CBSE Class 12 Maths Syllabus 2024-25

CBSE Class 12 Maths Syllabus

CBSE Class 12 Maths Syllabus 2024-25 includes a broad range of topics essential for comprehensive understanding and exam preparation. Key areas covered in the syllabus are Relations and Functions, Vectors and Three-Dimensional Geometry, Linear Programming, Probability, Calculus, and Algebra, among others. This well-rounded syllabus ensures that students acquire a deep understanding of fundamental concepts and develop problem-solving skills across various branches of mathematics.

For students looking to prepare effectively for the 2024-25 CBSE exams, it’s crucial to refer to the detailed CBSE Syllabus, which helps in focusing on key topics and managing study time. To enhance preparation, students can download the latest CBSE Class 12 Mathematics sample question papers.

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By using myCBSEGuide, students can stay organized, track their progress, and improve their understanding of the CBSE Class 12 Maths syllabus in an efficient manner. Download the app today to explore the syllabus, test papers, and revision notes, and begin your preparation for the upcoming exams!

Class 12 Mathematics Mobile App

CBSE Class 12
Mathematics (Code No. 041)
Syllabus (2024-25)

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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

Unit-I: Relations and Functions

1. Relations and Functions (15 Periods)
   Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions.
2. Inverse Trigonometric Functions (15 Periods)
   Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions.

Unit-II: Algebra

1. 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. 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). Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).
2. Determinants (25 Periods)
   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 (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.
2. 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)
3. 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.
   dxxadx∫dxx2±a2∫dxx2±a2,∫dxa2−x2, ∫dxa2+bx+c,∫dxa2+bx+c
   ∫px+qax2+bx+cdx,∫px+qax2+bx+cdx, ∫a2±x2dx,∫x2−a2dx
   ∫ax2+bx+cdx,
   Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.
4. Applications of the Integrals (15 Periods)
   Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only)
5. 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:
   dydxpydydx+py = q, where p and q are functions of x or constants.
   dxdypxdxdy+px = q, where p and q are functions of y or constants.

Unit-IV: Vectors and Three-Dimensional Geometry

1. 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.
2. Three-dimensional Geometry (15 Periods)
   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 (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 non-trivial constraints).

Unit-VI: Probability

1. 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
(2024-25)

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	16	20
	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
	Total	80	100

1. No. chapter wise weightage. Care to be taken to cover all the chapters
2. 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 tests 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:

1. Mode: The periodic test is to be taken in the form of pen-paper test.
2. Schedule: In the entire Academic Year, three Periodic Tests in each subject may be conducted as follows:
   

   Test	Pre Mid-term (PT-I)	Mid-Term (PT-II)	Post Mid-Term (PT-III)
   Tentative Month	July-August	November	December-January

   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.

3. 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.
4. The school will ensure simple documentation to keep a record of performance as suggested in detail circular no.Acad-05/2017.
5. 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 morale-boosting) 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.html a 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
  • Viva-voce: 2 marks

Prescribed Books:

1. 1. Mathematics Part I – Textbook for Class XII, NCERT Publication
   2. Mathematics Part II – Textbook for Class XII, NCERT Publication
   3. Mathematics Exemplar Problem for Class XII, Published by NCERT
   4. Mathematics Lab Manual class XII, published by NCERT

CBSE Syllabus 2024-25

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Frequently Asked Question:

When will the CBSE 2025 syllabus be released?

The CBSE 2025 syllabus has already been released by the board, and students can now access the most up-to-date and detailed syllabus for their exams. For those preparing for the upcoming exams, it’s crucial to stay informed and use reliable resources to maximize their study efforts. The myCBSEguide website provide the latest syllabus for all subjects, including CBSE Class 12 Physics Syllabus 2024-25, which is available in PDF format for easy access.

The myCBSEguide App platform offers comprehensive study materials, including sample papers, chapter-wise test papers, NCERT solutions, and revision notes. By using these resources, students can ensure they are well-prepared for their exams. The Examin8 App and Examin8 Website provide an added benefit for educators, enabling them to create personalized mock tests and practice papers. These tests can be customized with a teacher’s branding, enhancing the learning experience and helping students focus on areas that require improvement.

How to Download CBSE Class 12 Maths Syllabus in PDF Format:

To access the CBSE Class 12 Maths syllabus in PDF format, follow these simple steps:

1. Visit the official myCBSEguide website: Open your browser and go to myCBSEGuide Website.
2. Search for CBSE Class 12 Maths Syllabus: Use the search bar at the top of the homepage to search for “Class 12 Mathematics Syllabus.”
3. Select the correct syllabus: Once you find the syllabus for the 2024-25 session, click on the link to open the detailed syllabus.
4. Download the PDF: On the syllabus page, you will see an option to download the CBSE Class 12 Maths syllabus in PDF format. Simply click the “Download” button to save the file to your device.

With the syllabus downloaded, you can easily plan your study sessions, focus on key topics, and ensure a structured approach to your preparation.