Week No Learning Objectives Pupils will be taught to..... Learning Outcomes Pupils will be able to… No of Periods Suggested Teaching & Learning activities/Learning Skills/Values Points to Note Topic/Learning Area Al : FUNCTION --- 3 weeks First Term 1 3/1 - 4/1 ORIENTATIONS WEEK FORM 4 – 2 7/1 - 11/1 1 Understand the concept of relations. 1.1 Represent relations using (a) arrow diagrams (b) ordered pairs (c) graphs 1.2 Identify domain, co domain, object, image and range of a relation. 1.3 Classify a relation shown on a mapped diagram as: one to one, many to one, one to many or many to many 1 1 Use pictures, role-play and computer software to introduce the concept of relations. Skill : Interpretation, observe connection between domain, co domain, object, image and range of a relation. Discuss the idea of set and introduce set notation. Prepared by : Puan Senah Jan /2008 YEARLY LESSON PLAN – ADDITIONAL MATHEMATICS FORM 4 2008
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Yearly Plan Add Maths Form 4-Edit Kuching Senah 2008
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Use graphing calculators and computer software to explore the image of functions.
the function f”.Include examples of functions that are not mathematically based.Examples of functions include algebraic (linear and quadratic), trigonometric and absolute value. Define and sketch absolute value functions.
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3. Understand the concept of composite functions.
3.1 Determine composition of two functions.
3.2 Determine the image of composite functions given the object and vice versa
3.3 Determine one of the functions in a given composite function given the other related function.
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Use arrow diagrams or algebraic method to determine composite functions.
Give examples of finding images given the object and vice versa for composite functions
For example :Given f : x 3x – 4. Find (a) ff(2),(b) range of value of x if ff(x) > 8.
Give examples for finding a function when the composite function is given and one other function is also given.Example :Given f : x 2x – 1. find function g if
a. The composite function fg is given as fg : x 7 – 6x
b. composite function gf is given as gf : x 5/2x.
Involve algebraic functions only.
Images of composite functions include a range of values. (Limit to linear composite functions).Define composite functions
2 Geometer’s Sketchpad to explore the graphs of quadratic functions
Skills : mental process , interpretation
minimum value from the function and also the corresponding values of x.
1/3 Gantian Persekolahan (3.10.2008 – Jumaat)
10 PROGRESSIVE TEST 1(3/3- 7/3)
11FIRST MID TERM SCHOOL HOLIDAY (9 DAYS)
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Test Corrections 1
3. Sketch graphs of quadratic functions.
3.1 Sketch quadratic function graphs by determining the maximum or minimum point and two other points.
1 Use graphing calculators or
dynamic geometry software such as the Geometer’s Sketchpad to reinforce the understanding of graphs of quadratic functions.
Steps to sketch quadratic graphs:a) Determining the form“” or “”b) finding maximum or minimum point and axis of symmetry. c) finding the intercept with x-axis and y-axis.d) plot all points e) write the equation of the axis of
symmetry
Emphasise the marking of maximum or minimum point and two other points on the graphs drawn or by finding the axis of symmetry and the intersection with the y-axis.Determine other points by finding the intersection with the x-axis (if it exists).
4. Understand and use the concept of
quadratic inequalities.
4.1 Determine the ranges of values of x that satisfies quadratic inequalities.
2 Use graphing calculators or dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of quadratic inequalities.
Emphasise on sketching graphs and use of number lines when necessary.
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Topic A4: SIMULTANEOUS EQUATIONS- 1 weeks
1. Solve simultaneous equations in two unknowns: one linear equation and one non-linear equation.
1.1 Solve simultaneous equations using the substitution method.
2 Use graphing calculators or dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of simultaneous equations.Value: systematicSkills: interpretation of mathematical problem
Limit non-linear equations up to second degree only.
1.2 Solve simultaneous equations involving real- life situations.
Additional Exercises
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Use examples in real-life situations such as area, perimeter and others.
Pedagogy: Contextual Learning Values : Connection between mathematics and other subjects
Topic G1. Coordinate Geometry---5 weeks14
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1. Find distance between two points.
1.1 Find the distance between two
points , using formula.
1 Skill : Use of formula Use the Pythagoras’ Theorem to find the formula for distance between two points.
5.3 Determine whether two straight lines are perpendicular when the gradients of both lines are known and vice versa.
5.4 Determine the equation of a straight line that passes through a fixed point and perpendicular to a given line.
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Students to be exposed to SPM exam type of questions.
Values : hard work, cooperative
Pedagogy : Mastery learning
Emphasise that for perpendicular lines
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Derivation of is not required.
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5.5 Solve problems involving equations of straight lines.
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LABOUR DAY (1 May 2008)
6. Understand and use the concept of equation of locus involving distance between two points.
6.1 Find the equation of locus that satisfies the condition if:
a)the distance of a moving point from a fixed point is constant;
b) the ratio of the distances of a moving point from two fixed points is constant
6.2 Solve problems involving
2Use examples of real-life situations to explore equation of locus involving distance between two points.Use graphic calculators and dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of parallel and perpendicular lines.
Value : Patience, hard workingPedagogy: contextual learningSkill : drawing relevant diagrams
1 Use dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of circular measure.Students measure angle subtended at the centre by an arc length equal the length of radius. Repeat with different radius.Skill : contextual learningValue : Accurate, making conclusion.
Discuss the definition of one radian.“rad” is the abbreviation of radian.Include measurements in radians expressed in terms of π.
rad = 1800
2. Understand and use the concept of length of arc of a circle to solve problems.bulatan
2.1 Determine:
i) length of arc;
ii) radius; and
iii) angle subtended at the centre of a circle
based on given information.
3 Use examples of real-life situations to explore circular measure.Derivation of S = r θ by use of ratio or by deduction using definition of radian.Skill : Making conclusion or deduction, application of formula
Major and minor arc lengths discussed
Emphasize that the angle must be in radian.Students can also use formula
1.2 Use laws of indices to find the value of numbers in index form that are multiplied, divided or raised to a power.
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Use computer software such as the spreadsheet to enhance the understanding of indices.
Pedagogy : ConstructivismSkill : making inference, use of lawsValue : systematic, logical thinking
1.3 Use laws of indices to simplify algebraic expressions
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2. Understand and use the concept of logarithms and laws of logarithms to solve problems.
2.1 Express equation in index form to logarithm form and vice versa.
2.2 Find logarithm of a number
1 Use scientific calculators to enhance the understanding of the concept of logarithm.Explain definition of logarithm.N = ax; loga N = x with a > 0, a ≠ 1.
Value : systematic, abide by the laws
Pedagogy:Mastery learning
Emphasise that:loga 1 = 0; loga a = 1.
Emphasise that:a) logarithm of negative numbers
is undefined;b) logarithm of zero is undefined.Discuss cases where the given number is in:a) index formb) numerical form.
3.2 Solve problems involving the change of base and laws of logarithms.
2Activities : DemonstrationPedagogy: Mastery learning, problem solving.
12/7 Permuafakatan Ibu bapa Murid 2 (Ting 3 dan Ting 5)
4. Solve equations involving indices and logarithms
4.1 Solve equations involving indices.
2 Activities : Demonstration
Pedagogy: Mastery learning,
problem solving.
Equations that involve indices and logarithms are limited to equations with single solution only. Solve equations involving indices by: a) comparison of indices and
1 Understand and use the concept of measures of central tendency to solve problems.
1.1 Calculate the mean of ungrouped data.
1.2 Determine the mode of ungrouped data.
1.3 Determine the median of ungrouped data
1.4Determine the modal class of grouped data from frequency distribution tables.
1.5 Find the mode from histograms.
1.6 Calculate the mean of grouped data
1.7 Calculate the median of grouped data from cumulative frequency distribution tables.
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Use scientific calculators, graphing calculators and spreadsheets to explore measures of central tendency.
Students collect data from real-life situations to investigate measures of central tendency.Eg. 1) Length of leaves in school compound2). Marks for Add maths in the class.
iii) certain data is added or removed 1.10 Determine the most suitable
measure of central tendency for given data.
1Involve grouped and ungrouped data
32-33 PROGRESSIVE TEST 2 (6 August – 15 August )
34SECOND MID TERM SCHOOL HOLIDAY(9 DAYS)
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Test Corrections 2
2. Understand and use the concept of measures of dispersion to solve problems.
2.1 Find the range of ungrouped data.
2.2 Find the interquartile range of ungrouped data.
2.3 Find the range of grouped data
2 Activities : 1. Teacher gives real life examples where values of mean, mode adn medium are more or less the same and not sufficient to determine the consistency of the data and that lead to the need of finding measures of dispersion
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2.4 Find the interquartile range of grouped data from the cumulative frequency table
2.5 Determine the interquartile range of
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Values :1. Honest2. cooperative
Determine the upper and lower quartiles by using the first principle.
problems. 3.3 Solve problems involving maximum or minimum values. 1
Skills : Interpretation of problem ; Application of approprate method/formula
Limit problems to two variables only
4. Understand and use the concept of rates of change to solve problems.
4.1 Determine rates of change for related quantities.
1 Use graphing calculators with computer base ranger to explore the concept of rates of change.Skills : Interpretation of problem; Application of approprate method/formula
Limit problems to 3 variables only.
50* 5. Understand and
use the concept of small changes and approximations to solve problems.
5.1 Determine small changes in quantities
5.2 Determine approximate values using differentiation.
1 Skills : Interpretation of problem; Application of approprate method/formula
Exclude cases involving percentage change.
6. Understand and use the concept of second derivative to solve problems.
6.1 Determine the second derivative of .
6.2 Determine whether a turning point is maximum or minimum point of a curve using the second derivative