## Class 12 math(India)

#### Class 12 math(India) author

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### 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
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
Trigonometric function differentiation
Exponential function differentiation
Logarithmic function differentiation
Derivatives capstone

Implicit differentiation introduction
Inverse trig function differentiation
Derivatives of inverse function
Disguised function
Proof for the derivatives ex and In(x)
Logarithmic 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

### 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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