Unit-I: Sets and Functions

Chapter 1: Sets

10 Topics | 4 Quizzes

Introduction

Subset, Equality of Set, Proper Subset

Some Important Properties and Important Laws

Power Set

Important Properties

Practice Questions 1 – Sets – Class XI

Practice Questions 2 – Sets – Class XI

Practice Questions 3 – Sets – Class XI

Practice Questions 4 – Sets – Class XI

Chapter 2: Relations & Functions

14 Topics | 4 Quizzes

Ordered pairs & Cartesian Product

Relation

Domain and Range

Inverse Relation

Pictorial Representation of Different types of relation

Types of relation of a set, Equivalence Relation & Congruence Modulo Relation of Integers

Function

Diagrammatic representation of function

Some different types of functions

Real value functions and their graphs

Some real functions and their graphs

Different Categories of function

Equality of functions

Composition of functions

Practice Questions 1 – Relations and Functions – Class XI

Practice Questions 2 – Relations and Functions – Class XI

Practice Questions 3 – Relations and Functions – Class XI

Practice Questions 4 – Relations and Functions – Class XI

Chapter 3: Trigonometric Functions

9 Topics | 1 Quiz

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 sin2x + cos2x = 1, for all x

Signs of trigonometric functions

Domain and range of trigonometric functions and their graphs

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

General solution of trigonometric equations of the type sin y = sin a, cos y = cos a and tan y = tan a.

Concept Checkers – Trigonometric Functions

Unit-II: Algebra

Chapter 1: Principle of Mathematical Induction

3 Topics | 5 Quizzes

Introduction

The principle of mathematical induction

Applications

Practice Questions 1 – Principle of Mathematical Inductions – Class XI

Practice Questions 2 -Principle of Mathematical Inductions – Class XI

Practice Questions 3 -Principle of Mathematical Inductions – Class XI

Practice Questions 4 -Principle of Mathematical Inductions – Class XI

Practice Questions 5-Principle of Mathematical Inductions-Class XI

Chapter 2: Complex Numbers and Quadratic Equations

6 Topics | 2 Quizzes

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

Concept Checkers – Complex Numbers & Quadratic equations

Chapter 3: Linear Inequalities

6 Topics | 5 Quizzes

Inequalities and Linear inequalities

Types of Inequalities

Solution of Linear Inequality in one Variable

Solution of Linear Inequalities in two variable

System of Linear Inequalities in two variables – Graphical Representation

Properties of Inequality

Practice Questions 4-Linear Inequalities-Class XI

Practice Question 1a-Linear Inequalities-Class XI

Practice Question 1b-Linear Inequalities-Class XI

Practice Question 2-Linear Inequalities-Class XI

Practice Questions 3-Linear Inequalities-Class XI

Chapter 4: Permutations and Combinations

4 Topics | 5 Quizzes

Introduction to Permutation and Combination

Permutation

Combination

Number of Divisions (Applications)

Practice Questions 1-Permutation and Combinations-Class XI

Practice Questions 2-Permutations and Combinations-Class XI

Practice Questions 3-Permutation and Combinations-Class XI

Practice Questions 4-Permutation and Combination-Class XI

Practice Questions 5-Permutation and Combination-Class XI

Chapter 5: Binomial Theorem

5 Topics | 5 Quizzes

Introduction to Binomial Theorem

Statement of Binomial Theorem

Pascal’s triangle

Applications of Binomial Theorem

Properties of Binomial Co-efficient

Practice Questions 4-Binomial Theorem-Class XI

Practice Questions 1-Binomial Theorem-Class XI

Practice Questions 2-Binomial Theorem-Class XI

Practice Questions 3-Binomial Theorem-Class XI

Concept Checkers – Binomial Theorem

Chapter 6: Sequence and Series

9 Topics | 1 Quiz

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.

Concept Checkers – Sequence & Series

Unit-III: Coordinate Geometry

Chapter 1: Straight Lines

16 Topics | 5 Quizzes

Introduction to Straight Lines

Inclination of a line

Parallel Lines and Perpendicular Lines

Angle between a pair of intersecting lines

Some important Properties

Condition of Collinearity of three points

Formula to find coordinates

Locus

Equation of a line in various forms

Condition of coincidence of lines

Condition of Concurrency of three given lines

Some various forms of the equation of a line

Practice Questions 1-Straight Lines-Class XI

Practice Questions 2-Straight Lines-Class XI

Practice Questions 3-Straight lines-Class XI

Practice Questions 4-Straight lines-Class XI

Practice Questions 5-Straight Lines-Class XI

Chapter 2: Conic Sections

5 Topics | 4 Quizzes

Introduction to Conic Sections

Elementary Concepts of Parabola

Elementary Properties of Ellipse

Elementary Concepts of Hyperbola

Standard Equations

Practice Questions 1-Conic Sections-Class XI

Practice Questions 2-Conic Sections-Class XI

Practice Questions 3-Conic Sections-Class XI

Practice Questions 4-Conic Sections-Class XI

Chapter 3. Introduction to Three–dimensional Geometry

3 Topics | 1 Quiz

Coordinate axes and coordinate planes in three dimensions

Coordinates of a point

Distance between two points and section formula

Concept Checkers – 3D Geometry

Unit-IV: Calculus

Chapter 1: Limits and Derivatives

5 Topics | 1 Quiz

Derivative introduced as rate of change both as that of distance function and geometrically

Intuitive idea of limit

Limits of −Polynomials and rational functions, Trigonometric, 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 trigonometric functions

Concept Checkers – Limits & Derivatives

Unit-V: Mathematical Reasoning

Chapter 1: Mathematical Reasoning

15 Topics | 6 Quizzes

Statement and Negation of Statement

Conditional (Implification)

Equivalent Proposition

Tautology

Contradiction

Algebra of Statement: Some Standard Equivalence Relation

Negation of Compound Statement

Practice Questions 1 – Mathematical Reasoning – Class XI

Practice Questions 2 – Mathematical Reasoning – Class XI

Practice Questions 3-Mathematical Reasoning-Class XI

Practice Questions 4 – Mathematical Reasoning – Class XI

Practice Questions 5 – Mathematical Reasoning – Class XI

Practice Questions 6 – Mathematical Reasoning – Class XI

Unit-VI: Statistics and Probability

Chapter 1: Statistics

2 Topics | 1 Quiz

Measures of dispersion – Range, Mean deviation, Variance, Standard deviation of ungrouped/grouped data

Analysis of frequency distributions with equal means but different variances.

Concept Checkers – Statistics

Chapter 2: Probability

3 Topics | 1 Quiz

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

Concept Checkers – Probability

Concept Checkers – Conic Sections

Concept Checkers – Straight Lines

Concept Checkers – Linear Inequalities

Quiz 2

Quiz 3

Quiz 1

Concept Checkers – Permutations & Combinations

Concept Checkers – Relations & Functions

Concept Checkers – Sets

Concept Checkers – Algebra

Concept Checkers – Mathematical Reasoning

Practical Problems based on sets

Quiz 1 – Sets & Functions

Quiz 2 – Algebra

Quiz 3 – Coordinate Geometry

Quiz 4 – Calculus

Quiz 4 – Mathematical Reasoning

Quiz 5 – Statistics & Probability

Previous Topic

Composition of functions

Mathematics Class XI Chapter 2: Relations & Functions Composition of functions

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If $f: X \rightarrow Y$ and $g: Y\rightarrow Z$ , then the composition of $f$ and $g$ denoted by $\text {gof }$ (‘ $g$ composite $f$ ‘) is defined by

$(\text {gof })(x)=g (f(x)), x \in X$

$\text { dom }(\text {gof})=x$ and $\text {rng} (\text {gof})=g (\text {rng f})\subseteq Z$

Example:

$f_1(x)=\sin x^2$

$g(x)= \sin x, f(x)=x^2$ then $(\text {gof})(x)=g(f(x))$

$\begin{aligned} g(f(x))&=g(y)\\&=\sin y\\&=\sin x^2\\&=f_1(x)\end{aligned}$

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