CBSE Class 12 Syllabus For Maths 2019:20: The Central Board of Secondary Education (CBSE) conducts the Class 10 and Class 12 board exams for public and private schools affiliated to the board. As the Class 12 board exams are approaching, it is essential for students to be aware of the detailed CBSE Class 12 syllabus of the respective subjects. In this article, we have given detailed CBSE Class 12 syllabus for Maths. It will help in your preparation for not only the board exam but also national-level engineering exams, namely, JEE Main and JEE Advanced respectively, which too follows the CBSE Class 11 and Class 12 syllabus. These exams are conducted for admission to B.E./B.Tech./B.Arch in various engineering colleges across the country. Students must ensure they have finished the entire CBSE Class 12 syllabus for Maths. Read on to find out the CBSE Class 12 syllabus for Maths.
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CBSE Class 12 Syllabus For Maths 2019-20
The CBSE Class 12 Maths exam is conducted for 80 marks. Internal Assessment for the subject carries the remaining 20 marks. Let us now look into the different units, chapters, and marks distribution of CBSE Class 12 Maths syllabus (for the final exam):
Units |
Chapters |
Marks |
Unit I: Relations and Functions | – 1. Relations and Functions
– 2: Inverse Trigonometric Functions |
8 |
Unit II: Algebra | – 1. Matrices
– 2. Determinants |
10 |
Unit III: Calculus | – 1. Continuity and Differentiability
– 2. Applications of Derivatives – 3. Integrals – 4. Applications of the Integrals – 5. Differential Equations |
35 |
Unit IV: Vectors and Three-Dimensional Geometry | – 1. Vectors
– 2. Three-Dimensional Geometry |
14 |
Unit V: Linear Programming | – 1. Linear Programming |
5 |
Unit VI: Probability | – 1. Probability |
8 |
Total |
80 |
The evaluation scheme for Internal Assessment is as under:
Internal Assessment |
Marks |
Periodic Tests ( Best 2 out of 3 tests conducted) |
10 |
Mathematics Activities |
10 |
Total |
20 |
Let us now look at the detailed CBSE Class 12 syllabus for Maths:
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CBSE Class 12 Syllabus For Maths Unit 1 – Relations And Functions
1. Relations and Functions
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one andonto functions, composite functions, inverse of a function.
2. Inverse Trigonometric Functions
Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.
CBSE Class 12 Syllabus For Maths Unit 2 – Algebra
1. 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. Non- commutativity 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).
2. Determinants
Periods 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.
CBSE Class 12 Syllabus For Maths Unit 3 – Calculus
1. Continuity and Differentiability
Continuity and differentiability, derivative of composite functions, chain rule, derivative 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.
2. Applications 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).
3. Integrals
Periods 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.
4. Applications of the 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).
5. 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. Solutions of linear differential equation of the type: dy/dx + py = q, where p and q are functions of x or constants. d?/d? + px = q, where p and q are functions of y or constants.
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CBSE Class 12 Syllabus For Maths Unit 4 – Vectors And Three-Dimensional Geometry
1. 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, scalar triple product of vectors.
2. 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.
CBSE Class 12 Syllabus For Maths Unit 5 – Linear Programming
1. Linear Programming
Periods 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 or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).
CBSE Class 12 Syllabus For Maths Unit 6 – Probability
1. 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.
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