# Everything you must know about Class 12th Maths Syllabus

Author : Paakhi Jain

August 26, 2024

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Overview: Class 12th boards are significant to determine your eligibility for UG admissions. Mathematics is a significant subject in Class 12th boards and major entrance exams. Knowing the Class 12th Maths Syllabus will help you understand the marks distribution, units included and exam pattern.

The Class 12th Maths Syllabus for CBSE & ICSE board is different in terms of division and sub topics. The main highlights of Class 12th Maths paper are:

• There will be no overall choice in the question paper in CBSE however in ICSE there will be a choice to attempt any 1 section from Section B & C.
• Calculus is the unit with highest weightage in the both the boards.

## CBSE Class 12th Maths Syllabus

• 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 main highlights of Class 12th CBSE Maths paper are:

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

The table below shows the weightage of each topic in Class 12th Maths Syllabus(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

## 12th Class CBSE Maths Syllabus

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

### Unit I – Relations and Functions

#### 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, Range & Domain of Inverse Trigonometric Functions
• Principal Value Branch of Inverse Trigonometric Functions

### Unit II – Algebra

#### Chapter 1: Matrices

• Concept, Notation, Order, Equality and 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

Unit 3 in Class 12th Maths Syllabus in CBSE board is the highest weightage unit. Each topic from this unit must be prepared thoroughly.

#### 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
• 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

#### 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
• 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

#### 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

## Prescribed Books: CBSE Class 12th Maths Syllabus

• Mathematics Textbook for Class XI, NCERT Publications
• Mathematics Part I - Textbook for Class XII, NCERT Publication
• Mathematics Part II - Textbook for Class XII, NCERT Publication

## ICSE Class 12th Maths Syllabus Highlights

• 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 class12 mathematics syllabus (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 SECTION C: 15 MARKS 8 Application of Calculus 5 Marks 9 Linear Regression 6 Marks 10 Linear Programming 4 Marks Total 80 Marks

### Class 12th Maths Syllabus (ICSE)

#### 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

(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
• 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: Cost function, average cost, marginal cost and its interpretation, demand function
• Revenue function, marginal revenue function and its interpretation, Profit function and breakeven point.
• Rough sketching of the following curves: AR, MR, R, C, AC, MC and their mathematical interpretation using the concept of maxima & minima and increasing-decreasing functions.

#### 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).

### Key Takeaways

• You should have a strong grasp on formulas and usage to apply the right formulas and concepts.
• Mathematics is an optional subject for some but it is important for the PCM and Commerce with Maths students.
• Go through the previous year’s papers to know the exam pattern and syllabus.
• Create a balanced study plan after reviewing the previous year's papers.