CBSE Syllabus for Class 12 Maths plays a crucial role in students’ exam preparation. It makes them familiar with the course content of Mathematics subject. Also, students get to know the topics and sub-topics that they are going to study during the academic year. Here, we have provided the CBSE Class 12 Maths Syllabus for 2023-24. The board exam question paper is also designed by referring to the CBSE Class 12 Maths Syllabus. So, students are strictly recommended to follow the Mathematics syllabus for Class 12 and prepare accordingly. By covering the topics mentioned in the syllabus, students can easily score decent marks in the CBSE Class 12 exam.
CBSE Class 12 Maths Syllabus 2023-24
Students can download the latest released CBSE Class 12 Maths Syllabus PDF 2023-24 from the link below. Going through the syllabus will help students to know the topics they are going to study in Maths during the academic year. They must refer to it whenever they sit for studies. This CBSE Syllabus PDF will help students track a record of all topics they have covered till now and what they have to cover.
CBSE Class 12 Maths Syllabus 2023-24 with Marks Distribution
The table below shows the marks weightage along with the number of periods required for teaching. The Maths theory paper is of 80 marks, and the internal assessment is of 20 marks which totally comes out to be 100 marks.
CBSE Class 12 Maths Syllabus And Marks Distribution 2023-24
Max Marks: 80
No. | Units | Marks |
I. | Relations and Functions | 08 |
II. | Algebra | 10 |
III. | Calculus | 35 |
IV. | Vectors and Three – Dimensional Geometry | 14 |
V. | Linear Programming | 05 |
VI. | Probability | 08 |
Total Theory | 80 | |
Internal Assessment | 20 | |
Grand Total | 100 |
Unit-I: Relations and Functions
1. Relations and Functions
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions.
2. Inverse Trigonometric Functions
Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions.
Unit-II: Algebra
1. Matrices
Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operations 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). Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).
2. 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
1. Continuity and Differentiability
Continuity and differentiability, derivative of composite functions, 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.
2. Applications of Derivatives
Applications of derivatives: rate of change of quantities, 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 real-life situations).
3. IntegralsÂ
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.
4. Applications of the Integrals
Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only)
5. 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
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.
2. 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
1. 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
1. Probability
Conditional probability, multiplication theorem on probability, independent events, total probability, Bayesâ€™ theorem, Random variable and its probability distribution, mean of random variable.
Students can go through the CBSE Class 12 Syllabus to get the detailed syllabus of all subjects. Get access to interactive lessons and videos related to Maths and Science with BYJU’S App/ Tablet.
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