## CBSE Class 12 Maths Syllabus 2023-24

Central Board of Secondary Education has released the CBSE Class 12 Maths Syllabus 2023-24 at the official website www.cbseacademic.nic.in. The Class 12 Maths Syllabus is very important for the students who are going to give their board exams this year. We have provided the PDF of the CBSE 12th Maths Syllabus for 2023-24 in this article for ease of the students. The question paper for the board exam will also be prepared with context to the Class 12 Maths Syllabus for the academic year 2023-24 so the students are advised to go through the syllabus and cover the chapters much before the exams. Scroll through this page to know the complete Class 12th Maths Syllabus 2023-24.

## Maths Class 12 Syllabus 2023-24 [Basic Maths]

The Maths Class 12 Syllabus 2023-24 decodes the marks distribution for all the chapters. Students can take a look at the CBSE Class 12 Maths Syllabus 2023-24 and plan their study hours and strategy to score well in the Class 12th examination. The Class 12th Maths Syllabus 2023-24 serves as a blue print of the question paper as it helps the students know which chapter carries more marks and in this way students can decide on the chapters they want to invest more time.

CBSE Class 12 Maths Syllabus 2023-24 | |||

S.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 | ||

Total Marks | 100 |

## CBSE 12th Basic Maths Syllabus 2023-24 (Chapter-Wise)

The Chapter-wise CBSE 12th Basic Maths Syllabus 2023-24 has been detailed in this section. There are total of 8 units and 13 chapters from where the questions in the board exams are going to be framed. All the chapters are important and students must try to cover it all prioritising those chapters which carry more marks. Scroll through this page to know the CBSE Class 12 Syllabus 2023-24 for Maths and start with your preparations for the exams.

### Unit-I: Relations and Functions

**Chapter 1: Relations and Functions**

- Relations and Functions: Types of relations, reflexive, symmetric, transitive and equivalence relations. One-to-one and onto functions.

**Chapter 2: Inverse Trigonometric Functions**

- Inverse Trigonometric Functions: Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions

### Unit-II: Algebra

**Chapter 1: Matrices**

- 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. 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).

**Chapter 2: Determinants**

- 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 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

**Chapter 1: Continuity and Differentiability**

- Continuity and Differentiability: 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.

**Chapter 2: 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).

**Chapter 3: Integrals**

- 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 x 2 ± a 2, ∫ dx √x 2 ± a 2 , ∫ dx √a 2 − x 2 , ∫ dx ax2 + bx + c , ∫ dx √ax2+bx+c

∫ px + q ax2 + bx + c dx, ∫ px + q √ax2+bx + c dx, ∫ √a 2 ± x 2 dx, ∫ √x 2 − a 2

∫√𝑎𝑥2 + 𝑏𝑥 + 𝑐 𝑑𝑥, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

**Chapter 4: Applications of the Integrals**

- Applications of the Integrals: Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses(in standard form only)

**Chapter 5: Differential Equations**

- 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.

d𝑥 d𝑦 + px = q, where p and q are functions of y or constants.

### Unit-IV: Vectors and Three-Dimensional Geometry

**Chapter 1: Vectors**

- 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.

**Chapter 2: Three-dimensional Geometry**

- 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

**Chapter 1: 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

**Chapter 1: Probability**

- Probability: 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 Basic Maths Syllabus 2023-24 for Internal Assessment

CBSE Class 12 Basic Maths Syllabus 2023-24 for Internal Assessment carries 20 Marks which further gets divided into two parts-** **Periodic Tests and Mathematics Activities. The Periodic Test is a Pen and Paper Assessment for 10 Marks and the format of the periodic test are questions such as very short answer (VSA), short answer (SA) and long answer (LA) to effectively test the knowledge, understanding, application, skills, analysis. In Mathematics Activities, for activities, NCERT Lab Manual may be referred for 10 Marks.

CBSE Class 12 Basic Maths Syllabus 2023-24 for Internal Assessment | |

Internal Assessment | 20 Marks |

Periodic Tests ( Best 2 out of 3 tests conducted): Periodic Test is a Pen and Paper assessment. | 10 Marks |

Mathematics Activities: For activities NCERT Lab Manual may be referred. | 10 Marks |

## CBSE Maths Class 12 Syllabus 2023-24 [Applied Maths]

The CBSE Maths Class 12 Syllabus 2023-24 for applied maths consists of 8 units in total that further gets divided into more topics. CBSE has introduced the applied mathematics as an optional subject in the higher secondary classes for the students to apply the mathematical methods into various fields like physics, medicine, biology, etc. The CBSE Class 12 Maths Syllabus 2023-24 along with the marks distribution has been tabulated below.

CBSE Maths Class 12 Syllabus 2023-24 [Applied Maths] | ||

S. No. | Units | Marks |

I. | Numbers, Quantification and Numerical Applications | 11 |

II. | Algebra | 10 |

III. | Calculus | 15 |

IV. | Probability Distributions | 10 |

V. | Inferential Statistics | 05 |

VI. | Index Numbers and Time-based data | 06 |

VII. | Financial Mathematics | 15 |

VIII. | Linear Programming | 08 |

Total | 80 | |

Internal Assessment | 20 | |

Total Marks | 100 |

## CBSE 12th Applied Maths Syllabus 2023-24 (Chapter-wise)

CBSE 12th Applied Maths Syllabus 2023-24 must not be confused with basic maths as both papers are completely different and include different chapters. The chapters included in the CBSE Class 12 Applied Maths Syllabus 2023 are more of practical nature and are specially designed for students belonging to streams other than science. Go through this page to know the chapter-wise CBSE Class 12th Syllabus-24 2023 for Applied Maths.

### Unit-I: Numbers, Quantification and Numerical Applications

**Unit-I: Numbers, Quantification and Numerical Applications **

- Modulo Arithmetic
- Congruence Modulo
- Alligation and Mixture
- Numerical Problems: Solve real life problems mathematically
- Numerical Inequalities

### Unit-II: Algebra

**Unit-II: Algebra**

- Matrices and types of matrices
- Equality of matrices, Transpose of a matrix, Symmetric and Skew symmetric matrix
- Algebra of Matrices
- Determinants
- Inverse of a matrix
- Solving system of simultaneous equations using matrix method, Cramer’s rule

### Unit-III: Calculus

**Unit-III: Calculus**

- Higher Order Derivatives
- Application of Derivatives
- Marginal Cost and Marginal Revenue using derivatives
- Increasing /Decreasing Functions
- Maxima and Minima
- Integration
- Indefinite Integrals as family of curves
- Definite Integrals as area under the curve
- Application of Integration
- Differential Equations
- Formulating and Solving Differential Equations
- Application of Differential Equations

### Unit-IV: Probability Distributions

**Unit-IV: Probability Distributions **

- Probability Distribution
- Mathematical Expectation
- Variance
- Binomial Distribution
- Poison Distribution
- Normal Distribution

### Unit-V: Inferential Statistics

**Unit-V: Inferential Statistics**

- Population and Sample
- Parameter and Statistics and Statistical Interferences
- t-Test (one sample t-test and two independent groups t-test)

### Unit-VI: Index Numbers and Time-based data

**Unit-VI: Index Numbers and Time-based data**

- Time Series
- Components of Time Series
- Time Series analysis for univariate data
- Secular Trend
- Methods of Measuring trend

### Unit-VII: Financial Mathematics

**Unit-VII: Financial Mathematics**

- Perpetuity, Sinking Funds
- Calculation of EMI
- Calculation of Returns, Nominal Rate of Return
- Compound Annual Growth Rate
- Linear method of Depreciation

### Unit-VIII: Linear Programming

** Unit-VIII: Linear Programming**

- Introduction and related terminology
- Mathematical formulation of Linear Programming Problem
- Different types of Linear Programming Problems
- Graphical method of solution for problems in two variables
- Feasible and Infeasible Regions
- Feasible and infeasible solutions, optimal feasible solution

## CBSE Class 12 Applied Maths Syllabus 2023-24 for Internal Assessment

Refer to the table below to know the CBSE Class 12 Applied Maths Syllabus 2023-24 for Internal Assessment. Each comprises 10 marks, total of 20 marks. Students should perform well in periodic tests and Maths Activities conducted in the school to fetch maximum marks.

CBSE Class 12 Applied Maths Syllabus 2023-24 for Internal Assessment | |||

Sl. No | Area and Weightage | Assessment Area | Marks allocated |

1. | Project work (10 marks) | Project work and record | 5 |

Year-end Presentation/ Viva of the Project | 5 | ||

2. | Practical work (10 marks) | Performance of practical and record | 5 |

Year-end test of any one practical | 5 | ||

Total Marks | 20 |

### Special tips for Students

- Planning: Make a daily study plan based on the Maths syllabus and follow that plan religiously. Many students failed to follow their study plan, failing of plan depends upon lack of discipline. Discipline is hard to inculcate in life but it is not impossible.
- Practice: Go through the concepts and then solve problems based on those concepts, it will help students to understand concepts in-depth.
- Take Baby Steps: If you can’t achieve daily targets, then make short targets. Achieving targets will give you internal satisfaction, gradually increase your targets.
- Revision: Keep track of topics daily that have been completed. Revise them in short intervals of time, by revision you can retain them for a longer period.
- Study with a Group: Studying with classmates encourages an interactive environment to keep you engaged. This gives you a chance to test your knowledge with others. It will boost your confidence if you take part actively and make others understand the concepts if they are stuck anywhere.

Important Links | |

CBSE Class 12 Syllabus 2023-24 | CBSE Class 12 English Syllabus for 2023-24 |

CBSE Class 12 Physics Syllabus for 2023-24 | CBSE Class 12 Chemistry Syllabus for 2023-24 |