Grade 12 › Mathematics

Class 12 Mathematics

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Chapter 1

Relations and Functions

Types of Relations Types of Functions Composition of Functions Inverse of a Function Binary Operations

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Chapter 2

Inverse Trigonometric Functions

Principal Value Branches Properties of Inverse Trig Functions Simplification of Inverse Trig Expressions Addition Formulae for Inverse Trig

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Chapter 3

Matrices

Types of Matrices Operations on Matrices Transpose, Symmetric and Skew-Symmetric Matrices Invertible Matrices

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Chapter 4

Determinants

Determinant of a Matrix Properties of Determinants Minors, Cofactors and Adjoint Inverse of a Matrix Solution of Linear Equations

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Chapter 5

Continuity and Differentiability

Continuity of a Function Differentiability Standard Derivatives Chain Rule, Implicit and Parametric Differentiation Logarithmic Differentiation Second Order Derivatives Mean Value Theorems

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Chapter 6

Application of Derivatives

Rate of Change Increasing and Decreasing Functions Tangents and Normals Approximations Maxima and Minima

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Chapter 7

Integrals

Indefinite Integrals — Standard Forms Integration by Substitution Integration by Parts Integration by Partial Fractions Definite Integrals Properties of Definite Integrals

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Chapter 8

Application of Integrals

Area under a Curve Area between Two Curves Area of Standard Regions

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Chapter 9

Differential Equations

Order and Degree Formation of Differential Equations Variable Separable Method Homogeneous Differential Equations Linear Differential Equations

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Chapter 10

Vector Algebra

Scalars and Vectors Types and Operations on Vectors Dot (Scalar) Product Cross (Vector) Product Section Formula

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Chapter 11

Three-Dimensional Geometry

Direction Cosines and Direction Ratios Equation of a Line in Space Equation of a Plane Angle Between Lines and Planes Distance Formulas Skew Lines and Shortest Distance

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Chapter 12

Linear Programming

Formulation of LPP Graphical Method Corner Point Theorem Maximisation and Minimisation Problems

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Chapter 13

Probability

Conditional Probability Multiplication Theorem Independent Events Total Probability Theorem Bayes Theorem Random Variables, Mean and Variance

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Chapter 14

Application of Calculus (Commerce)

Cost, Revenue and Profit Functions Marginal Cost and Marginal Revenue Maximising Profit Elasticity of Demand

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Chapter 15

Linear Regression

Lines of Regression Regression Coefficients Correlation Coefficient Estimating Values using Regression Lines

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