CBSE Class 12 Mathematics Syllabus 202425
Course Structure
One Paper – Max Marks: 80
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 
UnitI: Relations and Functions
 Relations and Functions – 15 Periods
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions.
 Inverse Trigonometric Functions 15 Periods Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions.
UnitII: Algebra
 Matrices – 25 Periods
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. On commutativity of multiplication of matrices and existence of nonzero 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 – 25 Periods
Determinant of a square matrix (up to 3 x 3 matrices), minors, cofactors 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.
UnitIII: Calculus
 Continuity and Differentiability – 20 Periods
Continuity and differentiability, 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.
 Applications of Derivatives – 10 Periods
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 real life situations).
 Integrals – 20 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.
Fundamental Theoem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.
 Applications of the Integrals – 15 Periods
Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only)
 Differential Equations – 15 Periods
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:
UnitIV: Vectors and ThreeDimensional Geometry
 Vectors – 15 Periods
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 – 15 Periods
Direction cosines and direction ratios of a line joining two Cartesian equation and vector equation of a line, skew lines, shortest distance between two lines. Angle between two lines.
UnitV: Linear Programming
 Linear Programming – 20 Periods
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 nontrivial constraints).
UnitVI: Probability
 Probability – 30 Periods
Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean of random variable.
MATHEMATICS (Code No. – 041)
QUESTION PAPER DESIGN CLASS – XII
(202425)
Time: 3 hours Max. Marks: 80
S. No. 
Typology of Questions 
Total Marks 
% Weightage 
1 
Remembering: Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers. Understanding: Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas 
44 
55 
2 
Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way. 
20 
25 
3 
Analysing : Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations Evaluating: Present and defend opinions by making judgments about information, validity of ideas, or quality of work based on a set of criteria. Creating: Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions 
16 
20 
Total 
80 
100 
 No chapter wise Care to be taken to cover all the chapters
 Suitable internal variations may be made for generating various templates keeping the overall weightage to different form of questions and typology of questions same.
Choice(s):
There will be no overall choice in the question paper. However, 33% internal choices will be given in all the sections
INTERNAL ASSESSMENT 20 MARKS 
Periodic Tests ( Best 2 out of 3 test conducted) 10 Marks 
Mathematics Activities 10 Marks 
Note: For activities NCERT Lab Manual may be referred.
Conduct of Periodic Tests:
Periodic Test is a Pen and Paper assessment which is to be conducted by the respective subject teacher. The format of periodic test must have questions items with a balance mix, such as, very short answer (VSA), short answer (SA) and long answer (LA) to effectively assess the knowledge, understanding, application, skills, analysis, evaluation and synthesis. Depending on the nature of subject, the subject teacher will have the liberty of incorporating any other types of questions too. The modalities of the PT are as follows:
a) Mode: The periodic test is to be taken in the form of penpaper test.
b) Schedule: In the entire Academic Year, three Periodic Tests in each subject may be conducted as follows:
Test  Pre Midterm (PTI)  MidTerm (PTII)  Post MidTerm (PTIII) 
Tentative Month  JulyAugust  November  DecemberJanuary 
This is only a suggestive schedule and schools may conduct periodic tests as per their convenience. The winter bound schools would develop their own schedule with similar time gaps between two consecutive tests.
c) Average of Marks: Once schools complete the conduct of all the three periodic tests, they will convert the weightage of each of the three tests into ten marks each for identifying best two tests. The best two will be taken into consideration and the average of the two shall be taken as the final marks for PT.
d) The school will ensure simple documentation to keep a record of performance as suggested in detail circular no.Acad05/2017.
e) Sharing of Feedback/Performance: The students’ achievement in each test must be shared with the students and their parents to give them an overview of the level of learning that has taken place during different periods. Feedback will help parents formulate interventions (conducive ambience, support materials, motivation and moraleboosting) to further enhance learning. A teacher, while sharing the feedback with student or parent, should be empathetic, non judgmental and motivating. It is recommended that the teacher share best examples/performances of IA with the class to motivate all learners.
Assessment of Activity Work:
Throughout the year any 10 activities shall be performed by the student from the activities given in the NCERT Laboratory Manual for the respective class (XI or XII) which is available on the link: http://www.ncert.nic.in/exemplar/labmanuals.htmla record of the same may be kept by the student. An year end test on the activity may be conducted
The weightage are as under:
 The activities performed by the student throughout the year and record keeping : 5 marks
 Assessment of the activity performed during the year end test: 3 marks
 Vivavoce: 2 marks
Prescribed Books:
 Mathematics Textbook for Class XI, NCERT Publications
 Mathematics Part I – Textbook for Class XII, NCERT Publication
 Mathematics Part II – Textbook for Class XII, NCERT Publication
 Mathematics Exemplar Problem for Class XI, Published by NCERT
 Mathematics Exemplar Problem for Class XII, Published by NCERT
 Mathematics Lab Manual class XI, published by NCERT
 Mathematics Lab Manual class XII, published by NCERT
Important links:
Syllabus PDF  Download 
Class 12 Complete Syllabus  Class 12 Syllabus 