Mathematics XII – First In Class

Mathematics XII

Last updated: April 16, 2022

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Initially , stick to concept building. Be thorough with NCERT textbooks before moving on to R.S Aggarwal books for the Olympiads. NCERT contains many conceptual questions and will help you build a strong foundation.

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Relations and Functions 8 Topics Sample Lesson Free

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Introduction to Relations

Reflexive, Symmetric and Transitive Relations

Introduction to Functions

Types of Functions

Composition of Functions

Invertible Functions

Introduction to Binary Operations

Properties Of Binary Operations

Inverse Trigonometric Functions 18 Topics Paid

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Introduction to Inverse Trigonometric Functions

Inverse of Sine Function and its Graph

Inverse of Cosine Function and its Graph

Inverse of Tangent Function and its Graph

Inverse of Cotangent Function and its Graph

Inverse of Cosecant Function and its Graph

Inverse of Secant Function and its Graph

Properties of Inverse Trigonometric Functions-I

Properties of Inverse Trigonometric Functions-II

Properties of Inverse Trigonometric Functions-III

Properties of Inverse Trigonometric Functions-IV

Properties of Inverse Trigonometric Functions-V

Matrices 19 Topics Paid

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Introduction to Matrices

Representation of Vertices of Geometrical Figures

Types of Matrices

Equality of Matrices

Addition of Matrices

Multiplication of a Matrix by a Scalar

Difference of Matrices

Properties of Matrix Addition

Properties of Scalar Multiplication of a Matrix

Multiplication of Matrices

More about Multiplication of Matrices

Properties of Multiplication of Matrices-I

The Properties of Multiplication of Matrices-II

Transpose of a Matrix

Symmetric and Skew Symmetric Matrices

Theorems Relating Symmetric and Skew Symmetric Matrices

Elementary Operation (Transformation) of a Matrix

Invertible Matrices

Inverse of a Matrix by Elementary Operations

Continuity and Differentiability 22 Topics Paid

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Application of Derivatives 17 Topics Paid

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Rate of Change of Quantities

Introduction To Increasing and Decreasing Functions

Derivative test for Increasing and Decreasing Functions

Finding intervals in which a given Polynomial Function is Increasing or Decreasing

Equation of the Tangent

Equation of the Normal

Introduction to Approximations

Finding Approximate Value of Polynomials

Word Problem Involving Approximations

Introduction to Maxima and Minima

First Derivative Test

Second Derivative Test

Second Derivative Test: Example I

Second Derivative Test: Example II

Maximum and Minimum Values of a Function in a Closed Interval

Integrals 24 Topics Paid

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Application of Integrals 4 Topics Paid

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Finding area Under a Simple Curve

Problem Based on Finding the Area Under a Simple Curve

Area of the Region Bounded by a Curve and a Line

Area Between Two Curves

Differential Equations 9 Topics Paid

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Basic Concepts of Differential Equation

General and Particular Solutions of a Differential Equation

Formation of a Differential Equation

Equations in Variable Separable Form

Problem Based on Variable Separable Form

Introduction to Homogenous Functions

Solving Homogeneous Differential Equations

Linear Differential Equations

Solving Linear Differential Equations

Vector Algebra 13 Topics Paid

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Introduction to Vectors

Position Vector, Direction Cosines and Direction Ratios

Adding and Subtracting Vectors

Properties of Vector Addition

Components of a Vector

Scalar (or dot) Product of Two Vectors

Unit Vector in the Direction of a Given Vector

Section Formula-II

Scalar (or dot) Product of Two Vectors

Projection of a Vector on a Line and Another Vector

Vector Product of Two Vectors-I

Vector Product of Two Vectors-II

Vector Product of Two Vectors-III

Three Dimensional Geometry 11 Topics Paid

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Direction Cosines and Direction Ratios of a Line

Introduction to Three Dimensional Geometry

Direction Cosines and Direction Ratios of a Line

Equation of a Line in Space

Angle Between Two Lines

Shortest Distance Between Two Lines

Coplanarity of Two Lines

Angle Between Two Planes

Distance of a Point from a Plane

Angle Between a Line and a Plane

Linear Programming 14 Topics Paid

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Introduction to Linear Programming

Formulating Linear Programming Problems Mathematically

Rules of Solving the Linear Programming Problems Graphically

Solving LPP Graphically

Introduction to Linear Programming

Linear Programming Problem

Mathematical Formulation of the Linear Programming Problem

Graphical Method of Solving Linear Programming Problems

Different Types of Linear Programming Problems

Diet Problem Types of Linear Programming

Manufacturing Problems Types of Linear Programming

Allocation Problems Types of Linear Programming

Transportation Problems Types of Linear Programming

Corner Point Method of Solving linear Programming Problem

Probability 10 Topics Paid

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Introduction to Probability

Conditional Probability

Properties of Conditional Probability

Multiplication Theorem on Probability

Multiplication Theorem on Probability

Baye’s Theorem

Probability Distribution of a Random variable

Random Variables and its Probability Distributions

Mean of a Random Variable

Variance of a Random Variable

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