Class 12th is a significant step for the student's academic life because their future career depends on the marks obtained by them in the board examination. The CBSE Class 12 syllabus contains a few significant topics that form a major part of the higher education. Mathematics subject is a significant subject that shapes the career of the students after schooling. Mathematics subject is a very important subject in every competitive and school level examination. Having a decent hold on the Maths subject will be a reward for the students. So, students should know the 12^{th} Maths syllabus in detail.

- Students should have a strong grasp on mathematics this will help them in practicing many essential topics in which they have to apply formulas and concepts.
- In 12
^{th} class Commerce subjects, there are 4 main subjects i.e. Accountancy, Business Studies, Economics, and English. And many optional subjects like Maths, Informatics Practices, Hindi, Physical Education, Home Science, Entrepreneurship, and legal Studies.
- Mathematics is an optional subject but it is important for the students as much as other main subjects of class 12
^{th}

We are providing here the **previous year’s paper** for the students so that they will get to know the pattern and syllabus of the exam. Also, they will get some **preparation tips **after seeing the previous year's papers.

In this article, you will get to know about the detailed class 12^{th} maths syllabus, deleted portion of class 12^{th} maths syllabus, and weightage of each topic of the 12^{th} maths syllabus.

## Maths Weightage in CBSE Exam (Unit – Wise)

- The marks of class 12 maths are divided into 6 units i.e. Relations and Functions, Algebra, Calculus, Vector- Three Dimensional Geometry, Linear programming, and Probability. These 6 units are of 80 marks in total and of 240 periods.
- In this exam, 20 marks are allotted for the internal assessment (project work). So, the exam is of 100 marks in total.

The table below shows the weightage of each topic of class 12^{th} Maths subject (CBSE): -

**Units** |
**Topics** |
**Periods** |
**Marks** |

I |
Relations and Functions |
30 |
08 |

II |
Algebra |
50 |
10 |

III |
Calculus |
80 |
35 |

IV |
Vectors – Three Dimensional Geometry |
30 |
14 |

V |
Linear Programming |
20 |
05 |

VI |
Probability |
30 |
08 |

**Total** |
240 |
80 |

**Project Work (Internal Assessment) ** |
20 |

### Revised Class 12^{th} Commerce Maths Syllabus (CBSE)

Let us have a look at the detailed revised class 12th Maths syllabus from below.

#### Unit I – Relations and Functions

To help candidates, we have provided chapter-wise important topics for all the units. Go through the syllabus and plan your preparation accordingly.

#### Chapter 1: Relations and Functions

- Types of Relations
- Reflexive Relations
- Symmetric Relations
- Transitive and Equivalence Relations
- One to One and Onto Functions
- Binary Operations

#### Chapter 2: Inverse Trigonometric Functions

- Definition of Inverse Trigonometric Functions
- Range of Inverse Trigonometric Functions
- The domain of Inverse Trigonometric Functions
- Principal Value Branch of Inverse Trigonometric Functions

#### Unit II – Algebra

Candidates can check the detailed class 12 Maths Syllabus of Algebra from below.

#### Chapter 1: Matrices

- Concept of Matrices
- Notation of Matrices
- Order of Matrices,
- Equality of Matrices
- 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 commutatively of multiplication of matrices
- Invertible matrices

#### Chapter 2: Determinants

- The determinant of a square matrix (up to 3 × 3 matrices).
- Minors
- Co-factors
- Applications of determinants in finding the area of a triangle
- Ad joint.
- The inverse of a square matrix.
- Solving system of linear equations in two or three variables (having a unique solution) using the inverse of a matrix.

#### Unit III – Calculus

Here is the detailed chapter-wise syllabus of Calculus.

#### Chapter 1: Continuity and Differentiability

- Continuity and Differentiability
- The derivative of composite functions
- Chain rule
- Derivatives of inverse trigonometric functions
- The derivative of implicit functions
- Concept of exponential and logarithmic functions.
- Derivatives of logarithmic and exponential functions
- Logarithmic differentiation
- The derivative of functions expressed in parametric forms.
- Second-order derivatives

#### Chapter 2: Applications of Derivatives** **

- Applications of derivatives
- Increasing/decreasing functions
- Tangents and normal
- 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

- 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

$\int \frac{dx}{x^2\pm {a^2}'}$, $\int \frac{dx}{\sqrt{x^2\pm {a^2}'}}$, $\int \frac{dx}{\sqrt{a^2-x^2}}$, $\int \frac{dx}{ax^2+bx+c} \int \frac{dx}{\sqrt{ax^2+bx+c}}$

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

$\int \sqrt{ax^2+bx+c}dx$, $\int \left ( px+q \right )\sqrt{ax^2+bx+c}dx$

- Fundamental Theorem of Calculus (without proof)
- Basic properties of definite integrals
- Evaluation of definite integrals

#### Chapter 4: 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

- Definition of a Differential Equations
- Order and degree of a Differential Equations
- General and particular solutions of a differential equation
- The 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 the linear differential equation of the type
- dy/dx + py = q, where p and q are functions of x or constants

Unit IV: Vectors and Three-Dimensional Geometry

Go through the detailed syllabus of Vectors and three-dimensional geometry which is given below.

#### Chapter 1: 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
- The position vector of a point dividing a line segment in a given ratio
- Definition of Vectors
- Geometrical Interpretation
- Properties and application of scalar (dot) product of vectors
- Vector (cross) product of vectors

#### Chapter 2: Three - dimensional Geometry

- Direction cosines and direction ratios of a line joining two points
- Cartesian equation and vector equation of a line
- Coplanar and skew lines
- Shortest distance between two lines
- Cartesian and vector equation of a plane
- Distance of a point from a plane

#### Unit V: Linear Programming

Here is the detailed syllabus of Class 12th maths Syllabus for linear programming.

#### Chapter 1: Linear Programming

- Introduction of Linear Programming.
- Related terminology such as −
- Constraints
- Objective function
- Optimization
- Different types of linear programming (L.P.) Problems
- Graphical method of solution for problems in two variables
- Feasible and infeasible regions (bounded)
- Feasible and infeasible solutions
- Optimal feasible solutions (up to three non-trivial constraints)

#### Unit VI: Probability

#### Chapter 1: Probability

- Conditional probability
- Multiplication theorem on probability
- Independent events
- Total probability
- Baye's theorem
- Random variable and its probability distribution
- Repeated independent (Bernoulli) trials

### CBSE 12^{th} Maths Syllabus Deleted Portion for 2020-21

CBSE 12^{th} Maths Syllabus Deleted Portion for session 2020-21 Chapter-wise, is mentioned below:

#### Unit I: Relations and Functions

#### Chapter 1: Relations and Functions

- Composite Functions
- The inverse of a Function.

#### Chapter 2: Inverse Trigonometric Functions

- Graphs of inverse trigonometric functions
- Elementary properties of inverse trigonometric functions

#### Unit II: Algebra

#### Chapter 1: Matrices

- Existence of non-zero matrices whose product is the zero matrix.
- Concept of elementary row and column operations.
- Proof of the uniqueness of inverse, if it exists.

#### Chapter 2: Determinants

- Properties of determinants
- Consistency, inconsistency and number of solutions of system of linear equations by examples,

#### Unit-III: Calculus

#### Chapter 1: Continuity and Differentiability

- Rolle’s and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation.

#### Chapter 2: Applications of Derivatives

- Rate of change of bodies
- Use of derivatives in approximation

#### Chapter 3: Integrals

- ∫ √𝑎x2 + 𝑏𝑥 + 𝑐 dx,
- ∫(𝑎𝑥 + 𝑏)√𝑎𝑥2 + 𝑏𝑥 + 𝑐 dx
- Definite integrals as a limit of a sum

#### Chapter 4: Applications of the Integrals

- Area between any of the two above said curves

#### Chapter 5: Differential Equations

- Formation of differential equations whose general solution is given.

#### Unit-IV: Vectors and ThreeDimensional Geometry

#### Chapter 1: Vectors

- Vectors scalar triple product of vectors.

#### Chapter 2: Three - dimensional Geometry

- Angle between
- two lines,
- two planes,
- A-line and a Plane

#### Unit-V: Linear Programming

#### Chapter 1: Linear Programming

- The mathematical formulation of L.P. problems
- (unbounded)

#### Unit-VI: Probability

#### Chapter 1: Probability

- Mean and variance of a random variable.
- Binomial probability distribution.

### Maths Weightage in ICSE Exam (Unit – Wise)

- The Maths written exam is of 80 marks and 20 marks are allotted for project work.
- This written exam is divided into 3 sections i.e. section A, B, and C.
- In section A, students have to attempt all the six questions of 65 marks in total.
- In section B and section C, student have a choice either attempt section B of 15 marks or attempt section c of 15 marks.

The table below shows the weightage of each topic of class 12^{th} Maths subject (ICSE).

**S.No** |
**UNIT** |
**TOTAL WEIGHTAGE** |

**SECTION A: 65 MARKS** |

1 |
Relations and Functions |
10 Marks |

2 |
Algebra |
10 Marks |

3 |
Calculus |
32 Marks |

4 |
Probability |
13 Marks |

**SECTION B: 15 MARKS** |

5 |
Vectors |
5 Marks |

6 |
Three - Dimensional Geometry |
6 Marks |

7 |
Applications of Integrals |
4 Marks |

OR **SECTION C: 15 MARKS** |

8 |
Application of Calculus |
5 Marks |

9 |
Linear Regression |
6 Marks |

10 |
Linear Programming |
4 Marks |

**Total** |
80 Marks |

### Revised Class 12^{th} Commerce Maths Syllabus (ICSE)

#### SECTION A

Let us have a look at the detailed revised syllabus of Class 12th from below.

#### 1. Relations and Functions

**(i)** **Types of relations**

Reflexive, symmetric, transitive, and equivalence relations. One to one and onto functions, composite functions, the inverse of a function.

**(ii)** **Inverse Trigonometric Functions**

Definition, domain, range, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

#### 2. Algebra

#### Matrices and Determinants

**(i)** **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 up to 3). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists (Here all matrices will have real entries).

**(ii) Determinants**

The determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, 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 a system of linear equations by examples, solving system of linear equations in two or three variables (having a unique solution) using the inverse of a matrix.

#### 3. Calculus

**(i) Continuity and Differentiability **

Continuity, Differentiability, and Differentiation. Continuity and differentiability, a derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, 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. Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretation.

**(ii) Applications of Derivatives**

Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima, and minima (first derivative test motivated geometrically and second derivative test is given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).

**(iii) Integrals**

Integration as the 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.

Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

**(iv) Differential Equations**

Definition, order, and degree, general, and particular solutions of a differential equation. Formation of differential equations whose general solution is given. The 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 the linear differential equation.

#### 4. Probability

Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem.

#### SECTION B

#### 5. 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, a scalar triple product of vectors.

#### 6. Three – dimensional Geometry

Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, coplanar and skew lines, the shortest distance between two lines. Cartesian and vector equation of a plane. The angle between (i) two lines, (ii) two planes, (iii) a line and a plane. The distance of a point from a plane.

#### 7. Application of Integrals

Application in finding the area bounded by simple curves and coordinate axes. The area enclosed between two curves.

#### SECTION C

#### 8. Application of Calculus

Application of Calculus in Commerce and Economics.

#### 9. Linear Regression

- Lines of regression of x on y and y on x.
- Lines of best fit.
- Regression coefficient of x on y and y on x.
- Identification of regression equations
- The angle between regression line and the properties of regression lines.
- Estimation of the value of one variable using the value of other variables from the appropriate line of regression.

#### 10. Linear Programming

Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, Mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions(bounded and unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).