#### Class 12 math(India)

### Course Description

### Relations and functions

composite function

Intro to inverse function

verifying inverse functions by composition

Invertible function

### Inverse trigonometric functions

Intro to inverse trigonometric function

### Matrices

Introduction to matrices

Adding and subtracting matrices

Multiplying matrices by scalars

Properties of matrices addition and scalar multiplication

Multiplying matrices by matrices

properties of matrix multiplication

Transfer of a matrix

Elementary matrix row operation

Invertible matrix

Inverse of matrix by elementary operation

### Determinants

Determinants

Properties of determinants

Adjoint and inverse of matrix using minor and confactors

solving equation with inverse matrices

### Continuity & differentiability

continuity at a point

Review: Limits of combine &composite function

Continous function

Review: Intermediate value theorem

Differentiablility

Review: differentiation basics

product rule

Quotient rule

chain rule

Review: Produc, quotient& chain rule

Rational function differentiation

Radical function differentiation

Trigonometric function differentiation

Exponential function differentiation

Logarithmic function differentiation

Derivatives capstone

### Advanced differentiation

Implicit differentiation introduction

Implicit differentiation (advance example)

Inverse trig function differentiation

Derivatives of inverse function

Disguised function

Proof for the derivatives ex and In(x)

Logarithmic differentiation

Review: Advance differentiation

Higher -order derivatives

Mean value theorem

### Playing with graphs (using differentiation)

Critical point

Increasing and decreasing intervals

Relative minima and maxima

Absolute minima and maxima

Review : increasing/decreasing interval & extrema

Concavity

Point of inflection

Sketching graph using calculus

Review : concavity & points of inflection

### Applications of derivatives

Approximations

Related rates

Tangent and normal

Optimization

Applied rate of change

L’ Hospital’s rule

Review: Derivative and applications

### Indefinite Integrals

Antiderivatives

Indefinite integrals intro

Indefinite integrals of common function

Review: Indefinite integrals of common function

Integrative by parts

u-subsititution

Reverse chain rule

partial function expansion

Integration using trigonometrix

Trignometric Substitutuion

Definite Integrals

function defined by triangle

Fundamental theorem of calculus

fundamental theorem of calculus : chain rule

Definite integral as area

Definite integral properties

Review : Definite integral basics

Definition integral evaluation

Definite integrals of piecewise function

challenging definite integrals

Improper integrals

Riemann Sums

Trapezoidal rule

Definite integral as the limit of a rimann Sum

Review : rimann sums

### Application of integrals

Area under Simple curve

Area between two curve

Area define by polar curve

### Differential equations

Intro to differentiate equation

Separable equation

homogenous equation

Exact equality and integrating factor

### Vector algebra

vector basics

Magnitude and direction of vector

Dot product of vector

Cross product of vector

### Three dimensional geometry

Direction cosines and direction ratio of a live

Equation of a line

Angle between two lines

Shortest distance between two lines

Equation of a planes

coplanarity of two lines

Angle between two planes

distance of a point from a plane

Line and planes

Advance topic in planes

### Probability

conditional probability and independence

Discrete random variable

Binomial random variable

Binomial mean and standard deviation formulas

more or expected value

### COURCE CHALLENGE

Test your knowledge of the skills in this course. Have a test coming up? The Course challenge can help you understand what you need to review.

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