yala Songkhla Nakhon Pathom Surat Thani Ubon Ratchathani Nakhon Ratchasima Nonthabur Rayong Nakhon Sawan Nakhon Si Thammarat Nakhon Si Ayutthaya Bangkok Chiang Mai UAE Dubai Abu Dhabi Sharjah Al Ain Ajman UK Birmingham Bristol Edinburgh Glasgow Leeds Liverpool London Manchester United States New York Los Angeles California Chicago Ill Houston Tex Philadelphia Phoenix San Antonio San Diego Dallas San Jose Jacksonville Indianapolis San Francisco Austin Columbus Fort Worth Charlotte Detroit El Paso Memphis Baltimore Boston Seattle Washington DC Nashville-Davidson Denver Louisville-Jefferson Milwaukee Portland Las Vegas Oklahoma City Albuquerque Tucson Fresno Sacramento Long Beach Kansas City Mesa Virginia Beach Atlanta

Colorado Springs Omaha Nebr Raleigh NC Miami Fla Cleveland Ohio Tulsa Okla Oakland Calif Minneapolis Minn Wichita Kans Arlington Tex Vietnam Ho Chi Minh city Hanoi Hai Phong Da Nang Can Tho Nha Trang Hue Ha Long Da Lat Vung Tau Can Thi Sapa etc

Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc

MATHEMATICS Standard Level The portfolio ndash IA tasks

For use in 2012 and 2013

CIRCLES SL TYPE I Aim The aim of this task is to investigate positions of points in intersecting circles

The following diagram shows a circle with centre O and radius r and any point P 1 C

The circle has centre P and radius OP Let A be one of the points of intersection of and Circle has centre A and radius r The

point is the intersection of with (OP) This is shown in the diagram below

Let Use an analytic approach to find when and Describe what you notice and write a general statement to represent this Let Find when and Describe what you notice and write a general statement to represent this Comment whether or not this statement is consistent with your earlier statement Use technology to investigate other values of r and OP Find the general statement for OP Test the validity of your general statement by using different values of OP and r Discuss the scope andor limitations of the general statement

Explain how you arrived at the general statement

LACSAPrsquoS FRACTIONS SL TYPE I Aim In this task you will consider a set of numbers that are presented in a symmetrical pattern

Consider the five rows of numbers shown below

Describe how to find the numerator of the sixth row Using technology plot the relation between the row number n and the numerator in each row Describe what you notice from your plot and write a general statement to represent this Find the sixth and seventh rows Describe any patterns you used Let be the element in the nth row starting with Example Find the general statement for

Test the validity of the general statement by finding additional rows

Discuss the scope andor limitations of the general statement

Explain how you arrived at your general statement

FISH PRODUCTION SL TYPE II Aim This task considers commercial fishing in a particular country in two different environments ndash the sea and fish farms (aquaculture) The data is taken from the UN Statistics Division Common Database

The following table gives the total mass of fish caught in the sea in thousands of tonnes (1 tonne = 1000 kilograms)

Define suitable variables and discuss any parametersconstraints Using technology plot the data points from the table on a graph Comment on any apparent trends in your graph and suggest suitable models Analytically develop a model that fits the data points (You may find it useful to consider a combination of functions) On a new set of axes draw your model function and the original data points Comment on any differences Revise your model if necessary

The table below gives the total mass of fish in thousands of tonnes from fish farms

Plot the data points from this table on a graph and discuss whether your analytical model for the original data fits the new data

Use technology to find a suitable model for the new data On a new set of axes draw both models Discuss how trends in the first model could be explained by trends in the second model

By considering both models discuss possible future trends in both types of fishing

GOLD MEDAL HEIGHTS SL TYPE II Aim The aim of this task is to consider the winning height for the menrsquos high jump in the Olympic Games

The table below gives the height (in centimeters) achieved by the gold medalists at various Olympic Games

Note The Olympic Games were not held in 1940 and 1944 Using technology plot the data points on a graph Define all variables used and state any parameters clearly Discuss any possible constraints of the task What type of function models the behaviour of the graph Explain why you chose this function Analytically create an equation to model the data in the above table On a new set of axes draw your model function and the original graph Comment on any differences Discuss the limitations of your model Refine your model if necessary Use technology to find another function that models the data On a new set of axes draw both your model functions Comment on any differences Had the Games been held in 1940 and 1944 estimate what the winning heights would have been and justify your answers Use your model to predict the winning height in 1984 and in 2016 Comment on your answers

The following table gives the winning heights for all the other Olympic Games since 1896

How well does your model fit the additional data Discuss the overall trend from 1896 to 2008 with specific references to significant fluctuations

What modifications if any need to be made to your model to fit the new data

MATHEMATICSHigher LevelThe portfolio ndash IA tasks

For use in 2012 and 2013

SHADOW FUNCTIONS HL TYPE ITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatWhile real zeros of polynomial functions may be easily read off the graph of thepolynomial the same is not true for complex zeros In this task you will investigate themethod of shadow functions and their generators which helps identify the real andimaginary components of complex zeros from key points along the x-axisPart A (Quadratic Polynomials)

Consider the quadratic function 2 2Write down the coordinates of the vertexShow that 1 y has zeros whereThe ldquoshadow functionrdquo to 1 y is another quadratic 2 y which shares the same vertex asHowever 2 y has opposite concavity to that of 1 y and its zeros are in the form

Use various values for a and b to generate pairs of functions 1 y and

Hence or otherwise express 2 y in terms of 1 y and m y where m y is called the ldquoshadowgenerating functionrdquo_ On a labelled diagram illustrate how the zeros of 2 y may be helpful in the determination

of the real and imaginary components of the complex zeros of 1 y

Part B (Cubic Polynomials)Now consider the cubic function 1 _ _ _ _ y _ (x _ 2) x _ (3_ 2i) x _ (3_ 2i) The shadow function in this case is another cubic function 2 y which shares two points with 1 y has opposite concavity and its zeros are _2 and 3_ 2 as depicted in the figure below The shadow

generating function in this case passes through the two points of intersection

Write down an expression for 2 y and hence find the points of intersection between 1 y and 2 y

_ Hence or otherwise determine the equation of the shadow generating function m y in thiscase_ Once again express 2 y in terms of 1 y and m y Use technology to investigate similarcubic functions_ Write a general statement about the functions 1 y 2 y and m y and prove your statement_ On a labelled diagram illustrate how the zeros of 2 y may be helpful in the determinationof the real and imaginary components of the complex zeros of 1 y

_ How can the findings with quadratics and cubics be applied to quartics

PATTERNS FROM COMPLEX NUMBERS HL TYPE ITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo format

Part A

Use de Moivrersquos theorem to obtain solutions to the equation z3 _1 _ 0 _ Use graphing software to plot these roots on an Argand diagram as well as a unit circlewith centre origin_ Choose a root and draw line segments from this root to the other two roots

_ Measure these line segments and comment on your results_ Repeat the above for the equations z4 _1 _ 0 and z5 _1 _ 0 Comment on your results andtry to formulate a conjecture_ Factorize zn _1 for n _ 3 4 and 5_ Use graphing software to test your conjecture for some more values of n 1048576 __ and makemodifications to your conjecture if necessary_ Prove your conjecture

Part B

Use de Moivrersquos theorem to obtain solutions to zn _ i for n _ 3 4 and 5_ Use graphing software to represent each of these solutions on an Argand diagram_ Generalize and prove your results for zn _ a _ bi where a _ bi _1

_ What happens when a _ bi _1

THE DICE GAME HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatThe aim of this task is to create a dice game in a casino and model this usingprobability It is important to examine how best to run the game from both the

perspective of a player and the casino In doing so analyse the game to consider theoptimal payments by the player and payouts by the casino_ Consider a game with two players Ann and Bob Ann has a red die and Bob a white dieThey roll their dice and note the number on the upper face Ann wins if her score is higherthan Bobrsquos (note that Bob wins if the scores are the same) If both players roll their diceonce each what is the probability that Ann will win the game_ Now consider the same game where Ann can roll her die a second time and will note thehigher score of the two rolls but Bob rolls only once In this case what is the probabilitythat Ann will win_ Investigate the game when both players can roll their dice twice and also when bothplayers can roll their dice more than twice but not necessarily the same number of times_ Consider the game in a casino where the player has a red die and the bank has a white dieFind a model for a game so that the casino makes a reasonable profit in the case where theplayer rolls the red die once and the bank rolls the white die once (When creating yourmodel you will need to consider how much a player must pay to play a game and howmuch the bank will pay out if the player wins Do this from the perspective of both theplayer and the casino and consider carefully the criteria for whether the game can be

considered worthwhile for both the player and the casino)_ Now consider other models for the game including cases such as where the player or the

bank rolls their dice multiple times or where multiple players are involved in the game

FILLING UP THE PETROL TANK HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatIn this task you will develop a mathematical model that helps motorists decide which ofthe following two options is more economicalOption 1 to buy petrol from a station on their normal route at a relatively higher priceOption 2 to drive an extra distance out of their normal route to buy cheaper petrolConsider a situation in which two motorists Arwa and Bao share the same driving route but owndifferent sized vehicles Arwa fills up her vehiclersquos tank at a station along her normal route forUS$ 1 p per litre On the other hand Bao drives an extra d kilometres out of his normal route to fillup his vehiclersquos tank for US$ p2 per litre where p2 _ p1 _ Choose suitable parameters for Arwarsquos and Baorsquos vehicles Justify your choices

_ Suppose 1 p _ US$100 per litre 2 p _ US$098 per litre and d _10 km Which motorist is getting the better deal Show all calculations and justify any assumptions you make_ On a spreadsheet choose several sets of values for 1 p 2 p and d to investigate further_ Define a set of variables that would be relevant in the above situationldquoEffective litresrdquo is a method of comparing the cost of petrol bought under the two optionsdescribed above Effective litres for a given vehicle are those litres used when the vehicle travelsits normal route_ Use your variables and parameters to write algebraic expressions for 1 E and 2 E whichrepresent the cost per effective litre under options 1 and 2 respectively_ Write a model that helps motorists decide on the more economical option for theirvehiclesIn the remainder of this task you need to consider the two vehicles you have chosen for Arwaand Bao_ Use your model to find the farthest distance that Bao should drive to obtain a 2 pricesaving_ Investigate the relationship between d and 2 p when 2 E is kept constant (eg US$090US$100 hellip etc) Use technology to draw a family of curves for Arwarsquos vehicle Repeatfor Baorsquos vehicle

_ For 2 E _ US$090 provide Arwa with information on three different stations that yieldthis same cost per effective litre Discuss how such information may be useful to Arwa_ For 2 E _ US$100 and 2 p _ US$080 compare the maximum distance that each motoristshould drive and still save moneyArwa is a busy person and wonders whether the saving in money would be worth the time shewould lose in extra driving_ Modify your model to account for the time taken to drive to and from an off-route station

Clearly justify any assumptions you make

IB DP Math SL type 2 IA portfolio task Fish production Gold Medal heightsIB DP Math HL type 2 IA portfolio task The dice game Filling up the petrol tankIB DP Math HL type 1 IA portfolio task shadow function Patterns from complex numberIB DP Math SL type 1 IA portfolio task Lacsaprsquos fraction Circles

IB ToK Essay TutorIB ToK Essay Topics 201213

IB ToK Essay Help Choosing the Right Essay TitleIB ToK Essay Help Planning and Writing the Essay

IB ToK Essay Help Marking and Assessing the EssayIB ToK Essay Help Grammar and Punctuation Check

IB TOK Essay on Common Sense IB Sample TOK essays

Examiners mark essays against the title as set Respond to the title exactly as given do not alter it in any way

Your essay must be between 1200 and 1600 words in length double spaced and typed in size 12 font

1 In what ways may disagreement aid the pursuit of knowledge in the natural and human sciences

2 ldquoOnly seeing general patterns can give us knowledge Only seeing particular examples can give us understandingrdquo To what

extent do you agree with these assertions3 ldquoThe possession of knowledge carries an ethical

responsibilityrdquo Evaluate this claim4 The traditional TOK diagram indicates four ways of knowing

Propose the inclusion of a fifth way of knowing selected from intuition memory or imagination and explore the knowledge

issues it may raise in two areas of knowledge5 ldquoThat which can be asserted without evidence can be

dismissed without evidencerdquo (Christopher Hitchens) Do you agree

6 Can we know when to trust our emotions in the pursuit of knowledge Consider history and one other area of knowledge

IB TOK ESSAY WRITERS HELP SOLUTIONIB COMMENTARY ESSAY HELP IB ECONOMICS

COMMENTARIES IB TOK IB EXTENDED ESSAY IB IB TOK Essay Help Mathematics Physics Economics

ChemistryIB TOK TUTORS EXAMPLES SAMPLES IB TOK

PRESENTATION TUTORS HELP IB ESSAY EXTENDED ESSAY

Online tuitions Home tuitions and IndividualGroup coaching and tuitions in MathsMathMathematics and physics

Chemistry EconomicsBusiness Management for VI-XII standards for IGCSE IBAP A AS-level Ed-excelOverseas

Students studying in Grade(IV-XII ) from US UK Canada Australia Newzealand etc can contact for online tutoring in mathrsquos amp science Economics and Business Studies subjects

Teaching Exclusively International School Students for IB IGCSE and A levels Excellent and Consistent Results for IB

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HL Business IA Internal Assessment HLSL Tasks English IOCIOP Help Guidance

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heights Lacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essay computer dossierbusiness management IA helpeconomics commentaryLab reports tuition

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ups Project ESS English Spanish (Ab initio) French Hindi Extended Essay Help Tutors Examples Samples Solution

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Call or Email Ex-IB Examiner for Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website

httpwwwtopclassibtutorscom Online HelpTuition all over the world by the BestExpert IB Tutors Mail us or call

us for any queries

Essential Elements of a Math Portfolio Internal Assessment (IA) Task hlsl type 1 type 2 Problem Write-Up General

-‐

Name class and due date are clearly displayed

Introduction

-

Write up has an interesting (or pertinent) title

-‐

Task is properly introduced to the reader

-‐

This introduction should pose any major questions the task is seeking to answer

Body

-‐

Problem- solving process is completely explained throughout‐

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 2: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

Aali Isa Town Sitra Budaiya Jidhafs Al-Malikiyah Adliya Bahrain Doha Ar Rayyān Umm Şalāl Muḩammad Al Wakrah Al Khawr Ash Shaḩānīyah Dukhān Al Wukayr Ar Ruays Umm Bāb Qatar as-Salimiyah Jalib as-Suyuh Kuwait City Istanbul Ankara Izmir Bursa Adana Gaziantep Konya Antalya Mersin Kayseri Eskisehir Urfa Malatya Erzurum Samsun Turkey Cairo Alexandria Sharm el Sheikh Hurghada Marina Bur (Port) Said Ismailia Aswan Giza Luxor Egypt Baghdad Mosul Basrah Iraq Sanaa Aden Hodiedah Taiz Mukalla Yemen Aleppo Damascus Jaramana Duma Idlib Tartus Manbij Salamiyah Abu Kamal Jablah Darayya Nawa Baniyas Masyaf Qatana Syria Jerusalem West Jerusalem Haifa Tel Aviv Ashdod Rishon LeẔiyyon Petah Tikva Beersheba Netanya HE olon Israel Zarga Irbid Ramtha Aqaba Madaba Salt Karak Jerash Amman Jordan Aanjar Baalbeck Beiteddine Byblos The Cedars Eshmoun Sidon Tripoli Tyre Zahle Lebanon Gaza Jerusalem (PAL) Hebron Jabaliyah Nablus Rafah Ramallah Jericho Al Bireh Khan Yunus Bethlehem Tulkarm Jenin Palestinian territories Pakistan Islamabad Karachi Lahore Larnaca Lemesos Gazimagusa Nicosia Paphos Girne Guzelyurt Aradippou Paralimni Lefka Geri Ypsonas Livadia Dromolaxia Dipkarpaz Cyprus Canberra Melbourne Brisbane Adelaide Hobart Perth Darwin Cairns Central Coast Gold Coast Northern Territory Sunshine Coast Tasmania Townsville Wollongong Alice Spring Australia Argentina Buenos Aries Cordoba La Plata May del Plata Mendoza Rosario San Miguel de Tucuman San Carlos de Bariloche Bangladesh Dhaka Chittagong Somapuri Vihara Belgium Brussels Brugge Antwerp and Ghent Brazil Brasilia Rio de Janeiro Manaus Salvador Recife China Macao Shenyang QINGHUANGDAO SHENZHEN CHANGCHUN LHASA

KUNMING SANYA HARBIN TIANJIN URUMQI CHENGDU CHONGQING GUANGZHOU QINGDAO NANJING HANGZHOU XIAN Denmark Copenhagen Arhus Odense Aalborg Esbjerg Greece Athens Peloponnese Cyclades Crete Hungary Budapest Peacutecs Szeged Sopron Debrecen Indonesia Jakarta Makassar Medan Banda Aceh Surabaya Bandung Denpasar Ireland Dublin Cork Limerick Kilkenny Galway Waterford Wexford Sligo Kenmare Tralee Italy Rome Venice Florence Milan Naples Verona Turin Bologna Perugia Genova Japan Tokyo Yokohama Osaka Nagoya Sapporo Kobe Kyoto Fukuoka Kawasaki Saitama Hiroshima Sendai Kitakyushu Malaysia Kuala Lumpur Johor Bahru Ipoh Kuching Kuala Terengganu Kuantan Kota Bahru Seremban Georgetown Kota Kinabalu Sandakan Taiping Kajang-Sungai Chua Alor Setar Sibu Tawau Kluang Sungai Petani Miri Melaka Bandar Penggaram Mexico Mexico City Guadalajara Ecatepec Nezahualcoyotl Puebla Monterrey Tijuana Ciudad Juaacuterez Leon Zapopan Guadalupe Quereacutetaro Cuernavaca Tampico Veracruz Naucalpan Toluca Morelia Aguascalientes Netherlands Amsterdam Rotterdam Utrecht Den Haag(The Haugue) Eindhoven Tilburg Groningen Nijmegen Leiden Zwolle Venlo New Zealnd Auckland Hamilton Nelson Dunedin Napier Rotorua Taupo Tauranga Blenheim Invercargill Kaikoura Peru Lima (and Callao) Arequipa Trujillo Chiclayo Piura Iquitos Cusco Chimbote Huancayo Tacna Philippines Manila Cebu Baguio Boracay Palawan Albay Davao Zamboanga General Santos City Poland Cracow Gdansk Poznan Szczecin Warsaw

Wroclaw Poznari Tricity Russia Moscow Saint Petersburg Kazan Yekaterinburg Volgograd Irkutsk Vladivostok Nizhny Novgorod Saudi Arabia Abha Dhahran Jubail Qatif Al-Ahsa Hail Madinah Riyadh Al-khobar Jeddah Makkah Tabouk Baha Jizan Najran Taif Dammam Jouf Qassem Yanbu Singapore Bedok Seletar Woodlands Toa Payoh Ang Mo Kio Choa Chu Kang Tampines South Africa Alberton Benoni Cape Town Carltonville Durban East London Johannesburg Kimberley Klerksdorp Krugersdorp Mhluzi Midrand Msunduzi Newcastle Paarl Pretoria Soweto Port Elizabeth Spain Madrid Barcelona Valencia Sevilla Saragoza Malaga Zaragoza Murcia Palma de Mallorca Las Palmas Bilbao Switzerland Geneva Zuumlrich Bern Lausanne Base Luzern Thailand Phuket Chiang Rai Khon Kaen Chiang Mai Lampang Pak Kret Hat Yai Phitsanulok Trang Udon Thani Yala Samut Prakan Yala Songkhla Nakhon Pathom Surat Thani Ubon Ratchathani Nakhon Ratchasima Nonthabur Rayong Nakhon Sawan Nakhon Si Thammarat Nakhon Si Ayutthaya Bangkok Chiang Mai UAE Dubai Abu Dhabi Sharjah Al Ain Ajman UK Birmingham Bristol Edinburgh Glasgow Leeds Liverpool London Manchester United States New York Los Angeles California Chicago Ill Houston Tex Philadelphia Phoenix San Antonio San Diego Dallas San Jose Jacksonville Indianapolis San Francisco Austin Columbus Fort Worth Charlotte Detroit El Paso Memphis Baltimore Boston Seattle Washington DC Nashville-Davidson Denver Louisville-Jefferson Milwaukee Portland Las Vegas Oklahoma City Albuquerque Tucson Fresno Sacramento Long Beach Kansas City Mesa Virginia Beach Atlanta

Colorado Springs Omaha Nebr Raleigh NC Miami Fla Cleveland Ohio Tulsa Okla Oakland Calif Minneapolis Minn Wichita Kans Arlington Tex Vietnam Ho Chi Minh city Hanoi Hai Phong Da Nang Can Tho Nha Trang Hue Ha Long Da Lat Vung Tau Can Thi Sapa etc

Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc

MATHEMATICS Standard Level The portfolio ndash IA tasks

For use in 2012 and 2013

CIRCLES SL TYPE I Aim The aim of this task is to investigate positions of points in intersecting circles

The following diagram shows a circle with centre O and radius r and any point P 1 C

The circle has centre P and radius OP Let A be one of the points of intersection of and Circle has centre A and radius r The

point is the intersection of with (OP) This is shown in the diagram below

Let Use an analytic approach to find when and Describe what you notice and write a general statement to represent this Let Find when and Describe what you notice and write a general statement to represent this Comment whether or not this statement is consistent with your earlier statement Use technology to investigate other values of r and OP Find the general statement for OP Test the validity of your general statement by using different values of OP and r Discuss the scope andor limitations of the general statement

Explain how you arrived at the general statement

LACSAPrsquoS FRACTIONS SL TYPE I Aim In this task you will consider a set of numbers that are presented in a symmetrical pattern

Consider the five rows of numbers shown below

Describe how to find the numerator of the sixth row Using technology plot the relation between the row number n and the numerator in each row Describe what you notice from your plot and write a general statement to represent this Find the sixth and seventh rows Describe any patterns you used Let be the element in the nth row starting with Example Find the general statement for

Test the validity of the general statement by finding additional rows

Discuss the scope andor limitations of the general statement

Explain how you arrived at your general statement

FISH PRODUCTION SL TYPE II Aim This task considers commercial fishing in a particular country in two different environments ndash the sea and fish farms (aquaculture) The data is taken from the UN Statistics Division Common Database

The following table gives the total mass of fish caught in the sea in thousands of tonnes (1 tonne = 1000 kilograms)

Define suitable variables and discuss any parametersconstraints Using technology plot the data points from the table on a graph Comment on any apparent trends in your graph and suggest suitable models Analytically develop a model that fits the data points (You may find it useful to consider a combination of functions) On a new set of axes draw your model function and the original data points Comment on any differences Revise your model if necessary

The table below gives the total mass of fish in thousands of tonnes from fish farms

Plot the data points from this table on a graph and discuss whether your analytical model for the original data fits the new data

Use technology to find a suitable model for the new data On a new set of axes draw both models Discuss how trends in the first model could be explained by trends in the second model

By considering both models discuss possible future trends in both types of fishing

GOLD MEDAL HEIGHTS SL TYPE II Aim The aim of this task is to consider the winning height for the menrsquos high jump in the Olympic Games

The table below gives the height (in centimeters) achieved by the gold medalists at various Olympic Games

Note The Olympic Games were not held in 1940 and 1944 Using technology plot the data points on a graph Define all variables used and state any parameters clearly Discuss any possible constraints of the task What type of function models the behaviour of the graph Explain why you chose this function Analytically create an equation to model the data in the above table On a new set of axes draw your model function and the original graph Comment on any differences Discuss the limitations of your model Refine your model if necessary Use technology to find another function that models the data On a new set of axes draw both your model functions Comment on any differences Had the Games been held in 1940 and 1944 estimate what the winning heights would have been and justify your answers Use your model to predict the winning height in 1984 and in 2016 Comment on your answers

The following table gives the winning heights for all the other Olympic Games since 1896

How well does your model fit the additional data Discuss the overall trend from 1896 to 2008 with specific references to significant fluctuations

What modifications if any need to be made to your model to fit the new data

MATHEMATICSHigher LevelThe portfolio ndash IA tasks

For use in 2012 and 2013

SHADOW FUNCTIONS HL TYPE ITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatWhile real zeros of polynomial functions may be easily read off the graph of thepolynomial the same is not true for complex zeros In this task you will investigate themethod of shadow functions and their generators which helps identify the real andimaginary components of complex zeros from key points along the x-axisPart A (Quadratic Polynomials)

Consider the quadratic function 2 2Write down the coordinates of the vertexShow that 1 y has zeros whereThe ldquoshadow functionrdquo to 1 y is another quadratic 2 y which shares the same vertex asHowever 2 y has opposite concavity to that of 1 y and its zeros are in the form

Use various values for a and b to generate pairs of functions 1 y and

Hence or otherwise express 2 y in terms of 1 y and m y where m y is called the ldquoshadowgenerating functionrdquo_ On a labelled diagram illustrate how the zeros of 2 y may be helpful in the determination

of the real and imaginary components of the complex zeros of 1 y

Part B (Cubic Polynomials)Now consider the cubic function 1 _ _ _ _ y _ (x _ 2) x _ (3_ 2i) x _ (3_ 2i) The shadow function in this case is another cubic function 2 y which shares two points with 1 y has opposite concavity and its zeros are _2 and 3_ 2 as depicted in the figure below The shadow

generating function in this case passes through the two points of intersection

Write down an expression for 2 y and hence find the points of intersection between 1 y and 2 y

_ Hence or otherwise determine the equation of the shadow generating function m y in thiscase_ Once again express 2 y in terms of 1 y and m y Use technology to investigate similarcubic functions_ Write a general statement about the functions 1 y 2 y and m y and prove your statement_ On a labelled diagram illustrate how the zeros of 2 y may be helpful in the determinationof the real and imaginary components of the complex zeros of 1 y

_ How can the findings with quadratics and cubics be applied to quartics

PATTERNS FROM COMPLEX NUMBERS HL TYPE ITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo format

Part A

Use de Moivrersquos theorem to obtain solutions to the equation z3 _1 _ 0 _ Use graphing software to plot these roots on an Argand diagram as well as a unit circlewith centre origin_ Choose a root and draw line segments from this root to the other two roots

_ Measure these line segments and comment on your results_ Repeat the above for the equations z4 _1 _ 0 and z5 _1 _ 0 Comment on your results andtry to formulate a conjecture_ Factorize zn _1 for n _ 3 4 and 5_ Use graphing software to test your conjecture for some more values of n 1048576 __ and makemodifications to your conjecture if necessary_ Prove your conjecture

Part B

Use de Moivrersquos theorem to obtain solutions to zn _ i for n _ 3 4 and 5_ Use graphing software to represent each of these solutions on an Argand diagram_ Generalize and prove your results for zn _ a _ bi where a _ bi _1

_ What happens when a _ bi _1

THE DICE GAME HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatThe aim of this task is to create a dice game in a casino and model this usingprobability It is important to examine how best to run the game from both the

perspective of a player and the casino In doing so analyse the game to consider theoptimal payments by the player and payouts by the casino_ Consider a game with two players Ann and Bob Ann has a red die and Bob a white dieThey roll their dice and note the number on the upper face Ann wins if her score is higherthan Bobrsquos (note that Bob wins if the scores are the same) If both players roll their diceonce each what is the probability that Ann will win the game_ Now consider the same game where Ann can roll her die a second time and will note thehigher score of the two rolls but Bob rolls only once In this case what is the probabilitythat Ann will win_ Investigate the game when both players can roll their dice twice and also when bothplayers can roll their dice more than twice but not necessarily the same number of times_ Consider the game in a casino where the player has a red die and the bank has a white dieFind a model for a game so that the casino makes a reasonable profit in the case where theplayer rolls the red die once and the bank rolls the white die once (When creating yourmodel you will need to consider how much a player must pay to play a game and howmuch the bank will pay out if the player wins Do this from the perspective of both theplayer and the casino and consider carefully the criteria for whether the game can be

considered worthwhile for both the player and the casino)_ Now consider other models for the game including cases such as where the player or the

bank rolls their dice multiple times or where multiple players are involved in the game

FILLING UP THE PETROL TANK HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatIn this task you will develop a mathematical model that helps motorists decide which ofthe following two options is more economicalOption 1 to buy petrol from a station on their normal route at a relatively higher priceOption 2 to drive an extra distance out of their normal route to buy cheaper petrolConsider a situation in which two motorists Arwa and Bao share the same driving route but owndifferent sized vehicles Arwa fills up her vehiclersquos tank at a station along her normal route forUS$ 1 p per litre On the other hand Bao drives an extra d kilometres out of his normal route to fillup his vehiclersquos tank for US$ p2 per litre where p2 _ p1 _ Choose suitable parameters for Arwarsquos and Baorsquos vehicles Justify your choices

_ Suppose 1 p _ US$100 per litre 2 p _ US$098 per litre and d _10 km Which motorist is getting the better deal Show all calculations and justify any assumptions you make_ On a spreadsheet choose several sets of values for 1 p 2 p and d to investigate further_ Define a set of variables that would be relevant in the above situationldquoEffective litresrdquo is a method of comparing the cost of petrol bought under the two optionsdescribed above Effective litres for a given vehicle are those litres used when the vehicle travelsits normal route_ Use your variables and parameters to write algebraic expressions for 1 E and 2 E whichrepresent the cost per effective litre under options 1 and 2 respectively_ Write a model that helps motorists decide on the more economical option for theirvehiclesIn the remainder of this task you need to consider the two vehicles you have chosen for Arwaand Bao_ Use your model to find the farthest distance that Bao should drive to obtain a 2 pricesaving_ Investigate the relationship between d and 2 p when 2 E is kept constant (eg US$090US$100 hellip etc) Use technology to draw a family of curves for Arwarsquos vehicle Repeatfor Baorsquos vehicle

_ For 2 E _ US$090 provide Arwa with information on three different stations that yieldthis same cost per effective litre Discuss how such information may be useful to Arwa_ For 2 E _ US$100 and 2 p _ US$080 compare the maximum distance that each motoristshould drive and still save moneyArwa is a busy person and wonders whether the saving in money would be worth the time shewould lose in extra driving_ Modify your model to account for the time taken to drive to and from an off-route station

Clearly justify any assumptions you make

IB DP Math SL type 2 IA portfolio task Fish production Gold Medal heightsIB DP Math HL type 2 IA portfolio task The dice game Filling up the petrol tankIB DP Math HL type 1 IA portfolio task shadow function Patterns from complex numberIB DP Math SL type 1 IA portfolio task Lacsaprsquos fraction Circles

IB ToK Essay TutorIB ToK Essay Topics 201213

IB ToK Essay Help Choosing the Right Essay TitleIB ToK Essay Help Planning and Writing the Essay

IB ToK Essay Help Marking and Assessing the EssayIB ToK Essay Help Grammar and Punctuation Check

IB TOK Essay on Common Sense IB Sample TOK essays

Examiners mark essays against the title as set Respond to the title exactly as given do not alter it in any way

Your essay must be between 1200 and 1600 words in length double spaced and typed in size 12 font

1 In what ways may disagreement aid the pursuit of knowledge in the natural and human sciences

2 ldquoOnly seeing general patterns can give us knowledge Only seeing particular examples can give us understandingrdquo To what

extent do you agree with these assertions3 ldquoThe possession of knowledge carries an ethical

responsibilityrdquo Evaluate this claim4 The traditional TOK diagram indicates four ways of knowing

Propose the inclusion of a fifth way of knowing selected from intuition memory or imagination and explore the knowledge

issues it may raise in two areas of knowledge5 ldquoThat which can be asserted without evidence can be

dismissed without evidencerdquo (Christopher Hitchens) Do you agree

6 Can we know when to trust our emotions in the pursuit of knowledge Consider history and one other area of knowledge

IB TOK ESSAY WRITERS HELP SOLUTIONIB COMMENTARY ESSAY HELP IB ECONOMICS

COMMENTARIES IB TOK IB EXTENDED ESSAY IB IB TOK Essay Help Mathematics Physics Economics

ChemistryIB TOK TUTORS EXAMPLES SAMPLES IB TOK

PRESENTATION TUTORS HELP IB ESSAY EXTENDED ESSAY

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Chemistry EconomicsBusiness Management for VI-XII standards for IGCSE IBAP A AS-level Ed-excelOverseas

Students studying in Grade(IV-XII ) from US UK Canada Australia Newzealand etc can contact for online tutoring in mathrsquos amp science Economics and Business Studies subjects

Teaching Exclusively International School Students for IB IGCSE and A levels Excellent and Consistent Results for IB

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HL Business IA Internal Assessment HLSL Tasks English IOCIOP Help Guidance

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heights Lacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essay computer dossierbusiness management IA helpeconomics commentaryLab reports tuition

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heightsLacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essaycomputer dossierbusiness management IA helpeconomics commentary EVM Lab reports tuition

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IB Math Project Help Studies help IB World Literature Theatre Stimulus Essay Commentary storical Investigation

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ups Project ESS English Spanish (Ab initio) French Hindi Extended Essay Help Tutors Examples Samples Solution

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CADCAM Mathematics Physics Economics chemistryIB Business and Management Project Help Commentary storical

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ESS English Spanish French HindiIB Hindi HL SL help Mathematics Physics Economics

Chemistry Business EconomicsIB World Literature Help TOK Presentation ITGS IA Computer

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Call or Email Ex-IB Examiner for Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website

httpwwwtopclassibtutorscom Online HelpTuition all over the world by the BestExpert IB Tutors Mail us or call

us for any queries

Essential Elements of a Math Portfolio Internal Assessment (IA) Task hlsl type 1 type 2 Problem Write-Up General

-‐

Name class and due date are clearly displayed

Introduction

-

Write up has an interesting (or pertinent) title

-‐

Task is properly introduced to the reader

-‐

This introduction should pose any major questions the task is seeking to answer

Body

-‐

Problem- solving process is completely explained throughout‐

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 3: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

KUNMING SANYA HARBIN TIANJIN URUMQI CHENGDU CHONGQING GUANGZHOU QINGDAO NANJING HANGZHOU XIAN Denmark Copenhagen Arhus Odense Aalborg Esbjerg Greece Athens Peloponnese Cyclades Crete Hungary Budapest Peacutecs Szeged Sopron Debrecen Indonesia Jakarta Makassar Medan Banda Aceh Surabaya Bandung Denpasar Ireland Dublin Cork Limerick Kilkenny Galway Waterford Wexford Sligo Kenmare Tralee Italy Rome Venice Florence Milan Naples Verona Turin Bologna Perugia Genova Japan Tokyo Yokohama Osaka Nagoya Sapporo Kobe Kyoto Fukuoka Kawasaki Saitama Hiroshima Sendai Kitakyushu Malaysia Kuala Lumpur Johor Bahru Ipoh Kuching Kuala Terengganu Kuantan Kota Bahru Seremban Georgetown Kota Kinabalu Sandakan Taiping Kajang-Sungai Chua Alor Setar Sibu Tawau Kluang Sungai Petani Miri Melaka Bandar Penggaram Mexico Mexico City Guadalajara Ecatepec Nezahualcoyotl Puebla Monterrey Tijuana Ciudad Juaacuterez Leon Zapopan Guadalupe Quereacutetaro Cuernavaca Tampico Veracruz Naucalpan Toluca Morelia Aguascalientes Netherlands Amsterdam Rotterdam Utrecht Den Haag(The Haugue) Eindhoven Tilburg Groningen Nijmegen Leiden Zwolle Venlo New Zealnd Auckland Hamilton Nelson Dunedin Napier Rotorua Taupo Tauranga Blenheim Invercargill Kaikoura Peru Lima (and Callao) Arequipa Trujillo Chiclayo Piura Iquitos Cusco Chimbote Huancayo Tacna Philippines Manila Cebu Baguio Boracay Palawan Albay Davao Zamboanga General Santos City Poland Cracow Gdansk Poznan Szczecin Warsaw

Wroclaw Poznari Tricity Russia Moscow Saint Petersburg Kazan Yekaterinburg Volgograd Irkutsk Vladivostok Nizhny Novgorod Saudi Arabia Abha Dhahran Jubail Qatif Al-Ahsa Hail Madinah Riyadh Al-khobar Jeddah Makkah Tabouk Baha Jizan Najran Taif Dammam Jouf Qassem Yanbu Singapore Bedok Seletar Woodlands Toa Payoh Ang Mo Kio Choa Chu Kang Tampines South Africa Alberton Benoni Cape Town Carltonville Durban East London Johannesburg Kimberley Klerksdorp Krugersdorp Mhluzi Midrand Msunduzi Newcastle Paarl Pretoria Soweto Port Elizabeth Spain Madrid Barcelona Valencia Sevilla Saragoza Malaga Zaragoza Murcia Palma de Mallorca Las Palmas Bilbao Switzerland Geneva Zuumlrich Bern Lausanne Base Luzern Thailand Phuket Chiang Rai Khon Kaen Chiang Mai Lampang Pak Kret Hat Yai Phitsanulok Trang Udon Thani Yala Samut Prakan Yala Songkhla Nakhon Pathom Surat Thani Ubon Ratchathani Nakhon Ratchasima Nonthabur Rayong Nakhon Sawan Nakhon Si Thammarat Nakhon Si Ayutthaya Bangkok Chiang Mai UAE Dubai Abu Dhabi Sharjah Al Ain Ajman UK Birmingham Bristol Edinburgh Glasgow Leeds Liverpool London Manchester United States New York Los Angeles California Chicago Ill Houston Tex Philadelphia Phoenix San Antonio San Diego Dallas San Jose Jacksonville Indianapolis San Francisco Austin Columbus Fort Worth Charlotte Detroit El Paso Memphis Baltimore Boston Seattle Washington DC Nashville-Davidson Denver Louisville-Jefferson Milwaukee Portland Las Vegas Oklahoma City Albuquerque Tucson Fresno Sacramento Long Beach Kansas City Mesa Virginia Beach Atlanta

Colorado Springs Omaha Nebr Raleigh NC Miami Fla Cleveland Ohio Tulsa Okla Oakland Calif Minneapolis Minn Wichita Kans Arlington Tex Vietnam Ho Chi Minh city Hanoi Hai Phong Da Nang Can Tho Nha Trang Hue Ha Long Da Lat Vung Tau Can Thi Sapa etc

Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc

MATHEMATICS Standard Level The portfolio ndash IA tasks

For use in 2012 and 2013

CIRCLES SL TYPE I Aim The aim of this task is to investigate positions of points in intersecting circles

The following diagram shows a circle with centre O and radius r and any point P 1 C

The circle has centre P and radius OP Let A be one of the points of intersection of and Circle has centre A and radius r The

point is the intersection of with (OP) This is shown in the diagram below

Let Use an analytic approach to find when and Describe what you notice and write a general statement to represent this Let Find when and Describe what you notice and write a general statement to represent this Comment whether or not this statement is consistent with your earlier statement Use technology to investigate other values of r and OP Find the general statement for OP Test the validity of your general statement by using different values of OP and r Discuss the scope andor limitations of the general statement

Explain how you arrived at the general statement

LACSAPrsquoS FRACTIONS SL TYPE I Aim In this task you will consider a set of numbers that are presented in a symmetrical pattern

Consider the five rows of numbers shown below

Describe how to find the numerator of the sixth row Using technology plot the relation between the row number n and the numerator in each row Describe what you notice from your plot and write a general statement to represent this Find the sixth and seventh rows Describe any patterns you used Let be the element in the nth row starting with Example Find the general statement for

Test the validity of the general statement by finding additional rows

Discuss the scope andor limitations of the general statement

Explain how you arrived at your general statement

FISH PRODUCTION SL TYPE II Aim This task considers commercial fishing in a particular country in two different environments ndash the sea and fish farms (aquaculture) The data is taken from the UN Statistics Division Common Database

The following table gives the total mass of fish caught in the sea in thousands of tonnes (1 tonne = 1000 kilograms)

Define suitable variables and discuss any parametersconstraints Using technology plot the data points from the table on a graph Comment on any apparent trends in your graph and suggest suitable models Analytically develop a model that fits the data points (You may find it useful to consider a combination of functions) On a new set of axes draw your model function and the original data points Comment on any differences Revise your model if necessary

The table below gives the total mass of fish in thousands of tonnes from fish farms

Plot the data points from this table on a graph and discuss whether your analytical model for the original data fits the new data

Use technology to find a suitable model for the new data On a new set of axes draw both models Discuss how trends in the first model could be explained by trends in the second model

By considering both models discuss possible future trends in both types of fishing

GOLD MEDAL HEIGHTS SL TYPE II Aim The aim of this task is to consider the winning height for the menrsquos high jump in the Olympic Games

The table below gives the height (in centimeters) achieved by the gold medalists at various Olympic Games

Note The Olympic Games were not held in 1940 and 1944 Using technology plot the data points on a graph Define all variables used and state any parameters clearly Discuss any possible constraints of the task What type of function models the behaviour of the graph Explain why you chose this function Analytically create an equation to model the data in the above table On a new set of axes draw your model function and the original graph Comment on any differences Discuss the limitations of your model Refine your model if necessary Use technology to find another function that models the data On a new set of axes draw both your model functions Comment on any differences Had the Games been held in 1940 and 1944 estimate what the winning heights would have been and justify your answers Use your model to predict the winning height in 1984 and in 2016 Comment on your answers

The following table gives the winning heights for all the other Olympic Games since 1896

How well does your model fit the additional data Discuss the overall trend from 1896 to 2008 with specific references to significant fluctuations

What modifications if any need to be made to your model to fit the new data

MATHEMATICSHigher LevelThe portfolio ndash IA tasks

For use in 2012 and 2013

SHADOW FUNCTIONS HL TYPE ITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatWhile real zeros of polynomial functions may be easily read off the graph of thepolynomial the same is not true for complex zeros In this task you will investigate themethod of shadow functions and their generators which helps identify the real andimaginary components of complex zeros from key points along the x-axisPart A (Quadratic Polynomials)

Consider the quadratic function 2 2Write down the coordinates of the vertexShow that 1 y has zeros whereThe ldquoshadow functionrdquo to 1 y is another quadratic 2 y which shares the same vertex asHowever 2 y has opposite concavity to that of 1 y and its zeros are in the form

Use various values for a and b to generate pairs of functions 1 y and

Hence or otherwise express 2 y in terms of 1 y and m y where m y is called the ldquoshadowgenerating functionrdquo_ On a labelled diagram illustrate how the zeros of 2 y may be helpful in the determination

of the real and imaginary components of the complex zeros of 1 y

Part B (Cubic Polynomials)Now consider the cubic function 1 _ _ _ _ y _ (x _ 2) x _ (3_ 2i) x _ (3_ 2i) The shadow function in this case is another cubic function 2 y which shares two points with 1 y has opposite concavity and its zeros are _2 and 3_ 2 as depicted in the figure below The shadow

generating function in this case passes through the two points of intersection

Write down an expression for 2 y and hence find the points of intersection between 1 y and 2 y

_ Hence or otherwise determine the equation of the shadow generating function m y in thiscase_ Once again express 2 y in terms of 1 y and m y Use technology to investigate similarcubic functions_ Write a general statement about the functions 1 y 2 y and m y and prove your statement_ On a labelled diagram illustrate how the zeros of 2 y may be helpful in the determinationof the real and imaginary components of the complex zeros of 1 y

_ How can the findings with quadratics and cubics be applied to quartics

PATTERNS FROM COMPLEX NUMBERS HL TYPE ITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo format

Part A

Use de Moivrersquos theorem to obtain solutions to the equation z3 _1 _ 0 _ Use graphing software to plot these roots on an Argand diagram as well as a unit circlewith centre origin_ Choose a root and draw line segments from this root to the other two roots

_ Measure these line segments and comment on your results_ Repeat the above for the equations z4 _1 _ 0 and z5 _1 _ 0 Comment on your results andtry to formulate a conjecture_ Factorize zn _1 for n _ 3 4 and 5_ Use graphing software to test your conjecture for some more values of n 1048576 __ and makemodifications to your conjecture if necessary_ Prove your conjecture

Part B

Use de Moivrersquos theorem to obtain solutions to zn _ i for n _ 3 4 and 5_ Use graphing software to represent each of these solutions on an Argand diagram_ Generalize and prove your results for zn _ a _ bi where a _ bi _1

_ What happens when a _ bi _1

THE DICE GAME HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatThe aim of this task is to create a dice game in a casino and model this usingprobability It is important to examine how best to run the game from both the

perspective of a player and the casino In doing so analyse the game to consider theoptimal payments by the player and payouts by the casino_ Consider a game with two players Ann and Bob Ann has a red die and Bob a white dieThey roll their dice and note the number on the upper face Ann wins if her score is higherthan Bobrsquos (note that Bob wins if the scores are the same) If both players roll their diceonce each what is the probability that Ann will win the game_ Now consider the same game where Ann can roll her die a second time and will note thehigher score of the two rolls but Bob rolls only once In this case what is the probabilitythat Ann will win_ Investigate the game when both players can roll their dice twice and also when bothplayers can roll their dice more than twice but not necessarily the same number of times_ Consider the game in a casino where the player has a red die and the bank has a white dieFind a model for a game so that the casino makes a reasonable profit in the case where theplayer rolls the red die once and the bank rolls the white die once (When creating yourmodel you will need to consider how much a player must pay to play a game and howmuch the bank will pay out if the player wins Do this from the perspective of both theplayer and the casino and consider carefully the criteria for whether the game can be

considered worthwhile for both the player and the casino)_ Now consider other models for the game including cases such as where the player or the

bank rolls their dice multiple times or where multiple players are involved in the game

FILLING UP THE PETROL TANK HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatIn this task you will develop a mathematical model that helps motorists decide which ofthe following two options is more economicalOption 1 to buy petrol from a station on their normal route at a relatively higher priceOption 2 to drive an extra distance out of their normal route to buy cheaper petrolConsider a situation in which two motorists Arwa and Bao share the same driving route but owndifferent sized vehicles Arwa fills up her vehiclersquos tank at a station along her normal route forUS$ 1 p per litre On the other hand Bao drives an extra d kilometres out of his normal route to fillup his vehiclersquos tank for US$ p2 per litre where p2 _ p1 _ Choose suitable parameters for Arwarsquos and Baorsquos vehicles Justify your choices

_ Suppose 1 p _ US$100 per litre 2 p _ US$098 per litre and d _10 km Which motorist is getting the better deal Show all calculations and justify any assumptions you make_ On a spreadsheet choose several sets of values for 1 p 2 p and d to investigate further_ Define a set of variables that would be relevant in the above situationldquoEffective litresrdquo is a method of comparing the cost of petrol bought under the two optionsdescribed above Effective litres for a given vehicle are those litres used when the vehicle travelsits normal route_ Use your variables and parameters to write algebraic expressions for 1 E and 2 E whichrepresent the cost per effective litre under options 1 and 2 respectively_ Write a model that helps motorists decide on the more economical option for theirvehiclesIn the remainder of this task you need to consider the two vehicles you have chosen for Arwaand Bao_ Use your model to find the farthest distance that Bao should drive to obtain a 2 pricesaving_ Investigate the relationship between d and 2 p when 2 E is kept constant (eg US$090US$100 hellip etc) Use technology to draw a family of curves for Arwarsquos vehicle Repeatfor Baorsquos vehicle

_ For 2 E _ US$090 provide Arwa with information on three different stations that yieldthis same cost per effective litre Discuss how such information may be useful to Arwa_ For 2 E _ US$100 and 2 p _ US$080 compare the maximum distance that each motoristshould drive and still save moneyArwa is a busy person and wonders whether the saving in money would be worth the time shewould lose in extra driving_ Modify your model to account for the time taken to drive to and from an off-route station

Clearly justify any assumptions you make

IB DP Math SL type 2 IA portfolio task Fish production Gold Medal heightsIB DP Math HL type 2 IA portfolio task The dice game Filling up the petrol tankIB DP Math HL type 1 IA portfolio task shadow function Patterns from complex numberIB DP Math SL type 1 IA portfolio task Lacsaprsquos fraction Circles

IB ToK Essay TutorIB ToK Essay Topics 201213

IB ToK Essay Help Choosing the Right Essay TitleIB ToK Essay Help Planning and Writing the Essay

IB ToK Essay Help Marking and Assessing the EssayIB ToK Essay Help Grammar and Punctuation Check

IB TOK Essay on Common Sense IB Sample TOK essays

Examiners mark essays against the title as set Respond to the title exactly as given do not alter it in any way

Your essay must be between 1200 and 1600 words in length double spaced and typed in size 12 font

1 In what ways may disagreement aid the pursuit of knowledge in the natural and human sciences

2 ldquoOnly seeing general patterns can give us knowledge Only seeing particular examples can give us understandingrdquo To what

extent do you agree with these assertions3 ldquoThe possession of knowledge carries an ethical

responsibilityrdquo Evaluate this claim4 The traditional TOK diagram indicates four ways of knowing

Propose the inclusion of a fifth way of knowing selected from intuition memory or imagination and explore the knowledge

issues it may raise in two areas of knowledge5 ldquoThat which can be asserted without evidence can be

dismissed without evidencerdquo (Christopher Hitchens) Do you agree

6 Can we know when to trust our emotions in the pursuit of knowledge Consider history and one other area of knowledge

IB TOK ESSAY WRITERS HELP SOLUTIONIB COMMENTARY ESSAY HELP IB ECONOMICS

COMMENTARIES IB TOK IB EXTENDED ESSAY IB IB TOK Essay Help Mathematics Physics Economics

ChemistryIB TOK TUTORS EXAMPLES SAMPLES IB TOK

PRESENTATION TUTORS HELP IB ESSAY EXTENDED ESSAY

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Chemistry EconomicsBusiness Management for VI-XII standards for IGCSE IBAP A AS-level Ed-excelOverseas

Students studying in Grade(IV-XII ) from US UK Canada Australia Newzealand etc can contact for online tutoring in mathrsquos amp science Economics and Business Studies subjects

Teaching Exclusively International School Students for IB IGCSE and A levels Excellent and Consistent Results for IB

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HL Business IA Internal Assessment HLSL Tasks English IOCIOP Help Guidance

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heights Lacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essay computer dossierbusiness management IA helpeconomics commentaryLab reports tuition

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heightsLacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essaycomputer dossierbusiness management IA helpeconomics commentary EVM Lab reports tuition

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IB Math Project Help Studies help IB World Literature Theatre Stimulus Essay Commentary storical Investigation

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ups Project ESS English Spanish (Ab initio) French Hindi Extended Essay Help Tutors Examples Samples Solution

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StimulusIB Biology Lab writing Help Presentation ITGS IA Computer Dossier SLHL Design Technology Design Projects RAPA IA

CADCAM Mathematics Physics Economics chemistryIB Business and Management Project Help Commentary storical

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Economics Extended Essay IA Business IA IB Spanish Ab initio and Standard Level help Presentation ITGS

IA Computer DossierIB French Ab initio and Standard Level help Lab writing Project

ESS English Spanish French HindiIB Hindi HL SL help Mathematics Physics Economics

Chemistry Business EconomicsIB World Literature Help TOK Presentation ITGS IA Computer

Dossier EconomicsIB Theatre Stimulus help TOK Presentation ITGS IA Computer

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Call or Email Ex-IB Examiner for Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website

httpwwwtopclassibtutorscom Online HelpTuition all over the world by the BestExpert IB Tutors Mail us or call

us for any queries

Essential Elements of a Math Portfolio Internal Assessment (IA) Task hlsl type 1 type 2 Problem Write-Up General

-‐

Name class and due date are clearly displayed

Introduction

-

Write up has an interesting (or pertinent) title

-‐

Task is properly introduced to the reader

-‐

This introduction should pose any major questions the task is seeking to answer

Body

-‐

Problem- solving process is completely explained throughout‐

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 4: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

Wroclaw Poznari Tricity Russia Moscow Saint Petersburg Kazan Yekaterinburg Volgograd Irkutsk Vladivostok Nizhny Novgorod Saudi Arabia Abha Dhahran Jubail Qatif Al-Ahsa Hail Madinah Riyadh Al-khobar Jeddah Makkah Tabouk Baha Jizan Najran Taif Dammam Jouf Qassem Yanbu Singapore Bedok Seletar Woodlands Toa Payoh Ang Mo Kio Choa Chu Kang Tampines South Africa Alberton Benoni Cape Town Carltonville Durban East London Johannesburg Kimberley Klerksdorp Krugersdorp Mhluzi Midrand Msunduzi Newcastle Paarl Pretoria Soweto Port Elizabeth Spain Madrid Barcelona Valencia Sevilla Saragoza Malaga Zaragoza Murcia Palma de Mallorca Las Palmas Bilbao Switzerland Geneva Zuumlrich Bern Lausanne Base Luzern Thailand Phuket Chiang Rai Khon Kaen Chiang Mai Lampang Pak Kret Hat Yai Phitsanulok Trang Udon Thani Yala Samut Prakan Yala Songkhla Nakhon Pathom Surat Thani Ubon Ratchathani Nakhon Ratchasima Nonthabur Rayong Nakhon Sawan Nakhon Si Thammarat Nakhon Si Ayutthaya Bangkok Chiang Mai UAE Dubai Abu Dhabi Sharjah Al Ain Ajman UK Birmingham Bristol Edinburgh Glasgow Leeds Liverpool London Manchester United States New York Los Angeles California Chicago Ill Houston Tex Philadelphia Phoenix San Antonio San Diego Dallas San Jose Jacksonville Indianapolis San Francisco Austin Columbus Fort Worth Charlotte Detroit El Paso Memphis Baltimore Boston Seattle Washington DC Nashville-Davidson Denver Louisville-Jefferson Milwaukee Portland Las Vegas Oklahoma City Albuquerque Tucson Fresno Sacramento Long Beach Kansas City Mesa Virginia Beach Atlanta

Colorado Springs Omaha Nebr Raleigh NC Miami Fla Cleveland Ohio Tulsa Okla Oakland Calif Minneapolis Minn Wichita Kans Arlington Tex Vietnam Ho Chi Minh city Hanoi Hai Phong Da Nang Can Tho Nha Trang Hue Ha Long Da Lat Vung Tau Can Thi Sapa etc

Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc

MATHEMATICS Standard Level The portfolio ndash IA tasks

For use in 2012 and 2013

CIRCLES SL TYPE I Aim The aim of this task is to investigate positions of points in intersecting circles

The following diagram shows a circle with centre O and radius r and any point P 1 C

The circle has centre P and radius OP Let A be one of the points of intersection of and Circle has centre A and radius r The

point is the intersection of with (OP) This is shown in the diagram below

Let Use an analytic approach to find when and Describe what you notice and write a general statement to represent this Let Find when and Describe what you notice and write a general statement to represent this Comment whether or not this statement is consistent with your earlier statement Use technology to investigate other values of r and OP Find the general statement for OP Test the validity of your general statement by using different values of OP and r Discuss the scope andor limitations of the general statement

Explain how you arrived at the general statement

LACSAPrsquoS FRACTIONS SL TYPE I Aim In this task you will consider a set of numbers that are presented in a symmetrical pattern

Consider the five rows of numbers shown below

Describe how to find the numerator of the sixth row Using technology plot the relation between the row number n and the numerator in each row Describe what you notice from your plot and write a general statement to represent this Find the sixth and seventh rows Describe any patterns you used Let be the element in the nth row starting with Example Find the general statement for

Test the validity of the general statement by finding additional rows

Discuss the scope andor limitations of the general statement

Explain how you arrived at your general statement

FISH PRODUCTION SL TYPE II Aim This task considers commercial fishing in a particular country in two different environments ndash the sea and fish farms (aquaculture) The data is taken from the UN Statistics Division Common Database

The following table gives the total mass of fish caught in the sea in thousands of tonnes (1 tonne = 1000 kilograms)

Define suitable variables and discuss any parametersconstraints Using technology plot the data points from the table on a graph Comment on any apparent trends in your graph and suggest suitable models Analytically develop a model that fits the data points (You may find it useful to consider a combination of functions) On a new set of axes draw your model function and the original data points Comment on any differences Revise your model if necessary

The table below gives the total mass of fish in thousands of tonnes from fish farms

Plot the data points from this table on a graph and discuss whether your analytical model for the original data fits the new data

Use technology to find a suitable model for the new data On a new set of axes draw both models Discuss how trends in the first model could be explained by trends in the second model

By considering both models discuss possible future trends in both types of fishing

GOLD MEDAL HEIGHTS SL TYPE II Aim The aim of this task is to consider the winning height for the menrsquos high jump in the Olympic Games

The table below gives the height (in centimeters) achieved by the gold medalists at various Olympic Games

Note The Olympic Games were not held in 1940 and 1944 Using technology plot the data points on a graph Define all variables used and state any parameters clearly Discuss any possible constraints of the task What type of function models the behaviour of the graph Explain why you chose this function Analytically create an equation to model the data in the above table On a new set of axes draw your model function and the original graph Comment on any differences Discuss the limitations of your model Refine your model if necessary Use technology to find another function that models the data On a new set of axes draw both your model functions Comment on any differences Had the Games been held in 1940 and 1944 estimate what the winning heights would have been and justify your answers Use your model to predict the winning height in 1984 and in 2016 Comment on your answers

The following table gives the winning heights for all the other Olympic Games since 1896

How well does your model fit the additional data Discuss the overall trend from 1896 to 2008 with specific references to significant fluctuations

What modifications if any need to be made to your model to fit the new data

MATHEMATICSHigher LevelThe portfolio ndash IA tasks

For use in 2012 and 2013

SHADOW FUNCTIONS HL TYPE ITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatWhile real zeros of polynomial functions may be easily read off the graph of thepolynomial the same is not true for complex zeros In this task you will investigate themethod of shadow functions and their generators which helps identify the real andimaginary components of complex zeros from key points along the x-axisPart A (Quadratic Polynomials)

Consider the quadratic function 2 2Write down the coordinates of the vertexShow that 1 y has zeros whereThe ldquoshadow functionrdquo to 1 y is another quadratic 2 y which shares the same vertex asHowever 2 y has opposite concavity to that of 1 y and its zeros are in the form

Use various values for a and b to generate pairs of functions 1 y and

Hence or otherwise express 2 y in terms of 1 y and m y where m y is called the ldquoshadowgenerating functionrdquo_ On a labelled diagram illustrate how the zeros of 2 y may be helpful in the determination

of the real and imaginary components of the complex zeros of 1 y

Part B (Cubic Polynomials)Now consider the cubic function 1 _ _ _ _ y _ (x _ 2) x _ (3_ 2i) x _ (3_ 2i) The shadow function in this case is another cubic function 2 y which shares two points with 1 y has opposite concavity and its zeros are _2 and 3_ 2 as depicted in the figure below The shadow

generating function in this case passes through the two points of intersection

Write down an expression for 2 y and hence find the points of intersection between 1 y and 2 y

_ Hence or otherwise determine the equation of the shadow generating function m y in thiscase_ Once again express 2 y in terms of 1 y and m y Use technology to investigate similarcubic functions_ Write a general statement about the functions 1 y 2 y and m y and prove your statement_ On a labelled diagram illustrate how the zeros of 2 y may be helpful in the determinationof the real and imaginary components of the complex zeros of 1 y

_ How can the findings with quadratics and cubics be applied to quartics

PATTERNS FROM COMPLEX NUMBERS HL TYPE ITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo format

Part A

Use de Moivrersquos theorem to obtain solutions to the equation z3 _1 _ 0 _ Use graphing software to plot these roots on an Argand diagram as well as a unit circlewith centre origin_ Choose a root and draw line segments from this root to the other two roots

_ Measure these line segments and comment on your results_ Repeat the above for the equations z4 _1 _ 0 and z5 _1 _ 0 Comment on your results andtry to formulate a conjecture_ Factorize zn _1 for n _ 3 4 and 5_ Use graphing software to test your conjecture for some more values of n 1048576 __ and makemodifications to your conjecture if necessary_ Prove your conjecture

Part B

Use de Moivrersquos theorem to obtain solutions to zn _ i for n _ 3 4 and 5_ Use graphing software to represent each of these solutions on an Argand diagram_ Generalize and prove your results for zn _ a _ bi where a _ bi _1

_ What happens when a _ bi _1

THE DICE GAME HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatThe aim of this task is to create a dice game in a casino and model this usingprobability It is important to examine how best to run the game from both the

perspective of a player and the casino In doing so analyse the game to consider theoptimal payments by the player and payouts by the casino_ Consider a game with two players Ann and Bob Ann has a red die and Bob a white dieThey roll their dice and note the number on the upper face Ann wins if her score is higherthan Bobrsquos (note that Bob wins if the scores are the same) If both players roll their diceonce each what is the probability that Ann will win the game_ Now consider the same game where Ann can roll her die a second time and will note thehigher score of the two rolls but Bob rolls only once In this case what is the probabilitythat Ann will win_ Investigate the game when both players can roll their dice twice and also when bothplayers can roll their dice more than twice but not necessarily the same number of times_ Consider the game in a casino where the player has a red die and the bank has a white dieFind a model for a game so that the casino makes a reasonable profit in the case where theplayer rolls the red die once and the bank rolls the white die once (When creating yourmodel you will need to consider how much a player must pay to play a game and howmuch the bank will pay out if the player wins Do this from the perspective of both theplayer and the casino and consider carefully the criteria for whether the game can be

considered worthwhile for both the player and the casino)_ Now consider other models for the game including cases such as where the player or the

bank rolls their dice multiple times or where multiple players are involved in the game

FILLING UP THE PETROL TANK HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatIn this task you will develop a mathematical model that helps motorists decide which ofthe following two options is more economicalOption 1 to buy petrol from a station on their normal route at a relatively higher priceOption 2 to drive an extra distance out of their normal route to buy cheaper petrolConsider a situation in which two motorists Arwa and Bao share the same driving route but owndifferent sized vehicles Arwa fills up her vehiclersquos tank at a station along her normal route forUS$ 1 p per litre On the other hand Bao drives an extra d kilometres out of his normal route to fillup his vehiclersquos tank for US$ p2 per litre where p2 _ p1 _ Choose suitable parameters for Arwarsquos and Baorsquos vehicles Justify your choices

_ Suppose 1 p _ US$100 per litre 2 p _ US$098 per litre and d _10 km Which motorist is getting the better deal Show all calculations and justify any assumptions you make_ On a spreadsheet choose several sets of values for 1 p 2 p and d to investigate further_ Define a set of variables that would be relevant in the above situationldquoEffective litresrdquo is a method of comparing the cost of petrol bought under the two optionsdescribed above Effective litres for a given vehicle are those litres used when the vehicle travelsits normal route_ Use your variables and parameters to write algebraic expressions for 1 E and 2 E whichrepresent the cost per effective litre under options 1 and 2 respectively_ Write a model that helps motorists decide on the more economical option for theirvehiclesIn the remainder of this task you need to consider the two vehicles you have chosen for Arwaand Bao_ Use your model to find the farthest distance that Bao should drive to obtain a 2 pricesaving_ Investigate the relationship between d and 2 p when 2 E is kept constant (eg US$090US$100 hellip etc) Use technology to draw a family of curves for Arwarsquos vehicle Repeatfor Baorsquos vehicle

_ For 2 E _ US$090 provide Arwa with information on three different stations that yieldthis same cost per effective litre Discuss how such information may be useful to Arwa_ For 2 E _ US$100 and 2 p _ US$080 compare the maximum distance that each motoristshould drive and still save moneyArwa is a busy person and wonders whether the saving in money would be worth the time shewould lose in extra driving_ Modify your model to account for the time taken to drive to and from an off-route station

Clearly justify any assumptions you make

IB DP Math SL type 2 IA portfolio task Fish production Gold Medal heightsIB DP Math HL type 2 IA portfolio task The dice game Filling up the petrol tankIB DP Math HL type 1 IA portfolio task shadow function Patterns from complex numberIB DP Math SL type 1 IA portfolio task Lacsaprsquos fraction Circles

IB ToK Essay TutorIB ToK Essay Topics 201213

IB ToK Essay Help Choosing the Right Essay TitleIB ToK Essay Help Planning and Writing the Essay

IB ToK Essay Help Marking and Assessing the EssayIB ToK Essay Help Grammar and Punctuation Check

IB TOK Essay on Common Sense IB Sample TOK essays

Examiners mark essays against the title as set Respond to the title exactly as given do not alter it in any way

Your essay must be between 1200 and 1600 words in length double spaced and typed in size 12 font

1 In what ways may disagreement aid the pursuit of knowledge in the natural and human sciences

2 ldquoOnly seeing general patterns can give us knowledge Only seeing particular examples can give us understandingrdquo To what

extent do you agree with these assertions3 ldquoThe possession of knowledge carries an ethical

responsibilityrdquo Evaluate this claim4 The traditional TOK diagram indicates four ways of knowing

Propose the inclusion of a fifth way of knowing selected from intuition memory or imagination and explore the knowledge

issues it may raise in two areas of knowledge5 ldquoThat which can be asserted without evidence can be

dismissed without evidencerdquo (Christopher Hitchens) Do you agree

6 Can we know when to trust our emotions in the pursuit of knowledge Consider history and one other area of knowledge

IB TOK ESSAY WRITERS HELP SOLUTIONIB COMMENTARY ESSAY HELP IB ECONOMICS

COMMENTARIES IB TOK IB EXTENDED ESSAY IB IB TOK Essay Help Mathematics Physics Economics

ChemistryIB TOK TUTORS EXAMPLES SAMPLES IB TOK

PRESENTATION TUTORS HELP IB ESSAY EXTENDED ESSAY

Online tuitions Home tuitions and IndividualGroup coaching and tuitions in MathsMathMathematics and physics

Chemistry EconomicsBusiness Management for VI-XII standards for IGCSE IBAP A AS-level Ed-excelOverseas

Students studying in Grade(IV-XII ) from US UK Canada Australia Newzealand etc can contact for online tutoring in mathrsquos amp science Economics and Business Studies subjects

Teaching Exclusively International School Students for IB IGCSE and A levels Excellent and Consistent Results for IB

IGCSEGCSE O and A Level exam IGCSE O Level IB Maths Physics Chemistry Economics and Business and Management

HL Business IA Internal Assessment HLSL Tasks English IOCIOP Help Guidance

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heights Lacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essay computer dossierbusiness management IA helpeconomics commentaryLab reports tuition

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heightsLacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essaycomputer dossierbusiness management IA helpeconomics commentary EVM Lab reports tuition

IB MathsPortfolio urdu shayari

helpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow functionnumbersgold medal

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gurgoan IB maths home tuition in gurgoan IB math home tuition in gurgaon

IB Mathematics Physics Chemistry Economics Business and Management HL SL Studies Theatre Stimulus help

IB Physics Mathematics Chemistry Economics Business and Management Presentation ITGS IA Computer help

IB Chemistry HL SL help Mathematics Physics Economics Chemistry Business

IB Economics HL SL Management Math Portfolio TOK Economics Historical Investigation Extended help

IB Business and Management HL SL help Essay Commentary storical Investigation Lab writing

IB Math Portfolio Help HL SL help Lab writing Project ESS English Spanish French Hindi

IB Math Project Help Studies help IB World Literature Theatre Stimulus Essay Commentary storical Investigation

IB Extended Essay Help TOK Presentation ITGS IA Computer Dossier IB World Literature Theatre Stimulus

IB TOK Essay Help Mathematics Physics Economics Chemistry Business Presentation ITGS IA Computer

IB Economics Commentary Help Management Math Portfolio HL SL Extended

IB Historical Investigation Help Essay Commentary storical Investigation Lab writing

IB Physics Lab writing Help Lab writing EVM Lab Report write

ups Project ESS English Spanish (Ab initio) French Hindi Extended Essay Help Tutors Examples Samples Solution

GuidanceIB Chemistry Lab writing Help IB World Literature Theatre

StimulusIB Biology Lab writing Help Presentation ITGS IA Computer Dossier SLHL Design Technology Design Projects RAPA IA

CADCAM Mathematics Physics Economics chemistryIB Business and Management Project Help Commentary storical

Investigation Lab writingIB ESS lab report help Mathematics Physics Economics

Chemistry Business EconomicsIB English HL SL help IB World Literature Theatre Stimulus

Economics Extended Essay IA Business IA IB Spanish Ab initio and Standard Level help Presentation ITGS

IA Computer DossierIB French Ab initio and Standard Level help Lab writing Project

ESS English Spanish French HindiIB Hindi HL SL help Mathematics Physics Economics

Chemistry Business EconomicsIB World Literature Help TOK Presentation ITGS IA Computer

Dossier EconomicsIB Theatre Stimulus help TOK Presentation ITGS IA Computer

Dossier EconomicsIB TOK Presentation help Management Math Portfolio HL SL

Extended ITGS IA Computer Dossier MathIB ITGS IA help IB World Literature Theatre Stimulus Math

Portfolio TOK Economics investigation Extended helpIB Computer Dossier help TOK Presentation ITGS IA

Computer Dossier Math Portfolio TOK Economics

Call or Email Ex-IB Examiner for Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website

httpwwwtopclassibtutorscom Online HelpTuition all over the world by the BestExpert IB Tutors Mail us or call

us for any queries

Essential Elements of a Math Portfolio Internal Assessment (IA) Task hlsl type 1 type 2 Problem Write-Up General

-‐

Name class and due date are clearly displayed

Introduction

-

Write up has an interesting (or pertinent) title

-‐

Task is properly introduced to the reader

-‐

This introduction should pose any major questions the task is seeking to answer

Body

-‐

Problem- solving process is completely explained throughout‐

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 5: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

Colorado Springs Omaha Nebr Raleigh NC Miami Fla Cleveland Ohio Tulsa Okla Oakland Calif Minneapolis Minn Wichita Kans Arlington Tex Vietnam Ho Chi Minh city Hanoi Hai Phong Da Nang Can Tho Nha Trang Hue Ha Long Da Lat Vung Tau Can Thi Sapa etc

Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc

MATHEMATICS Standard Level The portfolio ndash IA tasks

For use in 2012 and 2013

CIRCLES SL TYPE I Aim The aim of this task is to investigate positions of points in intersecting circles

The following diagram shows a circle with centre O and radius r and any point P 1 C

The circle has centre P and radius OP Let A be one of the points of intersection of and Circle has centre A and radius r The

point is the intersection of with (OP) This is shown in the diagram below

Let Use an analytic approach to find when and Describe what you notice and write a general statement to represent this Let Find when and Describe what you notice and write a general statement to represent this Comment whether or not this statement is consistent with your earlier statement Use technology to investigate other values of r and OP Find the general statement for OP Test the validity of your general statement by using different values of OP and r Discuss the scope andor limitations of the general statement

Explain how you arrived at the general statement

LACSAPrsquoS FRACTIONS SL TYPE I Aim In this task you will consider a set of numbers that are presented in a symmetrical pattern

Consider the five rows of numbers shown below

Describe how to find the numerator of the sixth row Using technology plot the relation between the row number n and the numerator in each row Describe what you notice from your plot and write a general statement to represent this Find the sixth and seventh rows Describe any patterns you used Let be the element in the nth row starting with Example Find the general statement for

Test the validity of the general statement by finding additional rows

Discuss the scope andor limitations of the general statement

Explain how you arrived at your general statement

FISH PRODUCTION SL TYPE II Aim This task considers commercial fishing in a particular country in two different environments ndash the sea and fish farms (aquaculture) The data is taken from the UN Statistics Division Common Database

The following table gives the total mass of fish caught in the sea in thousands of tonnes (1 tonne = 1000 kilograms)

Define suitable variables and discuss any parametersconstraints Using technology plot the data points from the table on a graph Comment on any apparent trends in your graph and suggest suitable models Analytically develop a model that fits the data points (You may find it useful to consider a combination of functions) On a new set of axes draw your model function and the original data points Comment on any differences Revise your model if necessary

The table below gives the total mass of fish in thousands of tonnes from fish farms

Plot the data points from this table on a graph and discuss whether your analytical model for the original data fits the new data

Use technology to find a suitable model for the new data On a new set of axes draw both models Discuss how trends in the first model could be explained by trends in the second model

By considering both models discuss possible future trends in both types of fishing

GOLD MEDAL HEIGHTS SL TYPE II Aim The aim of this task is to consider the winning height for the menrsquos high jump in the Olympic Games

The table below gives the height (in centimeters) achieved by the gold medalists at various Olympic Games

Note The Olympic Games were not held in 1940 and 1944 Using technology plot the data points on a graph Define all variables used and state any parameters clearly Discuss any possible constraints of the task What type of function models the behaviour of the graph Explain why you chose this function Analytically create an equation to model the data in the above table On a new set of axes draw your model function and the original graph Comment on any differences Discuss the limitations of your model Refine your model if necessary Use technology to find another function that models the data On a new set of axes draw both your model functions Comment on any differences Had the Games been held in 1940 and 1944 estimate what the winning heights would have been and justify your answers Use your model to predict the winning height in 1984 and in 2016 Comment on your answers

The following table gives the winning heights for all the other Olympic Games since 1896

How well does your model fit the additional data Discuss the overall trend from 1896 to 2008 with specific references to significant fluctuations

What modifications if any need to be made to your model to fit the new data

MATHEMATICSHigher LevelThe portfolio ndash IA tasks

For use in 2012 and 2013

SHADOW FUNCTIONS HL TYPE ITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatWhile real zeros of polynomial functions may be easily read off the graph of thepolynomial the same is not true for complex zeros In this task you will investigate themethod of shadow functions and their generators which helps identify the real andimaginary components of complex zeros from key points along the x-axisPart A (Quadratic Polynomials)

Consider the quadratic function 2 2Write down the coordinates of the vertexShow that 1 y has zeros whereThe ldquoshadow functionrdquo to 1 y is another quadratic 2 y which shares the same vertex asHowever 2 y has opposite concavity to that of 1 y and its zeros are in the form

Use various values for a and b to generate pairs of functions 1 y and

Hence or otherwise express 2 y in terms of 1 y and m y where m y is called the ldquoshadowgenerating functionrdquo_ On a labelled diagram illustrate how the zeros of 2 y may be helpful in the determination

of the real and imaginary components of the complex zeros of 1 y

Part B (Cubic Polynomials)Now consider the cubic function 1 _ _ _ _ y _ (x _ 2) x _ (3_ 2i) x _ (3_ 2i) The shadow function in this case is another cubic function 2 y which shares two points with 1 y has opposite concavity and its zeros are _2 and 3_ 2 as depicted in the figure below The shadow

generating function in this case passes through the two points of intersection

Write down an expression for 2 y and hence find the points of intersection between 1 y and 2 y

_ Hence or otherwise determine the equation of the shadow generating function m y in thiscase_ Once again express 2 y in terms of 1 y and m y Use technology to investigate similarcubic functions_ Write a general statement about the functions 1 y 2 y and m y and prove your statement_ On a labelled diagram illustrate how the zeros of 2 y may be helpful in the determinationof the real and imaginary components of the complex zeros of 1 y

_ How can the findings with quadratics and cubics be applied to quartics

PATTERNS FROM COMPLEX NUMBERS HL TYPE ITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo format

Part A

Use de Moivrersquos theorem to obtain solutions to the equation z3 _1 _ 0 _ Use graphing software to plot these roots on an Argand diagram as well as a unit circlewith centre origin_ Choose a root and draw line segments from this root to the other two roots

_ Measure these line segments and comment on your results_ Repeat the above for the equations z4 _1 _ 0 and z5 _1 _ 0 Comment on your results andtry to formulate a conjecture_ Factorize zn _1 for n _ 3 4 and 5_ Use graphing software to test your conjecture for some more values of n 1048576 __ and makemodifications to your conjecture if necessary_ Prove your conjecture

Part B

Use de Moivrersquos theorem to obtain solutions to zn _ i for n _ 3 4 and 5_ Use graphing software to represent each of these solutions on an Argand diagram_ Generalize and prove your results for zn _ a _ bi where a _ bi _1

_ What happens when a _ bi _1

THE DICE GAME HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatThe aim of this task is to create a dice game in a casino and model this usingprobability It is important to examine how best to run the game from both the

perspective of a player and the casino In doing so analyse the game to consider theoptimal payments by the player and payouts by the casino_ Consider a game with two players Ann and Bob Ann has a red die and Bob a white dieThey roll their dice and note the number on the upper face Ann wins if her score is higherthan Bobrsquos (note that Bob wins if the scores are the same) If both players roll their diceonce each what is the probability that Ann will win the game_ Now consider the same game where Ann can roll her die a second time and will note thehigher score of the two rolls but Bob rolls only once In this case what is the probabilitythat Ann will win_ Investigate the game when both players can roll their dice twice and also when bothplayers can roll their dice more than twice but not necessarily the same number of times_ Consider the game in a casino where the player has a red die and the bank has a white dieFind a model for a game so that the casino makes a reasonable profit in the case where theplayer rolls the red die once and the bank rolls the white die once (When creating yourmodel you will need to consider how much a player must pay to play a game and howmuch the bank will pay out if the player wins Do this from the perspective of both theplayer and the casino and consider carefully the criteria for whether the game can be

considered worthwhile for both the player and the casino)_ Now consider other models for the game including cases such as where the player or the

bank rolls their dice multiple times or where multiple players are involved in the game

FILLING UP THE PETROL TANK HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatIn this task you will develop a mathematical model that helps motorists decide which ofthe following two options is more economicalOption 1 to buy petrol from a station on their normal route at a relatively higher priceOption 2 to drive an extra distance out of their normal route to buy cheaper petrolConsider a situation in which two motorists Arwa and Bao share the same driving route but owndifferent sized vehicles Arwa fills up her vehiclersquos tank at a station along her normal route forUS$ 1 p per litre On the other hand Bao drives an extra d kilometres out of his normal route to fillup his vehiclersquos tank for US$ p2 per litre where p2 _ p1 _ Choose suitable parameters for Arwarsquos and Baorsquos vehicles Justify your choices

_ Suppose 1 p _ US$100 per litre 2 p _ US$098 per litre and d _10 km Which motorist is getting the better deal Show all calculations and justify any assumptions you make_ On a spreadsheet choose several sets of values for 1 p 2 p and d to investigate further_ Define a set of variables that would be relevant in the above situationldquoEffective litresrdquo is a method of comparing the cost of petrol bought under the two optionsdescribed above Effective litres for a given vehicle are those litres used when the vehicle travelsits normal route_ Use your variables and parameters to write algebraic expressions for 1 E and 2 E whichrepresent the cost per effective litre under options 1 and 2 respectively_ Write a model that helps motorists decide on the more economical option for theirvehiclesIn the remainder of this task you need to consider the two vehicles you have chosen for Arwaand Bao_ Use your model to find the farthest distance that Bao should drive to obtain a 2 pricesaving_ Investigate the relationship between d and 2 p when 2 E is kept constant (eg US$090US$100 hellip etc) Use technology to draw a family of curves for Arwarsquos vehicle Repeatfor Baorsquos vehicle

_ For 2 E _ US$090 provide Arwa with information on three different stations that yieldthis same cost per effective litre Discuss how such information may be useful to Arwa_ For 2 E _ US$100 and 2 p _ US$080 compare the maximum distance that each motoristshould drive and still save moneyArwa is a busy person and wonders whether the saving in money would be worth the time shewould lose in extra driving_ Modify your model to account for the time taken to drive to and from an off-route station

Clearly justify any assumptions you make

IB DP Math SL type 2 IA portfolio task Fish production Gold Medal heightsIB DP Math HL type 2 IA portfolio task The dice game Filling up the petrol tankIB DP Math HL type 1 IA portfolio task shadow function Patterns from complex numberIB DP Math SL type 1 IA portfolio task Lacsaprsquos fraction Circles

IB ToK Essay TutorIB ToK Essay Topics 201213

IB ToK Essay Help Choosing the Right Essay TitleIB ToK Essay Help Planning and Writing the Essay

IB ToK Essay Help Marking and Assessing the EssayIB ToK Essay Help Grammar and Punctuation Check

IB TOK Essay on Common Sense IB Sample TOK essays

Examiners mark essays against the title as set Respond to the title exactly as given do not alter it in any way

Your essay must be between 1200 and 1600 words in length double spaced and typed in size 12 font

1 In what ways may disagreement aid the pursuit of knowledge in the natural and human sciences

2 ldquoOnly seeing general patterns can give us knowledge Only seeing particular examples can give us understandingrdquo To what

extent do you agree with these assertions3 ldquoThe possession of knowledge carries an ethical

responsibilityrdquo Evaluate this claim4 The traditional TOK diagram indicates four ways of knowing

Propose the inclusion of a fifth way of knowing selected from intuition memory or imagination and explore the knowledge

issues it may raise in two areas of knowledge5 ldquoThat which can be asserted without evidence can be

dismissed without evidencerdquo (Christopher Hitchens) Do you agree

6 Can we know when to trust our emotions in the pursuit of knowledge Consider history and one other area of knowledge

IB TOK ESSAY WRITERS HELP SOLUTIONIB COMMENTARY ESSAY HELP IB ECONOMICS

COMMENTARIES IB TOK IB EXTENDED ESSAY IB IB TOK Essay Help Mathematics Physics Economics

ChemistryIB TOK TUTORS EXAMPLES SAMPLES IB TOK

PRESENTATION TUTORS HELP IB ESSAY EXTENDED ESSAY

Online tuitions Home tuitions and IndividualGroup coaching and tuitions in MathsMathMathematics and physics

Chemistry EconomicsBusiness Management for VI-XII standards for IGCSE IBAP A AS-level Ed-excelOverseas

Students studying in Grade(IV-XII ) from US UK Canada Australia Newzealand etc can contact for online tutoring in mathrsquos amp science Economics and Business Studies subjects

Teaching Exclusively International School Students for IB IGCSE and A levels Excellent and Consistent Results for IB

IGCSEGCSE O and A Level exam IGCSE O Level IB Maths Physics Chemistry Economics and Business and Management

HL Business IA Internal Assessment HLSL Tasks English IOCIOP Help Guidance

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heights Lacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essay computer dossierbusiness management IA helpeconomics commentaryLab reports tuition

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heightsLacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essaycomputer dossierbusiness management IA helpeconomics commentary EVM Lab reports tuition

IB MathsPortfolio urdu shayari

helpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow functionnumbersgold medal

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maths home tuition in delhi IB math home tuition in delhiIB math home tuition in gurgaon IB maths home tuition in

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IB Mathematics Physics Chemistry Economics Business and Management HL SL Studies Theatre Stimulus help

IB Physics Mathematics Chemistry Economics Business and Management Presentation ITGS IA Computer help

IB Chemistry HL SL help Mathematics Physics Economics Chemistry Business

IB Economics HL SL Management Math Portfolio TOK Economics Historical Investigation Extended help

IB Business and Management HL SL help Essay Commentary storical Investigation Lab writing

IB Math Portfolio Help HL SL help Lab writing Project ESS English Spanish French Hindi

IB Math Project Help Studies help IB World Literature Theatre Stimulus Essay Commentary storical Investigation

IB Extended Essay Help TOK Presentation ITGS IA Computer Dossier IB World Literature Theatre Stimulus

IB TOK Essay Help Mathematics Physics Economics Chemistry Business Presentation ITGS IA Computer

IB Economics Commentary Help Management Math Portfolio HL SL Extended

IB Historical Investigation Help Essay Commentary storical Investigation Lab writing

IB Physics Lab writing Help Lab writing EVM Lab Report write

ups Project ESS English Spanish (Ab initio) French Hindi Extended Essay Help Tutors Examples Samples Solution

GuidanceIB Chemistry Lab writing Help IB World Literature Theatre

StimulusIB Biology Lab writing Help Presentation ITGS IA Computer Dossier SLHL Design Technology Design Projects RAPA IA

CADCAM Mathematics Physics Economics chemistryIB Business and Management Project Help Commentary storical

Investigation Lab writingIB ESS lab report help Mathematics Physics Economics

Chemistry Business EconomicsIB English HL SL help IB World Literature Theatre Stimulus

Economics Extended Essay IA Business IA IB Spanish Ab initio and Standard Level help Presentation ITGS

IA Computer DossierIB French Ab initio and Standard Level help Lab writing Project

ESS English Spanish French HindiIB Hindi HL SL help Mathematics Physics Economics

Chemistry Business EconomicsIB World Literature Help TOK Presentation ITGS IA Computer

Dossier EconomicsIB Theatre Stimulus help TOK Presentation ITGS IA Computer

Dossier EconomicsIB TOK Presentation help Management Math Portfolio HL SL

Extended ITGS IA Computer Dossier MathIB ITGS IA help IB World Literature Theatre Stimulus Math

Portfolio TOK Economics investigation Extended helpIB Computer Dossier help TOK Presentation ITGS IA

Computer Dossier Math Portfolio TOK Economics

Call or Email Ex-IB Examiner for Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website

httpwwwtopclassibtutorscom Online HelpTuition all over the world by the BestExpert IB Tutors Mail us or call

us for any queries

Essential Elements of a Math Portfolio Internal Assessment (IA) Task hlsl type 1 type 2 Problem Write-Up General

-‐

Name class and due date are clearly displayed

Introduction

-

Write up has an interesting (or pertinent) title

-‐

Task is properly introduced to the reader

-‐

This introduction should pose any major questions the task is seeking to answer

Body

-‐

Problem- solving process is completely explained throughout‐

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 6: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

The circle has centre P and radius OP Let A be one of the points of intersection of and Circle has centre A and radius r The

point is the intersection of with (OP) This is shown in the diagram below

Let Use an analytic approach to find when and Describe what you notice and write a general statement to represent this Let Find when and Describe what you notice and write a general statement to represent this Comment whether or not this statement is consistent with your earlier statement Use technology to investigate other values of r and OP Find the general statement for OP Test the validity of your general statement by using different values of OP and r Discuss the scope andor limitations of the general statement

Explain how you arrived at the general statement

LACSAPrsquoS FRACTIONS SL TYPE I Aim In this task you will consider a set of numbers that are presented in a symmetrical pattern

Consider the five rows of numbers shown below

Describe how to find the numerator of the sixth row Using technology plot the relation between the row number n and the numerator in each row Describe what you notice from your plot and write a general statement to represent this Find the sixth and seventh rows Describe any patterns you used Let be the element in the nth row starting with Example Find the general statement for

Test the validity of the general statement by finding additional rows

Discuss the scope andor limitations of the general statement

Explain how you arrived at your general statement

FISH PRODUCTION SL TYPE II Aim This task considers commercial fishing in a particular country in two different environments ndash the sea and fish farms (aquaculture) The data is taken from the UN Statistics Division Common Database

The following table gives the total mass of fish caught in the sea in thousands of tonnes (1 tonne = 1000 kilograms)

Define suitable variables and discuss any parametersconstraints Using technology plot the data points from the table on a graph Comment on any apparent trends in your graph and suggest suitable models Analytically develop a model that fits the data points (You may find it useful to consider a combination of functions) On a new set of axes draw your model function and the original data points Comment on any differences Revise your model if necessary

The table below gives the total mass of fish in thousands of tonnes from fish farms

Plot the data points from this table on a graph and discuss whether your analytical model for the original data fits the new data

Use technology to find a suitable model for the new data On a new set of axes draw both models Discuss how trends in the first model could be explained by trends in the second model

By considering both models discuss possible future trends in both types of fishing

GOLD MEDAL HEIGHTS SL TYPE II Aim The aim of this task is to consider the winning height for the menrsquos high jump in the Olympic Games

The table below gives the height (in centimeters) achieved by the gold medalists at various Olympic Games

Note The Olympic Games were not held in 1940 and 1944 Using technology plot the data points on a graph Define all variables used and state any parameters clearly Discuss any possible constraints of the task What type of function models the behaviour of the graph Explain why you chose this function Analytically create an equation to model the data in the above table On a new set of axes draw your model function and the original graph Comment on any differences Discuss the limitations of your model Refine your model if necessary Use technology to find another function that models the data On a new set of axes draw both your model functions Comment on any differences Had the Games been held in 1940 and 1944 estimate what the winning heights would have been and justify your answers Use your model to predict the winning height in 1984 and in 2016 Comment on your answers

The following table gives the winning heights for all the other Olympic Games since 1896

How well does your model fit the additional data Discuss the overall trend from 1896 to 2008 with specific references to significant fluctuations

What modifications if any need to be made to your model to fit the new data

MATHEMATICSHigher LevelThe portfolio ndash IA tasks

For use in 2012 and 2013

SHADOW FUNCTIONS HL TYPE ITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatWhile real zeros of polynomial functions may be easily read off the graph of thepolynomial the same is not true for complex zeros In this task you will investigate themethod of shadow functions and their generators which helps identify the real andimaginary components of complex zeros from key points along the x-axisPart A (Quadratic Polynomials)

Consider the quadratic function 2 2Write down the coordinates of the vertexShow that 1 y has zeros whereThe ldquoshadow functionrdquo to 1 y is another quadratic 2 y which shares the same vertex asHowever 2 y has opposite concavity to that of 1 y and its zeros are in the form

Use various values for a and b to generate pairs of functions 1 y and

Hence or otherwise express 2 y in terms of 1 y and m y where m y is called the ldquoshadowgenerating functionrdquo_ On a labelled diagram illustrate how the zeros of 2 y may be helpful in the determination

of the real and imaginary components of the complex zeros of 1 y

Part B (Cubic Polynomials)Now consider the cubic function 1 _ _ _ _ y _ (x _ 2) x _ (3_ 2i) x _ (3_ 2i) The shadow function in this case is another cubic function 2 y which shares two points with 1 y has opposite concavity and its zeros are _2 and 3_ 2 as depicted in the figure below The shadow

generating function in this case passes through the two points of intersection

Write down an expression for 2 y and hence find the points of intersection between 1 y and 2 y

_ Hence or otherwise determine the equation of the shadow generating function m y in thiscase_ Once again express 2 y in terms of 1 y and m y Use technology to investigate similarcubic functions_ Write a general statement about the functions 1 y 2 y and m y and prove your statement_ On a labelled diagram illustrate how the zeros of 2 y may be helpful in the determinationof the real and imaginary components of the complex zeros of 1 y

_ How can the findings with quadratics and cubics be applied to quartics

PATTERNS FROM COMPLEX NUMBERS HL TYPE ITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo format

Part A

Use de Moivrersquos theorem to obtain solutions to the equation z3 _1 _ 0 _ Use graphing software to plot these roots on an Argand diagram as well as a unit circlewith centre origin_ Choose a root and draw line segments from this root to the other two roots

_ Measure these line segments and comment on your results_ Repeat the above for the equations z4 _1 _ 0 and z5 _1 _ 0 Comment on your results andtry to formulate a conjecture_ Factorize zn _1 for n _ 3 4 and 5_ Use graphing software to test your conjecture for some more values of n 1048576 __ and makemodifications to your conjecture if necessary_ Prove your conjecture

Part B

Use de Moivrersquos theorem to obtain solutions to zn _ i for n _ 3 4 and 5_ Use graphing software to represent each of these solutions on an Argand diagram_ Generalize and prove your results for zn _ a _ bi where a _ bi _1

_ What happens when a _ bi _1

THE DICE GAME HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatThe aim of this task is to create a dice game in a casino and model this usingprobability It is important to examine how best to run the game from both the

perspective of a player and the casino In doing so analyse the game to consider theoptimal payments by the player and payouts by the casino_ Consider a game with two players Ann and Bob Ann has a red die and Bob a white dieThey roll their dice and note the number on the upper face Ann wins if her score is higherthan Bobrsquos (note that Bob wins if the scores are the same) If both players roll their diceonce each what is the probability that Ann will win the game_ Now consider the same game where Ann can roll her die a second time and will note thehigher score of the two rolls but Bob rolls only once In this case what is the probabilitythat Ann will win_ Investigate the game when both players can roll their dice twice and also when bothplayers can roll their dice more than twice but not necessarily the same number of times_ Consider the game in a casino where the player has a red die and the bank has a white dieFind a model for a game so that the casino makes a reasonable profit in the case where theplayer rolls the red die once and the bank rolls the white die once (When creating yourmodel you will need to consider how much a player must pay to play a game and howmuch the bank will pay out if the player wins Do this from the perspective of both theplayer and the casino and consider carefully the criteria for whether the game can be

considered worthwhile for both the player and the casino)_ Now consider other models for the game including cases such as where the player or the

bank rolls their dice multiple times or where multiple players are involved in the game

FILLING UP THE PETROL TANK HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatIn this task you will develop a mathematical model that helps motorists decide which ofthe following two options is more economicalOption 1 to buy petrol from a station on their normal route at a relatively higher priceOption 2 to drive an extra distance out of their normal route to buy cheaper petrolConsider a situation in which two motorists Arwa and Bao share the same driving route but owndifferent sized vehicles Arwa fills up her vehiclersquos tank at a station along her normal route forUS$ 1 p per litre On the other hand Bao drives an extra d kilometres out of his normal route to fillup his vehiclersquos tank for US$ p2 per litre where p2 _ p1 _ Choose suitable parameters for Arwarsquos and Baorsquos vehicles Justify your choices

_ Suppose 1 p _ US$100 per litre 2 p _ US$098 per litre and d _10 km Which motorist is getting the better deal Show all calculations and justify any assumptions you make_ On a spreadsheet choose several sets of values for 1 p 2 p and d to investigate further_ Define a set of variables that would be relevant in the above situationldquoEffective litresrdquo is a method of comparing the cost of petrol bought under the two optionsdescribed above Effective litres for a given vehicle are those litres used when the vehicle travelsits normal route_ Use your variables and parameters to write algebraic expressions for 1 E and 2 E whichrepresent the cost per effective litre under options 1 and 2 respectively_ Write a model that helps motorists decide on the more economical option for theirvehiclesIn the remainder of this task you need to consider the two vehicles you have chosen for Arwaand Bao_ Use your model to find the farthest distance that Bao should drive to obtain a 2 pricesaving_ Investigate the relationship between d and 2 p when 2 E is kept constant (eg US$090US$100 hellip etc) Use technology to draw a family of curves for Arwarsquos vehicle Repeatfor Baorsquos vehicle

_ For 2 E _ US$090 provide Arwa with information on three different stations that yieldthis same cost per effective litre Discuss how such information may be useful to Arwa_ For 2 E _ US$100 and 2 p _ US$080 compare the maximum distance that each motoristshould drive and still save moneyArwa is a busy person and wonders whether the saving in money would be worth the time shewould lose in extra driving_ Modify your model to account for the time taken to drive to and from an off-route station

Clearly justify any assumptions you make

IB DP Math SL type 2 IA portfolio task Fish production Gold Medal heightsIB DP Math HL type 2 IA portfolio task The dice game Filling up the petrol tankIB DP Math HL type 1 IA portfolio task shadow function Patterns from complex numberIB DP Math SL type 1 IA portfolio task Lacsaprsquos fraction Circles

IB ToK Essay TutorIB ToK Essay Topics 201213

IB ToK Essay Help Choosing the Right Essay TitleIB ToK Essay Help Planning and Writing the Essay

IB ToK Essay Help Marking and Assessing the EssayIB ToK Essay Help Grammar and Punctuation Check

IB TOK Essay on Common Sense IB Sample TOK essays

Examiners mark essays against the title as set Respond to the title exactly as given do not alter it in any way

Your essay must be between 1200 and 1600 words in length double spaced and typed in size 12 font

1 In what ways may disagreement aid the pursuit of knowledge in the natural and human sciences

2 ldquoOnly seeing general patterns can give us knowledge Only seeing particular examples can give us understandingrdquo To what

extent do you agree with these assertions3 ldquoThe possession of knowledge carries an ethical

responsibilityrdquo Evaluate this claim4 The traditional TOK diagram indicates four ways of knowing

Propose the inclusion of a fifth way of knowing selected from intuition memory or imagination and explore the knowledge

issues it may raise in two areas of knowledge5 ldquoThat which can be asserted without evidence can be

dismissed without evidencerdquo (Christopher Hitchens) Do you agree

6 Can we know when to trust our emotions in the pursuit of knowledge Consider history and one other area of knowledge

IB TOK ESSAY WRITERS HELP SOLUTIONIB COMMENTARY ESSAY HELP IB ECONOMICS

COMMENTARIES IB TOK IB EXTENDED ESSAY IB IB TOK Essay Help Mathematics Physics Economics

ChemistryIB TOK TUTORS EXAMPLES SAMPLES IB TOK

PRESENTATION TUTORS HELP IB ESSAY EXTENDED ESSAY

Online tuitions Home tuitions and IndividualGroup coaching and tuitions in MathsMathMathematics and physics

Chemistry EconomicsBusiness Management for VI-XII standards for IGCSE IBAP A AS-level Ed-excelOverseas

Students studying in Grade(IV-XII ) from US UK Canada Australia Newzealand etc can contact for online tutoring in mathrsquos amp science Economics and Business Studies subjects

Teaching Exclusively International School Students for IB IGCSE and A levels Excellent and Consistent Results for IB

IGCSEGCSE O and A Level exam IGCSE O Level IB Maths Physics Chemistry Economics and Business and Management

HL Business IA Internal Assessment HLSL Tasks English IOCIOP Help Guidance

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heights Lacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essay computer dossierbusiness management IA helpeconomics commentaryLab reports tuition

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heightsLacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essaycomputer dossierbusiness management IA helpeconomics commentary EVM Lab reports tuition

IB MathsPortfolio urdu shayari

helpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow functionnumbersgold medal

heightsLacasprsquos fractioncirclestutorIB math home tuition in delhi IB maths home tuition in delhi IB

maths home tuition in delhi IB math home tuition in delhiIB math home tuition in gurgaon IB maths home tuition in

gurgoan IB maths home tuition in gurgoan IB math home tuition in gurgaon

IB Mathematics Physics Chemistry Economics Business and Management HL SL Studies Theatre Stimulus help

IB Physics Mathematics Chemistry Economics Business and Management Presentation ITGS IA Computer help

IB Chemistry HL SL help Mathematics Physics Economics Chemistry Business

IB Economics HL SL Management Math Portfolio TOK Economics Historical Investigation Extended help

IB Business and Management HL SL help Essay Commentary storical Investigation Lab writing

IB Math Portfolio Help HL SL help Lab writing Project ESS English Spanish French Hindi

IB Math Project Help Studies help IB World Literature Theatre Stimulus Essay Commentary storical Investigation

IB Extended Essay Help TOK Presentation ITGS IA Computer Dossier IB World Literature Theatre Stimulus

IB TOK Essay Help Mathematics Physics Economics Chemistry Business Presentation ITGS IA Computer

IB Economics Commentary Help Management Math Portfolio HL SL Extended

IB Historical Investigation Help Essay Commentary storical Investigation Lab writing

IB Physics Lab writing Help Lab writing EVM Lab Report write

ups Project ESS English Spanish (Ab initio) French Hindi Extended Essay Help Tutors Examples Samples Solution

GuidanceIB Chemistry Lab writing Help IB World Literature Theatre

StimulusIB Biology Lab writing Help Presentation ITGS IA Computer Dossier SLHL Design Technology Design Projects RAPA IA

CADCAM Mathematics Physics Economics chemistryIB Business and Management Project Help Commentary storical

Investigation Lab writingIB ESS lab report help Mathematics Physics Economics

Chemistry Business EconomicsIB English HL SL help IB World Literature Theatre Stimulus

Economics Extended Essay IA Business IA IB Spanish Ab initio and Standard Level help Presentation ITGS

IA Computer DossierIB French Ab initio and Standard Level help Lab writing Project

ESS English Spanish French HindiIB Hindi HL SL help Mathematics Physics Economics

Chemistry Business EconomicsIB World Literature Help TOK Presentation ITGS IA Computer

Dossier EconomicsIB Theatre Stimulus help TOK Presentation ITGS IA Computer

Dossier EconomicsIB TOK Presentation help Management Math Portfolio HL SL

Extended ITGS IA Computer Dossier MathIB ITGS IA help IB World Literature Theatre Stimulus Math

Portfolio TOK Economics investigation Extended helpIB Computer Dossier help TOK Presentation ITGS IA

Computer Dossier Math Portfolio TOK Economics

Call or Email Ex-IB Examiner for Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website

httpwwwtopclassibtutorscom Online HelpTuition all over the world by the BestExpert IB Tutors Mail us or call

us for any queries

Essential Elements of a Math Portfolio Internal Assessment (IA) Task hlsl type 1 type 2 Problem Write-Up General

-‐

Name class and due date are clearly displayed

Introduction

-

Write up has an interesting (or pertinent) title

-‐

Task is properly introduced to the reader

-‐

This introduction should pose any major questions the task is seeking to answer

Body

-‐

Problem- solving process is completely explained throughout‐

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 7: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

Test the validity of the general statement by finding additional rows

Discuss the scope andor limitations of the general statement

Explain how you arrived at your general statement

FISH PRODUCTION SL TYPE II Aim This task considers commercial fishing in a particular country in two different environments ndash the sea and fish farms (aquaculture) The data is taken from the UN Statistics Division Common Database

The following table gives the total mass of fish caught in the sea in thousands of tonnes (1 tonne = 1000 kilograms)

Define suitable variables and discuss any parametersconstraints Using technology plot the data points from the table on a graph Comment on any apparent trends in your graph and suggest suitable models Analytically develop a model that fits the data points (You may find it useful to consider a combination of functions) On a new set of axes draw your model function and the original data points Comment on any differences Revise your model if necessary

The table below gives the total mass of fish in thousands of tonnes from fish farms

Plot the data points from this table on a graph and discuss whether your analytical model for the original data fits the new data

Use technology to find a suitable model for the new data On a new set of axes draw both models Discuss how trends in the first model could be explained by trends in the second model

By considering both models discuss possible future trends in both types of fishing

GOLD MEDAL HEIGHTS SL TYPE II Aim The aim of this task is to consider the winning height for the menrsquos high jump in the Olympic Games

The table below gives the height (in centimeters) achieved by the gold medalists at various Olympic Games

Note The Olympic Games were not held in 1940 and 1944 Using technology plot the data points on a graph Define all variables used and state any parameters clearly Discuss any possible constraints of the task What type of function models the behaviour of the graph Explain why you chose this function Analytically create an equation to model the data in the above table On a new set of axes draw your model function and the original graph Comment on any differences Discuss the limitations of your model Refine your model if necessary Use technology to find another function that models the data On a new set of axes draw both your model functions Comment on any differences Had the Games been held in 1940 and 1944 estimate what the winning heights would have been and justify your answers Use your model to predict the winning height in 1984 and in 2016 Comment on your answers

The following table gives the winning heights for all the other Olympic Games since 1896

How well does your model fit the additional data Discuss the overall trend from 1896 to 2008 with specific references to significant fluctuations

What modifications if any need to be made to your model to fit the new data

MATHEMATICSHigher LevelThe portfolio ndash IA tasks

For use in 2012 and 2013

SHADOW FUNCTIONS HL TYPE ITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatWhile real zeros of polynomial functions may be easily read off the graph of thepolynomial the same is not true for complex zeros In this task you will investigate themethod of shadow functions and their generators which helps identify the real andimaginary components of complex zeros from key points along the x-axisPart A (Quadratic Polynomials)

Consider the quadratic function 2 2Write down the coordinates of the vertexShow that 1 y has zeros whereThe ldquoshadow functionrdquo to 1 y is another quadratic 2 y which shares the same vertex asHowever 2 y has opposite concavity to that of 1 y and its zeros are in the form

Use various values for a and b to generate pairs of functions 1 y and

Hence or otherwise express 2 y in terms of 1 y and m y where m y is called the ldquoshadowgenerating functionrdquo_ On a labelled diagram illustrate how the zeros of 2 y may be helpful in the determination

of the real and imaginary components of the complex zeros of 1 y

Part B (Cubic Polynomials)Now consider the cubic function 1 _ _ _ _ y _ (x _ 2) x _ (3_ 2i) x _ (3_ 2i) The shadow function in this case is another cubic function 2 y which shares two points with 1 y has opposite concavity and its zeros are _2 and 3_ 2 as depicted in the figure below The shadow

generating function in this case passes through the two points of intersection

Write down an expression for 2 y and hence find the points of intersection between 1 y and 2 y

_ Hence or otherwise determine the equation of the shadow generating function m y in thiscase_ Once again express 2 y in terms of 1 y and m y Use technology to investigate similarcubic functions_ Write a general statement about the functions 1 y 2 y and m y and prove your statement_ On a labelled diagram illustrate how the zeros of 2 y may be helpful in the determinationof the real and imaginary components of the complex zeros of 1 y

_ How can the findings with quadratics and cubics be applied to quartics

PATTERNS FROM COMPLEX NUMBERS HL TYPE ITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo format

Part A

Use de Moivrersquos theorem to obtain solutions to the equation z3 _1 _ 0 _ Use graphing software to plot these roots on an Argand diagram as well as a unit circlewith centre origin_ Choose a root and draw line segments from this root to the other two roots

_ Measure these line segments and comment on your results_ Repeat the above for the equations z4 _1 _ 0 and z5 _1 _ 0 Comment on your results andtry to formulate a conjecture_ Factorize zn _1 for n _ 3 4 and 5_ Use graphing software to test your conjecture for some more values of n 1048576 __ and makemodifications to your conjecture if necessary_ Prove your conjecture

Part B

Use de Moivrersquos theorem to obtain solutions to zn _ i for n _ 3 4 and 5_ Use graphing software to represent each of these solutions on an Argand diagram_ Generalize and prove your results for zn _ a _ bi where a _ bi _1

_ What happens when a _ bi _1

THE DICE GAME HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatThe aim of this task is to create a dice game in a casino and model this usingprobability It is important to examine how best to run the game from both the

perspective of a player and the casino In doing so analyse the game to consider theoptimal payments by the player and payouts by the casino_ Consider a game with two players Ann and Bob Ann has a red die and Bob a white dieThey roll their dice and note the number on the upper face Ann wins if her score is higherthan Bobrsquos (note that Bob wins if the scores are the same) If both players roll their diceonce each what is the probability that Ann will win the game_ Now consider the same game where Ann can roll her die a second time and will note thehigher score of the two rolls but Bob rolls only once In this case what is the probabilitythat Ann will win_ Investigate the game when both players can roll their dice twice and also when bothplayers can roll their dice more than twice but not necessarily the same number of times_ Consider the game in a casino where the player has a red die and the bank has a white dieFind a model for a game so that the casino makes a reasonable profit in the case where theplayer rolls the red die once and the bank rolls the white die once (When creating yourmodel you will need to consider how much a player must pay to play a game and howmuch the bank will pay out if the player wins Do this from the perspective of both theplayer and the casino and consider carefully the criteria for whether the game can be

considered worthwhile for both the player and the casino)_ Now consider other models for the game including cases such as where the player or the

bank rolls their dice multiple times or where multiple players are involved in the game

FILLING UP THE PETROL TANK HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatIn this task you will develop a mathematical model that helps motorists decide which ofthe following two options is more economicalOption 1 to buy petrol from a station on their normal route at a relatively higher priceOption 2 to drive an extra distance out of their normal route to buy cheaper petrolConsider a situation in which two motorists Arwa and Bao share the same driving route but owndifferent sized vehicles Arwa fills up her vehiclersquos tank at a station along her normal route forUS$ 1 p per litre On the other hand Bao drives an extra d kilometres out of his normal route to fillup his vehiclersquos tank for US$ p2 per litre where p2 _ p1 _ Choose suitable parameters for Arwarsquos and Baorsquos vehicles Justify your choices

_ Suppose 1 p _ US$100 per litre 2 p _ US$098 per litre and d _10 km Which motorist is getting the better deal Show all calculations and justify any assumptions you make_ On a spreadsheet choose several sets of values for 1 p 2 p and d to investigate further_ Define a set of variables that would be relevant in the above situationldquoEffective litresrdquo is a method of comparing the cost of petrol bought under the two optionsdescribed above Effective litres for a given vehicle are those litres used when the vehicle travelsits normal route_ Use your variables and parameters to write algebraic expressions for 1 E and 2 E whichrepresent the cost per effective litre under options 1 and 2 respectively_ Write a model that helps motorists decide on the more economical option for theirvehiclesIn the remainder of this task you need to consider the two vehicles you have chosen for Arwaand Bao_ Use your model to find the farthest distance that Bao should drive to obtain a 2 pricesaving_ Investigate the relationship between d and 2 p when 2 E is kept constant (eg US$090US$100 hellip etc) Use technology to draw a family of curves for Arwarsquos vehicle Repeatfor Baorsquos vehicle

_ For 2 E _ US$090 provide Arwa with information on three different stations that yieldthis same cost per effective litre Discuss how such information may be useful to Arwa_ For 2 E _ US$100 and 2 p _ US$080 compare the maximum distance that each motoristshould drive and still save moneyArwa is a busy person and wonders whether the saving in money would be worth the time shewould lose in extra driving_ Modify your model to account for the time taken to drive to and from an off-route station

Clearly justify any assumptions you make

IB DP Math SL type 2 IA portfolio task Fish production Gold Medal heightsIB DP Math HL type 2 IA portfolio task The dice game Filling up the petrol tankIB DP Math HL type 1 IA portfolio task shadow function Patterns from complex numberIB DP Math SL type 1 IA portfolio task Lacsaprsquos fraction Circles

IB ToK Essay TutorIB ToK Essay Topics 201213

IB ToK Essay Help Choosing the Right Essay TitleIB ToK Essay Help Planning and Writing the Essay

IB ToK Essay Help Marking and Assessing the EssayIB ToK Essay Help Grammar and Punctuation Check

IB TOK Essay on Common Sense IB Sample TOK essays

Examiners mark essays against the title as set Respond to the title exactly as given do not alter it in any way

Your essay must be between 1200 and 1600 words in length double spaced and typed in size 12 font

1 In what ways may disagreement aid the pursuit of knowledge in the natural and human sciences

2 ldquoOnly seeing general patterns can give us knowledge Only seeing particular examples can give us understandingrdquo To what

extent do you agree with these assertions3 ldquoThe possession of knowledge carries an ethical

responsibilityrdquo Evaluate this claim4 The traditional TOK diagram indicates four ways of knowing

Propose the inclusion of a fifth way of knowing selected from intuition memory or imagination and explore the knowledge

issues it may raise in two areas of knowledge5 ldquoThat which can be asserted without evidence can be

dismissed without evidencerdquo (Christopher Hitchens) Do you agree

6 Can we know when to trust our emotions in the pursuit of knowledge Consider history and one other area of knowledge

IB TOK ESSAY WRITERS HELP SOLUTIONIB COMMENTARY ESSAY HELP IB ECONOMICS

COMMENTARIES IB TOK IB EXTENDED ESSAY IB IB TOK Essay Help Mathematics Physics Economics

ChemistryIB TOK TUTORS EXAMPLES SAMPLES IB TOK

PRESENTATION TUTORS HELP IB ESSAY EXTENDED ESSAY

Online tuitions Home tuitions and IndividualGroup coaching and tuitions in MathsMathMathematics and physics

Chemistry EconomicsBusiness Management for VI-XII standards for IGCSE IBAP A AS-level Ed-excelOverseas

Students studying in Grade(IV-XII ) from US UK Canada Australia Newzealand etc can contact for online tutoring in mathrsquos amp science Economics and Business Studies subjects

Teaching Exclusively International School Students for IB IGCSE and A levels Excellent and Consistent Results for IB

IGCSEGCSE O and A Level exam IGCSE O Level IB Maths Physics Chemistry Economics and Business and Management

HL Business IA Internal Assessment HLSL Tasks English IOCIOP Help Guidance

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heights Lacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essay computer dossierbusiness management IA helpeconomics commentaryLab reports tuition

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heightsLacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essaycomputer dossierbusiness management IA helpeconomics commentary EVM Lab reports tuition

IB MathsPortfolio urdu shayari

helpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow functionnumbersgold medal

heightsLacasprsquos fractioncirclestutorIB math home tuition in delhi IB maths home tuition in delhi IB

maths home tuition in delhi IB math home tuition in delhiIB math home tuition in gurgaon IB maths home tuition in

gurgoan IB maths home tuition in gurgoan IB math home tuition in gurgaon

IB Mathematics Physics Chemistry Economics Business and Management HL SL Studies Theatre Stimulus help

IB Physics Mathematics Chemistry Economics Business and Management Presentation ITGS IA Computer help

IB Chemistry HL SL help Mathematics Physics Economics Chemistry Business

IB Economics HL SL Management Math Portfolio TOK Economics Historical Investigation Extended help

IB Business and Management HL SL help Essay Commentary storical Investigation Lab writing

IB Math Portfolio Help HL SL help Lab writing Project ESS English Spanish French Hindi

IB Math Project Help Studies help IB World Literature Theatre Stimulus Essay Commentary storical Investigation

IB Extended Essay Help TOK Presentation ITGS IA Computer Dossier IB World Literature Theatre Stimulus

IB TOK Essay Help Mathematics Physics Economics Chemistry Business Presentation ITGS IA Computer

IB Economics Commentary Help Management Math Portfolio HL SL Extended

IB Historical Investigation Help Essay Commentary storical Investigation Lab writing

IB Physics Lab writing Help Lab writing EVM Lab Report write

ups Project ESS English Spanish (Ab initio) French Hindi Extended Essay Help Tutors Examples Samples Solution

GuidanceIB Chemistry Lab writing Help IB World Literature Theatre

StimulusIB Biology Lab writing Help Presentation ITGS IA Computer Dossier SLHL Design Technology Design Projects RAPA IA

CADCAM Mathematics Physics Economics chemistryIB Business and Management Project Help Commentary storical

Investigation Lab writingIB ESS lab report help Mathematics Physics Economics

Chemistry Business EconomicsIB English HL SL help IB World Literature Theatre Stimulus

Economics Extended Essay IA Business IA IB Spanish Ab initio and Standard Level help Presentation ITGS

IA Computer DossierIB French Ab initio and Standard Level help Lab writing Project

ESS English Spanish French HindiIB Hindi HL SL help Mathematics Physics Economics

Chemistry Business EconomicsIB World Literature Help TOK Presentation ITGS IA Computer

Dossier EconomicsIB Theatre Stimulus help TOK Presentation ITGS IA Computer

Dossier EconomicsIB TOK Presentation help Management Math Portfolio HL SL

Extended ITGS IA Computer Dossier MathIB ITGS IA help IB World Literature Theatre Stimulus Math

Portfolio TOK Economics investigation Extended helpIB Computer Dossier help TOK Presentation ITGS IA

Computer Dossier Math Portfolio TOK Economics

Call or Email Ex-IB Examiner for Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website

httpwwwtopclassibtutorscom Online HelpTuition all over the world by the BestExpert IB Tutors Mail us or call

us for any queries

Essential Elements of a Math Portfolio Internal Assessment (IA) Task hlsl type 1 type 2 Problem Write-Up General

-‐

Name class and due date are clearly displayed

Introduction

-

Write up has an interesting (or pertinent) title

-‐

Task is properly introduced to the reader

-‐

This introduction should pose any major questions the task is seeking to answer

Body

-‐

Problem- solving process is completely explained throughout‐

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 8: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

Use technology to find a suitable model for the new data On a new set of axes draw both models Discuss how trends in the first model could be explained by trends in the second model

By considering both models discuss possible future trends in both types of fishing

GOLD MEDAL HEIGHTS SL TYPE II Aim The aim of this task is to consider the winning height for the menrsquos high jump in the Olympic Games

The table below gives the height (in centimeters) achieved by the gold medalists at various Olympic Games

Note The Olympic Games were not held in 1940 and 1944 Using technology plot the data points on a graph Define all variables used and state any parameters clearly Discuss any possible constraints of the task What type of function models the behaviour of the graph Explain why you chose this function Analytically create an equation to model the data in the above table On a new set of axes draw your model function and the original graph Comment on any differences Discuss the limitations of your model Refine your model if necessary Use technology to find another function that models the data On a new set of axes draw both your model functions Comment on any differences Had the Games been held in 1940 and 1944 estimate what the winning heights would have been and justify your answers Use your model to predict the winning height in 1984 and in 2016 Comment on your answers

The following table gives the winning heights for all the other Olympic Games since 1896

How well does your model fit the additional data Discuss the overall trend from 1896 to 2008 with specific references to significant fluctuations

What modifications if any need to be made to your model to fit the new data

MATHEMATICSHigher LevelThe portfolio ndash IA tasks

For use in 2012 and 2013

SHADOW FUNCTIONS HL TYPE ITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatWhile real zeros of polynomial functions may be easily read off the graph of thepolynomial the same is not true for complex zeros In this task you will investigate themethod of shadow functions and their generators which helps identify the real andimaginary components of complex zeros from key points along the x-axisPart A (Quadratic Polynomials)

Consider the quadratic function 2 2Write down the coordinates of the vertexShow that 1 y has zeros whereThe ldquoshadow functionrdquo to 1 y is another quadratic 2 y which shares the same vertex asHowever 2 y has opposite concavity to that of 1 y and its zeros are in the form

Use various values for a and b to generate pairs of functions 1 y and

Hence or otherwise express 2 y in terms of 1 y and m y where m y is called the ldquoshadowgenerating functionrdquo_ On a labelled diagram illustrate how the zeros of 2 y may be helpful in the determination

of the real and imaginary components of the complex zeros of 1 y

Part B (Cubic Polynomials)Now consider the cubic function 1 _ _ _ _ y _ (x _ 2) x _ (3_ 2i) x _ (3_ 2i) The shadow function in this case is another cubic function 2 y which shares two points with 1 y has opposite concavity and its zeros are _2 and 3_ 2 as depicted in the figure below The shadow

generating function in this case passes through the two points of intersection

Write down an expression for 2 y and hence find the points of intersection between 1 y and 2 y

_ Hence or otherwise determine the equation of the shadow generating function m y in thiscase_ Once again express 2 y in terms of 1 y and m y Use technology to investigate similarcubic functions_ Write a general statement about the functions 1 y 2 y and m y and prove your statement_ On a labelled diagram illustrate how the zeros of 2 y may be helpful in the determinationof the real and imaginary components of the complex zeros of 1 y

_ How can the findings with quadratics and cubics be applied to quartics

PATTERNS FROM COMPLEX NUMBERS HL TYPE ITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo format

Part A

Use de Moivrersquos theorem to obtain solutions to the equation z3 _1 _ 0 _ Use graphing software to plot these roots on an Argand diagram as well as a unit circlewith centre origin_ Choose a root and draw line segments from this root to the other two roots

_ Measure these line segments and comment on your results_ Repeat the above for the equations z4 _1 _ 0 and z5 _1 _ 0 Comment on your results andtry to formulate a conjecture_ Factorize zn _1 for n _ 3 4 and 5_ Use graphing software to test your conjecture for some more values of n 1048576 __ and makemodifications to your conjecture if necessary_ Prove your conjecture

Part B

Use de Moivrersquos theorem to obtain solutions to zn _ i for n _ 3 4 and 5_ Use graphing software to represent each of these solutions on an Argand diagram_ Generalize and prove your results for zn _ a _ bi where a _ bi _1

_ What happens when a _ bi _1

THE DICE GAME HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatThe aim of this task is to create a dice game in a casino and model this usingprobability It is important to examine how best to run the game from both the

perspective of a player and the casino In doing so analyse the game to consider theoptimal payments by the player and payouts by the casino_ Consider a game with two players Ann and Bob Ann has a red die and Bob a white dieThey roll their dice and note the number on the upper face Ann wins if her score is higherthan Bobrsquos (note that Bob wins if the scores are the same) If both players roll their diceonce each what is the probability that Ann will win the game_ Now consider the same game where Ann can roll her die a second time and will note thehigher score of the two rolls but Bob rolls only once In this case what is the probabilitythat Ann will win_ Investigate the game when both players can roll their dice twice and also when bothplayers can roll their dice more than twice but not necessarily the same number of times_ Consider the game in a casino where the player has a red die and the bank has a white dieFind a model for a game so that the casino makes a reasonable profit in the case where theplayer rolls the red die once and the bank rolls the white die once (When creating yourmodel you will need to consider how much a player must pay to play a game and howmuch the bank will pay out if the player wins Do this from the perspective of both theplayer and the casino and consider carefully the criteria for whether the game can be

considered worthwhile for both the player and the casino)_ Now consider other models for the game including cases such as where the player or the

bank rolls their dice multiple times or where multiple players are involved in the game

FILLING UP THE PETROL TANK HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatIn this task you will develop a mathematical model that helps motorists decide which ofthe following two options is more economicalOption 1 to buy petrol from a station on their normal route at a relatively higher priceOption 2 to drive an extra distance out of their normal route to buy cheaper petrolConsider a situation in which two motorists Arwa and Bao share the same driving route but owndifferent sized vehicles Arwa fills up her vehiclersquos tank at a station along her normal route forUS$ 1 p per litre On the other hand Bao drives an extra d kilometres out of his normal route to fillup his vehiclersquos tank for US$ p2 per litre where p2 _ p1 _ Choose suitable parameters for Arwarsquos and Baorsquos vehicles Justify your choices

_ Suppose 1 p _ US$100 per litre 2 p _ US$098 per litre and d _10 km Which motorist is getting the better deal Show all calculations and justify any assumptions you make_ On a spreadsheet choose several sets of values for 1 p 2 p and d to investigate further_ Define a set of variables that would be relevant in the above situationldquoEffective litresrdquo is a method of comparing the cost of petrol bought under the two optionsdescribed above Effective litres for a given vehicle are those litres used when the vehicle travelsits normal route_ Use your variables and parameters to write algebraic expressions for 1 E and 2 E whichrepresent the cost per effective litre under options 1 and 2 respectively_ Write a model that helps motorists decide on the more economical option for theirvehiclesIn the remainder of this task you need to consider the two vehicles you have chosen for Arwaand Bao_ Use your model to find the farthest distance that Bao should drive to obtain a 2 pricesaving_ Investigate the relationship between d and 2 p when 2 E is kept constant (eg US$090US$100 hellip etc) Use technology to draw a family of curves for Arwarsquos vehicle Repeatfor Baorsquos vehicle

_ For 2 E _ US$090 provide Arwa with information on three different stations that yieldthis same cost per effective litre Discuss how such information may be useful to Arwa_ For 2 E _ US$100 and 2 p _ US$080 compare the maximum distance that each motoristshould drive and still save moneyArwa is a busy person and wonders whether the saving in money would be worth the time shewould lose in extra driving_ Modify your model to account for the time taken to drive to and from an off-route station

Clearly justify any assumptions you make

IB DP Math SL type 2 IA portfolio task Fish production Gold Medal heightsIB DP Math HL type 2 IA portfolio task The dice game Filling up the petrol tankIB DP Math HL type 1 IA portfolio task shadow function Patterns from complex numberIB DP Math SL type 1 IA portfolio task Lacsaprsquos fraction Circles

IB ToK Essay TutorIB ToK Essay Topics 201213

IB ToK Essay Help Choosing the Right Essay TitleIB ToK Essay Help Planning and Writing the Essay

IB ToK Essay Help Marking and Assessing the EssayIB ToK Essay Help Grammar and Punctuation Check

IB TOK Essay on Common Sense IB Sample TOK essays

Examiners mark essays against the title as set Respond to the title exactly as given do not alter it in any way

Your essay must be between 1200 and 1600 words in length double spaced and typed in size 12 font

1 In what ways may disagreement aid the pursuit of knowledge in the natural and human sciences

2 ldquoOnly seeing general patterns can give us knowledge Only seeing particular examples can give us understandingrdquo To what

extent do you agree with these assertions3 ldquoThe possession of knowledge carries an ethical

responsibilityrdquo Evaluate this claim4 The traditional TOK diagram indicates four ways of knowing

Propose the inclusion of a fifth way of knowing selected from intuition memory or imagination and explore the knowledge

issues it may raise in two areas of knowledge5 ldquoThat which can be asserted without evidence can be

dismissed without evidencerdquo (Christopher Hitchens) Do you agree

6 Can we know when to trust our emotions in the pursuit of knowledge Consider history and one other area of knowledge

IB TOK ESSAY WRITERS HELP SOLUTIONIB COMMENTARY ESSAY HELP IB ECONOMICS

COMMENTARIES IB TOK IB EXTENDED ESSAY IB IB TOK Essay Help Mathematics Physics Economics

ChemistryIB TOK TUTORS EXAMPLES SAMPLES IB TOK

PRESENTATION TUTORS HELP IB ESSAY EXTENDED ESSAY

Online tuitions Home tuitions and IndividualGroup coaching and tuitions in MathsMathMathematics and physics

Chemistry EconomicsBusiness Management for VI-XII standards for IGCSE IBAP A AS-level Ed-excelOverseas

Students studying in Grade(IV-XII ) from US UK Canada Australia Newzealand etc can contact for online tutoring in mathrsquos amp science Economics and Business Studies subjects

Teaching Exclusively International School Students for IB IGCSE and A levels Excellent and Consistent Results for IB

IGCSEGCSE O and A Level exam IGCSE O Level IB Maths Physics Chemistry Economics and Business and Management

HL Business IA Internal Assessment HLSL Tasks English IOCIOP Help Guidance

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heights Lacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essay computer dossierbusiness management IA helpeconomics commentaryLab reports tuition

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heightsLacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essaycomputer dossierbusiness management IA helpeconomics commentary EVM Lab reports tuition

IB MathsPortfolio urdu shayari

helpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow functionnumbersgold medal

heightsLacasprsquos fractioncirclestutorIB math home tuition in delhi IB maths home tuition in delhi IB

maths home tuition in delhi IB math home tuition in delhiIB math home tuition in gurgaon IB maths home tuition in

gurgoan IB maths home tuition in gurgoan IB math home tuition in gurgaon

IB Mathematics Physics Chemistry Economics Business and Management HL SL Studies Theatre Stimulus help

IB Physics Mathematics Chemistry Economics Business and Management Presentation ITGS IA Computer help

IB Chemistry HL SL help Mathematics Physics Economics Chemistry Business

IB Economics HL SL Management Math Portfolio TOK Economics Historical Investigation Extended help

IB Business and Management HL SL help Essay Commentary storical Investigation Lab writing

IB Math Portfolio Help HL SL help Lab writing Project ESS English Spanish French Hindi

IB Math Project Help Studies help IB World Literature Theatre Stimulus Essay Commentary storical Investigation

IB Extended Essay Help TOK Presentation ITGS IA Computer Dossier IB World Literature Theatre Stimulus

IB TOK Essay Help Mathematics Physics Economics Chemistry Business Presentation ITGS IA Computer

IB Economics Commentary Help Management Math Portfolio HL SL Extended

IB Historical Investigation Help Essay Commentary storical Investigation Lab writing

IB Physics Lab writing Help Lab writing EVM Lab Report write

ups Project ESS English Spanish (Ab initio) French Hindi Extended Essay Help Tutors Examples Samples Solution

GuidanceIB Chemistry Lab writing Help IB World Literature Theatre

StimulusIB Biology Lab writing Help Presentation ITGS IA Computer Dossier SLHL Design Technology Design Projects RAPA IA

CADCAM Mathematics Physics Economics chemistryIB Business and Management Project Help Commentary storical

Investigation Lab writingIB ESS lab report help Mathematics Physics Economics

Chemistry Business EconomicsIB English HL SL help IB World Literature Theatre Stimulus

Economics Extended Essay IA Business IA IB Spanish Ab initio and Standard Level help Presentation ITGS

IA Computer DossierIB French Ab initio and Standard Level help Lab writing Project

ESS English Spanish French HindiIB Hindi HL SL help Mathematics Physics Economics

Chemistry Business EconomicsIB World Literature Help TOK Presentation ITGS IA Computer

Dossier EconomicsIB Theatre Stimulus help TOK Presentation ITGS IA Computer

Dossier EconomicsIB TOK Presentation help Management Math Portfolio HL SL

Extended ITGS IA Computer Dossier MathIB ITGS IA help IB World Literature Theatre Stimulus Math

Portfolio TOK Economics investigation Extended helpIB Computer Dossier help TOK Presentation ITGS IA

Computer Dossier Math Portfolio TOK Economics

Call or Email Ex-IB Examiner for Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website

httpwwwtopclassibtutorscom Online HelpTuition all over the world by the BestExpert IB Tutors Mail us or call

us for any queries

Essential Elements of a Math Portfolio Internal Assessment (IA) Task hlsl type 1 type 2 Problem Write-Up General

-‐

Name class and due date are clearly displayed

Introduction

-

Write up has an interesting (or pertinent) title

-‐

Task is properly introduced to the reader

-‐

This introduction should pose any major questions the task is seeking to answer

Body

-‐

Problem- solving process is completely explained throughout‐

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 9: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

The following table gives the winning heights for all the other Olympic Games since 1896

How well does your model fit the additional data Discuss the overall trend from 1896 to 2008 with specific references to significant fluctuations

What modifications if any need to be made to your model to fit the new data

MATHEMATICSHigher LevelThe portfolio ndash IA tasks

For use in 2012 and 2013

SHADOW FUNCTIONS HL TYPE ITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatWhile real zeros of polynomial functions may be easily read off the graph of thepolynomial the same is not true for complex zeros In this task you will investigate themethod of shadow functions and their generators which helps identify the real andimaginary components of complex zeros from key points along the x-axisPart A (Quadratic Polynomials)

Consider the quadratic function 2 2Write down the coordinates of the vertexShow that 1 y has zeros whereThe ldquoshadow functionrdquo to 1 y is another quadratic 2 y which shares the same vertex asHowever 2 y has opposite concavity to that of 1 y and its zeros are in the form

Use various values for a and b to generate pairs of functions 1 y and

Hence or otherwise express 2 y in terms of 1 y and m y where m y is called the ldquoshadowgenerating functionrdquo_ On a labelled diagram illustrate how the zeros of 2 y may be helpful in the determination

of the real and imaginary components of the complex zeros of 1 y

Part B (Cubic Polynomials)Now consider the cubic function 1 _ _ _ _ y _ (x _ 2) x _ (3_ 2i) x _ (3_ 2i) The shadow function in this case is another cubic function 2 y which shares two points with 1 y has opposite concavity and its zeros are _2 and 3_ 2 as depicted in the figure below The shadow

generating function in this case passes through the two points of intersection

Write down an expression for 2 y and hence find the points of intersection between 1 y and 2 y

_ Hence or otherwise determine the equation of the shadow generating function m y in thiscase_ Once again express 2 y in terms of 1 y and m y Use technology to investigate similarcubic functions_ Write a general statement about the functions 1 y 2 y and m y and prove your statement_ On a labelled diagram illustrate how the zeros of 2 y may be helpful in the determinationof the real and imaginary components of the complex zeros of 1 y

_ How can the findings with quadratics and cubics be applied to quartics

PATTERNS FROM COMPLEX NUMBERS HL TYPE ITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo format

Part A

Use de Moivrersquos theorem to obtain solutions to the equation z3 _1 _ 0 _ Use graphing software to plot these roots on an Argand diagram as well as a unit circlewith centre origin_ Choose a root and draw line segments from this root to the other two roots

_ Measure these line segments and comment on your results_ Repeat the above for the equations z4 _1 _ 0 and z5 _1 _ 0 Comment on your results andtry to formulate a conjecture_ Factorize zn _1 for n _ 3 4 and 5_ Use graphing software to test your conjecture for some more values of n 1048576 __ and makemodifications to your conjecture if necessary_ Prove your conjecture

Part B

Use de Moivrersquos theorem to obtain solutions to zn _ i for n _ 3 4 and 5_ Use graphing software to represent each of these solutions on an Argand diagram_ Generalize and prove your results for zn _ a _ bi where a _ bi _1

_ What happens when a _ bi _1

THE DICE GAME HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatThe aim of this task is to create a dice game in a casino and model this usingprobability It is important to examine how best to run the game from both the

perspective of a player and the casino In doing so analyse the game to consider theoptimal payments by the player and payouts by the casino_ Consider a game with two players Ann and Bob Ann has a red die and Bob a white dieThey roll their dice and note the number on the upper face Ann wins if her score is higherthan Bobrsquos (note that Bob wins if the scores are the same) If both players roll their diceonce each what is the probability that Ann will win the game_ Now consider the same game where Ann can roll her die a second time and will note thehigher score of the two rolls but Bob rolls only once In this case what is the probabilitythat Ann will win_ Investigate the game when both players can roll their dice twice and also when bothplayers can roll their dice more than twice but not necessarily the same number of times_ Consider the game in a casino where the player has a red die and the bank has a white dieFind a model for a game so that the casino makes a reasonable profit in the case where theplayer rolls the red die once and the bank rolls the white die once (When creating yourmodel you will need to consider how much a player must pay to play a game and howmuch the bank will pay out if the player wins Do this from the perspective of both theplayer and the casino and consider carefully the criteria for whether the game can be

considered worthwhile for both the player and the casino)_ Now consider other models for the game including cases such as where the player or the

bank rolls their dice multiple times or where multiple players are involved in the game

FILLING UP THE PETROL TANK HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatIn this task you will develop a mathematical model that helps motorists decide which ofthe following two options is more economicalOption 1 to buy petrol from a station on their normal route at a relatively higher priceOption 2 to drive an extra distance out of their normal route to buy cheaper petrolConsider a situation in which two motorists Arwa and Bao share the same driving route but owndifferent sized vehicles Arwa fills up her vehiclersquos tank at a station along her normal route forUS$ 1 p per litre On the other hand Bao drives an extra d kilometres out of his normal route to fillup his vehiclersquos tank for US$ p2 per litre where p2 _ p1 _ Choose suitable parameters for Arwarsquos and Baorsquos vehicles Justify your choices

_ Suppose 1 p _ US$100 per litre 2 p _ US$098 per litre and d _10 km Which motorist is getting the better deal Show all calculations and justify any assumptions you make_ On a spreadsheet choose several sets of values for 1 p 2 p and d to investigate further_ Define a set of variables that would be relevant in the above situationldquoEffective litresrdquo is a method of comparing the cost of petrol bought under the two optionsdescribed above Effective litres for a given vehicle are those litres used when the vehicle travelsits normal route_ Use your variables and parameters to write algebraic expressions for 1 E and 2 E whichrepresent the cost per effective litre under options 1 and 2 respectively_ Write a model that helps motorists decide on the more economical option for theirvehiclesIn the remainder of this task you need to consider the two vehicles you have chosen for Arwaand Bao_ Use your model to find the farthest distance that Bao should drive to obtain a 2 pricesaving_ Investigate the relationship between d and 2 p when 2 E is kept constant (eg US$090US$100 hellip etc) Use technology to draw a family of curves for Arwarsquos vehicle Repeatfor Baorsquos vehicle

_ For 2 E _ US$090 provide Arwa with information on three different stations that yieldthis same cost per effective litre Discuss how such information may be useful to Arwa_ For 2 E _ US$100 and 2 p _ US$080 compare the maximum distance that each motoristshould drive and still save moneyArwa is a busy person and wonders whether the saving in money would be worth the time shewould lose in extra driving_ Modify your model to account for the time taken to drive to and from an off-route station

Clearly justify any assumptions you make

IB DP Math SL type 2 IA portfolio task Fish production Gold Medal heightsIB DP Math HL type 2 IA portfolio task The dice game Filling up the petrol tankIB DP Math HL type 1 IA portfolio task shadow function Patterns from complex numberIB DP Math SL type 1 IA portfolio task Lacsaprsquos fraction Circles

IB ToK Essay TutorIB ToK Essay Topics 201213

IB ToK Essay Help Choosing the Right Essay TitleIB ToK Essay Help Planning and Writing the Essay

IB ToK Essay Help Marking and Assessing the EssayIB ToK Essay Help Grammar and Punctuation Check

IB TOK Essay on Common Sense IB Sample TOK essays

Examiners mark essays against the title as set Respond to the title exactly as given do not alter it in any way

Your essay must be between 1200 and 1600 words in length double spaced and typed in size 12 font

1 In what ways may disagreement aid the pursuit of knowledge in the natural and human sciences

2 ldquoOnly seeing general patterns can give us knowledge Only seeing particular examples can give us understandingrdquo To what

extent do you agree with these assertions3 ldquoThe possession of knowledge carries an ethical

responsibilityrdquo Evaluate this claim4 The traditional TOK diagram indicates four ways of knowing

Propose the inclusion of a fifth way of knowing selected from intuition memory or imagination and explore the knowledge

issues it may raise in two areas of knowledge5 ldquoThat which can be asserted without evidence can be

dismissed without evidencerdquo (Christopher Hitchens) Do you agree

6 Can we know when to trust our emotions in the pursuit of knowledge Consider history and one other area of knowledge

IB TOK ESSAY WRITERS HELP SOLUTIONIB COMMENTARY ESSAY HELP IB ECONOMICS

COMMENTARIES IB TOK IB EXTENDED ESSAY IB IB TOK Essay Help Mathematics Physics Economics

ChemistryIB TOK TUTORS EXAMPLES SAMPLES IB TOK

PRESENTATION TUTORS HELP IB ESSAY EXTENDED ESSAY

Online tuitions Home tuitions and IndividualGroup coaching and tuitions in MathsMathMathematics and physics

Chemistry EconomicsBusiness Management for VI-XII standards for IGCSE IBAP A AS-level Ed-excelOverseas

Students studying in Grade(IV-XII ) from US UK Canada Australia Newzealand etc can contact for online tutoring in mathrsquos amp science Economics and Business Studies subjects

Teaching Exclusively International School Students for IB IGCSE and A levels Excellent and Consistent Results for IB

IGCSEGCSE O and A Level exam IGCSE O Level IB Maths Physics Chemistry Economics and Business and Management

HL Business IA Internal Assessment HLSL Tasks English IOCIOP Help Guidance

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heights Lacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essay computer dossierbusiness management IA helpeconomics commentaryLab reports tuition

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heightsLacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essaycomputer dossierbusiness management IA helpeconomics commentary EVM Lab reports tuition

IB MathsPortfolio urdu shayari

helpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow functionnumbersgold medal

heightsLacasprsquos fractioncirclestutorIB math home tuition in delhi IB maths home tuition in delhi IB

maths home tuition in delhi IB math home tuition in delhiIB math home tuition in gurgaon IB maths home tuition in

gurgoan IB maths home tuition in gurgoan IB math home tuition in gurgaon

IB Mathematics Physics Chemistry Economics Business and Management HL SL Studies Theatre Stimulus help

IB Physics Mathematics Chemistry Economics Business and Management Presentation ITGS IA Computer help

IB Chemistry HL SL help Mathematics Physics Economics Chemistry Business

IB Economics HL SL Management Math Portfolio TOK Economics Historical Investigation Extended help

IB Business and Management HL SL help Essay Commentary storical Investigation Lab writing

IB Math Portfolio Help HL SL help Lab writing Project ESS English Spanish French Hindi

IB Math Project Help Studies help IB World Literature Theatre Stimulus Essay Commentary storical Investigation

IB Extended Essay Help TOK Presentation ITGS IA Computer Dossier IB World Literature Theatre Stimulus

IB TOK Essay Help Mathematics Physics Economics Chemistry Business Presentation ITGS IA Computer

IB Economics Commentary Help Management Math Portfolio HL SL Extended

IB Historical Investigation Help Essay Commentary storical Investigation Lab writing

IB Physics Lab writing Help Lab writing EVM Lab Report write

ups Project ESS English Spanish (Ab initio) French Hindi Extended Essay Help Tutors Examples Samples Solution

GuidanceIB Chemistry Lab writing Help IB World Literature Theatre

StimulusIB Biology Lab writing Help Presentation ITGS IA Computer Dossier SLHL Design Technology Design Projects RAPA IA

CADCAM Mathematics Physics Economics chemistryIB Business and Management Project Help Commentary storical

Investigation Lab writingIB ESS lab report help Mathematics Physics Economics

Chemistry Business EconomicsIB English HL SL help IB World Literature Theatre Stimulus

Economics Extended Essay IA Business IA IB Spanish Ab initio and Standard Level help Presentation ITGS

IA Computer DossierIB French Ab initio and Standard Level help Lab writing Project

ESS English Spanish French HindiIB Hindi HL SL help Mathematics Physics Economics

Chemistry Business EconomicsIB World Literature Help TOK Presentation ITGS IA Computer

Dossier EconomicsIB Theatre Stimulus help TOK Presentation ITGS IA Computer

Dossier EconomicsIB TOK Presentation help Management Math Portfolio HL SL

Extended ITGS IA Computer Dossier MathIB ITGS IA help IB World Literature Theatre Stimulus Math

Portfolio TOK Economics investigation Extended helpIB Computer Dossier help TOK Presentation ITGS IA

Computer Dossier Math Portfolio TOK Economics

Call or Email Ex-IB Examiner for Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website

httpwwwtopclassibtutorscom Online HelpTuition all over the world by the BestExpert IB Tutors Mail us or call

us for any queries

Essential Elements of a Math Portfolio Internal Assessment (IA) Task hlsl type 1 type 2 Problem Write-Up General

-‐

Name class and due date are clearly displayed

Introduction

-

Write up has an interesting (or pertinent) title

-‐

Task is properly introduced to the reader

-‐

This introduction should pose any major questions the task is seeking to answer

Body

-‐

Problem- solving process is completely explained throughout‐

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 10: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

Consider the quadratic function 2 2Write down the coordinates of the vertexShow that 1 y has zeros whereThe ldquoshadow functionrdquo to 1 y is another quadratic 2 y which shares the same vertex asHowever 2 y has opposite concavity to that of 1 y and its zeros are in the form

Use various values for a and b to generate pairs of functions 1 y and

Hence or otherwise express 2 y in terms of 1 y and m y where m y is called the ldquoshadowgenerating functionrdquo_ On a labelled diagram illustrate how the zeros of 2 y may be helpful in the determination

of the real and imaginary components of the complex zeros of 1 y

Part B (Cubic Polynomials)Now consider the cubic function 1 _ _ _ _ y _ (x _ 2) x _ (3_ 2i) x _ (3_ 2i) The shadow function in this case is another cubic function 2 y which shares two points with 1 y has opposite concavity and its zeros are _2 and 3_ 2 as depicted in the figure below The shadow

generating function in this case passes through the two points of intersection

Write down an expression for 2 y and hence find the points of intersection between 1 y and 2 y

_ Hence or otherwise determine the equation of the shadow generating function m y in thiscase_ Once again express 2 y in terms of 1 y and m y Use technology to investigate similarcubic functions_ Write a general statement about the functions 1 y 2 y and m y and prove your statement_ On a labelled diagram illustrate how the zeros of 2 y may be helpful in the determinationof the real and imaginary components of the complex zeros of 1 y

_ How can the findings with quadratics and cubics be applied to quartics

PATTERNS FROM COMPLEX NUMBERS HL TYPE ITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo format

Part A

Use de Moivrersquos theorem to obtain solutions to the equation z3 _1 _ 0 _ Use graphing software to plot these roots on an Argand diagram as well as a unit circlewith centre origin_ Choose a root and draw line segments from this root to the other two roots

_ Measure these line segments and comment on your results_ Repeat the above for the equations z4 _1 _ 0 and z5 _1 _ 0 Comment on your results andtry to formulate a conjecture_ Factorize zn _1 for n _ 3 4 and 5_ Use graphing software to test your conjecture for some more values of n 1048576 __ and makemodifications to your conjecture if necessary_ Prove your conjecture

Part B

Use de Moivrersquos theorem to obtain solutions to zn _ i for n _ 3 4 and 5_ Use graphing software to represent each of these solutions on an Argand diagram_ Generalize and prove your results for zn _ a _ bi where a _ bi _1

_ What happens when a _ bi _1

THE DICE GAME HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatThe aim of this task is to create a dice game in a casino and model this usingprobability It is important to examine how best to run the game from both the

perspective of a player and the casino In doing so analyse the game to consider theoptimal payments by the player and payouts by the casino_ Consider a game with two players Ann and Bob Ann has a red die and Bob a white dieThey roll their dice and note the number on the upper face Ann wins if her score is higherthan Bobrsquos (note that Bob wins if the scores are the same) If both players roll their diceonce each what is the probability that Ann will win the game_ Now consider the same game where Ann can roll her die a second time and will note thehigher score of the two rolls but Bob rolls only once In this case what is the probabilitythat Ann will win_ Investigate the game when both players can roll their dice twice and also when bothplayers can roll their dice more than twice but not necessarily the same number of times_ Consider the game in a casino where the player has a red die and the bank has a white dieFind a model for a game so that the casino makes a reasonable profit in the case where theplayer rolls the red die once and the bank rolls the white die once (When creating yourmodel you will need to consider how much a player must pay to play a game and howmuch the bank will pay out if the player wins Do this from the perspective of both theplayer and the casino and consider carefully the criteria for whether the game can be

considered worthwhile for both the player and the casino)_ Now consider other models for the game including cases such as where the player or the

bank rolls their dice multiple times or where multiple players are involved in the game

FILLING UP THE PETROL TANK HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatIn this task you will develop a mathematical model that helps motorists decide which ofthe following two options is more economicalOption 1 to buy petrol from a station on their normal route at a relatively higher priceOption 2 to drive an extra distance out of their normal route to buy cheaper petrolConsider a situation in which two motorists Arwa and Bao share the same driving route but owndifferent sized vehicles Arwa fills up her vehiclersquos tank at a station along her normal route forUS$ 1 p per litre On the other hand Bao drives an extra d kilometres out of his normal route to fillup his vehiclersquos tank for US$ p2 per litre where p2 _ p1 _ Choose suitable parameters for Arwarsquos and Baorsquos vehicles Justify your choices

_ Suppose 1 p _ US$100 per litre 2 p _ US$098 per litre and d _10 km Which motorist is getting the better deal Show all calculations and justify any assumptions you make_ On a spreadsheet choose several sets of values for 1 p 2 p and d to investigate further_ Define a set of variables that would be relevant in the above situationldquoEffective litresrdquo is a method of comparing the cost of petrol bought under the two optionsdescribed above Effective litres for a given vehicle are those litres used when the vehicle travelsits normal route_ Use your variables and parameters to write algebraic expressions for 1 E and 2 E whichrepresent the cost per effective litre under options 1 and 2 respectively_ Write a model that helps motorists decide on the more economical option for theirvehiclesIn the remainder of this task you need to consider the two vehicles you have chosen for Arwaand Bao_ Use your model to find the farthest distance that Bao should drive to obtain a 2 pricesaving_ Investigate the relationship between d and 2 p when 2 E is kept constant (eg US$090US$100 hellip etc) Use technology to draw a family of curves for Arwarsquos vehicle Repeatfor Baorsquos vehicle

_ For 2 E _ US$090 provide Arwa with information on three different stations that yieldthis same cost per effective litre Discuss how such information may be useful to Arwa_ For 2 E _ US$100 and 2 p _ US$080 compare the maximum distance that each motoristshould drive and still save moneyArwa is a busy person and wonders whether the saving in money would be worth the time shewould lose in extra driving_ Modify your model to account for the time taken to drive to and from an off-route station

Clearly justify any assumptions you make

IB DP Math SL type 2 IA portfolio task Fish production Gold Medal heightsIB DP Math HL type 2 IA portfolio task The dice game Filling up the petrol tankIB DP Math HL type 1 IA portfolio task shadow function Patterns from complex numberIB DP Math SL type 1 IA portfolio task Lacsaprsquos fraction Circles

IB ToK Essay TutorIB ToK Essay Topics 201213

IB ToK Essay Help Choosing the Right Essay TitleIB ToK Essay Help Planning and Writing the Essay

IB ToK Essay Help Marking and Assessing the EssayIB ToK Essay Help Grammar and Punctuation Check

IB TOK Essay on Common Sense IB Sample TOK essays

Examiners mark essays against the title as set Respond to the title exactly as given do not alter it in any way

Your essay must be between 1200 and 1600 words in length double spaced and typed in size 12 font

1 In what ways may disagreement aid the pursuit of knowledge in the natural and human sciences

2 ldquoOnly seeing general patterns can give us knowledge Only seeing particular examples can give us understandingrdquo To what

extent do you agree with these assertions3 ldquoThe possession of knowledge carries an ethical

responsibilityrdquo Evaluate this claim4 The traditional TOK diagram indicates four ways of knowing

Propose the inclusion of a fifth way of knowing selected from intuition memory or imagination and explore the knowledge

issues it may raise in two areas of knowledge5 ldquoThat which can be asserted without evidence can be

dismissed without evidencerdquo (Christopher Hitchens) Do you agree

6 Can we know when to trust our emotions in the pursuit of knowledge Consider history and one other area of knowledge

IB TOK ESSAY WRITERS HELP SOLUTIONIB COMMENTARY ESSAY HELP IB ECONOMICS

COMMENTARIES IB TOK IB EXTENDED ESSAY IB IB TOK Essay Help Mathematics Physics Economics

ChemistryIB TOK TUTORS EXAMPLES SAMPLES IB TOK

PRESENTATION TUTORS HELP IB ESSAY EXTENDED ESSAY

Online tuitions Home tuitions and IndividualGroup coaching and tuitions in MathsMathMathematics and physics

Chemistry EconomicsBusiness Management for VI-XII standards for IGCSE IBAP A AS-level Ed-excelOverseas

Students studying in Grade(IV-XII ) from US UK Canada Australia Newzealand etc can contact for online tutoring in mathrsquos amp science Economics and Business Studies subjects

Teaching Exclusively International School Students for IB IGCSE and A levels Excellent and Consistent Results for IB

IGCSEGCSE O and A Level exam IGCSE O Level IB Maths Physics Chemistry Economics and Business and Management

HL Business IA Internal Assessment HLSL Tasks English IOCIOP Help Guidance

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heights Lacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essay computer dossierbusiness management IA helpeconomics commentaryLab reports tuition

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heightsLacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essaycomputer dossierbusiness management IA helpeconomics commentary EVM Lab reports tuition

IB MathsPortfolio urdu shayari

helpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow functionnumbersgold medal

heightsLacasprsquos fractioncirclestutorIB math home tuition in delhi IB maths home tuition in delhi IB

maths home tuition in delhi IB math home tuition in delhiIB math home tuition in gurgaon IB maths home tuition in

gurgoan IB maths home tuition in gurgoan IB math home tuition in gurgaon

IB Mathematics Physics Chemistry Economics Business and Management HL SL Studies Theatre Stimulus help

IB Physics Mathematics Chemistry Economics Business and Management Presentation ITGS IA Computer help

IB Chemistry HL SL help Mathematics Physics Economics Chemistry Business

IB Economics HL SL Management Math Portfolio TOK Economics Historical Investigation Extended help

IB Business and Management HL SL help Essay Commentary storical Investigation Lab writing

IB Math Portfolio Help HL SL help Lab writing Project ESS English Spanish French Hindi

IB Math Project Help Studies help IB World Literature Theatre Stimulus Essay Commentary storical Investigation

IB Extended Essay Help TOK Presentation ITGS IA Computer Dossier IB World Literature Theatre Stimulus

IB TOK Essay Help Mathematics Physics Economics Chemistry Business Presentation ITGS IA Computer

IB Economics Commentary Help Management Math Portfolio HL SL Extended

IB Historical Investigation Help Essay Commentary storical Investigation Lab writing

IB Physics Lab writing Help Lab writing EVM Lab Report write

ups Project ESS English Spanish (Ab initio) French Hindi Extended Essay Help Tutors Examples Samples Solution

GuidanceIB Chemistry Lab writing Help IB World Literature Theatre

StimulusIB Biology Lab writing Help Presentation ITGS IA Computer Dossier SLHL Design Technology Design Projects RAPA IA

CADCAM Mathematics Physics Economics chemistryIB Business and Management Project Help Commentary storical

Investigation Lab writingIB ESS lab report help Mathematics Physics Economics

Chemistry Business EconomicsIB English HL SL help IB World Literature Theatre Stimulus

Economics Extended Essay IA Business IA IB Spanish Ab initio and Standard Level help Presentation ITGS

IA Computer DossierIB French Ab initio and Standard Level help Lab writing Project

ESS English Spanish French HindiIB Hindi HL SL help Mathematics Physics Economics

Chemistry Business EconomicsIB World Literature Help TOK Presentation ITGS IA Computer

Dossier EconomicsIB Theatre Stimulus help TOK Presentation ITGS IA Computer

Dossier EconomicsIB TOK Presentation help Management Math Portfolio HL SL

Extended ITGS IA Computer Dossier MathIB ITGS IA help IB World Literature Theatre Stimulus Math

Portfolio TOK Economics investigation Extended helpIB Computer Dossier help TOK Presentation ITGS IA

Computer Dossier Math Portfolio TOK Economics

Call or Email Ex-IB Examiner for Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website

httpwwwtopclassibtutorscom Online HelpTuition all over the world by the BestExpert IB Tutors Mail us or call

us for any queries

Essential Elements of a Math Portfolio Internal Assessment (IA) Task hlsl type 1 type 2 Problem Write-Up General

-‐

Name class and due date are clearly displayed

Introduction

-

Write up has an interesting (or pertinent) title

-‐

Task is properly introduced to the reader

-‐

This introduction should pose any major questions the task is seeking to answer

Body

-‐

Problem- solving process is completely explained throughout‐

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 11: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

_ Hence or otherwise determine the equation of the shadow generating function m y in thiscase_ Once again express 2 y in terms of 1 y and m y Use technology to investigate similarcubic functions_ Write a general statement about the functions 1 y 2 y and m y and prove your statement_ On a labelled diagram illustrate how the zeros of 2 y may be helpful in the determinationof the real and imaginary components of the complex zeros of 1 y

_ How can the findings with quadratics and cubics be applied to quartics

PATTERNS FROM COMPLEX NUMBERS HL TYPE ITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo format

Part A

Use de Moivrersquos theorem to obtain solutions to the equation z3 _1 _ 0 _ Use graphing software to plot these roots on an Argand diagram as well as a unit circlewith centre origin_ Choose a root and draw line segments from this root to the other two roots

_ Measure these line segments and comment on your results_ Repeat the above for the equations z4 _1 _ 0 and z5 _1 _ 0 Comment on your results andtry to formulate a conjecture_ Factorize zn _1 for n _ 3 4 and 5_ Use graphing software to test your conjecture for some more values of n 1048576 __ and makemodifications to your conjecture if necessary_ Prove your conjecture

Part B

Use de Moivrersquos theorem to obtain solutions to zn _ i for n _ 3 4 and 5_ Use graphing software to represent each of these solutions on an Argand diagram_ Generalize and prove your results for zn _ a _ bi where a _ bi _1

_ What happens when a _ bi _1

THE DICE GAME HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatThe aim of this task is to create a dice game in a casino and model this usingprobability It is important to examine how best to run the game from both the

perspective of a player and the casino In doing so analyse the game to consider theoptimal payments by the player and payouts by the casino_ Consider a game with two players Ann and Bob Ann has a red die and Bob a white dieThey roll their dice and note the number on the upper face Ann wins if her score is higherthan Bobrsquos (note that Bob wins if the scores are the same) If both players roll their diceonce each what is the probability that Ann will win the game_ Now consider the same game where Ann can roll her die a second time and will note thehigher score of the two rolls but Bob rolls only once In this case what is the probabilitythat Ann will win_ Investigate the game when both players can roll their dice twice and also when bothplayers can roll their dice more than twice but not necessarily the same number of times_ Consider the game in a casino where the player has a red die and the bank has a white dieFind a model for a game so that the casino makes a reasonable profit in the case where theplayer rolls the red die once and the bank rolls the white die once (When creating yourmodel you will need to consider how much a player must pay to play a game and howmuch the bank will pay out if the player wins Do this from the perspective of both theplayer and the casino and consider carefully the criteria for whether the game can be

considered worthwhile for both the player and the casino)_ Now consider other models for the game including cases such as where the player or the

bank rolls their dice multiple times or where multiple players are involved in the game

FILLING UP THE PETROL TANK HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatIn this task you will develop a mathematical model that helps motorists decide which ofthe following two options is more economicalOption 1 to buy petrol from a station on their normal route at a relatively higher priceOption 2 to drive an extra distance out of their normal route to buy cheaper petrolConsider a situation in which two motorists Arwa and Bao share the same driving route but owndifferent sized vehicles Arwa fills up her vehiclersquos tank at a station along her normal route forUS$ 1 p per litre On the other hand Bao drives an extra d kilometres out of his normal route to fillup his vehiclersquos tank for US$ p2 per litre where p2 _ p1 _ Choose suitable parameters for Arwarsquos and Baorsquos vehicles Justify your choices

_ Suppose 1 p _ US$100 per litre 2 p _ US$098 per litre and d _10 km Which motorist is getting the better deal Show all calculations and justify any assumptions you make_ On a spreadsheet choose several sets of values for 1 p 2 p and d to investigate further_ Define a set of variables that would be relevant in the above situationldquoEffective litresrdquo is a method of comparing the cost of petrol bought under the two optionsdescribed above Effective litres for a given vehicle are those litres used when the vehicle travelsits normal route_ Use your variables and parameters to write algebraic expressions for 1 E and 2 E whichrepresent the cost per effective litre under options 1 and 2 respectively_ Write a model that helps motorists decide on the more economical option for theirvehiclesIn the remainder of this task you need to consider the two vehicles you have chosen for Arwaand Bao_ Use your model to find the farthest distance that Bao should drive to obtain a 2 pricesaving_ Investigate the relationship between d and 2 p when 2 E is kept constant (eg US$090US$100 hellip etc) Use technology to draw a family of curves for Arwarsquos vehicle Repeatfor Baorsquos vehicle

_ For 2 E _ US$090 provide Arwa with information on three different stations that yieldthis same cost per effective litre Discuss how such information may be useful to Arwa_ For 2 E _ US$100 and 2 p _ US$080 compare the maximum distance that each motoristshould drive and still save moneyArwa is a busy person and wonders whether the saving in money would be worth the time shewould lose in extra driving_ Modify your model to account for the time taken to drive to and from an off-route station

Clearly justify any assumptions you make

IB DP Math SL type 2 IA portfolio task Fish production Gold Medal heightsIB DP Math HL type 2 IA portfolio task The dice game Filling up the petrol tankIB DP Math HL type 1 IA portfolio task shadow function Patterns from complex numberIB DP Math SL type 1 IA portfolio task Lacsaprsquos fraction Circles

IB ToK Essay TutorIB ToK Essay Topics 201213

IB ToK Essay Help Choosing the Right Essay TitleIB ToK Essay Help Planning and Writing the Essay

IB ToK Essay Help Marking and Assessing the EssayIB ToK Essay Help Grammar and Punctuation Check

IB TOK Essay on Common Sense IB Sample TOK essays

Examiners mark essays against the title as set Respond to the title exactly as given do not alter it in any way

Your essay must be between 1200 and 1600 words in length double spaced and typed in size 12 font

1 In what ways may disagreement aid the pursuit of knowledge in the natural and human sciences

2 ldquoOnly seeing general patterns can give us knowledge Only seeing particular examples can give us understandingrdquo To what

extent do you agree with these assertions3 ldquoThe possession of knowledge carries an ethical

responsibilityrdquo Evaluate this claim4 The traditional TOK diagram indicates four ways of knowing

Propose the inclusion of a fifth way of knowing selected from intuition memory or imagination and explore the knowledge

issues it may raise in two areas of knowledge5 ldquoThat which can be asserted without evidence can be

dismissed without evidencerdquo (Christopher Hitchens) Do you agree

6 Can we know when to trust our emotions in the pursuit of knowledge Consider history and one other area of knowledge

IB TOK ESSAY WRITERS HELP SOLUTIONIB COMMENTARY ESSAY HELP IB ECONOMICS

COMMENTARIES IB TOK IB EXTENDED ESSAY IB IB TOK Essay Help Mathematics Physics Economics

ChemistryIB TOK TUTORS EXAMPLES SAMPLES IB TOK

PRESENTATION TUTORS HELP IB ESSAY EXTENDED ESSAY

Online tuitions Home tuitions and IndividualGroup coaching and tuitions in MathsMathMathematics and physics

Chemistry EconomicsBusiness Management for VI-XII standards for IGCSE IBAP A AS-level Ed-excelOverseas

Students studying in Grade(IV-XII ) from US UK Canada Australia Newzealand etc can contact for online tutoring in mathrsquos amp science Economics and Business Studies subjects

Teaching Exclusively International School Students for IB IGCSE and A levels Excellent and Consistent Results for IB

IGCSEGCSE O and A Level exam IGCSE O Level IB Maths Physics Chemistry Economics and Business and Management

HL Business IA Internal Assessment HLSL Tasks English IOCIOP Help Guidance

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heights Lacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essay computer dossierbusiness management IA helpeconomics commentaryLab reports tuition

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heightsLacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essaycomputer dossierbusiness management IA helpeconomics commentary EVM Lab reports tuition

IB MathsPortfolio urdu shayari

helpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow functionnumbersgold medal

heightsLacasprsquos fractioncirclestutorIB math home tuition in delhi IB maths home tuition in delhi IB

maths home tuition in delhi IB math home tuition in delhiIB math home tuition in gurgaon IB maths home tuition in

gurgoan IB maths home tuition in gurgoan IB math home tuition in gurgaon

IB Mathematics Physics Chemistry Economics Business and Management HL SL Studies Theatre Stimulus help

IB Physics Mathematics Chemistry Economics Business and Management Presentation ITGS IA Computer help

IB Chemistry HL SL help Mathematics Physics Economics Chemistry Business

IB Economics HL SL Management Math Portfolio TOK Economics Historical Investigation Extended help

IB Business and Management HL SL help Essay Commentary storical Investigation Lab writing

IB Math Portfolio Help HL SL help Lab writing Project ESS English Spanish French Hindi

IB Math Project Help Studies help IB World Literature Theatre Stimulus Essay Commentary storical Investigation

IB Extended Essay Help TOK Presentation ITGS IA Computer Dossier IB World Literature Theatre Stimulus

IB TOK Essay Help Mathematics Physics Economics Chemistry Business Presentation ITGS IA Computer

IB Economics Commentary Help Management Math Portfolio HL SL Extended

IB Historical Investigation Help Essay Commentary storical Investigation Lab writing

IB Physics Lab writing Help Lab writing EVM Lab Report write

ups Project ESS English Spanish (Ab initio) French Hindi Extended Essay Help Tutors Examples Samples Solution

GuidanceIB Chemistry Lab writing Help IB World Literature Theatre

StimulusIB Biology Lab writing Help Presentation ITGS IA Computer Dossier SLHL Design Technology Design Projects RAPA IA

CADCAM Mathematics Physics Economics chemistryIB Business and Management Project Help Commentary storical

Investigation Lab writingIB ESS lab report help Mathematics Physics Economics

Chemistry Business EconomicsIB English HL SL help IB World Literature Theatre Stimulus

Economics Extended Essay IA Business IA IB Spanish Ab initio and Standard Level help Presentation ITGS

IA Computer DossierIB French Ab initio and Standard Level help Lab writing Project

ESS English Spanish French HindiIB Hindi HL SL help Mathematics Physics Economics

Chemistry Business EconomicsIB World Literature Help TOK Presentation ITGS IA Computer

Dossier EconomicsIB Theatre Stimulus help TOK Presentation ITGS IA Computer

Dossier EconomicsIB TOK Presentation help Management Math Portfolio HL SL

Extended ITGS IA Computer Dossier MathIB ITGS IA help IB World Literature Theatre Stimulus Math

Portfolio TOK Economics investigation Extended helpIB Computer Dossier help TOK Presentation ITGS IA

Computer Dossier Math Portfolio TOK Economics

Call or Email Ex-IB Examiner for Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website

httpwwwtopclassibtutorscom Online HelpTuition all over the world by the BestExpert IB Tutors Mail us or call

us for any queries

Essential Elements of a Math Portfolio Internal Assessment (IA) Task hlsl type 1 type 2 Problem Write-Up General

-‐

Name class and due date are clearly displayed

Introduction

-

Write up has an interesting (or pertinent) title

-‐

Task is properly introduced to the reader

-‐

This introduction should pose any major questions the task is seeking to answer

Body

-‐

Problem- solving process is completely explained throughout‐

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 12: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

_ Measure these line segments and comment on your results_ Repeat the above for the equations z4 _1 _ 0 and z5 _1 _ 0 Comment on your results andtry to formulate a conjecture_ Factorize zn _1 for n _ 3 4 and 5_ Use graphing software to test your conjecture for some more values of n 1048576 __ and makemodifications to your conjecture if necessary_ Prove your conjecture

Part B

Use de Moivrersquos theorem to obtain solutions to zn _ i for n _ 3 4 and 5_ Use graphing software to represent each of these solutions on an Argand diagram_ Generalize and prove your results for zn _ a _ bi where a _ bi _1

_ What happens when a _ bi _1

THE DICE GAME HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatThe aim of this task is to create a dice game in a casino and model this usingprobability It is important to examine how best to run the game from both the

perspective of a player and the casino In doing so analyse the game to consider theoptimal payments by the player and payouts by the casino_ Consider a game with two players Ann and Bob Ann has a red die and Bob a white dieThey roll their dice and note the number on the upper face Ann wins if her score is higherthan Bobrsquos (note that Bob wins if the scores are the same) If both players roll their diceonce each what is the probability that Ann will win the game_ Now consider the same game where Ann can roll her die a second time and will note thehigher score of the two rolls but Bob rolls only once In this case what is the probabilitythat Ann will win_ Investigate the game when both players can roll their dice twice and also when bothplayers can roll their dice more than twice but not necessarily the same number of times_ Consider the game in a casino where the player has a red die and the bank has a white dieFind a model for a game so that the casino makes a reasonable profit in the case where theplayer rolls the red die once and the bank rolls the white die once (When creating yourmodel you will need to consider how much a player must pay to play a game and howmuch the bank will pay out if the player wins Do this from the perspective of both theplayer and the casino and consider carefully the criteria for whether the game can be

considered worthwhile for both the player and the casino)_ Now consider other models for the game including cases such as where the player or the

bank rolls their dice multiple times or where multiple players are involved in the game

FILLING UP THE PETROL TANK HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatIn this task you will develop a mathematical model that helps motorists decide which ofthe following two options is more economicalOption 1 to buy petrol from a station on their normal route at a relatively higher priceOption 2 to drive an extra distance out of their normal route to buy cheaper petrolConsider a situation in which two motorists Arwa and Bao share the same driving route but owndifferent sized vehicles Arwa fills up her vehiclersquos tank at a station along her normal route forUS$ 1 p per litre On the other hand Bao drives an extra d kilometres out of his normal route to fillup his vehiclersquos tank for US$ p2 per litre where p2 _ p1 _ Choose suitable parameters for Arwarsquos and Baorsquos vehicles Justify your choices

_ Suppose 1 p _ US$100 per litre 2 p _ US$098 per litre and d _10 km Which motorist is getting the better deal Show all calculations and justify any assumptions you make_ On a spreadsheet choose several sets of values for 1 p 2 p and d to investigate further_ Define a set of variables that would be relevant in the above situationldquoEffective litresrdquo is a method of comparing the cost of petrol bought under the two optionsdescribed above Effective litres for a given vehicle are those litres used when the vehicle travelsits normal route_ Use your variables and parameters to write algebraic expressions for 1 E and 2 E whichrepresent the cost per effective litre under options 1 and 2 respectively_ Write a model that helps motorists decide on the more economical option for theirvehiclesIn the remainder of this task you need to consider the two vehicles you have chosen for Arwaand Bao_ Use your model to find the farthest distance that Bao should drive to obtain a 2 pricesaving_ Investigate the relationship between d and 2 p when 2 E is kept constant (eg US$090US$100 hellip etc) Use technology to draw a family of curves for Arwarsquos vehicle Repeatfor Baorsquos vehicle

_ For 2 E _ US$090 provide Arwa with information on three different stations that yieldthis same cost per effective litre Discuss how such information may be useful to Arwa_ For 2 E _ US$100 and 2 p _ US$080 compare the maximum distance that each motoristshould drive and still save moneyArwa is a busy person and wonders whether the saving in money would be worth the time shewould lose in extra driving_ Modify your model to account for the time taken to drive to and from an off-route station

Clearly justify any assumptions you make

IB DP Math SL type 2 IA portfolio task Fish production Gold Medal heightsIB DP Math HL type 2 IA portfolio task The dice game Filling up the petrol tankIB DP Math HL type 1 IA portfolio task shadow function Patterns from complex numberIB DP Math SL type 1 IA portfolio task Lacsaprsquos fraction Circles

IB ToK Essay TutorIB ToK Essay Topics 201213

IB ToK Essay Help Choosing the Right Essay TitleIB ToK Essay Help Planning and Writing the Essay

IB ToK Essay Help Marking and Assessing the EssayIB ToK Essay Help Grammar and Punctuation Check

IB TOK Essay on Common Sense IB Sample TOK essays

Examiners mark essays against the title as set Respond to the title exactly as given do not alter it in any way

Your essay must be between 1200 and 1600 words in length double spaced and typed in size 12 font

1 In what ways may disagreement aid the pursuit of knowledge in the natural and human sciences

2 ldquoOnly seeing general patterns can give us knowledge Only seeing particular examples can give us understandingrdquo To what

extent do you agree with these assertions3 ldquoThe possession of knowledge carries an ethical

responsibilityrdquo Evaluate this claim4 The traditional TOK diagram indicates four ways of knowing

Propose the inclusion of a fifth way of knowing selected from intuition memory or imagination and explore the knowledge

issues it may raise in two areas of knowledge5 ldquoThat which can be asserted without evidence can be

dismissed without evidencerdquo (Christopher Hitchens) Do you agree

6 Can we know when to trust our emotions in the pursuit of knowledge Consider history and one other area of knowledge

IB TOK ESSAY WRITERS HELP SOLUTIONIB COMMENTARY ESSAY HELP IB ECONOMICS

COMMENTARIES IB TOK IB EXTENDED ESSAY IB IB TOK Essay Help Mathematics Physics Economics

ChemistryIB TOK TUTORS EXAMPLES SAMPLES IB TOK

PRESENTATION TUTORS HELP IB ESSAY EXTENDED ESSAY

Online tuitions Home tuitions and IndividualGroup coaching and tuitions in MathsMathMathematics and physics

Chemistry EconomicsBusiness Management for VI-XII standards for IGCSE IBAP A AS-level Ed-excelOverseas

Students studying in Grade(IV-XII ) from US UK Canada Australia Newzealand etc can contact for online tutoring in mathrsquos amp science Economics and Business Studies subjects

Teaching Exclusively International School Students for IB IGCSE and A levels Excellent and Consistent Results for IB

IGCSEGCSE O and A Level exam IGCSE O Level IB Maths Physics Chemistry Economics and Business and Management

HL Business IA Internal Assessment HLSL Tasks English IOCIOP Help Guidance

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heights Lacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essay computer dossierbusiness management IA helpeconomics commentaryLab reports tuition

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heightsLacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essaycomputer dossierbusiness management IA helpeconomics commentary EVM Lab reports tuition

IB MathsPortfolio urdu shayari

helpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow functionnumbersgold medal

heightsLacasprsquos fractioncirclestutorIB math home tuition in delhi IB maths home tuition in delhi IB

maths home tuition in delhi IB math home tuition in delhiIB math home tuition in gurgaon IB maths home tuition in

gurgoan IB maths home tuition in gurgoan IB math home tuition in gurgaon

IB Mathematics Physics Chemistry Economics Business and Management HL SL Studies Theatre Stimulus help

IB Physics Mathematics Chemistry Economics Business and Management Presentation ITGS IA Computer help

IB Chemistry HL SL help Mathematics Physics Economics Chemistry Business

IB Economics HL SL Management Math Portfolio TOK Economics Historical Investigation Extended help

IB Business and Management HL SL help Essay Commentary storical Investigation Lab writing

IB Math Portfolio Help HL SL help Lab writing Project ESS English Spanish French Hindi

IB Math Project Help Studies help IB World Literature Theatre Stimulus Essay Commentary storical Investigation

IB Extended Essay Help TOK Presentation ITGS IA Computer Dossier IB World Literature Theatre Stimulus

IB TOK Essay Help Mathematics Physics Economics Chemistry Business Presentation ITGS IA Computer

IB Economics Commentary Help Management Math Portfolio HL SL Extended

IB Historical Investigation Help Essay Commentary storical Investigation Lab writing

IB Physics Lab writing Help Lab writing EVM Lab Report write

ups Project ESS English Spanish (Ab initio) French Hindi Extended Essay Help Tutors Examples Samples Solution

GuidanceIB Chemistry Lab writing Help IB World Literature Theatre

StimulusIB Biology Lab writing Help Presentation ITGS IA Computer Dossier SLHL Design Technology Design Projects RAPA IA

CADCAM Mathematics Physics Economics chemistryIB Business and Management Project Help Commentary storical

Investigation Lab writingIB ESS lab report help Mathematics Physics Economics

Chemistry Business EconomicsIB English HL SL help IB World Literature Theatre Stimulus

Economics Extended Essay IA Business IA IB Spanish Ab initio and Standard Level help Presentation ITGS

IA Computer DossierIB French Ab initio and Standard Level help Lab writing Project

ESS English Spanish French HindiIB Hindi HL SL help Mathematics Physics Economics

Chemistry Business EconomicsIB World Literature Help TOK Presentation ITGS IA Computer

Dossier EconomicsIB Theatre Stimulus help TOK Presentation ITGS IA Computer

Dossier EconomicsIB TOK Presentation help Management Math Portfolio HL SL

Extended ITGS IA Computer Dossier MathIB ITGS IA help IB World Literature Theatre Stimulus Math

Portfolio TOK Economics investigation Extended helpIB Computer Dossier help TOK Presentation ITGS IA

Computer Dossier Math Portfolio TOK Economics

Call or Email Ex-IB Examiner for Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website

httpwwwtopclassibtutorscom Online HelpTuition all over the world by the BestExpert IB Tutors Mail us or call

us for any queries

Essential Elements of a Math Portfolio Internal Assessment (IA) Task hlsl type 1 type 2 Problem Write-Up General

-‐

Name class and due date are clearly displayed

Introduction

-

Write up has an interesting (or pertinent) title

-‐

Task is properly introduced to the reader

-‐

This introduction should pose any major questions the task is seeking to answer

Body

-‐

Problem- solving process is completely explained throughout‐

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 13: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

perspective of a player and the casino In doing so analyse the game to consider theoptimal payments by the player and payouts by the casino_ Consider a game with two players Ann and Bob Ann has a red die and Bob a white dieThey roll their dice and note the number on the upper face Ann wins if her score is higherthan Bobrsquos (note that Bob wins if the scores are the same) If both players roll their diceonce each what is the probability that Ann will win the game_ Now consider the same game where Ann can roll her die a second time and will note thehigher score of the two rolls but Bob rolls only once In this case what is the probabilitythat Ann will win_ Investigate the game when both players can roll their dice twice and also when bothplayers can roll their dice more than twice but not necessarily the same number of times_ Consider the game in a casino where the player has a red die and the bank has a white dieFind a model for a game so that the casino makes a reasonable profit in the case where theplayer rolls the red die once and the bank rolls the white die once (When creating yourmodel you will need to consider how much a player must pay to play a game and howmuch the bank will pay out if the player wins Do this from the perspective of both theplayer and the casino and consider carefully the criteria for whether the game can be

considered worthwhile for both the player and the casino)_ Now consider other models for the game including cases such as where the player or the

bank rolls their dice multiple times or where multiple players are involved in the game

FILLING UP THE PETROL TANK HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatIn this task you will develop a mathematical model that helps motorists decide which ofthe following two options is more economicalOption 1 to buy petrol from a station on their normal route at a relatively higher priceOption 2 to drive an extra distance out of their normal route to buy cheaper petrolConsider a situation in which two motorists Arwa and Bao share the same driving route but owndifferent sized vehicles Arwa fills up her vehiclersquos tank at a station along her normal route forUS$ 1 p per litre On the other hand Bao drives an extra d kilometres out of his normal route to fillup his vehiclersquos tank for US$ p2 per litre where p2 _ p1 _ Choose suitable parameters for Arwarsquos and Baorsquos vehicles Justify your choices

_ Suppose 1 p _ US$100 per litre 2 p _ US$098 per litre and d _10 km Which motorist is getting the better deal Show all calculations and justify any assumptions you make_ On a spreadsheet choose several sets of values for 1 p 2 p and d to investigate further_ Define a set of variables that would be relevant in the above situationldquoEffective litresrdquo is a method of comparing the cost of petrol bought under the two optionsdescribed above Effective litres for a given vehicle are those litres used when the vehicle travelsits normal route_ Use your variables and parameters to write algebraic expressions for 1 E and 2 E whichrepresent the cost per effective litre under options 1 and 2 respectively_ Write a model that helps motorists decide on the more economical option for theirvehiclesIn the remainder of this task you need to consider the two vehicles you have chosen for Arwaand Bao_ Use your model to find the farthest distance that Bao should drive to obtain a 2 pricesaving_ Investigate the relationship between d and 2 p when 2 E is kept constant (eg US$090US$100 hellip etc) Use technology to draw a family of curves for Arwarsquos vehicle Repeatfor Baorsquos vehicle

_ For 2 E _ US$090 provide Arwa with information on three different stations that yieldthis same cost per effective litre Discuss how such information may be useful to Arwa_ For 2 E _ US$100 and 2 p _ US$080 compare the maximum distance that each motoristshould drive and still save moneyArwa is a busy person and wonders whether the saving in money would be worth the time shewould lose in extra driving_ Modify your model to account for the time taken to drive to and from an off-route station

Clearly justify any assumptions you make

IB DP Math SL type 2 IA portfolio task Fish production Gold Medal heightsIB DP Math HL type 2 IA portfolio task The dice game Filling up the petrol tankIB DP Math HL type 1 IA portfolio task shadow function Patterns from complex numberIB DP Math SL type 1 IA portfolio task Lacsaprsquos fraction Circles

IB ToK Essay TutorIB ToK Essay Topics 201213

IB ToK Essay Help Choosing the Right Essay TitleIB ToK Essay Help Planning and Writing the Essay

IB ToK Essay Help Marking and Assessing the EssayIB ToK Essay Help Grammar and Punctuation Check

IB TOK Essay on Common Sense IB Sample TOK essays

Examiners mark essays against the title as set Respond to the title exactly as given do not alter it in any way

Your essay must be between 1200 and 1600 words in length double spaced and typed in size 12 font

1 In what ways may disagreement aid the pursuit of knowledge in the natural and human sciences

2 ldquoOnly seeing general patterns can give us knowledge Only seeing particular examples can give us understandingrdquo To what

extent do you agree with these assertions3 ldquoThe possession of knowledge carries an ethical

responsibilityrdquo Evaluate this claim4 The traditional TOK diagram indicates four ways of knowing

Propose the inclusion of a fifth way of knowing selected from intuition memory or imagination and explore the knowledge

issues it may raise in two areas of knowledge5 ldquoThat which can be asserted without evidence can be

dismissed without evidencerdquo (Christopher Hitchens) Do you agree

6 Can we know when to trust our emotions in the pursuit of knowledge Consider history and one other area of knowledge

IB TOK ESSAY WRITERS HELP SOLUTIONIB COMMENTARY ESSAY HELP IB ECONOMICS

COMMENTARIES IB TOK IB EXTENDED ESSAY IB IB TOK Essay Help Mathematics Physics Economics

ChemistryIB TOK TUTORS EXAMPLES SAMPLES IB TOK

PRESENTATION TUTORS HELP IB ESSAY EXTENDED ESSAY

Online tuitions Home tuitions and IndividualGroup coaching and tuitions in MathsMathMathematics and physics

Chemistry EconomicsBusiness Management for VI-XII standards for IGCSE IBAP A AS-level Ed-excelOverseas

Students studying in Grade(IV-XII ) from US UK Canada Australia Newzealand etc can contact for online tutoring in mathrsquos amp science Economics and Business Studies subjects

Teaching Exclusively International School Students for IB IGCSE and A levels Excellent and Consistent Results for IB

IGCSEGCSE O and A Level exam IGCSE O Level IB Maths Physics Chemistry Economics and Business and Management

HL Business IA Internal Assessment HLSL Tasks English IOCIOP Help Guidance

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heights Lacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essay computer dossierbusiness management IA helpeconomics commentaryLab reports tuition

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heightsLacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essaycomputer dossierbusiness management IA helpeconomics commentary EVM Lab reports tuition

IB MathsPortfolio urdu shayari

helpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow functionnumbersgold medal

heightsLacasprsquos fractioncirclestutorIB math home tuition in delhi IB maths home tuition in delhi IB

maths home tuition in delhi IB math home tuition in delhiIB math home tuition in gurgaon IB maths home tuition in

gurgoan IB maths home tuition in gurgoan IB math home tuition in gurgaon

IB Mathematics Physics Chemistry Economics Business and Management HL SL Studies Theatre Stimulus help

IB Physics Mathematics Chemistry Economics Business and Management Presentation ITGS IA Computer help

IB Chemistry HL SL help Mathematics Physics Economics Chemistry Business

IB Economics HL SL Management Math Portfolio TOK Economics Historical Investigation Extended help

IB Business and Management HL SL help Essay Commentary storical Investigation Lab writing

IB Math Portfolio Help HL SL help Lab writing Project ESS English Spanish French Hindi

IB Math Project Help Studies help IB World Literature Theatre Stimulus Essay Commentary storical Investigation

IB Extended Essay Help TOK Presentation ITGS IA Computer Dossier IB World Literature Theatre Stimulus

IB TOK Essay Help Mathematics Physics Economics Chemistry Business Presentation ITGS IA Computer

IB Economics Commentary Help Management Math Portfolio HL SL Extended

IB Historical Investigation Help Essay Commentary storical Investigation Lab writing

IB Physics Lab writing Help Lab writing EVM Lab Report write

ups Project ESS English Spanish (Ab initio) French Hindi Extended Essay Help Tutors Examples Samples Solution

GuidanceIB Chemistry Lab writing Help IB World Literature Theatre

StimulusIB Biology Lab writing Help Presentation ITGS IA Computer Dossier SLHL Design Technology Design Projects RAPA IA

CADCAM Mathematics Physics Economics chemistryIB Business and Management Project Help Commentary storical

Investigation Lab writingIB ESS lab report help Mathematics Physics Economics

Chemistry Business EconomicsIB English HL SL help IB World Literature Theatre Stimulus

Economics Extended Essay IA Business IA IB Spanish Ab initio and Standard Level help Presentation ITGS

IA Computer DossierIB French Ab initio and Standard Level help Lab writing Project

ESS English Spanish French HindiIB Hindi HL SL help Mathematics Physics Economics

Chemistry Business EconomicsIB World Literature Help TOK Presentation ITGS IA Computer

Dossier EconomicsIB Theatre Stimulus help TOK Presentation ITGS IA Computer

Dossier EconomicsIB TOK Presentation help Management Math Portfolio HL SL

Extended ITGS IA Computer Dossier MathIB ITGS IA help IB World Literature Theatre Stimulus Math

Portfolio TOK Economics investigation Extended helpIB Computer Dossier help TOK Presentation ITGS IA

Computer Dossier Math Portfolio TOK Economics

Call or Email Ex-IB Examiner for Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website

httpwwwtopclassibtutorscom Online HelpTuition all over the world by the BestExpert IB Tutors Mail us or call

us for any queries

Essential Elements of a Math Portfolio Internal Assessment (IA) Task hlsl type 1 type 2 Problem Write-Up General

-‐

Name class and due date are clearly displayed

Introduction

-

Write up has an interesting (or pertinent) title

-‐

Task is properly introduced to the reader

-‐

This introduction should pose any major questions the task is seeking to answer

Body

-‐

Problem- solving process is completely explained throughout‐

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 14: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

considered worthwhile for both the player and the casino)_ Now consider other models for the game including cases such as where the player or the

bank rolls their dice multiple times or where multiple players are involved in the game

FILLING UP THE PETROL TANK HL Type IITo the student The work that you produce to address the questions in this task should be a reportthat can stand on its own It is best to avoid copying the questions in the task to adopt a ldquoquestionand answerrdquo formatIn this task you will develop a mathematical model that helps motorists decide which ofthe following two options is more economicalOption 1 to buy petrol from a station on their normal route at a relatively higher priceOption 2 to drive an extra distance out of their normal route to buy cheaper petrolConsider a situation in which two motorists Arwa and Bao share the same driving route but owndifferent sized vehicles Arwa fills up her vehiclersquos tank at a station along her normal route forUS$ 1 p per litre On the other hand Bao drives an extra d kilometres out of his normal route to fillup his vehiclersquos tank for US$ p2 per litre where p2 _ p1 _ Choose suitable parameters for Arwarsquos and Baorsquos vehicles Justify your choices

_ Suppose 1 p _ US$100 per litre 2 p _ US$098 per litre and d _10 km Which motorist is getting the better deal Show all calculations and justify any assumptions you make_ On a spreadsheet choose several sets of values for 1 p 2 p and d to investigate further_ Define a set of variables that would be relevant in the above situationldquoEffective litresrdquo is a method of comparing the cost of petrol bought under the two optionsdescribed above Effective litres for a given vehicle are those litres used when the vehicle travelsits normal route_ Use your variables and parameters to write algebraic expressions for 1 E and 2 E whichrepresent the cost per effective litre under options 1 and 2 respectively_ Write a model that helps motorists decide on the more economical option for theirvehiclesIn the remainder of this task you need to consider the two vehicles you have chosen for Arwaand Bao_ Use your model to find the farthest distance that Bao should drive to obtain a 2 pricesaving_ Investigate the relationship between d and 2 p when 2 E is kept constant (eg US$090US$100 hellip etc) Use technology to draw a family of curves for Arwarsquos vehicle Repeatfor Baorsquos vehicle

_ For 2 E _ US$090 provide Arwa with information on three different stations that yieldthis same cost per effective litre Discuss how such information may be useful to Arwa_ For 2 E _ US$100 and 2 p _ US$080 compare the maximum distance that each motoristshould drive and still save moneyArwa is a busy person and wonders whether the saving in money would be worth the time shewould lose in extra driving_ Modify your model to account for the time taken to drive to and from an off-route station

Clearly justify any assumptions you make

IB DP Math SL type 2 IA portfolio task Fish production Gold Medal heightsIB DP Math HL type 2 IA portfolio task The dice game Filling up the petrol tankIB DP Math HL type 1 IA portfolio task shadow function Patterns from complex numberIB DP Math SL type 1 IA portfolio task Lacsaprsquos fraction Circles

IB ToK Essay TutorIB ToK Essay Topics 201213

IB ToK Essay Help Choosing the Right Essay TitleIB ToK Essay Help Planning and Writing the Essay

IB ToK Essay Help Marking and Assessing the EssayIB ToK Essay Help Grammar and Punctuation Check

IB TOK Essay on Common Sense IB Sample TOK essays

Examiners mark essays against the title as set Respond to the title exactly as given do not alter it in any way

Your essay must be between 1200 and 1600 words in length double spaced and typed in size 12 font

1 In what ways may disagreement aid the pursuit of knowledge in the natural and human sciences

2 ldquoOnly seeing general patterns can give us knowledge Only seeing particular examples can give us understandingrdquo To what

extent do you agree with these assertions3 ldquoThe possession of knowledge carries an ethical

responsibilityrdquo Evaluate this claim4 The traditional TOK diagram indicates four ways of knowing

Propose the inclusion of a fifth way of knowing selected from intuition memory or imagination and explore the knowledge

issues it may raise in two areas of knowledge5 ldquoThat which can be asserted without evidence can be

dismissed without evidencerdquo (Christopher Hitchens) Do you agree

6 Can we know when to trust our emotions in the pursuit of knowledge Consider history and one other area of knowledge

IB TOK ESSAY WRITERS HELP SOLUTIONIB COMMENTARY ESSAY HELP IB ECONOMICS

COMMENTARIES IB TOK IB EXTENDED ESSAY IB IB TOK Essay Help Mathematics Physics Economics

ChemistryIB TOK TUTORS EXAMPLES SAMPLES IB TOK

PRESENTATION TUTORS HELP IB ESSAY EXTENDED ESSAY

Online tuitions Home tuitions and IndividualGroup coaching and tuitions in MathsMathMathematics and physics

Chemistry EconomicsBusiness Management for VI-XII standards for IGCSE IBAP A AS-level Ed-excelOverseas

Students studying in Grade(IV-XII ) from US UK Canada Australia Newzealand etc can contact for online tutoring in mathrsquos amp science Economics and Business Studies subjects

Teaching Exclusively International School Students for IB IGCSE and A levels Excellent and Consistent Results for IB

IGCSEGCSE O and A Level exam IGCSE O Level IB Maths Physics Chemistry Economics and Business and Management

HL Business IA Internal Assessment HLSL Tasks English IOCIOP Help Guidance

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heights Lacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essay computer dossierbusiness management IA helpeconomics commentaryLab reports tuition

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heightsLacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essaycomputer dossierbusiness management IA helpeconomics commentary EVM Lab reports tuition

IB MathsPortfolio urdu shayari

helpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow functionnumbersgold medal

heightsLacasprsquos fractioncirclestutorIB math home tuition in delhi IB maths home tuition in delhi IB

maths home tuition in delhi IB math home tuition in delhiIB math home tuition in gurgaon IB maths home tuition in

gurgoan IB maths home tuition in gurgoan IB math home tuition in gurgaon

IB Mathematics Physics Chemistry Economics Business and Management HL SL Studies Theatre Stimulus help

IB Physics Mathematics Chemistry Economics Business and Management Presentation ITGS IA Computer help

IB Chemistry HL SL help Mathematics Physics Economics Chemistry Business

IB Economics HL SL Management Math Portfolio TOK Economics Historical Investigation Extended help

IB Business and Management HL SL help Essay Commentary storical Investigation Lab writing

IB Math Portfolio Help HL SL help Lab writing Project ESS English Spanish French Hindi

IB Math Project Help Studies help IB World Literature Theatre Stimulus Essay Commentary storical Investigation

IB Extended Essay Help TOK Presentation ITGS IA Computer Dossier IB World Literature Theatre Stimulus

IB TOK Essay Help Mathematics Physics Economics Chemistry Business Presentation ITGS IA Computer

IB Economics Commentary Help Management Math Portfolio HL SL Extended

IB Historical Investigation Help Essay Commentary storical Investigation Lab writing

IB Physics Lab writing Help Lab writing EVM Lab Report write

ups Project ESS English Spanish (Ab initio) French Hindi Extended Essay Help Tutors Examples Samples Solution

GuidanceIB Chemistry Lab writing Help IB World Literature Theatre

StimulusIB Biology Lab writing Help Presentation ITGS IA Computer Dossier SLHL Design Technology Design Projects RAPA IA

CADCAM Mathematics Physics Economics chemistryIB Business and Management Project Help Commentary storical

Investigation Lab writingIB ESS lab report help Mathematics Physics Economics

Chemistry Business EconomicsIB English HL SL help IB World Literature Theatre Stimulus

Economics Extended Essay IA Business IA IB Spanish Ab initio and Standard Level help Presentation ITGS

IA Computer DossierIB French Ab initio and Standard Level help Lab writing Project

ESS English Spanish French HindiIB Hindi HL SL help Mathematics Physics Economics

Chemistry Business EconomicsIB World Literature Help TOK Presentation ITGS IA Computer

Dossier EconomicsIB Theatre Stimulus help TOK Presentation ITGS IA Computer

Dossier EconomicsIB TOK Presentation help Management Math Portfolio HL SL

Extended ITGS IA Computer Dossier MathIB ITGS IA help IB World Literature Theatre Stimulus Math

Portfolio TOK Economics investigation Extended helpIB Computer Dossier help TOK Presentation ITGS IA

Computer Dossier Math Portfolio TOK Economics

Call or Email Ex-IB Examiner for Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website

httpwwwtopclassibtutorscom Online HelpTuition all over the world by the BestExpert IB Tutors Mail us or call

us for any queries

Essential Elements of a Math Portfolio Internal Assessment (IA) Task hlsl type 1 type 2 Problem Write-Up General

-‐

Name class and due date are clearly displayed

Introduction

-

Write up has an interesting (or pertinent) title

-‐

Task is properly introduced to the reader

-‐

This introduction should pose any major questions the task is seeking to answer

Body

-‐

Problem- solving process is completely explained throughout‐

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 15: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

_ Suppose 1 p _ US$100 per litre 2 p _ US$098 per litre and d _10 km Which motorist is getting the better deal Show all calculations and justify any assumptions you make_ On a spreadsheet choose several sets of values for 1 p 2 p and d to investigate further_ Define a set of variables that would be relevant in the above situationldquoEffective litresrdquo is a method of comparing the cost of petrol bought under the two optionsdescribed above Effective litres for a given vehicle are those litres used when the vehicle travelsits normal route_ Use your variables and parameters to write algebraic expressions for 1 E and 2 E whichrepresent the cost per effective litre under options 1 and 2 respectively_ Write a model that helps motorists decide on the more economical option for theirvehiclesIn the remainder of this task you need to consider the two vehicles you have chosen for Arwaand Bao_ Use your model to find the farthest distance that Bao should drive to obtain a 2 pricesaving_ Investigate the relationship between d and 2 p when 2 E is kept constant (eg US$090US$100 hellip etc) Use technology to draw a family of curves for Arwarsquos vehicle Repeatfor Baorsquos vehicle

_ For 2 E _ US$090 provide Arwa with information on three different stations that yieldthis same cost per effective litre Discuss how such information may be useful to Arwa_ For 2 E _ US$100 and 2 p _ US$080 compare the maximum distance that each motoristshould drive and still save moneyArwa is a busy person and wonders whether the saving in money would be worth the time shewould lose in extra driving_ Modify your model to account for the time taken to drive to and from an off-route station

Clearly justify any assumptions you make

IB DP Math SL type 2 IA portfolio task Fish production Gold Medal heightsIB DP Math HL type 2 IA portfolio task The dice game Filling up the petrol tankIB DP Math HL type 1 IA portfolio task shadow function Patterns from complex numberIB DP Math SL type 1 IA portfolio task Lacsaprsquos fraction Circles

IB ToK Essay TutorIB ToK Essay Topics 201213

IB ToK Essay Help Choosing the Right Essay TitleIB ToK Essay Help Planning and Writing the Essay

IB ToK Essay Help Marking and Assessing the EssayIB ToK Essay Help Grammar and Punctuation Check

IB TOK Essay on Common Sense IB Sample TOK essays

Examiners mark essays against the title as set Respond to the title exactly as given do not alter it in any way

Your essay must be between 1200 and 1600 words in length double spaced and typed in size 12 font

1 In what ways may disagreement aid the pursuit of knowledge in the natural and human sciences

2 ldquoOnly seeing general patterns can give us knowledge Only seeing particular examples can give us understandingrdquo To what

extent do you agree with these assertions3 ldquoThe possession of knowledge carries an ethical

responsibilityrdquo Evaluate this claim4 The traditional TOK diagram indicates four ways of knowing

Propose the inclusion of a fifth way of knowing selected from intuition memory or imagination and explore the knowledge

issues it may raise in two areas of knowledge5 ldquoThat which can be asserted without evidence can be

dismissed without evidencerdquo (Christopher Hitchens) Do you agree

6 Can we know when to trust our emotions in the pursuit of knowledge Consider history and one other area of knowledge

IB TOK ESSAY WRITERS HELP SOLUTIONIB COMMENTARY ESSAY HELP IB ECONOMICS

COMMENTARIES IB TOK IB EXTENDED ESSAY IB IB TOK Essay Help Mathematics Physics Economics

ChemistryIB TOK TUTORS EXAMPLES SAMPLES IB TOK

PRESENTATION TUTORS HELP IB ESSAY EXTENDED ESSAY

Online tuitions Home tuitions and IndividualGroup coaching and tuitions in MathsMathMathematics and physics

Chemistry EconomicsBusiness Management for VI-XII standards for IGCSE IBAP A AS-level Ed-excelOverseas

Students studying in Grade(IV-XII ) from US UK Canada Australia Newzealand etc can contact for online tutoring in mathrsquos amp science Economics and Business Studies subjects

Teaching Exclusively International School Students for IB IGCSE and A levels Excellent and Consistent Results for IB

IGCSEGCSE O and A Level exam IGCSE O Level IB Maths Physics Chemistry Economics and Business and Management

HL Business IA Internal Assessment HLSL Tasks English IOCIOP Help Guidance

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heights Lacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essay computer dossierbusiness management IA helpeconomics commentaryLab reports tuition

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heightsLacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essaycomputer dossierbusiness management IA helpeconomics commentary EVM Lab reports tuition

IB MathsPortfolio urdu shayari

helpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow functionnumbersgold medal

heightsLacasprsquos fractioncirclestutorIB math home tuition in delhi IB maths home tuition in delhi IB

maths home tuition in delhi IB math home tuition in delhiIB math home tuition in gurgaon IB maths home tuition in

gurgoan IB maths home tuition in gurgoan IB math home tuition in gurgaon

IB Mathematics Physics Chemistry Economics Business and Management HL SL Studies Theatre Stimulus help

IB Physics Mathematics Chemistry Economics Business and Management Presentation ITGS IA Computer help

IB Chemistry HL SL help Mathematics Physics Economics Chemistry Business

IB Economics HL SL Management Math Portfolio TOK Economics Historical Investigation Extended help

IB Business and Management HL SL help Essay Commentary storical Investigation Lab writing

IB Math Portfolio Help HL SL help Lab writing Project ESS English Spanish French Hindi

IB Math Project Help Studies help IB World Literature Theatre Stimulus Essay Commentary storical Investigation

IB Extended Essay Help TOK Presentation ITGS IA Computer Dossier IB World Literature Theatre Stimulus

IB TOK Essay Help Mathematics Physics Economics Chemistry Business Presentation ITGS IA Computer

IB Economics Commentary Help Management Math Portfolio HL SL Extended

IB Historical Investigation Help Essay Commentary storical Investigation Lab writing

IB Physics Lab writing Help Lab writing EVM Lab Report write

ups Project ESS English Spanish (Ab initio) French Hindi Extended Essay Help Tutors Examples Samples Solution

GuidanceIB Chemistry Lab writing Help IB World Literature Theatre

StimulusIB Biology Lab writing Help Presentation ITGS IA Computer Dossier SLHL Design Technology Design Projects RAPA IA

CADCAM Mathematics Physics Economics chemistryIB Business and Management Project Help Commentary storical

Investigation Lab writingIB ESS lab report help Mathematics Physics Economics

Chemistry Business EconomicsIB English HL SL help IB World Literature Theatre Stimulus

Economics Extended Essay IA Business IA IB Spanish Ab initio and Standard Level help Presentation ITGS

IA Computer DossierIB French Ab initio and Standard Level help Lab writing Project

ESS English Spanish French HindiIB Hindi HL SL help Mathematics Physics Economics

Chemistry Business EconomicsIB World Literature Help TOK Presentation ITGS IA Computer

Dossier EconomicsIB Theatre Stimulus help TOK Presentation ITGS IA Computer

Dossier EconomicsIB TOK Presentation help Management Math Portfolio HL SL

Extended ITGS IA Computer Dossier MathIB ITGS IA help IB World Literature Theatre Stimulus Math

Portfolio TOK Economics investigation Extended helpIB Computer Dossier help TOK Presentation ITGS IA

Computer Dossier Math Portfolio TOK Economics

Call or Email Ex-IB Examiner for Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website

httpwwwtopclassibtutorscom Online HelpTuition all over the world by the BestExpert IB Tutors Mail us or call

us for any queries

Essential Elements of a Math Portfolio Internal Assessment (IA) Task hlsl type 1 type 2 Problem Write-Up General

-‐

Name class and due date are clearly displayed

Introduction

-

Write up has an interesting (or pertinent) title

-‐

Task is properly introduced to the reader

-‐

This introduction should pose any major questions the task is seeking to answer

Body

-‐

Problem- solving process is completely explained throughout‐

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 16: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

_ For 2 E _ US$090 provide Arwa with information on three different stations that yieldthis same cost per effective litre Discuss how such information may be useful to Arwa_ For 2 E _ US$100 and 2 p _ US$080 compare the maximum distance that each motoristshould drive and still save moneyArwa is a busy person and wonders whether the saving in money would be worth the time shewould lose in extra driving_ Modify your model to account for the time taken to drive to and from an off-route station

Clearly justify any assumptions you make

IB DP Math SL type 2 IA portfolio task Fish production Gold Medal heightsIB DP Math HL type 2 IA portfolio task The dice game Filling up the petrol tankIB DP Math HL type 1 IA portfolio task shadow function Patterns from complex numberIB DP Math SL type 1 IA portfolio task Lacsaprsquos fraction Circles

IB ToK Essay TutorIB ToK Essay Topics 201213

IB ToK Essay Help Choosing the Right Essay TitleIB ToK Essay Help Planning and Writing the Essay

IB ToK Essay Help Marking and Assessing the EssayIB ToK Essay Help Grammar and Punctuation Check

IB TOK Essay on Common Sense IB Sample TOK essays

Examiners mark essays against the title as set Respond to the title exactly as given do not alter it in any way

Your essay must be between 1200 and 1600 words in length double spaced and typed in size 12 font

1 In what ways may disagreement aid the pursuit of knowledge in the natural and human sciences

2 ldquoOnly seeing general patterns can give us knowledge Only seeing particular examples can give us understandingrdquo To what

extent do you agree with these assertions3 ldquoThe possession of knowledge carries an ethical

responsibilityrdquo Evaluate this claim4 The traditional TOK diagram indicates four ways of knowing

Propose the inclusion of a fifth way of knowing selected from intuition memory or imagination and explore the knowledge

issues it may raise in two areas of knowledge5 ldquoThat which can be asserted without evidence can be

dismissed without evidencerdquo (Christopher Hitchens) Do you agree

6 Can we know when to trust our emotions in the pursuit of knowledge Consider history and one other area of knowledge

IB TOK ESSAY WRITERS HELP SOLUTIONIB COMMENTARY ESSAY HELP IB ECONOMICS

COMMENTARIES IB TOK IB EXTENDED ESSAY IB IB TOK Essay Help Mathematics Physics Economics

ChemistryIB TOK TUTORS EXAMPLES SAMPLES IB TOK

PRESENTATION TUTORS HELP IB ESSAY EXTENDED ESSAY

Online tuitions Home tuitions and IndividualGroup coaching and tuitions in MathsMathMathematics and physics

Chemistry EconomicsBusiness Management for VI-XII standards for IGCSE IBAP A AS-level Ed-excelOverseas

Students studying in Grade(IV-XII ) from US UK Canada Australia Newzealand etc can contact for online tutoring in mathrsquos amp science Economics and Business Studies subjects

Teaching Exclusively International School Students for IB IGCSE and A levels Excellent and Consistent Results for IB

IGCSEGCSE O and A Level exam IGCSE O Level IB Maths Physics Chemistry Economics and Business and Management

HL Business IA Internal Assessment HLSL Tasks English IOCIOP Help Guidance

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heights Lacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essay computer dossierbusiness management IA helpeconomics commentaryLab reports tuition

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heightsLacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essaycomputer dossierbusiness management IA helpeconomics commentary EVM Lab reports tuition

IB MathsPortfolio urdu shayari

helpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow functionnumbersgold medal

heightsLacasprsquos fractioncirclestutorIB math home tuition in delhi IB maths home tuition in delhi IB

maths home tuition in delhi IB math home tuition in delhiIB math home tuition in gurgaon IB maths home tuition in

gurgoan IB maths home tuition in gurgoan IB math home tuition in gurgaon

IB Mathematics Physics Chemistry Economics Business and Management HL SL Studies Theatre Stimulus help

IB Physics Mathematics Chemistry Economics Business and Management Presentation ITGS IA Computer help

IB Chemistry HL SL help Mathematics Physics Economics Chemistry Business

IB Economics HL SL Management Math Portfolio TOK Economics Historical Investigation Extended help

IB Business and Management HL SL help Essay Commentary storical Investigation Lab writing

IB Math Portfolio Help HL SL help Lab writing Project ESS English Spanish French Hindi

IB Math Project Help Studies help IB World Literature Theatre Stimulus Essay Commentary storical Investigation

IB Extended Essay Help TOK Presentation ITGS IA Computer Dossier IB World Literature Theatre Stimulus

IB TOK Essay Help Mathematics Physics Economics Chemistry Business Presentation ITGS IA Computer

IB Economics Commentary Help Management Math Portfolio HL SL Extended

IB Historical Investigation Help Essay Commentary storical Investigation Lab writing

IB Physics Lab writing Help Lab writing EVM Lab Report write

ups Project ESS English Spanish (Ab initio) French Hindi Extended Essay Help Tutors Examples Samples Solution

GuidanceIB Chemistry Lab writing Help IB World Literature Theatre

StimulusIB Biology Lab writing Help Presentation ITGS IA Computer Dossier SLHL Design Technology Design Projects RAPA IA

CADCAM Mathematics Physics Economics chemistryIB Business and Management Project Help Commentary storical

Investigation Lab writingIB ESS lab report help Mathematics Physics Economics

Chemistry Business EconomicsIB English HL SL help IB World Literature Theatre Stimulus

Economics Extended Essay IA Business IA IB Spanish Ab initio and Standard Level help Presentation ITGS

IA Computer DossierIB French Ab initio and Standard Level help Lab writing Project

ESS English Spanish French HindiIB Hindi HL SL help Mathematics Physics Economics

Chemistry Business EconomicsIB World Literature Help TOK Presentation ITGS IA Computer

Dossier EconomicsIB Theatre Stimulus help TOK Presentation ITGS IA Computer

Dossier EconomicsIB TOK Presentation help Management Math Portfolio HL SL

Extended ITGS IA Computer Dossier MathIB ITGS IA help IB World Literature Theatre Stimulus Math

Portfolio TOK Economics investigation Extended helpIB Computer Dossier help TOK Presentation ITGS IA

Computer Dossier Math Portfolio TOK Economics

Call or Email Ex-IB Examiner for Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website

httpwwwtopclassibtutorscom Online HelpTuition all over the world by the BestExpert IB Tutors Mail us or call

us for any queries

Essential Elements of a Math Portfolio Internal Assessment (IA) Task hlsl type 1 type 2 Problem Write-Up General

-‐

Name class and due date are clearly displayed

Introduction

-

Write up has an interesting (or pertinent) title

-‐

Task is properly introduced to the reader

-‐

This introduction should pose any major questions the task is seeking to answer

Body

-‐

Problem- solving process is completely explained throughout‐

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 17: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

IB TOK Essay on Common Sense IB Sample TOK essays

Examiners mark essays against the title as set Respond to the title exactly as given do not alter it in any way

Your essay must be between 1200 and 1600 words in length double spaced and typed in size 12 font

1 In what ways may disagreement aid the pursuit of knowledge in the natural and human sciences

2 ldquoOnly seeing general patterns can give us knowledge Only seeing particular examples can give us understandingrdquo To what

extent do you agree with these assertions3 ldquoThe possession of knowledge carries an ethical

responsibilityrdquo Evaluate this claim4 The traditional TOK diagram indicates four ways of knowing

Propose the inclusion of a fifth way of knowing selected from intuition memory or imagination and explore the knowledge

issues it may raise in two areas of knowledge5 ldquoThat which can be asserted without evidence can be

dismissed without evidencerdquo (Christopher Hitchens) Do you agree

6 Can we know when to trust our emotions in the pursuit of knowledge Consider history and one other area of knowledge

IB TOK ESSAY WRITERS HELP SOLUTIONIB COMMENTARY ESSAY HELP IB ECONOMICS

COMMENTARIES IB TOK IB EXTENDED ESSAY IB IB TOK Essay Help Mathematics Physics Economics

ChemistryIB TOK TUTORS EXAMPLES SAMPLES IB TOK

PRESENTATION TUTORS HELP IB ESSAY EXTENDED ESSAY

Online tuitions Home tuitions and IndividualGroup coaching and tuitions in MathsMathMathematics and physics

Chemistry EconomicsBusiness Management for VI-XII standards for IGCSE IBAP A AS-level Ed-excelOverseas

Students studying in Grade(IV-XII ) from US UK Canada Australia Newzealand etc can contact for online tutoring in mathrsquos amp science Economics and Business Studies subjects

Teaching Exclusively International School Students for IB IGCSE and A levels Excellent and Consistent Results for IB

IGCSEGCSE O and A Level exam IGCSE O Level IB Maths Physics Chemistry Economics and Business and Management

HL Business IA Internal Assessment HLSL Tasks English IOCIOP Help Guidance

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heights Lacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essay computer dossierbusiness management IA helpeconomics commentaryLab reports tuition

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heightsLacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essaycomputer dossierbusiness management IA helpeconomics commentary EVM Lab reports tuition

IB MathsPortfolio urdu shayari

helpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow functionnumbersgold medal

heightsLacasprsquos fractioncirclestutorIB math home tuition in delhi IB maths home tuition in delhi IB

maths home tuition in delhi IB math home tuition in delhiIB math home tuition in gurgaon IB maths home tuition in

gurgoan IB maths home tuition in gurgoan IB math home tuition in gurgaon

IB Mathematics Physics Chemistry Economics Business and Management HL SL Studies Theatre Stimulus help

IB Physics Mathematics Chemistry Economics Business and Management Presentation ITGS IA Computer help

IB Chemistry HL SL help Mathematics Physics Economics Chemistry Business

IB Economics HL SL Management Math Portfolio TOK Economics Historical Investigation Extended help

IB Business and Management HL SL help Essay Commentary storical Investigation Lab writing

IB Math Portfolio Help HL SL help Lab writing Project ESS English Spanish French Hindi

IB Math Project Help Studies help IB World Literature Theatre Stimulus Essay Commentary storical Investigation

IB Extended Essay Help TOK Presentation ITGS IA Computer Dossier IB World Literature Theatre Stimulus

IB TOK Essay Help Mathematics Physics Economics Chemistry Business Presentation ITGS IA Computer

IB Economics Commentary Help Management Math Portfolio HL SL Extended

IB Historical Investigation Help Essay Commentary storical Investigation Lab writing

IB Physics Lab writing Help Lab writing EVM Lab Report write

ups Project ESS English Spanish (Ab initio) French Hindi Extended Essay Help Tutors Examples Samples Solution

GuidanceIB Chemistry Lab writing Help IB World Literature Theatre

StimulusIB Biology Lab writing Help Presentation ITGS IA Computer Dossier SLHL Design Technology Design Projects RAPA IA

CADCAM Mathematics Physics Economics chemistryIB Business and Management Project Help Commentary storical

Investigation Lab writingIB ESS lab report help Mathematics Physics Economics

Chemistry Business EconomicsIB English HL SL help IB World Literature Theatre Stimulus

Economics Extended Essay IA Business IA IB Spanish Ab initio and Standard Level help Presentation ITGS

IA Computer DossierIB French Ab initio and Standard Level help Lab writing Project

ESS English Spanish French HindiIB Hindi HL SL help Mathematics Physics Economics

Chemistry Business EconomicsIB World Literature Help TOK Presentation ITGS IA Computer

Dossier EconomicsIB Theatre Stimulus help TOK Presentation ITGS IA Computer

Dossier EconomicsIB TOK Presentation help Management Math Portfolio HL SL

Extended ITGS IA Computer Dossier MathIB ITGS IA help IB World Literature Theatre Stimulus Math

Portfolio TOK Economics investigation Extended helpIB Computer Dossier help TOK Presentation ITGS IA

Computer Dossier Math Portfolio TOK Economics

Call or Email Ex-IB Examiner for Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website

httpwwwtopclassibtutorscom Online HelpTuition all over the world by the BestExpert IB Tutors Mail us or call

us for any queries

Essential Elements of a Math Portfolio Internal Assessment (IA) Task hlsl type 1 type 2 Problem Write-Up General

-‐

Name class and due date are clearly displayed

Introduction

-

Write up has an interesting (or pertinent) title

-‐

Task is properly introduced to the reader

-‐

This introduction should pose any major questions the task is seeking to answer

Body

-‐

Problem- solving process is completely explained throughout‐

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 18: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

PRESENTATION TUTORS HELP IB ESSAY EXTENDED ESSAY

Online tuitions Home tuitions and IndividualGroup coaching and tuitions in MathsMathMathematics and physics

Chemistry EconomicsBusiness Management for VI-XII standards for IGCSE IBAP A AS-level Ed-excelOverseas

Students studying in Grade(IV-XII ) from US UK Canada Australia Newzealand etc can contact for online tutoring in mathrsquos amp science Economics and Business Studies subjects

Teaching Exclusively International School Students for IB IGCSE and A levels Excellent and Consistent Results for IB

IGCSEGCSE O and A Level exam IGCSE O Level IB Maths Physics Chemistry Economics and Business and Management

HL Business IA Internal Assessment HLSL Tasks English IOCIOP Help Guidance

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heights Lacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essay computer dossierbusiness management IA helpeconomics commentaryLab reports tuition

IB MathsPortfoliohelpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow

functionnumbersgold medal heightsLacasprsquos fractioncirclestutortuition solution writer TOK essay

extended essaycomputer dossierbusiness management IA helpeconomics commentary EVM Lab reports tuition

IB MathsPortfolio urdu shayari

helpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow functionnumbersgold medal

heightsLacasprsquos fractioncirclestutorIB math home tuition in delhi IB maths home tuition in delhi IB

maths home tuition in delhi IB math home tuition in delhiIB math home tuition in gurgaon IB maths home tuition in

gurgoan IB maths home tuition in gurgoan IB math home tuition in gurgaon

IB Mathematics Physics Chemistry Economics Business and Management HL SL Studies Theatre Stimulus help

IB Physics Mathematics Chemistry Economics Business and Management Presentation ITGS IA Computer help

IB Chemistry HL SL help Mathematics Physics Economics Chemistry Business

IB Economics HL SL Management Math Portfolio TOK Economics Historical Investigation Extended help

IB Business and Management HL SL help Essay Commentary storical Investigation Lab writing

IB Math Portfolio Help HL SL help Lab writing Project ESS English Spanish French Hindi

IB Math Project Help Studies help IB World Literature Theatre Stimulus Essay Commentary storical Investigation

IB Extended Essay Help TOK Presentation ITGS IA Computer Dossier IB World Literature Theatre Stimulus

IB TOK Essay Help Mathematics Physics Economics Chemistry Business Presentation ITGS IA Computer

IB Economics Commentary Help Management Math Portfolio HL SL Extended

IB Historical Investigation Help Essay Commentary storical Investigation Lab writing

IB Physics Lab writing Help Lab writing EVM Lab Report write

ups Project ESS English Spanish (Ab initio) French Hindi Extended Essay Help Tutors Examples Samples Solution

GuidanceIB Chemistry Lab writing Help IB World Literature Theatre

StimulusIB Biology Lab writing Help Presentation ITGS IA Computer Dossier SLHL Design Technology Design Projects RAPA IA

CADCAM Mathematics Physics Economics chemistryIB Business and Management Project Help Commentary storical

Investigation Lab writingIB ESS lab report help Mathematics Physics Economics

Chemistry Business EconomicsIB English HL SL help IB World Literature Theatre Stimulus

Economics Extended Essay IA Business IA IB Spanish Ab initio and Standard Level help Presentation ITGS

IA Computer DossierIB French Ab initio and Standard Level help Lab writing Project

ESS English Spanish French HindiIB Hindi HL SL help Mathematics Physics Economics

Chemistry Business EconomicsIB World Literature Help TOK Presentation ITGS IA Computer

Dossier EconomicsIB Theatre Stimulus help TOK Presentation ITGS IA Computer

Dossier EconomicsIB TOK Presentation help Management Math Portfolio HL SL

Extended ITGS IA Computer Dossier MathIB ITGS IA help IB World Literature Theatre Stimulus Math

Portfolio TOK Economics investigation Extended helpIB Computer Dossier help TOK Presentation ITGS IA

Computer Dossier Math Portfolio TOK Economics

Call or Email Ex-IB Examiner for Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website

httpwwwtopclassibtutorscom Online HelpTuition all over the world by the BestExpert IB Tutors Mail us or call

us for any queries

Essential Elements of a Math Portfolio Internal Assessment (IA) Task hlsl type 1 type 2 Problem Write-Up General

-‐

Name class and due date are clearly displayed

Introduction

-

Write up has an interesting (or pertinent) title

-‐

Task is properly introduced to the reader

-‐

This introduction should pose any major questions the task is seeking to answer

Body

-‐

Problem- solving process is completely explained throughout‐

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 19: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

helpHLSLcomplex numberdice gamefish productionIb filling uppetrol tank shadow functionnumbersgold medal

heightsLacasprsquos fractioncirclestutorIB math home tuition in delhi IB maths home tuition in delhi IB

maths home tuition in delhi IB math home tuition in delhiIB math home tuition in gurgaon IB maths home tuition in

gurgoan IB maths home tuition in gurgoan IB math home tuition in gurgaon

IB Mathematics Physics Chemistry Economics Business and Management HL SL Studies Theatre Stimulus help

IB Physics Mathematics Chemistry Economics Business and Management Presentation ITGS IA Computer help

IB Chemistry HL SL help Mathematics Physics Economics Chemistry Business

IB Economics HL SL Management Math Portfolio TOK Economics Historical Investigation Extended help

IB Business and Management HL SL help Essay Commentary storical Investigation Lab writing

IB Math Portfolio Help HL SL help Lab writing Project ESS English Spanish French Hindi

IB Math Project Help Studies help IB World Literature Theatre Stimulus Essay Commentary storical Investigation

IB Extended Essay Help TOK Presentation ITGS IA Computer Dossier IB World Literature Theatre Stimulus

IB TOK Essay Help Mathematics Physics Economics Chemistry Business Presentation ITGS IA Computer

IB Economics Commentary Help Management Math Portfolio HL SL Extended

IB Historical Investigation Help Essay Commentary storical Investigation Lab writing

IB Physics Lab writing Help Lab writing EVM Lab Report write

ups Project ESS English Spanish (Ab initio) French Hindi Extended Essay Help Tutors Examples Samples Solution

GuidanceIB Chemistry Lab writing Help IB World Literature Theatre

StimulusIB Biology Lab writing Help Presentation ITGS IA Computer Dossier SLHL Design Technology Design Projects RAPA IA

CADCAM Mathematics Physics Economics chemistryIB Business and Management Project Help Commentary storical

Investigation Lab writingIB ESS lab report help Mathematics Physics Economics

Chemistry Business EconomicsIB English HL SL help IB World Literature Theatre Stimulus

Economics Extended Essay IA Business IA IB Spanish Ab initio and Standard Level help Presentation ITGS

IA Computer DossierIB French Ab initio and Standard Level help Lab writing Project

ESS English Spanish French HindiIB Hindi HL SL help Mathematics Physics Economics

Chemistry Business EconomicsIB World Literature Help TOK Presentation ITGS IA Computer

Dossier EconomicsIB Theatre Stimulus help TOK Presentation ITGS IA Computer

Dossier EconomicsIB TOK Presentation help Management Math Portfolio HL SL

Extended ITGS IA Computer Dossier MathIB ITGS IA help IB World Literature Theatre Stimulus Math

Portfolio TOK Economics investigation Extended helpIB Computer Dossier help TOK Presentation ITGS IA

Computer Dossier Math Portfolio TOK Economics

Call or Email Ex-IB Examiner for Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website

httpwwwtopclassibtutorscom Online HelpTuition all over the world by the BestExpert IB Tutors Mail us or call

us for any queries

Essential Elements of a Math Portfolio Internal Assessment (IA) Task hlsl type 1 type 2 Problem Write-Up General

-‐

Name class and due date are clearly displayed

Introduction

-

Write up has an interesting (or pertinent) title

-‐

Task is properly introduced to the reader

-‐

This introduction should pose any major questions the task is seeking to answer

Body

-‐

Problem- solving process is completely explained throughout‐

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 20: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

ups Project ESS English Spanish (Ab initio) French Hindi Extended Essay Help Tutors Examples Samples Solution

GuidanceIB Chemistry Lab writing Help IB World Literature Theatre

StimulusIB Biology Lab writing Help Presentation ITGS IA Computer Dossier SLHL Design Technology Design Projects RAPA IA

CADCAM Mathematics Physics Economics chemistryIB Business and Management Project Help Commentary storical

Investigation Lab writingIB ESS lab report help Mathematics Physics Economics

Chemistry Business EconomicsIB English HL SL help IB World Literature Theatre Stimulus

Economics Extended Essay IA Business IA IB Spanish Ab initio and Standard Level help Presentation ITGS

IA Computer DossierIB French Ab initio and Standard Level help Lab writing Project

ESS English Spanish French HindiIB Hindi HL SL help Mathematics Physics Economics

Chemistry Business EconomicsIB World Literature Help TOK Presentation ITGS IA Computer

Dossier EconomicsIB Theatre Stimulus help TOK Presentation ITGS IA Computer

Dossier EconomicsIB TOK Presentation help Management Math Portfolio HL SL

Extended ITGS IA Computer Dossier MathIB ITGS IA help IB World Literature Theatre Stimulus Math

Portfolio TOK Economics investigation Extended helpIB Computer Dossier help TOK Presentation ITGS IA

Computer Dossier Math Portfolio TOK Economics

Call or Email Ex-IB Examiner for Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website

httpwwwtopclassibtutorscom Online HelpTuition all over the world by the BestExpert IB Tutors Mail us or call

us for any queries

Essential Elements of a Math Portfolio Internal Assessment (IA) Task hlsl type 1 type 2 Problem Write-Up General

-‐

Name class and due date are clearly displayed

Introduction

-

Write up has an interesting (or pertinent) title

-‐

Task is properly introduced to the reader

-‐

This introduction should pose any major questions the task is seeking to answer

Body

-‐

Problem- solving process is completely explained throughout‐

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 21: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

Call or Email Ex-IB Examiner for Help +91 9911918255 or +91 9716570693 Email ramprhrgmailcom Website

httpwwwtopclassibtutorscom Online HelpTuition all over the world by the BestExpert IB Tutors Mail us or call

us for any queries

Essential Elements of a Math Portfolio Internal Assessment (IA) Task hlsl type 1 type 2 Problem Write-Up General

-‐

Name class and due date are clearly displayed

Introduction

-

Write up has an interesting (or pertinent) title

-‐

Task is properly introduced to the reader

-‐

This introduction should pose any major questions the task is seeking to answer

Body

-‐

Problem- solving process is completely explained throughout‐

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 22: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

-‐

Write- up is written in a way that would allow a younger ‐student to completely understand the problem posed and the reasoning that lead to the solution

-‐

Write- up is written as a technical paper not a piece of prose‐

-‐

Paragraphs are concise and to the point

-‐

Use of a variety of technology is regularly used and cited

-‐

Graphs and pictures are inserted in meaningful and organized ways

-‐

Graphs and pictures are completely visible properly cited and labeled in appropriate and meaningful ways

-‐

All equations are displayed using an

equation- writing program‐

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 23: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

-‐

Questions are answered in a logical order without

necessarily restating each question

-‐

All answers are correct and well supported by mathematical evidence or reasoning that is obvious to the reader

Conclusion

- ‐

All questions posed throughout the task are thoroughly answered

-‐

A general form of a solution has been reached and

explained

-‐

Investigation beyond the stated task has been

attempted

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 24: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

Basic Elements of a Good IB Mathematics Portfolio IB Math Internal Assessment (IA) Task HLSL Type 2 Type 1 Project

Correct answers throughout

All questions answered in a logical order

Audience is the teacher

Identify and address the principal goal of the assignment

Written explanations of difficult or less obvious steps in work

Word-processed including use of technology for graphs and equations

Elements of Superior Work

Attention to detail

Consistent use of significant figures or decimal place rounding

Use of proper notation such as ldquoasymprdquo or approximations

Avoid calculator notation such as 45 x^2 or 23E4

Graphs are clear with logical scales and labeled axes

Clearly define all variable that are introduced

Work stands alone

Audience is another student of the same level

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 25: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

Reader doesnrsquot have to refer to the assignment sheet

Reads smoothly and effortlessly

Answers are not numbered unless required

Single word-processed document

Integrate an equation-writing program spreadsheets graphing program etc

Comment on everything included

Explain all steps each time a new mathematical process is used

Avoid repetition of processes already explained

Graphs charts etc appear on the same page where they are explained

Student goes beyond the assignment with insight and sophistication

Identify and address the hidden goals of the assignment

Try to get into the mind of the writer of the assignment

Most tasks leave some space for the top students to explore

Student uses a variety of mathematical approaches

A good assignment will require the use of many kinds of math

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 26: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

A good question will often have several possible approaches for the solution

All math used is relevant to the task

No fluff or space-fillers

Tips to the Students

Work through all problems with pencil and calculator before writing it up

Gives an overall feel for the project so that that student can start to address the main goal and

even insights right from the start

Write a brief introduction rather than jumping right in to the first question

Sets a tone of readability

Math SLHL students can pretend that they are writing a chapter in a textbook

Encourages students to fully explain each step remembering that their audience is another

student from their course of average ability

Students can have fun with creative formatting

Take pride in the look and feel of their work

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 27: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

Math Studies students can approach the IA Project as they would a science lab

Write a hypothesis

Collect data

Analyze data

Draw conclusions

Discuss possible errors or improvements

Common Problems

Solutions to individual problems are cut in half by the page break

It is ok to leave space on the bottom of a page

Use the ldquoInsert Page-Breakrdquo feature of most word-processing programs when a new problem is

started (If there is not enough space on the current page)

Proof for comments like ldquosee the graph belowrdquo when the graph was accidentally bumped to the

next page during editing

Pages of graphs or charts with comments and explanations at end

Full-page graphs should be avoided if possible

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 28: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

Include small (but clear) graphs with an explanation on the same page

Use features like ldquotext-wrappingrdquo to make graphs or charts look and feel like an integrated part

of the work

If a graph must take up a full page include a full discussion of it on the next page

Pages of raw data in the main body of text

Raw data should be organized as concisely as possible and included in the appendix

The main body should only include the compiled data used in the relevant calculation

Frequent reference to appendix

Cuts the flow of the work

If what is in the appendix is very important move it to the body

Over-researching

IB Math Internal Assessments are not research projects

IB is looking for student work and it is obvious when it is not

Grading

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 29: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

Read paper from start to finish before assigning grades

Detail is important

Overall feel is important

Make comments or corrections in the text

Comments help the IB moderator to understand how you have assigned marks

Reference the IB Rubric on a regular basis

IB has two rubrics which could be used for students at many levels

Math Studies (Open-ended project)

Math SLHL (Answering an assigned problem)

We are expert ib math tutors who have been helping ib students across the world through online We do all types of ib mathematics iaportfolio type 2 type 1 hl and sl Here are some tips on how to do math ia circles sl type 1Always begin with Good impressive introduction predict what you are going to do in whole iaMention what technological tool you are going to useIf asked about model then dont forget to validate your model a model without validation has no meaning Put Proper Heading Figure Caption well labelled graph and Table heading followed by some explanation what is happeningFor further help you can contact us we give 100 guarantee for top class grades Top class IB tutors top class results

Please feel free to contact us for any queries or help on ib math ia circles sl type 1 portfolio write up ib

tutors sample example solution guidance mail us or call us +91 9911918255 or +91 9716570693

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013
Page 30: Ib math hl portfolio ia the dice game/filling up the petrol tank/shadow functions/patterns from complex numbers help tutors sample example solution guide

Email ramprhrgmailcom Website wwwtopclassibtutorscomNow Ex-IB Examiner for online help Tuition across the world

  • Get Expert Top Class Help by the Best IB Tutors Expert IB Tutors 100 Guaranteed help on IB Mathematics IB Maths Studies SL IA Math portfolio (SLHL Type 1I Type 2II) IA (Internal Assessment) Circles Lacsaprsquos Fractions Gold Medal Heights Fish Production Shadow Functions Patterns from Complex Numbers The Dice Game Filling up the Petrol Tank Extended Essays (EE) Help Tutors HLSL Design Technology Design Projects RAPA IA SL IB DP IA Samples Examples Solution Tutors Guidance TOK Essay TOK Presentation English IOPIOC etc
  • For use in 2012 and 2013