Mathematics

Algebra covers chapters such as Sets, Matrices, Permutation and Combination, Binomial Theorem, Determinants, Sequences and Series, Relations and Functions, Linear Programming, Mathematical Reasoning, Mathematical Induction and, Linear Inequalities

Algebra

Trigonometry covers chapters such as Inverse Trigonometric Functions and Trigonometric Functions

Trigonometry

Coordinate Geometry covers chapters such as Circles, Straight Lines and, Conic Sections

Coordinate Geometry

Differential Calculus covers chapters such as Application of Derivatives, Continuity and Differentiability and, Limits and Derivatives

Differential Calculus

Integral Calculus covers chapters such as Differential Equations, Definite Integrals, Indefinite Integrals and, Application of Integrals

Integral Calculus

Vectors and 3D Geometry covers chapters such as Vector Algebra and Three Dimensional Geometry

Vectors and 3D Geometry

Statistics and Probability covers chapters such as Probability and Statistics

Statistics and Probability

Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book

MATHEMATICS PART II Textbook for Class XII

MATHEMATICS PART I Textbook for Class XII

Mathematics Textbook for Class 11

Validating Statements Using Direct Method

Solving System of Linear Equations using Matrices

Counter Example Method for Validity of a Statement

General Term in a Multinomial Expansion

Distance Between Two Parallel Lines in 3D

Distance of a Point From a Plane

Applications of Section Formula

Implications of Conditional Statements

Biconditional Statements and Their Negations

Section Formula in Three-Dimensional Space

Number of Distinct Terms in a Multinomial Expansion

Deriving the Multinomial Theorem

The Shortest Distance Between Two Skew Lines

Linear Programming: Manufacturing Problem

Variance and Standard Deviation for Ungrouped Distribution

Derivative of Functions in Parametric Form

Derivatives of Exponential and Logarithmic Functions

Formation of Differential Equations

Finding Inverse by Elementary Transformations

Elementary Operations or Transformations of a Matrix

Properties of Binary Operations

Mean Deviation About Mean and Median for Ungrouped Data

Discrete Frequency Stats: Mean, Variance, SD

Linear Programming: Diet Problem

Linear Programming Problem: Graphical Method

Mean Deviation, Its Merits, and Demerits

Quartile Deviation

Relations

Coefficient of Variation

Measures of Dispersion

Mean Deviation of Ungrouped Data

Variance - Properties, Merits and Demerits

Standard Deviation - Properties, Merits and Demerits

Variance and SD for Grouped Frequency Distribution

Linear Programming Transportation Problem

Formulation of a Linear Programming Problem

Binary Operations and Operation Tables

Intervals and Subsets of Real Numbers

Variance and SD of Continuous Distribution

Mean Deviation of Grouped Data

Linear Programming Resource Allocation Problem

Minor and Cofactor of Elements of a Determinant

Examples on Logarithms

Working Rules for Logarithms

The Mantissa of Log

Logarithm: Characteristic and Mantissa

Properties of Determinants (Part 3)

Properties of Determinants (Part 2)

Properties of Determinants (Part 1)

n- Geometric Means Between Two Numbers

Mathematical Induction: Illustration

Illustration on Properties of Determinant

Properties of Determinant (Part 4)

Special Types of Matrices

Properties of ITF: Illustration-3

Properties of ITF: Illustration-2

Properties of ITF: Illustration-1

Properties of Inverse Trigonometric Functions

Principal Value of ITF: Illustrations 2

The Inverse of Cot Function

Reflection of a Graph of tanx on the Line y=x

Graph of cos⁻¹ x

Graph of sin⁻¹ x

The Inverse of Sine Function

Inverse Function: Theorem

Inverse Function

One-one and Onto of Composition of Functions

Composite Functions: Illustration

Composition of Functions: Theorem

Composition of Functions

Types of Functions

Definition and Equation of a Circle

Angle Between Two Lines

Conditions for Two Lines to Be Parallel

Finding N Arithmetic Means Between Two Numbers

Arithmetic Mean

Roots of Quadratic Equation: Illustration

Convert Degree Into Radian & Radian Into Degree

Relation Between Radian and Degree

Systems for Measurement of Angles

Modulus Function

The Reciprocal Function

Graphs of Linear Real-Valued Functions

Real-Valued Functions

Range of a Function: Illustration

Domain, Co-Domain and Range of a Function

Concept of a Function

Properties of Cartesian Product : Example

Example on Cartesian Product of Sets

Cartesian Product of Sets: Example

Cartesian Product of Two Sets: Illustration

Cartesian Product of Sets

Equality of Ordered Pairs

Ordered Pairs

Verification: n(A∪B)=n(A)+n(B)-n(A∩B)

Complement of Set

Symmetric Difference of Sets

Difference of Sets

Distributive Law of Sets

Examples of De Morgan’s Law and Distributive Law

This chapter covers topics, such as Properties of Definite Integrals and Definite Integration.

Definite Integrals

This chapter covers topics, such as Basics of Vectors, Multiplication of a Vector by a Scalar, Product of Vectors, and Addition of Vectors.

Vector Algebra

This chapter covers topics, such as Types of Sets, Complement of a Set, Subsets, Practical Problems on Union and Intersection of Two Sets, Difference of Sets, Venn Diagrams, Sets and their Representations, and Operations on Sets.

Sets

This chapter covers topics, such as Derivatives of Polynomials and Trigonometric Functions, Algebra of Derivative of Functions, Limits of Trigonometric Functions, First Principle of Differentiation, Limits of Polynomials and Rational Functions, etc.

Limits and Derivatives

This chapter covers topics, such as Distance of a Point From a Line, General Equation of a Line, Basics of 2D Coordinate Geometry, Slope of a Line, Various Forms of the Equation of a Line, and Family of Straight Lines.

Straight Lines

This chapter covers topics, such as Solutions of Linear Inequalities in One Variable, Types of Inequalities, and Solutions of Linear Inequalities in Two Variables.

Linear Inequalities

This chapter covers topics, such as Properties of Inverse Trigonometric Functions and Basic Concepts in Inverse Trigonometric Functions.

Inverse Trigonometric Functions

This chapter covers topics, such as Introduction to Trigonometric Functions, Angles, Trigonometric Equations, and Trigonometric Functions of Sum and Difference of Two Angles.

Trigonometric Functions

This chapter covers topics, such as Integration as an Inverse Process of Differentiation, Integration by Parts, Methods of Integration, and Integration by Partial Fractions.

Indefinite Integrals

This chapter covers topics, such as Area Under Simple Curves and Area between Two Curves.

Application of Integrals

This chapter covers the topic of The Principle of Mathematical Induction.

Mathematical Induction

This chapter covers topics, such as Basics of Matrices, Types of Matrices, Operation on Matrices, Symmetric and Skew-symmetric Matrices, Elementary Operation (Transformation) of a Matrix, and Inverse Matrix.

Matrices

This chapter covers topics, such as Coordinate Axes and Coordinate Planes in 3D, Angle between Two Lines, Distance of a Point From a Plane, Distance Formula in 3D, Section Formula in 3D, Plane, Direction Cosines and Direction Ratios of a Line, etc.

Three Dimensional Geometry

This chapter covers topics, such as Statements, Validating Statements, Logical Connectives and Quantifiers, Implications, and New Statements from Old.

Mathematical Reasoning

This chapter covers topics, such as Methods of Solving First Order, First Degree Differential Equation, Basics of Differential Equation, Formation of Differential Equation, General and Particular Solutions of Differential Equation, etc.

Differential Equations

This chapter covers topics, such as Continuity, Exponential and Logarithmic Functions, Mean Value Theorem, Derivatives of Composite and Implicit Functions, Differentiability, Derivative of Functions in Parametric Forms, etc.

Continuity and Differentiability

This chapter covers topics, such as Different Types of Linear Programming Problems and Mathematical Formulation of a Linear Programming Problem.

Linear Programming

This chapter covers topics, such as Hyperbola, Ellipse, Parabola, and Sections of a Cone.

Conic Sections

This chapter covers topics, such as Sum to n Terms of Special Series, Arithmetic Progression, Arithmetic Mean, Introduction to Sequences and Series, Relationship Between Arithmetic Mean and Geometric Mean, Geometric Progression, etc.

Sequences and Series

This chapter covers topics, such as Determinants, Applications of Determinants and Matrices, Adjoint and Inverse of a Matrix, Minor and Cofactors, Area of a Triangle, and Properties of Determinants.

Determinants

This chapter covers topics, such as Multinomial Theorem, Binomial Theorem for Positive Integral Indices, and General and Middle Terms.

Binomial Theorem

This chapter covers topics, such as Analysis of Frequency Distributions, Mean Deviation, Variance and Standard Deviation, and Measures of Dispersion.

Statistics

This chapter covers topics, such as Rate of Change of Quantities, Approximation, Tangents and Normals, Maxima and Minima, and Increasing and Decreasing Function.

Application of Derivatives

This chapter covers topics, such as De Moivre's Theorem, Argand Plane and Polar Representation, The Modulus and the Conjugate of a Complex Number, Roots of Unity, Complex Numbers, Algebra of Complex Numbers, and Quadratic Equations.

Complex Numbers and Quadratic Equations

This chapter covers topics, such as Permutations, Combinations, Permutations when All the Objects are not Distinct Objects, Factorial Notation, Fundamental Principle of Counting, and Permutations when All the Objects are Distinct.

Permutation and Combination

This chapter covers topics, such as Types of Functions, Invertible Functions, Basics of Functions, Cartesian Products of Sets, Basics of Relations, Composition of Functions, Algebra of Real Functions, Domain and Range of Functions, etc.

Relations and Functions

This chapter covers topics, such as Basics of Circle, Family of Circles, and Circle and a Point.

Circles

This chapter covers topics, such as Random Variables and its Probability Distributions, Independent Events, Events, Bayes Theorem, Axiomatic Approach to Probability, Random Experiments, Bernoulli Trials and Binomial Distribution, etc.

Probability

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