Chapter 1

Relations and Functions

Types of relations: Reflexive, Symmetric, Transitive

medium • 1 min read

One-to-one and onto functions, domain/range

medium • 2 min read

Composite functions and inverse of a function

medium • 3 min read

Invertible functions and their graphs

medium • 4 min read

Binary operations and their properties

medium • 5 min read

Chapter 2

Algebra (Matrices and Determinants)

Types of matrices and elementary transformations

medium • 1 min read

Multiplication of matrices and its properties

medium • 2 min read

Adjoint and Inverse of a square matrix

medium • 3 min read

Solving linear equations using matrix method

medium • 4 min read

Cramer's Rule and properties of determinants

medium • 5 min read

Chapter 3

Calculus (Differential and Integral)

Continuity and differentiability of functions

medium • 1 min read

Application of derivatives: Tangents and Normals

medium • 2 min read

Integration by substitution, parts, and partial fractions

medium • 3 min read

Definite integrals and their properties

medium • 4 min read

Area bounded by curves using integration

medium • 5 min read

Chapter 4

Vectors and 3D Geometry

Scalar and vector products of two vectors

medium • 1 min read

Direction cosines and direction ratios of a line

medium • 2 min read

Equation of a line and a plane in space

medium • 3 min read

Angle between two lines/planes

medium • 4 min read

Shortest distance between two skew lines

medium • 5 min read

Chapter 5

Linear Programming and Probability

LPP: Formulation and graphical method of solution

medium • 1 min read

Feasible and optimal regions in LPP

medium • 2 min read

Conditional probability and Bayes' Theorem

medium • 3 min read

Independent events and Bernoulli trials

medium • 4 min read

Binomial distribution and its applications

medium • 5 min read