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Class 12 Maths

13 Chapters

Class 12


Class 12 Maths aims to solidify students in the field of Maths. There are 13 chapters in Maths of class 12. The first chapter is Relations and Functions which involves the concept of relation and functions, domain, co-domain, range, etc. Inverse Trigonometric Functions chapter deals with restrictions on domains and trigonometric functions ranges that facilitate visibility of their inverses. Furthermore, the Matrix chapter takes you deeper into the concept of matrix as well as matrix algebra. In the Determinants chapter, you will learn about determinants which are up to order three only with real entries. Continuity and Differentiability is the fifth chapter which deals with important concepts of continuity, differentiability, and the relations existing between them. In the Application of Derivatives chapter, you will go through the derivative of composite functions, exponential functions, implicit functions, logarithmic functions, and inverse trigonometric functions. Moreover, the Integrals chapter revolves around the concept of Integral. Application of Integrals is another chapter here and it will teach you about the specific application of integrals. Differential Equations chapter will teach you the basic concepts of differential equations. Vector Algebra revolves around the concept of vectors. Three Dimensional geometry is also included in maths of class 12 which deals with the study of direction cosines and direction ratios related to a line. This chapter also has equations of lines and planes. Linear Programming teaches linear programming by graphical method only. Finally, Probability chapter deals with the concepts of probability and its related aspects.

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Relations and FunctionsInverse Trigonometric FunctionsMatricesDeterminantsContinuity and DifferentiabilityApplication of DerivativesIntegralsApplication of IntegralsDifferential EquationsVector AlgebraThree Dimensional GeometryLinear ProgrammingProbability

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Chapter 1 : Relations and Functions

Can you relate which school buses go to which schools? Does there exist a relation between them? The buses with a school name written on it will belong to that particular school. Therefore, the school name as a function defines the relation between buses and schools. Let's read all about a relation and function.

Important topic links

Introduction to RelationsTypes of FunctionsComposition of FunctionsInvertible FunctionsBinary Operations

Chapter 2 : Inverse Trigonometric Functions

Do you know what inverse trigonometric functions are? They find their applications across multiple fields. For example, if you find the ration of two sides of a right triangle, can you find the angle between them? Well, yes you can. Let's find out more in the sections below.

Important topic links

Inverse Trigonometric FunctionsGraphs of Inverse Trigonometric FunctionProperties of Inverse Trigonometric FunctionsIdentities Related to Inverse Trigonometric Functions

Chapter 3 : Matrices

When some numbers are arranged in rows and columns and are surrounded on both sides by square brackets, we call it as a Matrix. A Matrix or Matrices have very important applications in Mathematics. In this chapter, we will learn about matrices, their types and various operations on them.

Important topic links

Introduction to MatricesOperations on MatricesMultiplication of Matrices and their PropertiesTranspose of a MatrixSymmetric and Skew Symmetric Matrices

Chapter 4 : Determinants

Learning about Matrices is incomplete without learning about Determinants. The determinant of a Matrix is computed by all the elements of that Matrix. In this chapter, we will learn about Adjoint and Inverse of Matrix, Applications of Determinants, Minors and Cofactors of Determinants and so on.

Important topic links

Introduction to DeterminantsProperties of DeterminantsArea of Triangles using DeterminantsMinors and CofactorsAdjoint of a Matrix

Chapter 5 : Continuity and Differentiability

Continuity of a function is the characteristic of a function by virtue of which, the graphical form of that function is a continuous wave. A differentiable function is a function whose derivative exists at each point in its domain. Here, we will learn everything about Continuity and Differentiability of a function.

Important topic links

ContinuityAlgebra of Continuous FunctionsDifferentiability of a FunctionDerivatives of Composite Functions and Chain RuleDerivatives of Implicit Functions

Chapter 6 : Application of Derivatives

The derivative is defined as something which is based on some other thing. In Mathematics, the derivative is an expression that gives the rate of change of a function with respect to an independent variable. The application of derivatives exists in Mathematics, Science, and Engineering. Let's find out more.

Important topic links

Derivative as Rate of ChangeIncreasing and Decreasing FunctionsTangents and NormalsApproximationsMaxima and Minima

Chapter 7 : Integrals

Do you know that all I do is join things? Like if I cut a paper in a lot of strips and then place them side by side, that’s an indefinite integral. Yes, that’s what integration is. Don’t believe me? Why don’t you go through the integrals concepts below to see how right I am?

Important topic links

Introduction and Interpretation to IntegralsIntegration by SubstitutionIntegration by Partial FractionsIntegration by PartsNine Special Formula

Chapter 8 : Application of Integrals

Calculus is widely seen as functions, differentiation, and integration. It has a lot of applications in the fields of Engineering, Science, and Mathematics. In this chapter, we will learn how to use integrals to find out areas under different conditions. So, let's find the application of integrals in the topics below.

Important topic links

Area Under Simple CurvesArea Between Two Curves

Chapter 9 : Differential Equations

Do you find some equations very complex to solve? Well, a differential equation can ease your problems. Here you will be able to find the methods to find the orders and degrees and will be able to solve different types of differential equations. Let's study more in this section.

Important topic links

Introduction to Differential EquationsFormation of Differential EquationSolving Differential Equations - Variable Separable MethodSolving Homogeneous Differential EquationSolving Linear Differential Equation

Chapter 10 : Vector Algebra

Do you know how to represent a quantity with a direction? Can we represent 5 km to North in one single entity? Yes, we can with the help of vectors. In the section, we will learn about the Vector Algebra which will consist of the basic concepts, components, types and operations on the vectors.

Important topic links

Introduction to VectorsOperations on VectorsComponents of VectorSection Formula Related to VectorsScalar or Dot Product

Chapter 11 : Three Dimensional Geometry

Everything in the real world is in a three-dimensional shape. You can simply look around and observe! A strand of your hair or a big-sized bus, all of them have a three dimensional geometry. And it is necessary to learn their properties. So, let's start by understanding lines, planes, and angles from the topics below.

Important topic links

Direction Cosines and Direction RatiosEquation of a Line in GeometryAngles between Two lines in 3D SpaceShortest Distance Between Two lines in 3D SpacePlanes

Chapter 12 : Linear Programming

Linear programming is the method used in mathematics to optimize the outcome of a function. It is widely used in the fields of Mathematics, Economics and Statistics. In this chapter, we will learn about different types of Linear Programming Problems and the methods to solve them.

Important topic links

Introduction to Linear ProgrammingGraphical Solution of a Linear Programming Problems

Chapter 13 : Probability

Did you know the origins of Probability can be linked to gambling? The theory of probability may have been discovered to help gamblers, but now it assists many of our everyday activities. The chances of your school team winning the tournament, the possibility of rain on a given day, are all applications of probability.

Important topic links

Conditional ProbabilityMultiplication TheoremBayes TheoremProbability DistributionBernoulli Trials and Binomial Distribution