Central Board of Secondary Education (CBSE) has released the latest CBSE Class 12 Maths Syllabus 2022-23. This latest CBSE Class 12 Mathematics Syllabus 2022-23 is beneficial for CBSE Board Exam 2023. All important topics related to CBSE Class 12 Maths Syllabus 2022-23 are discussed in this article. We also provide the direct link to download CBSE Class 12 Mathematics Syllabus 2022-23 PDF.

Students of class 12 can download the new CBSE Maths Syllabus 2022-23 through the official website of CBSE at cbseacademic.nic.in or cbse.gov.in or the direct link is given below. After downloading this latest maths syllabus the student should go through all the topics thoroughly.

The syllabus of Mathematics subject has been changing from time to time according to the growth of the subject and the emerging needs of society. The senior secondary stage is the initial stage from which students go for higher academic education in mathematics or for vocational courses such as engineering, physical and biological sciences, commerce, or computer applications.

**Also Read: CBSE Class 10 Syllabus 2022-23 PDF**

**Also Read: Secondary and Senior Secondary School Curriculum 2022-23**

The present revised curriculum has been designed as per the National Curriculum Framework 2005 and guidelines laid down in the Focus Group 2005 on Teaching of Mathematics to meet the emerging needs of all categories of students. There is a greater emphasis on the application of various concepts, inspiring subjects from real-life situations and other subject areas.

**CBSE Class 12 Maths Syllabus 2022-23 Overview**

Unit No. | Unit Name | No. of Periods | Marks |

I | Relations and Functions | 30 | 08 |

II | Algebra | 50 | 10 |

III | Calculus | 80 | 35 |

IV | Vector and Three-Dimensional Geometry | 30 | 14 |

V | Linear Programming | 20 | 05 |

VI | Probability | 30 | 08 |

Internal Assessment | 20 | ||

Total | 100 |

**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 matrices (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:** Determinants 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 the number of solutions of the system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using the inverse of a matrix.

**Unit III: Calculus**

**Continuity and Differentiability: **Continuity and differentiability, chain rule, the 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 is the 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 real-life situations).

**Also Read: CBSE Syllabus 2022-23 for Class 11 and 12**

**Integrals:** Integration is an 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.

**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 the method of separation of variables, solutions of homogeneous differential equations of the 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**

**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.

**Three-dimensional Geometry:** Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, skew lines, the shortest distance between two lines. The 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 the random variable.

**CBSE Class 12 Mathematics Question Paper Design 2022-23**

Typology of Questions | Total Marks | % Weightage |

Remembering: Exhibit memory of previously learned materialby recalling facts, terms, basic concepts, and answers. Understanding: Demonstrate understanding of facts andideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas. | 44 | 55 |

Applying: Solve problems to new situations by applyingacquired knowledge, facts, techniques, and rules in a different way. | 20 | 25 |

Analyzing: Examine and break information into parts by identifyingmotives or causes. Make inferences and find evidence to support generalizations Evaluating: Present and defend opinions by making judgments about information, the validity of ideas, or the 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 weightage. Care to be taken to cover all the chapters.
- Suitable internal variations may be made for generating various templates keeping the overall weightage to a different form of questions and typology of questions same.

**Choice(s):**

- There will be no overall choice in the question paper.
- However, 33% of internal choices will be given in all the sections.

**Internal Assessment of Class 12 Maths Syllabus 2022-23**

- Periodic Tests (Best 2 out of 3 tests conducted) = 10 Marks
- Mathematics Activities = 10 Marks

**Conduct of Periodic Tests**

A periodic test is a pen and paper evaluation that is to be conducted by the concerned subject teacher. To effectively assess knowledge, understanding, application, skills, analysis, and assessment, the format of the periodic test should contain question items with a balanced mix, such as Very Short Answer (VSA), Short Answer (SA), and Long Answer (LA) and synthesis. The subject teacher will be at liberty to include other types of questions depending on the nature of the subject. The modalities of PT are as follows:

**a) Mode:** The periodic test is to be taken in the form of a pen-paper test.**b) 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 a suggestive program only and schools may conduct tests from time to time as per their convenience. Winter-bound schools will develop their own schedules with equal time intervals between two consecutive tests.

**c) Average of marks:** Once schools have completed conducting all three periodic tests, they will convert the weightage of each of the three tests to ten marks to identify the best two tests. The best two will be taken into account and the average of both will be taken as the final score for PT.

d) The school shall ensure simple documentation for record-keeping of performance as suggested in the detailed circular no. Acad-05/2017.

**e) Sharing of Feedback/Performance:** Students’ achievements in each test should be shared with the students and their parents to give them an overview of the level of learning achieved during different periods. Feedback will help parents to design interventions (conducive environment, support material, motivation, and morale-boosting) to further enhance learning. When sharing feedback with a teacher, student, or parent, one should be empathetic, non-judgmental, and persuasive. It is recommended that teachers share the best examples/demonstrations of IA with the class to motivate all the learners.

**Prescribed Books for CBSE Class 12 Board Exam 2023**

1) Mathematics Textbook for Class XI, NCERT Publications

2) Mathematics Part I – Textbook for Class XII, NCERT Publication

3) Mathematics Part II – Textbook for Class XII, NCERT Publication

4) Mathematics Exemplar Problem for Class XI, Published by NCERT

5) Mathematics Exemplar Problem for Class XII, Published by NCERT

6) Mathematics Lab Manual class XI, published by NCERT

7) Mathematics Lab Manual class XII, published by NCERT

**CBSE Class 12 Maths Syllabus 2022-23 PDF**

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