# CBSE Revision Notes for class 12 Mathematics

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## Quick Revision Notes for Class 12 Mathematics

When your exams date is coming closer we know stress level goes up. We know maths not an easy subject for some students. The first thing students do is revise whole syllabus that's why we provide you the maths revision notes for your good preparation for exams. These class 11 notes are created by our expert teachers helps you to score well in board exams. You can download CBSE Revision Notes for class 12 Maths in myCBSEguide website and mobile app for free.Download CBSE Revision Notes for CBSE Class 12 Mathematics Relations and Functions Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations.

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Download CBSE Revision Notes for CBSE Class 12 Mathematics Inverse Trigonometric Functions Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

Download CBSE Revision Notes for CBSE Class 12 Mathematics 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. Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2).Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

Download CBSE Revision Notes for CBSE Class 12 Mathematics Determinants Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, 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.

Download CBSE Revision Notes for CBSE Class 12 Mathematics Continuity and Differentiability Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, 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. Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation.

Download CBSE Revision Notes for CBSE Class 12 Mathematics Application of Derivatives Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, 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 real-life situations).

Download CBSE Revision Notes for CBSE Class 12 Mathematics 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. Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof).Basic properties of definite integrals and evaluation of definite integrals.

Download CBSE Revision Notes for CBSE Class 12 Mathematics Application of Integrals Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only), Area between any of the two above said curves (the region should be clearly identifiable).

Download CBSE Revision Notes for CBSE Class 12 Mathematics Differential Equations Definition, order and degree, general and particular solutions of a differential equation.Formation of differential equation whose general solution is given.Solution of differential equations by method of separation of variables solutions of homogeneous differential equations of first order and first degree.

Download CBSE Revision Notes for CBSE Class 12 Mathematics Vector Algebra 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, scalar triple product of vectors.

Download CBSE Revision Notes for CBSE Class 12 Mathematics Three Dimensional Geometry Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes, (iii) a line and a plane.Distance of a point from a plane.

Download CBSE Revision Notes for CBSE Class 12 Mathematics Linear Programming Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions(bounded and unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

Download CBSE Revision Notes for CBSE Class 12 Mathematics Probability Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution.

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**CBSE Class 12 Mathematics Chapter-wise Revision Notes**

- Chapter 1 - Relations and Functions
- Chapter 2 - Inverse Trigonometric Functions
- Chapter 3 - Matrices
- Chapter 4 - Determinants
- Chapter 5 - Continuity and Differentiability
- Chapter 6 - Application of Derivatives
- Chapter 7 - Integrals
- Chapter 8 - Application of Integrals
- Chapter 9 - Differential Equations
- Chapter 10 - Vector Algebra
- Chapter 11 - Three Dimensional Geometry
- Chapter 12 - Linear Programming
- Chapter 13 - Probability

**CBSE Class-12 Revision Notes and Key Points**

CBSE quick revision note for class-12 Physics, Chemistry, Maths, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.

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