Sample - KopyKitab...Cartesian product of the sets of reals with itself (upto R × R × R). Definition of relation, pictorial diagrams, domain, codomain and range of a relation. Function

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MATHEMATICS

Strictly Based on Latest Syllabus Issued by CBSEfor 2015 Examination

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( iii )

CONTENTS

q Sample Question Papers (Solved)Sample Question Paper 1 9 - 11

Sample Question Paper 2 12 - 14

Sample Question Paper 3 15 - 17

Sample Question Paper 4 18 - 20

Sample Question Paper 5 21 - 23

q Sample Question Papers for self assessmentSample Question Paper 6 24 - 26

Sample Question Paper 7 27 - 29

Sample Question Paper 8 30 - 32

Sample Question Paper 9 33 - 35

Sample Question Paper 10 .36 - 38

q SolutionsSample Question Paper 1 39 - 49

Sample Question Paper 2 50 - 62

Sample Question Paper 3 63 - 72

Sample Question Paper 4 73 - 84

Sample Question Paper 5 85 - 96

* SOLUTIONS for Sample Question Paper 6 to 10 can be downloaded from www.OswaalBooks.com

qq

Believe in YourselfThis is the foremost barrier to be crossed for scoring high marks in exams. One needs to believe in his / her

ability to learn, memorize and reproduce what has been learnt. Exams are nothing but the test of our faith, confidence and knowledge.

Follow a Time – TableA well set time table allotting specific durations for studying, sleeping, playing/surfing the net and eating

can help every student a lot. Every above quoted thing has to be done every day. A proper schedule can help a student beat examination stress.

Set Every Day GoalsPreparations should be done every day to excel at the day of exams without depending upon any miracle

capsule to bail you out at the last moment. By setting everyday targets and goals, one can achieve incredible results in terms of efficiency and performance.

Take care of your HealthHealth is wealth. This adage never fails. Only a sound body and sound mind can work effectively towards

achieving any objective. Thus to sum up, healthy body is a mandate for rigorous mental exercise that comes up during examinations.

Practice DailyWe eat daily, we sleep daily, so why not study daily?

Regular practice in every subject will keep students close to a subject. If one avoids any subject for more than three days in a go, he/she is bound to lose interest in it.

1.TIPS N

How to Score

2.

3.

OSWAAL Your Elixir of Positivity & Confidence Positivity and confidence can do wonders to your grades,

far more than you can think. By studying from Oswaal Sample Question papers, you develop confidence in yourself which makes you positive and hence gives you the winners advantage!! A bunch of important questions along with their systematic presentation helps you tremendously in studying effectively.

OSWAAL - Your Planner For Examination PreparationsYou must make a schedule for your studies followed by

strict implementation of that schedule. Oswaal SQP's give you questions on the important topics or topics which need more practice or time. Oswaal SQP's include last year exam questions as well as sample papers for the proper schedule of your study. You may also study with your friends and make the entire learning process fun!!

OSWAAL - Your Confidence Booster Just before the ExamOne should never try to read, study or cram anything new

just before the beginning of your exam. You can just open your Oswaal SQP's and read through the answers highlighted by you a night before for the last time and then put away all your books. This gives you a new wave of confidence just before the commencement of your exam!

4.

5.

High in your Examination?

How to get 6.

7.

8.

9.

10.

1.

2.

3.

Play GamesPlaying games – both the indoors and

outdoors, help in inculcating a practical approach towards dealing with a problem along with beating the examination stress.

PresentationTill now we have discussed the pre-exam tips.

This is a crucial tip while writing the examinations. A systematic and neat display of answers can boost your chances of scoring high.

Time ManagementYou need to manage time not only during

exam preparations, but also at the time of solving the Question paper. Carrying a wrist watch during exams is an excellent way to manage time well. You should also try to save some time at the end of the paper to recheck the answers.

Sleep WellA sound sleep a night before exam helps us

relax and rejuvenates our mind. The tired brain needs and we need to understand the needs of our brain, only then we will be able to make the most out of it especially during examinations.

Relax YourselfThis is last but not the least. Relaxing is

like meditating. When we are relaxed we are the most efficient in reproducing what we have learnt.

The 'OSWAAL' Advantage?

SYLLABUSTotal Periods : 240

One Paper 3 Hours 100 Marks

Units No. of Periods Marks

I. SETS AND FUNCTIONS 60 29

II. ALGEBRA 70 37

III. COORDINATE GEOMETRY 40 13

IV. CALCULUS 30 06

V. MATHEMATICAL REASONING 10 03

VI. STATISTICS AND PROBABILITY 30 12

Total 240 100

UNIT-I : SETS AND FUNCTIONS

1. Sets : (20 Periods)Sets and their representations. Empty set. Finite & Infinite sets. Equal sets. Subsets. Subsets of a set of realnumbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and Intersectionof sets. Difference of sets. Complement of a set. Properties of Complement Sets.

2. Relations & Functions : (20 Periods)

Ordered pairs, Cartesian product of sets. Number of elements in the cartesian product of two finite sets.Cartesian product of the sets of reals with itself (upto R × R × R). Definition of relation, pictorial diagrams,domain, codomain and range of a relation. Function as a special kind of relation from one set to another.Pictorial representation of a function, domain, co-domain & range of a function. Real valued function of thereal variable, domain and range of these functions, constant, identity, polynomial, rational, modulus, signumand greatest integer functions with their graphs. Sum, difference, product and quotients of functions.

3. Trigonometric Functions : (20 Periods)

Positive and negative angles. Measuring angles in radians & in degrees and conversion from onemeasure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identitysin2 x + cos2 x = 1, for all x. Signs of trigonometric functions and sketch of their graphs. Domain and rangeof trignometric functions and their graphs. Expressiong sin (x ± y) and cos (x ± y) in terms of sin x, sin y,cos x & cos y. Deducing the identities like following :

tan (x ± y) = tan tan

1 tan tanx y

x y±

±, cot (x ± y) =

cot cot 1cot cot

x yx y

±±

sin x + sin y = 2 sin 2

x y+ cos

2x y− , cos x + cos y = 2 cos

2x y+

cos 2

x y− ,

sin x – sin y = 2 cos 2

x y+ sin

2x y− , cos x – cos y = – 2 sin

2x y+

sin 2

x y− ,

Identities related to sin 2x, cos 2x, tan 2x, sin 3x, cos 3x and tan 3x. General solution of trigonometricequations of the type sin θ = sin α, cos θ = cos α and tan θ = tan α. Proofs and simple applications of sineand cosine formulae.

( v )

ijh{kk lEcU/kh vko';d tkudkjhUNIT-II : ALGEBRA

1. Principle of Mathematical Induction : (10 Periods)Processes of the proof by induction, motivating the application of the method by looking at naturalnumbers as the least inductive subset of real numbers. The principle of mathematical induction and simpleapplications.

2. Complex Numbers and Quadratic Equations : (15 Periods)Need for complex numbers, especially 1− , to be motivated by inability to solve some of the quadraticequations. Brief description of algebraic properties of complex numbers. Argand plane and polarrepresentation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadraticequations in the complex number system. Source root of a complex number.

3. Linear Inequalities : (15 Periods)Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on thenumber line. Graphical solution of linear inequalities in two variables. Graphical solution of system oflinear inequalities in two variables.

4. Permutations & Combinations : (10 Periods)Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of formulaeand their connections, simple applications.

5. Binomial Theorem : (10 Periods)History, statement and proof of the binomial theorem for positive integral indices, Pascal's triangle, generaland middle term in binomial expansion, simple applications.

6. Sequence and Series : (10 Periods)Sequence and Series. Arithmetic progression (A.P.). arithmetic mean (A.M.) Geometric progression (G.P.),general term of a G.P., sum of n terms of a G.P., Arithmetic and Geometric series, infinite G.P. and its sum,geometric mean (G.M.), relation between A.M. and G.M. Sum to n terms of the special series

2 31

1 1 1, , ,

= = =∑ ∑ ∑n n n

k k kk k k

UNIT-III : COORDINATE GEOMETRY

1. Straight Lines : (10 Periods)Brief recall of Dimensional Geometry from earlier classes. Shifting of origins. Slope of a line and anglebetween two lines. Various forms of equations of a line : parallel to axes, point-slope form, slope-interceptform, two-point form, intercepts form and normal form. General equation of a line. Equation of family oflines passing through the point of intersection of two lines. Distance of a point from a line.

2. Conic Sections : (20 Periods)Sections of a cone : circles, ellipse, parabola, hyperbola, a point, a straight line and pair of intersecting linesas a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse andhyperbola. Standard equation of a circle.

3. Introduction to Three-dimensional Geometry : (10 Periods)Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between twopoints and section formula.

UNIT-IV : CALCULUS

1. Limits and Derivatives : (30 Periods)Derivative introduced as rate of change both as that of distance function and geometrically. Intutive idea oflimit. Limits of polynomials and rational functions trignometric, exponential and logarithmic functions.

( vi )

Definition of derivative, relate it to slope of tangent of the curve, derivative of sum, difference, product andquotient of functions. Derivatives of polynomial and trigonometric functions.

UNIT-V : MATHEMATICAL REASONING

1. Mathematical Reasoning : (10 Periods)

Mathematically acceptable statements. Connecting words/ phrases - consolidating the understanding of "ifand only if (necessary and sufficient) condition", "implies", "and/or", "implied by", "and", "or", "there exists"and their use through variety of examples related to real life and Mathematics. Validating the statementsinvolving the connecting words-difference between contradiction, converse and contrapositive.

UNIT-VI : STATISTICS & PROBABILITY

1. Statistics : (15 Periods)Measures of dispersion; mean deviation, variance and standard deviation of ungrouped/grouped data. Analysisof frequency distributions with equal means but different variances.

2. Probability : (15 Periods)Random experiments : outcomes, sample spaces (set representation). Events : occurrence of events, 'not','and' and 'or' events, exhaustive events, mutually exclusive events. Axiomatic (set theoretic) probability,connections with the theories of earlier classes. Probability of an event, probability of 'not', 'and' & 'or'events.

qq

( vii )

MATHEMATICS (CODE - 041)QUESTION PAPER DESIGN

CLASS - XI (2014-15)Time : 3 Hours Max. Marks : 100

S. Typology of Questions Learning Very Long Long Marks %No. Outcomes Short Answer I Answer II Weightage

and Answer (4 marks) (6 marks)Testing (1 mark)

Competencies1. Remembering : • Reasoning 2 3 1 20 20%

(Knowledge based Simple • Analyticalrecall questions, to know Skillsspecific, facts, terms, • Criticalconcepts, principles, or thinkingtheories, identify, define • Derivativeor recite, information)

2. Understanding : 2 2 1 16 16%(Comprehension to befamiliar with meaning andto understandconceptually, interpret,compare, contrast, explain,parapharase information)

3. Application (Use abstract 1 3 2 25 25%information in concretesituation, to applyknowledge to newsituations. Use givencontent to interpret asituation, provide anexample, or solve aproblem)

4. High Order Thinking 1 2 2 21 21%Skills (Analysis &Synthesis : Classify,comare, contrast, ordifferentiate betweendifferent pieces ofinformation, Organizeand/or integrate uniquepieces of informationfrom a veriety of sources)

5. Evaluation and Multi- – 2+1 1 18 18%Disciplinary (Appraise, (valuesjudge, and/or justify the based)value or worth of a decisionor outcome, or to predictoutcomes based on values) TOTAL 6×1=6 13×4=52 7×6=42 100 100%

QUESTION WISE BREAK UP

Type of Question Mark per Total No. of TotalQuestion Questions Marks

VSA 1 6 06LA-I 4 13 52LA-II 6 7 42Total 26 100

1. No chapter wise weightage. Care to be taken to cover all the chapters.2. The above template is only a sample. Suitable internal variants may be made for generating similar

templates keeping the overall weightage to different form of questions and typology of questions same.( viii )

SAMPLE QUESTION PAPER–1(Solved)

Time : 3 hrs.] [M.M. : 100

General Instructions :

1. All questions are compulsory.2. The question paper consists of 26 questions divided into 3 sections A, B and C. Section A

comprises of 6 questions of 1 mark each, Section B comprises of 13 questions of 4 markseach and Section C comprises of 7 questions of 6 marks each.

3. There is no overall choice. However internal choice has been provided in 4 questions of 4marks each and 2 questions of 6 marks each. You have to attempt only one of thealternatives in all such questions.

4. Write the serial number of question before attempting.5. Use of calculator is not permitted. However, you may ask for logarithmic and statistical

tables, if required.

Section-AQuestion numbers 1 to 6 carry 1 mark each.

1. If U = {1, 2, 3, 4, 5, 6, 7, 8, 9} A = {1, 2, 3, 4} and B = {3, 4, 5, 6},find (A B).

2. If (x + 1, y – 2) = (3, 1), find the values of x and y.

3. Find the value of cosec

19·

34. Find the multiplicative inverse of 2 – 3i.

5. Find the equation of the ellipse, whose length of the major axis is 20 and foci are (0, ± 5).

6. Find : x

x x x2 10

1lim (1 ... ).

Section-BQuestion numbers 7 to 19 carry 4 marks each.

7. Let A and B be two sets. If A X = B X = and A X = B X for some set X, show thatA = B.

ORShow that A B = A B implies A = B.

8. In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennisonly and not cricket ? How many like tennis ?

9. Find the domain and the range of the real function f defined by f (x) = 1.x

10. Solve : 2 cos2 x + 3 sin x = 0.OR

Find the value of tan ·8

cont inue

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