# CBSE Class 12 Maths Syllabus 2023-24

CBSE has released the Latest Updated Syllabus for the New Academic Session 2023-24 on March 31st, 2023, for class 12.

CBSE Board has released the latest Class 12 Maths syllabus which is to be strictly followed. Below please find our detailed analysis of Board Paper pattern, Unit-wise summary for the New Session 2023-24.

We have also updated Oswal Gurukul Books as per the Latest Paper Pattern prescribed by Board for each Subject Curriculum.

Students can directly access the CBSE Mathematics Syllabus for Class 12 of the academic year 2023-24 by clicking on the link below.

## CBSE Class 12 Maths Syllabus 2023-24: Unit-wise Summary

### Unit-I:

Relations and Functions

 NO Units No. of Periods Marks 1 Relations and Functions 30 08 2 Algebra 50 10 3 Calculus 80 35 4 Vectors and Three - Dimensional Geometry 30 14 5 Linear Programming 20 05 6 Probability 30 08 Total 240 80 Internal Assessment 20

1. Relations and 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. Operations 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 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. 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.

$$\int\frac{dx}{x^2 ± a^2}\int\frac{dx}{\sqrt{x^2 ± a^2}},\int\frac{dx}{\sqrt{x^2 - a^2}},\int\frac{dx}{ax^2 +bx+c},\int\frac{dx}{\sqrt{ax^2 +bx+c}}\\\int\frac{px+q}{ax^2 +bx+c}dx,\int\frac{px+q}{\sqrt{ax^2 +bx+c}}dx,\int{\sqrt{a^2 +x^2}}dx,\int{\sqrt{x^2 -a^2}}dx,\\\int{\sqrt{ax^2 +bx+c}}\space dx,$$

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:

$$\frac{dy}{dx}+py=q,\text{where p and q are functions of x or constants.}\\\frac{dx}{dy}+px=q,\text{where p and q are functions of y or constants.}$$

### 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.

## CBSE Class 12 Mathematics Standard Question Paper Design 2023-24

Time: 3 Hours

Max. Marks: 80

S.
No.

Typology of Questions

Total
Marks

%
Weightage
(approx.)

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

43

54

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

## Internal Assessment

 Internal assessment 20 Marks Periodic Tests ( Best 2 out of 3 tests conducted) 10 Marks Mathematics Activities 10 Marks

## The Changes for Class 12 (2023-24) Year-end Board Examinations are as under:

 (Class-12) Particulars Academic Session 2022-23 Academic Session 2023-24 Composition of question paperyear-end examination/ Board Examination (Theory) Competency Based Questions are 30% in the form of Multiple-Choice Questions, Case Based Questions, Source Based Integrated Questions or any other type. Objective Question are 20%Remaining 50% Questions are Short Answer/Long Answer Questions 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%

## 2022-23 Reduced Syllabus

(for reference purposes only)

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