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CONTENTS

• Syllabus v - viii

• Examination Paper (KVS), 2014 1 - 4

1. Sets 1 - 15

2. Relations and Functions 16 - 27

3. Trigonometric Functions 28 - 50

4. Principle of Mathematical Induction 51 - 65

5. Complex Number and Quadratic Equations 66 - 81

6. Linear Inequalities 82 - 98

7. Permutations and Combinations 99 - 112

8. Binomial Theorem 113 - 127

9. Sequences and Series 128 - 160

10. Straight Lines 161 - 193

11. Conic Sections 194 - 218

12. Introduction to Three Dimensional Geometry 219 - 225

13. Limits and Derivatives 226 - 241

14. Mathematical Reasoning 242 - 249

15. Statistics 250 - 264

16. Probability 265 - 284

( iii )

Note : BSM - Board Supplementary Material, NCT - National Capital Territory, KVS - Kendriya VidyalayaSangathan

Syllabus

MathematicsCourse Structure

Class XI (2014-15)

One Paper Total Hours—Periods of 35 Minutes each

Three Hours Max. Marks. 100

Units No. of Periods Marks

I. Sets and Functions 60 29

II. Algebra 70 37

III. Coordinate Geometry 4019

IV. Calculus 30

V. Mathematical Reasoning 1015

VI. Statistics and Probability 30

Total 240 100

*No chapter/unitwise weightage. Care to be taken to cover all the chapters.

Unit-I : Sets and Functions

1. Sets : 20 Periods

Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of a

set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams.

Union and Intersection of sets. Difference of sets. Complement of a set. Properties of Complement Sets.

Practical Problems based on 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 real (upto R x R). Definition of relation, pictorial diagrams,

domain, co-domain 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 and range of a function. Real

valued functions, domain and range of these functions; constant, identity, polynomial, rational,

modulus, signum and 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 and in degrees and conversion of one into

other. Definition of trigonometric functions with the help of unit circle. Truth of the sin2 x + cos2 x=1,

for all x. Signs of trigonometric functions. Domain and range of trignometric functions and their

graphs. Expressing sin (x ± y) and cos (x ± y) in terms of sinx, siny, cosx & cosy and their simple

application. Deducing identities like the following :

[ vi ]

tan (x ± y) =

tan tan

1 tan tan

x y

x y , cot (x ± y) =

cot cot 1

cot cot

x y

y x

sin x + sin y = 2sin

2

x ycos

2

x y, cos x + cos y = 2cos

2

x ycos

2

x y,

sin x – sin y = 2cos

2

x ysin

2

x y, cos x – cos y = – 2sin

2

x ysin

2

x y,

Identities related to sin 2x, cos 2x, tan 2x, sin 3x, cos 3x and tan 3x. General solution of trigonometric

equations of the type siny = sin a, cos y = cos a and tan y = tan a.

Unit-II : Algebra

1. Principle of Mathematical Induction : 10 Periods

Process of the proof by induction, motivating the application of the method by looking at natural

numbers as the least inductive subset of real numbers. The principle of mathematical induction and

simple applications.

2. Complex Numbers and Quadratic Equations : 15 Periods

Need for complex numbers, especially 1 , to be motivated by inability to solve some of the quardratic

equations. Algebraic properties of complex numbers. Argand plane and polar representation of complex

numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex

number system. Square root of a complex number.

3. Linear Inequalities : 15 Periods

Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation

on the number line. Graphical solution of linear inequalities in two variables. Graphical solution of

system of linear inequalities in two variables.

4. Permutations and Combinations : 10 Periods

Fundamental principle of counting. Factorial n. (n!)Permutations and combinations, derivation of

formulae and their connections, simple applications.

5. Binomial Theorem : 10 Periods

History, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle,

General and 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. Formula for the following

special sum :

2 3

1 1 1

, andn n n

k k k

k k k

Unit-III : Coordinate Geometry

1. Straight Lines : 10 Periods

Brief recall of two dimensional geometry from earlier classes. Shifting of origin. Slope of a line and

angle between two lines. Various forms of equations of a line: parallel to axis, point-slope form, slope-

[ vii ]

intercept form, two-point form, intercept form and normal form. General equation of a line. Equation

of family of lines 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 a pair of inter-

secting lines as a degenerated case of a conic section. Standard equations and simple properties of

parabola, ellipse and hyperbola. 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

two points 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 of limit. Limits of polynomials and rational functions, trignometric, exponential and

logarithmic functions. Definition of derivative, relate it to slope of tangent of a curve, derivative of

sum, difference, product and quotient of functions. The derivative of polynomial and trignometric

functions.

Unit-V : Mathematical Reasoning

1. Mathematical Reasoning : 10 Periods

Mathematically acceptable statements. Connecting words/ phrases - consolidating the understand-

ing of “if and 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 statements involving the connecting words difference between contradiction, converse

and contrapositive.

Unit-VI : Statistics and Probability

1. Statistics : 15 Periods

Measures of dispersion; mean deviation, variance and standard deviation of ungrouped/grouped

data. Analysis of 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’ and ‘or’ events.

[ viii ]

Mathematics (Code No. 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 and Short Answer 1 Answer Weightage

Testing Answer (4 marks) II

Competencies (1 marks) (6 marks)

1. Remembering-(Knowledge based Simple Reasoning 2 3 1 20 20%

recall questions, to know specific facts, Analytical

terms, concepts, principles, or theories, Skills

Identify, define, or recite, information) Critcal

thinking

Derivative

2. Understanding-(Comprehension to be 2 2 1 16 16%

familiar with meaning and to understand

conceptually, interpret, compare, contrast,

explain, paraphrase information)

3. Application (Use abstract information in 1 3 2 25 25%

concrete situation, to apply knowledge to

new situations, Use given content to

interpret a situation, provide an example,

or solve a problem)

4. High Order Thinking Skills (Analysis 1 2 2 21 21%

& Synthesis- Classify, compare, contrast,

or differentiate between different pieces of

information, Organize and/or integrate

unique pieces of information from a variety

of sources)

5. Evaluation and Multi-Disciplinary – 2+1 1 18 18%

(Appraise, judge, and/or justify the value (Value

or worth of a decision or outcome, or to based)

predict outcomes based on values)

TOTAL 6x1=6 13x4=52 7x6=42 100 100%

QUESTION WISE BREAK UP

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

VSA 1 6 06

LA-I 4 13 52

LA-II 6 7 42

Total 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 variations may be made for generating similar templates

keeping the overall weightage to different form of questions and typology of questions same.

KENDRIYA VIDYALAYA SANGATHAN

COMMON SESSION ENDING EXAMINATION 2013-14

SUBJECT : MATHEMATICS

CLASS-XI

(EXAMINATION PAPER)Time Allowed : 3.00 Hours Maximum Marks : 100

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

6 questions of 1 mark each. Section B consists of 13 questions of 4 marks each. Section C consistsof 7 questions of 6 marks each.

3. All the questions in section A are to be answered in one word, one sentence or as per the exactrequirement of the question.

4. There is no overall choice. However internal choice has been provided in 4 questions of 4 markseach and 2 questions of 6 marks each. You have to attempt only one of the alternative in all suchquestions.

5. Use of calculators in not permitted.

SECTION – A (1 × 6 = 6)

1. Write all the subsets of the set A = {a, b, c}.

2. Find the slope of the line 6x + 3y – 5 = 0.

3. Write the contra positive of the statement : "If x is a prime number, then x is odd."

4. Write the converse of the statement : "x is an even number implies that x is divisible by 4".

5. If C (n, 8) = C (n, 6), find C (n, 2).

6. Write the negation of the statement p : x2 > x, for every real number x.

SECTION – B (4 × 13 = 52)

7. Fine the general solution of the following equation : 2 cos2 x + 3 sin x = 0

8. Prove thatsin5 – 2sin3 sin

cos5 – cos

x x x

x x

= tan x

OR

In any triangle ABC, prove thata b

c

=

cos( – ) / 2

sin / 2

B C

C

9. Using the principle of mathematical induction, prove that for every positive integer n, 7n – 3n isdivisible by 4.

10. Find the square root of (–7 – 24i).OR

If (x + iy)3 = u + iv, then show thatu

x+

v

y= 4 (x2 – y2)

11. Let A = {9, 10, 11, 12, 13} and f : A N be defined by f (n) = the highest prime factor of n. Listthe elements of f and find the range of f.

cont inue

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z #

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