# CBSE Class 12 Mathematics Syllabus 2019-20 – Chapters, Topics, Weightage

CBSE Class 12 Mathematics Syllabus 2019-20 – Chapters, Topics are available here in this article. This information design is completely similar to the Central Board Of Secondary Education. CBSE Class 12 Mathematics Syllabus PDF is also available in this article. Check once in this article (सीबीएसई कक्षा 12 गणित का सिलेबस) and refer your regulation syllabus after that we start the examination preparation immediately. CBSE (Central Board Of Secondary Education) changes the syllabus curriculum year to year. That may know the CBSE  Class 11 Mathematics Syllabus 2019-20 – Chapters, Topics.

• Relations and functions
• Algebra
• Calculus
• Vectors and 3-D Geometry
• Linear Programming
• Probability

### CBSE Class 12 Mathematics Syllabus & Mark Weightage

 Chapter Marks Total Marks 1. Relations and functions 10 100 Marks 2. Algebra 13 3. Calculus 44 4. Vectors and 3-D Geometry 17 5. Linear Programming 06 6. Probability 10

Time of an examination is 3 hours

Total marks awarded is 100

### Units in CBSE Class 12 Mathematics Syllabus  & No. of Periods

Relations and functions-(30 Periods)

Algebra-(50 Periods)

Calculus-(80 Periods)

Vectors and 3-D Geometry-(30 Periods)

Linear Programming-(20 Periods)

Probability-(30 Periods)

### Units in CBSE Class 12 Mathematics Syllabus Chapters, topics

Unit 1: Relations and Functions

• Relations and Functions
• Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and
• Onto functions, composite functions, the inverse of a function. Binary operations.
• Inverse Trigonometric Functions
• Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions.
• Elementary properties of inverse trigonometric functions.

Unit 2: Algebra

1. Matrices

(a)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- commutatively of multiplication of matrices and existence of non-zero matrices whose product is the zero matrices (restrict to square matrices of order.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).

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

Unit 3: Calculus

1. Continuity and Differentiability
• Continuity and differentiability, a 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.
1. 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 is given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).
1. Integrals
• Integration as inverse process ofdifferentiation. Integrationofavariety 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.
1. 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).
1. DifferentialEquations
• Definition, order, and degree, general and particular solutions of a differential equation. formation of differential equations whose general solution is given. The solution of differential equations by the method of separation of variables, solutions of homogeneous differential equations of the first order and first degree.

Unit 4: Vectors and 3-D 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, the 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, a scalar triple product of vectors.
1. 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, the shortest distance between two lines. Cartesian and vector equation of a plane. The angle between (i)two lines, (ii)two planes, (iii) a line and aplane.A distance of a point from a plane.

Unit 5: Linear Programming

1. 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 or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

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 a random variable. Repeated independent (Bernoulli) trials and Binomial distribution.

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