## Class 12 Maths Syllabus 2023

**Class 12 Maths Syllabus 2023: **Maths is a science that studies numbers, logical interpretation, and the shapes of practical situations. Class 11th and Class 12 Maths Syllabus is very helpful to clear engineering entrance examinations such as IIT JEE, BITSAT, VITEEE, etc. In this article, we have covered the entire syllabus of the Class 12 Maths Syllabus with some Special tips, these tips are very helpful to lift the overall scores do check them out and bookmark this page.

## Class 12 Maths Syllabus 2023 [Basic Maths]

Students study day and night to score well in the Class 12th examination, without a syllabus it becomes difficult to score good marks. Thus, we have mentioned the detailed CBSE Class 12 Maths Syllabus 2023. Refer to this syllabus and score well in 12th boards, because Class 12th result plays a key role in deciding the career of students ahead.

Class 12 Maths Syllabus 2023 | ||

S.No. | Units | Marks |

I. | Relations and Functions | 08 |

II. | Algebra | 10 |

III. | Calculus | 35 |

IV. | Vectors and Three - Dimensional Geometry | 14 |

V. | Linear Programming | 05 |

VI | Probability | 08 |

Total | 80 | |

Internal Assessment | 20 | |

Total Marks | 100 |

**CBSE Class 12 Maths 2023 Sample Paper**** **

## CBSE Class 12 Basic Maths Syllabus 2023

Prepare for CBSE Class 12 Basic Maths Syllabus 2023 Board Exam with the chapters as mentioned in CBSE Class 12 Basic Maths Syllabus 2023 which consists in 80 Marks-

### CBSE Class 12 Basic Maths Syllabus Unit-I: Relations and Functions

**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

### CBSE Class 12 Basic Maths Syllabus Unit-II: Algebra

**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 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: 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.

### CBSE Class 12 Basic Maths Syllabus Unit-III: Calculus

**Unit-III: Calculus**

- 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.
- 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).
- 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.

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

5. 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.

### CBSE Class 12 Basic Maths Syllabus Unit-IV: Vectors and Three-Dimensional Geometry

**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, 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, shortest distance between two lines. Angle between two lines.

### CBSE Class 12 Basic Maths Syllabus Unit-V: Linear Programming

**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).

### CBSE Class 12 Basic Maths Syllabus Unit-VI: Probability

**Unit-VI: 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 Internal Assessment 2023

Internal Assessment consist of 20 Marks which further is divided into two parts, that is,** Periodic Tests, Mathematics Activities.** Periodic Tests is a Pen and Paper Assessment for 10 Marks, 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. In Mathematics Activities, for activities NCERT Lab Manual may be referred for 10 Marks.

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 Class 12 Applied Maths Syllabus 2023

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 Class 12 Applied Maths Syllabus 2023

Prepare for CBSE Class 12 Applied Maths Syllabus 2023 Board Exam with the chapters as mentioned in CBSE Class 12 Applied Maths Syllabus 2023 which consists in 80 Marks-

### CBSE Class 12 Basic Maths Syllabus 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

### CBSE Class 12 Basic Maths Syllabus 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

### CBSE Class 12 Basic Maths Syllabus 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

### CBSE Class 12 Basic Maths Syllabus Unit-IV: Probability Distributions

**Unit-IV: Probability Distributions **

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

### CBSE Class 12 Basic Maths Syllabus 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)

### CBSE Class 12 Basic Maths Syllabus 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

### CBSE Class 12 Basic Maths Syllabus 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

### CBSE Class 12 Basic Maths Syllabus 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 Internal Assessment 2023

Refer to the table below to know the Internal Assessment for Applied Maths. 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.

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 |

**CBSE Class 12 Basic Maths Syllabus PDF- Click to Download**

**CBSE Class 12 Applied Maths Syllabus PDF- Click to Download**

### 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.