Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
10 Topics | 4 Quizzes
Introduction
Subset, Equality of Set, Proper Subset
Null set
Universal Set
Finite Set
Infinite Set
Set Operations
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
Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and tan3x
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
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
Distance Formula
Division Formula
Mid Point Formula
Area of a Triangle
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
Compound Statement
Conjunction
Disjunction
Quantifiers
Conditional (Implification)
Converse
Inverse
Contrapositive
Biconditional
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
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Disjunction

Mathematics Class XI Chapter 1: Mathematical Reasoning Disjunction
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Disjunction:

If p & q are two statements, can be combined by the word “or” to form a new sentence, is called disjunction and writing as p \cup q.

Axiom:

If  p, q are statement, then p \cup q is true if p is true or q is true and it is false when both p & q are false.

Truth table

The disjunction table

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Example:

Two lines intersect at a point or they are parallel.

p: Two lines intersect at a point.

q: two lines are parallel.

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