Chapter 1

Relations and Functions

Types of relations: Reflexive, Symmetric, Transitive

medium • 1 min read

Equivalence relation

medium • 2 min read

One to one and onto functions

medium • 3 min read

Composite functions

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Inverse of a function

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Chapter 2

Inverse Trigonometric Functions

Definition and Range

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Domain and Principal value branch

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Graphs of inverse trigonometric functions

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Elementary properties of inverse trigonometric functions

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Solving inverse trigonometric equations

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Chapter 3

Matrices

Concept and notation

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Order and equality of matrices

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Operations on Matrices

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Transpose and symmetric matrices

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Invertible matrices and proof of uniqueness of inverse

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Chapter 4

Determinants

Determinant of a square matrix (up to 3x3)

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Properties of Determinants

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Minors and Cofactors

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Adjoint and inverse of a square matrix

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Solving system of linear equations

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Chapter 5

Continuity and Differentiability

Continuity concept and examples

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Differentiability concept

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Derivative of composite functions

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Derivative of implicit functions

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Logarithmic and exponential differentiation

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Chapter 6

Applications of Derivatives

Rate of change of bodies

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Increasing and decreasing functions

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Tangents and normals

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Maxima and minima concept

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Simple problems on maxima/minima

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Chapter 7

Integrals

Integration as inverse process of differentiation

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Integration by substitution

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Integration by Parts

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Integration by Partial Fractions

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Definite integrals as limit of a sum

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Chapter 8

Applications of the Integrals

Applications in finding area

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Area under simple curves

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Area of circles/parabolas/ellipses

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Area between two curves

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Word problems using integration

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Chapter 9

Differential Equations

Definition, order and degree

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Formation of differential equation

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Solution of differential equations by variable separation

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Homogeneous differential equations

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Linear differential equations

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Chapter 10

Vectors

Vectors and scalars

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Magnitude and direction

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Direction cosines and ratios

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Types of vectors

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Scalar and vector products

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Chapter 11

Three Dimensional Geometry

Direction cosines and ratios of a line

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Equation of a Line in Space

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Angle between Two Lines

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Shortest distance between two lines

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Equation of a plane

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Chapter 12

Probability

Conditional probability

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Multiplication Theorem on Probability

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Independent Events

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Bayes theorem

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Random variable and its probability distribution

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