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

15 Topics | 4 Quizzes

Introduction to Trigonometry

Angles

Degree & Radians

Cartesian Coordinate System & Polar Coordinate System

Trigonometric Ratios and Trigonometric Functions

Relation between Cartesian & Polar Coordinates

Trigonometric Identities

Graphs of Trigonometric Functions

Trigonometric Functions with Negative Angles

Some Trigonometric Measures

Transforming of Trigonometric Expression to Product

Transforming of Trigonometric Expression to Sum

Trigonometric Ratio of some Specific Angles

Trigonometric Equations

Applications of Trigonometric Formulas

Practice Questions 1-Trigonometric Functions-Class XI

Practice Questions 2-Trigonometric Functions-Class XI

Practice Questions 3-Trigonometric Functions-Class XI

Practice Questions 4-Trigonometric Functions-Class XI

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

9 Topics | 4 Quizzes

Introduction to Quadratic Equations and Complex Numbers

Algebra of complex numbers

Some important identities of Complex Numbers

Graphical representation of Complex numbers and its conjugate

Some important properties of complex numbers

Properties of the cube roots of unity

Polar representation of Complex Numbers

De-Moivre’s Theorem

Fundamental Theorem of Algebra

Practice Questions 1-Complex Numbers & Quadratic Equations-Class XI

Practice Questions 2-Complex Numbers & Quadratic Equations-Class XI

Practice Questions 3-Complex Numbers & Quadratic Equations-Class XI

Practice Questions 4-Complex Numbers & Quadratic Equations-Class XI

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

10 Topics | 4 Quizzes

Introduction and types of Sequence

Series and types of Series

Arithmetic Progression (A.P.)

Arithmetic Mean (A.M.)

Geometric Progression (G.P.)

Geometric Mean (G.M.)

Harmonic Progression (H.P.) & Harmonic Mean (H.M.)

Relation between A.M, G.M and H.M

Sum of some series of Natural numbers

Arithmetico-geometric series

Practice Questions 1-Sequence ans Series-Class XI

Practice Questions 2-Sequence ans Series-Class XI

Practice Questions 3-Sequence ans Series-Class XI

Practice Questions 4-Sequence ans Series-Class XI

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

7 Topics | 4 Quizzes

Introduction to three-dimensional geometry

Space and its dimension

Lines and Planes in Space

Rectangle Cartesian coordinates in space

Projection of a point on a line or a plane

Projection of a segment on a line or a plane

Division Formula

Practice Questions 1-3D Geometry-Class XI

Practice Questions 2-3D Geometry-Class XI

Practice Questions 3-3D Geometry-Class XI

Practice Questions 4-3D Geometry-Class XI

Unit-IV: Calculus

Chapter 1: Limits and Derivatives

6 Topics | 4 Quizzes

Introduction and historical background

Sequence

Limit of functions

Limits and their Applications

Differentiation

Algebra of Derivatives

Practice Questions 1-Limits and Derivatives-Class XI

Practice Questions 2-Limits and Derivatives-Class XI

Practice Questions 3-Limits and Derivatives-Class XI

Practice Questions 4-Limits and Derivatives-Class XI

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

4 Topics | 1 Quiz

Introduction and historical background

Basic Concepts

Random Experiment

Concept Checkers – Statistics

Chapter 2: Probability

7 Topics | 4 Quizzes

Introduction and historical background

Random Experiment

Sample Space and Event

Types of Events

Equiprobable Space or Uniform Space

Independency of Events

Baye’s Theorem

Practice Question 1-Probability-Class XI

Practice Question 2-Probability-Class XI

Practice Question 3-Probability-Class XI

Practice Question 4-Probability-Class XI

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Relation between Cartesian & Polar Coordinates

Mathematics Class XI Chapter 3: Trigonometric Functions Relation between Cartesian & Polar Coordinates

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If $P(r,\theta) = P(x,y),$ then by definition of sine and cosine functions,

$x=r\cos\theta\quad \text { and }\quad y=r\sin\theta$

Hence, $(r,\theta) \text { and } (x,y)$ are respectively polar and cartesian coordinates of the point $P$

(i) $\sin\theta=0\Rightarrow \theta=n\pi$ , where $n$ is an integer.

(ii) $\cos\theta=0\Rightarrow \theta=(2n+1)\dfrac{\pi}{2}, \text { where } n\in Z$ .

(iii) $\csc\theta=\dfrac{1}{\sin\theta},\quad \theta\neq n\pi, n\in Z$

(iv) $\sec\theta=\dfrac{1}{\cos\theta}, \quad \theta\neq (2n+1)\dfrac{\pi}{2}, n\in Z$

(v) $\tan\theta=\dfrac{\sin\theta}{\cos\theta}, \quad \theta\neq (2n+1)\dfrac{\pi}{2}, \quad n\in Z$

(vi) $\cot\theta=\dfrac{\cos\theta}{\sin\theta}, \quad \theta\neq n\pi,\quad n\in Z$

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