CBSE Class 12 Syllabus 2024 – 25 For Class 12 Maths Download Online CBSE Syllabus Class 12 Maths Syllabus As per Guidelines.
CBSE पाठ्यक्रम 12th Class Maths As Per NCERT
सीबीएसई बोर्ड 12वीं सिलेबस 2024 | CBSE Syllabus 2024 2025 | CBSE Maths Syllabus for Class XII | CBSE Class 12 Maths Syllabus www.cbse.gov.in
CBSE Latest Syllabus for Class 12 Maths is important for students to prepare their study time to time. Here we are provided New Edition CBSE Syllabus 2024. Stay tuned with Us for Get All Subjects Solution Biology MCQ, Physics MCQ, Difference between in Physics, Difference between in Biology
Exam Pattern for Year 2024 – 25
- Competency Focused Questions in the form of MCQs/ Case Based Questions, Source-based Integrated Questions or any other type = 40%
- Select response type questions(MCQ) = 20%
- Constructed response questions (Short Answer Questions/ Long Answer type Questions, as per existing pattern) = 40%
In case you have missed:- NCERT Solutions for Class 12
CBSE Class 12 Maths Syllabus 2024 2025
CLASS-XII
Mathematics Part I
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
Mathematics Part II
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
No. | Units | No. of Periods | Marks |
I. | Relations and Functions | 30 | 08 |
II. | Algebra | 50 | 10 |
III | Calculus | 80 | 35 |
IV. | Vectors and Three – Dimensional Geometry | 30 | 14 |
V | Linear Programming | 20 | 05 |
VI | Probability | 30 | 08 |
Total | 240 | 80 | |
Internal Assessment | 20 |
Unit-I: Relations and Functions
- Relations and Functions
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions.
- Inverse Trigonometric Functions
Definition, range, domain, principal value branch.Graphs of inverse trigonometric functions.
Unit-II: Algebra
- 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.Oncommutativity 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).
- 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
- Continuity and Differentiability
Continuity and differentiability, chain rule, derivative of inverse trigonometric functions, sin−1 , cos−1 and tan−1 , 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.
- 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).
- 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.
∫dx/x2 ± a2,∫ dx/√x2 ± a2,∫ dx/√a2 − x2,∫ dx/ax2 + bx + c,∫ dx √ax2+bx+c
∫px + q/ax2 + bx + c dx,∫px + q/√ax2+bx + c dx,∫ √a2 ± x2 dx, ∫ √x2 − a2 dx
∫√ax2 + + ,
Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.
- Applications of the Integrals
Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only)
- 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.
d d + 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
- 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
- Probability
Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean of random variable.