Mathematics

Differential Calculus covers chapters such as Differentiation, Relations and Functions, Application of Derivatives, Mean Value Theorems, Indeterminate Forms of Limits and, Continuity and Differentiability of Functions

Differential Calculus

Trigonometry contains chapter Inverse Trigonometric Functions

Trigonometry

Algebra covers chapters such as Matrices, Probability, Determinants, Linear Programming and, Theoretical Probability Distribution

Algebra

Integral Calculus covers chapters such as Differential Equations, Definite Integrals, Indefinite Integral, Application of Integrals and, Application of Calculus

Integral Calculus

Coordinate Geometry covers chapters such as Vectors and Three Dimensional Geometry

Coordinate Geometry

Statistics contains chapter Linear Regression

Statistics

Mathematics Crash Course (Based on Revised Syllabus-2023)

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS

Understanding ISC Mathematics Class 12 Volume 2

Understanding ISC Mathematics Class 12 Volume 1

Volume of a Prism Using Scalar Triple Product

Solving System of Linear Equations using Matrices

Distance of a Point From a Plane

Derivative of Functions in Parametric Form

Derivatives of Exponential and Logarithmic Functions

Formation of Differential Equations

Elementary Operations or Transformations of a Matrix

Properties of Binary Operations

Equivalence Relations and Equivalence Classes

Empty and Universal Relations

Linear Programming: Diet Problem

Linear Programming Problem: Graphical Method

Linear Programming Transportation Problem

Formulation of a Linear Programming Problem

Binary Operations and Operation Tables

Mean Deviation of Grouped Data

Linear Programming Resource Allocation Problem

Value of Determinant (Cofactor Expansion)

Properties of Determinants (Part 3)

Properties of Determinants (Part 2)

Properties of Determinants (Part 1)

Illustration on Properties of Determinant

Properties of Determinant (Part 4)

Special Types of Matrices

Properties of ITF: Illustration-3

Properties of ITF: Illustration-2

Properties of ITF: Illustration-1

Properties of Inverse Trigonometric Functions

Principal Value of ITF: Illustrations 2

The Inverse of Cot Function

Reflection of a Graph of tanx on the Line y=x

Graph of cos⁻¹ x

Graph of sin⁻¹ x

The Inverse of Sine Function

Inverse Function: Theorem

Inverse Function

One-one and Onto of Composition of Functions

Composite Functions: Illustration

Composition of Functions: Theorem

Composition of Functions

Illustration on Binomial Distribution

Example on Binomial Distribution

Bernoulli Trials and Binomial Distribution

Probability Distribution: Illustration

Probability Distribution: Example

Illustration on Probability Distribution

Results Related to Mathematical Expectation

Mean, Variance and S.D. of Random Variable

Probability Distribution of a Random Variable

Random Variable and Probability Distribution

Introduction to Random Variable

Bayes' Theorem

The Law of Total Probability

Illustration on Pairwise Independent Events

Independency of More Than Two Events

Illustration on Conditional Probability

Problem on Conditional Probability

Angle Between a Line and a Plane

Angle Between Two Planes: Illustration

Angle Between Two Planes

Skew Lines

Line and a Plane

Equation of Plane Making Intercepts on Axes

Equation of a Plane: Illustration

Cartesian Equation of the Plane

Plane and Its Equation

Angle Between Two Lines

Equation of a Line in Vector Form

Cross Product

Scalar Product of Vectors: Illustration

Properties of Scalar Product

Scalar Product

The Centroid of a Triangle

Vector Joining Two Points

Multiplication of Vectors by Scalars: Properties

Multiplication of a Vector With a Scalar

Examples on Addition of Vectors

Addition of Vectors

Unit Vector in the Direction of a Given Vector

Unit Vector and Linear Combination of Vectors

Direction Cosine

Definition of Vector and its Magnitude

Linear Differential Equation: Illustration

Homogeneous Differential Equations

Solutions of a Differential Equation: Illustration

Solutions of a Differential Equation

Order and the Degree of Differential Equations

Area Enclosed by a Curve and a Line: Illustration

Area Under Curve: Illustration

Standard Form of Indefinite Integral - 3

Standard Form of Indefinite Integral - 2

Standard Form of Indefinite Integral

Integration by Parts: Illustration

Integration by Parts

Method of Partial Fractions

Proper and Improper Rational Functions

Indefinite Integral Illustration

Integration of Trigonometric Form

Integrals of Different Forms

Integrals With Trigonometric Substitutions

This chapter covers topics such as Points of Inflection, Turning Points or Stationary Points or Maxima and Minima Points, Maximum and Minimum Values in Closed Intervals, Maximum and Minimum Values, Monotonicity of Functions, etc.

Application of Derivatives

This chapter covers topics such as Rolle's Theorem and Lagrange's Mean Value Theorem.

Mean Value Theorems

In this chapter, we will study the concept of linear programming via examples. It explains the meaning of feasible regions and mentions the basic requirements of linear programming. We will also learn the graphical method of solving an L.P.P.

Linear Programming

This chapter covers the concept of linear regression. It highlights the regression coefficients. It also covers the properties of lines of regression.

Linear Regression

This chapter discusses the basic concepts of economics like fixed and variable costs, revenue, and profit. It explains how to find the marginal cost using the first derivative. It also highlights the concept of minimum cost and maximum revenue.

Application of Calculus

This chapter discusses the application of integrals. It teaches us how to find the areas of bounded regions. It derives the formula which is used to calculate the areas enclosed by closed curves.

Application of Integrals

In this chapter, we will study the concept of direction cosines and direction ratios of a line. We will learn how to find the shortest distance between two lines via examples. It also discusses the vector and Cartesian equation of a plane.

Three Dimensional Geometry

This chapter describes scalar and vector quantities including their representation. We will learn how to carry out mathematical operations on vectors. It also explains the laws of vector addition and dot and cross product with their properties.

Vectors

The theories of probabilities are of great practical importance. In this chapter, we recollect the experimental probability learnt in previous class and learn about theoretical probability.

Theoretical Probability Distribution

This chapter explains the concept of probability. It discusses the terms related to probability such as sample space, event, random experiment, etc., and problems based on them.

Probability

This chapter discusses differential equations. We will learn how to find the solution of an equation. Different methods of solving differential equations are explained here.

Differential Equations

This chapter covers the concept of differential calculus and definite integral. It explains the methods of integration along with fundamental theorems of calculus.

Definite Integrals

This chapter covers the concept of differential calculus, integral calculus, and indefinite integral. It explains the methods of integration along with fundamental theorems of calculus.

Indefinite Integral

This chapter describes different types of indeterminate forms such as subtraction of ∞ from ∞ and multiplication of 0 and ∞. It also explains the L’Hopital’s rule via solved examples.

Indeterminate Forms of Limits

This chapter covers topics like basic formulas and differentiation of composite functions- chain rule, differentiation of different type of functions, derivatives of implicit functions, and derivative of parametric functions.

Differentiation

This chapter discusses continuity and the derivatives of trigonometric functions, composite functions, and inverse trigonometric functions. It also explains second-order derivatives, Rolle’s theorem and Lagrange’s mean value theorem.

Continuity and Differentiability of Functions

In this chapter, we will learn about matrices and its types with the help of examples. It details the operations on matrices, including addition and multiplication. We will also solve the previous year questions based on it.

Matrices

This chapter deals with determinants. It explains the different properties of determinants. We will learn how to find the area of a triangle. It explains the method of finding the adjoint and inverse of a matrix.

Determinants

This chapter discusses the inverse trigonometric functions. It describes the inverse functions of sine, cosine, tangent, etc. It also explains the properties of inverse trigonometric functions.

Inverse Trigonometric Functions

This chapter defines the terms relations and functions. It discusses various methods for representing relations. We will learn how to find the domain and range of a relation with the aid of examples.

Relations and Functions

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