# CBSE Class 12 Maths Notes NCERT Solution Sample Papers

Class 12 Maths Study Notes Previous year question papers , sample paper , NCERT Solutions, and all other study material for Maths subject of class 12th are present here for students and teachers.

Contents

## Class 12 Maths

Senior Secondary stage is a launching stage from where the students go either for higher academic education in Mathematics or for professional courses like Engineering, Physical and Biological science, Commerce or Computer Applications. The Syllabus in the subject of Mathematics has undergone changes from time to time in accordance with growth of the subject and emerging needs of the society

Class 12 Maths NCERT Text book consists of the following chapters : Relations and Functions, Inverse Trigonometric Functions, Matrices , Determinants , Continuity and Differentiability, Application of Derivatives, Integrals , Application of Integrals, Differential Equations, Vector Algebra, Three Dimensional Geometry, Linear Programming, Probability

## CBSE Class 12th Maths Syllabus

Unit-I: Relations and Functions
Chapter 1 : Relations and Function
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions.

Chapter 2 : Inverse Trigonometric Functions
Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions.

Unit-II: Algebra
Chapter 3: Matrices
Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. On commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

Chapter 4 : Determinants
Determinant of a square matrix (up to 3 x 3 matrices), minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

Unit-III: Calculus
Chapter 5 : Continuity and Differentiability
Continuity and differentiability, chain rule, derivative of inverse trigonometric functions, 𝑙𝑖𝑘𝑒 sin−1 𝑥 , cos−1 𝑥 and tan−1 𝑥, derivative of implicit functions. Concept of exponential and logarithmic functions.
Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions
expressed in parametric forms. Second order derivatives

Chapter 6 : Applications of Derivatives
Applications of derivatives: rate of change of bodies, increasing/decreasing functions, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as reallife situations).

Chapter 7 : . Integrals
Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.
Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

Chapter 8 : Applications of the Integrals
Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only)

Chapter 9 : Differential Equations
Definition, order and degree, general and particular solutions of a differential equation. Solution of differential equations by method of separation of variables, solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type:
dy/dx + py = q, where p and q are functions of x or constants.
d𝑥/d𝑦 +px = q, where p and q are functions of y or constants.

Unit-IV: Vectors and Three-Dimensional Geometry
Vectors
Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors.

Three – dimensional Geometry
Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, skew lines, shortest distance between two lines. Angle between two lines.

Unit-V: Linear Programming
Introduction, related terminology such as constraints, objective function, optimization, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints)

Unit-VI: Probability
Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean of random variable

## CBSE Class 12 Maths Study Notes

NCERT Text Book Class 12 Maths- Part I
Study Notes Chapter 1 ( Relations and Functions )
Study Notes Chapter 2 ( Inverse Trigonometric Functions )
Study Notes Chapter 3 ( Matrices )
Study Notes Chapter 4 ( Determinants )
Study Notes Chapter 5 ( Continuity and Differentiability )
Study Notes Chapter 6 ( Application of Derivatives )

NCERT Text Book Class 12 Maths – Part II
Study Notes Chapter 7 ( Integrals )
Study Notes Chapter 8 ( Application of Integrals )
Study Notes Chapter 9 ( Differential Equations )
Study Notes Chapter 10 ( Vector Algebra )
Study Notes Chapter 11 ( Three Dimensional Geometry )
Study Notes Chapter 12 ( Linear Programming )
Study Notes Chapter 13 ( Probability )

## CBSE Class 12 Maths NCERT Solutions

NCERT Text Book Class 12 Maths- Part I
NCERT Solution Chapter 1 ( Relations and Functions )
NCERT Solution Chapter 2 ( Inverse Trigonometric Functions )
NCERT Solution Chapter 3 ( Matrices )
NCERT Solution Chapter 4 ( Determinants )
NCERT Solution Chapter 5 ( Continuity and Differentiability )
NCERT Solution Chapter 6 ( Application of Derivatives )

NCERT Text Book Class 12 Maths – Part II
NCERT Solution Chapter 7 ( Integrals )
NCERT Solution Chapter 8 ( Application of Integrals )
NCERT Solution Chapter 9 ( Differential Equations )
NCERT Solution Chapter 10 ( Vector Algebra )
NCERT Solution Chapter 11 ( Three Dimensional Geometry )
NCERT Solution Chapter 12 ( Linear Programming )
NCERT Solution Chapter 13 ( Probability )

## CBSE Class 12 Maths Previous Year Question Papers

CBSE Class 12 Maths Question Paper 2022
CBSE Class 12 Maths Question Paper 2021
CBSE Class 12 Maths Question Paper 2020
CBSE Class 12 Maths Question Paper 2019
CBSE Class 12 Maths Question Paper 2018
CBSE Class 12 Maths Question Paper 2017
CBSE Class 12 Maths Question Paper 2016
CBSE Class 12 Maths Question Paper 2015
CBSE Class 12 Maths Question Paper 2014
CBSE Class 12 Maths Question Paper 2013
CBSE Class 12 Maths Question Paper 2012
CBSE Class 12 Maths Question Paper 2011
CBSE Class 12 Maths Question Paper 2010