HBSE Class 12th Mathematics Syllabus

Chapter

Sub-Topics

Marks

Chapter 1: Relations and Functions

1.1: Introduction 

1.2 Types of Relations: Empty Relation, Universal Relation, Reflexive  Relation, Symmetric Relation, Transitive Relation, Equivalence Relation 

1.3 Types of Functions: Injective Function, Surjective Function, Bijective Function

1.4: Composition of Functions and Invertible Function: fog , gof ,  Invertible Function definition 

8

Chapter 2: Inverse Trigonometric Functions

2.1 Introduction 

2.2 Basic Concepts: Domain, Range ,Graphs and Principal value of  Trigonometric Functions  

2.3 Properties of Inverse Trigonometric Functions: Related to sin(sin1x) = x, x € [-1,1] and sin-1 (sin x) = x , x € [-π/2,π/2] ,Conversion of some trigonometric functions in their simplest forms using trigonometric properties.

Chapter 3: Matrices

3.1 Introduction  

3.2 Matrix: Definition and Order of a matrix. 

3.3 Types of Matrices : Column Matrix ,Row Matrix , Square Matrix ,Diagonal Matrix , Scalar Matrix , Identity Matrix ,Zero Matrix 

3.3.1 Equality of Matrices 

3.4 Operations on Matrices : Addition of matrices, Multiplication of a matrix by a scalar, Properties of matrix addition ,Properties of scalar multiplication of a matrix , Multiplication of matrices ,Properties of multiplication of matrices    

3.5 Transpose of a Matrix : Properties of transpose of the matrices  

3.6 Symmetric and Skew Symmetric Matrices  

3.7 Invertible Matrices : Definition of invertible matrix , Uniqueness of  Inverse (Theorem and its applications) 

13

Chapter 4: Determinants

4.1 Introduction  

4.2 Determinant: Determinants of matrices of order one, two and three  

4.3 Area of a Triangle  

4.4 Minors and Cofactors  

4.5 Adjoint and Inverse of a Matrix  

4.6 Applications of Determinants and Matrices: Solution of system of linear equations using inverse of a matrix 

Chapter 5: Continuity and Differentiability

5.1 Introduction 

5.2 Continuity: Definition of continuity , Algebra of continuous functions

5.3 Differentiability: Derivatives of composite functions , Chain Rule, Derivatives of implicit functions, Derivatives of inverse trigonometric functions  

5.4 Exponential and Logarithmic Functions 

5.5 Logarithmic Differentiation 

5.6 Derivatives of Functions in Parametric Forms  

5.7 Second Order Derivative  

14

Chapter 6: Application of Derivatives

6.1 Introduction  

6.2 Rate of change of Quantities  

6.3 Increasing and Decreasing Functions  

6.4 Maxima and Minima : Local Maxima , Local Minima , First Derivative Test, Second Derivative Test , Maximum and Minimum Values of a Function in a closed Interval ,Absolute Maximum, Absolute Minimum   

Chapter 7: Integrals

7.1 Introduction  

7.2 Integration as an Inverse Process of Differentiation : Some properties of indefinite integral  

7.3 Methods of Integration : Integration by Substitution, Integration using Trigonometric Identities 

7.4 Integrals of Some Particular Functions  

7.5 Integration by Partial Fractions  

7.6 Integration by Parts: Integral of the type ∫ ex [ f (x)+f1 (x) ] dx ,  Integrals of some more types 

7.7 Definite Integral 

7.8 Fundamental Theorem of Calculus : Area function and related numerical problems  

7.9 Evaluation of Definite Integrals by Substitution  

7.10 Some properties of Definite Integrals and Related Problems 

19

Chapter 8: Application of Integrals

8.1 Introduction 

8.2 Area under Simple Curves Using Definite Integrals 

Chapter 9: Differential Equations

9.1 Introduction 

9.2 Basic Concepts :Order and Degree of a Differential Equation 

9.3 General and Particular Solutions of a Differential Equation 

9.4 Methods of Solving First Order ,First Degree Differential Equations: Differential Equations with variables separable, Homogeneous Differential Equations , Linear Differential Equations 

Chapter 10: Vector Algebra

10.1 Introduction

10.2 Some Basic Concepts : Definition of Vector ,Position Vector , Direction Cosines  

10.3 Types of Vectors : Zero Vector, Unit Vector , Coinitial Vector ,  Collinear Vector , Equal Vectors ,Negative of a Vector.

10.4 Addition of Vectors

10.5 Multiplication of a vector by a Scalar : Components of a Vector,  Vector joining Two Points , Section Formula 

10.6 Product of Two Vectors : Scalar (or dot) Product of Two Vectors, Projection of a Vector on a line ,Vector ( or cross ) product of Two Vectors  

12

Chapter 11: Three Dimensional Geometry

11.1 Introduction 

11.2 Direction Cosines and Direction Ratios of a Line : Direction cosines of a line passing through two points 

11.3 Equation of a Line in Space : Equation of a Line through a given point and parallel to a given vector.

11.4 Angle between two Lines

11.5 Shortest Distance between Two Lines : Distance between two skew lines, Distance between two parallel lines  

Chapter 12: Linear Programming

12.1 Introduction 

12.2 Linear Programming Problem and its Mathematical Formation: Mathematical Formulation of the Problem , Graphical Method of solving Linear Programming Problems     

5

Chapter 13: Probability

13.1 Introduction 

13.2 Condition Probability : Properties of conditional probability 

13.3 Multiplication Theorem on Probability

13.4 Independent Events 

13.5 Bayes’ Theorem and Related Problems:Partition of a sample space,  Theorem of total probability 

9

HBSE Class 12th Mathematics Syllabus PDF

Competencies

Percentage 

Marks

Knowledge

40%

32

Understanding

30%

24

Application

20%

16

Skill

10%

08

Total

100%

80

Type of Question

Marks

Number 

Description

Total Marks

Objective Questions

1

20

12 MCQs, 3 one-word answers, 3 fill in the blanks, 2 assertion-reason questions. Internal choice in two questions.

20

Very Short Answer Type Questions

2

5

Internal choice will be given in any two questions.

10

Short Answer Type Questions

2

6

Internal choice will be given in any two questions.   

One question will be of High Order Thinking Skill (HOTS) /  Competency Based Question (CBC)

18

Long Answer Type Questions

5

4

Internal choice will be given in any two questions.   

20

Source-Based Questions

4

3

3 Source based /case based/ passage based /integrated units of    assessment 4 marks each 

12

Total

38

80

Prescribed Books for HBSE Class 12th Mathematics

1. Textbook for class 12th : Mathematics Part-1, NCERT- Latest Edition 

                                            Mathematics Part-2, NCERT- Latest Edition 

2. Exemplar Problems: Mathematics - Class XII (NCERT)