TBSE Class 12 Syllabus 2024 Mathematics

Half-Yearly Syllabus (2023-24)
Class : XII
Subject : MATHEMATICS
Max. Marks : 80
Unit-I : Relations and Functions
1. Relation and Functions : 15 Periods
Types of relations : reflexive, symmetric, transitive and equivalence relations. One to one and onto
functions.
Unit-II : Algebra
1. Matrices : 25 Periods
Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix,
symmetric and skew symmetric matrices. Operations 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).
Unit-III : Calculus
1. Continuity and Differentiability : 20 Periods
Continuity and differentiability, chain rule, derivative of inverse trigonometric functions, like
sin–1x, cos–1 and tan–1x, 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.
3. Integrals : 20 Periods
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 a following types and problems
based on them.
dx dx dx dx dx
f–––––– , f––––––– , f ––––––– , f––––––––––– , f––––––––––
x² ± a² Öx² ± a² Öa² – x² ax² + bx + c Öax² + bx + c
px + q px + q
f––––––––––– dx, f––––––––––– dx, fÖa² ± x² dx, fÖx²– a² dx
ax² + bx + c Öax² + bx + c
fÖax² + bx + c dx.
Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and
evaluation of definite integrals.
5. Differential Equations : 15 Periods
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 equations of the type :
dx
––– + py = q, where p and q are functions of x or constants.
dy
dx
––– + px = q, where p and q are functions of y or constants.
dy

Unit-IV : Vectors and Three-Dimentional Geometry
1. Vectors : 15 Periods
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.
Unit-V : Linear Programming
1. Linear Programming : 20 Periods
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).

Syllabus
Class - XII
Subject : Mathematics
Half-Yearly Examination- 2023-24
Time : 3 hrs. Blue Print of Marks Distribution Total Marks : 80 (Eighty)
Unit’s No. & Name Chapter’s Name MCQ VSA SA-I SA-II LA-I LA-II Total
(1 Mark) (1 Mark) (2 Marks) (3 Marks) (4 Marks) (5 Marks) Marks
I. Relations & 1. Relation & Function 2 1 1 1 - - 08
Functions
II. Algebra 1. Matrices 1 3 1 - 1 - 10
III. Calculus 1. Continuity & Differen-
tiability 1 1 1 - 2 -
2. Integrals (Indefinite) 1 1 1 1 2 - 35
3. Differential Equations 2 2 - - 1 -
IV. Vectors & 1. Vectors 2 1 - 2 - 1 14
3D-Geometry
V. Linear Progra- 1. Linear Programming - - - - - 1 05
mming
VI. Probability 1. Probability (Conditional
Probability, multiplication
theorem on probability, 1 1 1 - 1 - 08
Independent events,
total probability)
Total Marks (Nos. of questions) 1x10 1x10 2x5 3x4 4x7 5x2 80
(10 Nos) (10 Nos) (5 Nos) (4 Nos) (7 Nos) (2 Nos) (38 Nos)

Internal Assessment -20

Pre-Board / Board Final Exam. (2023-24)
Class : XII
Subject : Mathematics
Course Structure Max Marks : 80

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

Unit-I : Relations and Functions
1. Relations and Functions : 15 Periods
Types of relations : reflexive, symmetric, transitive and equivalence relations. One to one and onto
functions.
2. Inverse Trigonometric Functions : 15 Periods
Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions.
Unit-II : Algebra
1. Matrices 25 Periods
Concept, notation, order, equality, typesd of matrices, zero and identity matrix, transppse of a
matrix, symmetric and skew symmetric matrices. Operations 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).
2. Determinants : 25 Periods
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.
Unit-III : Calculus
1. Continuity and Differentiability : 20 Periods
Continuity and differentiability, chain rule, derivative of inverse trigonometric functions, like
sin–1x, cos–1 and tan–1x, 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.
2. Applications of Derivatives 10 Periods
Applications of derivatives : rate of change of quantities, 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).
3. Integrals : 20 Periods
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 a following types and problems
based on them.
dx dx dx dx dx
f–––––– , f––––––– , f ––––––– , f––––––––––– , f––––––––––
x² ± a² Öx² ± a² Öa² – x² ax² + bx + c Öax² + bx + c
px + q px + q
f––––––––––– dx, f––––––––––– dx, fÖa² ± x² dx, fÖx²– a² dx
ax² + bx + c Öax² + bx + c
fÖax² + bx + c dx.

Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and
evaluation of definite integrals.
4. Applications of the Integrals : 15 Periods
Applications in finding the area under simple curves, especially lines, circles/parabolus/ellipses
(in standard form only).
5. Differential Equations : 15 Periods
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 equations of the type :
dx
––– + py = q, where p and q are functions of x or constants.
dy
dx
–––
dy + px = q, where p and q are functions of y or constants.
Unit-IV : Vectors and Three-Dimentional Geometry
1. Vectors : 15 Periods
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.
2. Three-dimensional Geometry : 15 Periods
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
1. Linear Programming : 20 Periods
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
1. Probability : 30 Periods
Conditional probability, multiplication theorem on probability, independent events, total probability,
Bayes’ theorem, Random variable and its probability distribution, mean of random variable.

Pre-Board / Board Final Examination- 2023-24
Class : XII (Twelve)

Subject : Mathematics
Unit/Chapter-wise Marks Distribution
Time : 3 hrs. Total Marks : 80 (Eighty)
Unit’s No. & Name Chapter’s Name MCQ VSA SA-I SA-II LA-I LA-II Total
(1 Mark) (1 Mark) (2 Marks) (3 Marks) (4 Marks) (5 Marks) Marks
I. Relations & 1. Relation & Function 1 - 1 - - -
Functions 2. Inverse Trigonometric 08
Functions 1 1 - 1 - -
II. Algebra 1. Matrices - 2 - - 1 -
10
2. Determinants 1 1 1 - - -
III. Calculus 1. Continuity & Differen-
tiability - - 1 - 1 -
2. Application of Derivatives 1 - 1 - 1 -
3. Integrals 1 2 - 1 1 - 35
4. Application of Integrals 1 - - - 1 -
5. Differential Equations 1 2 - - 1 -
IV. Vectors & 1. Vectors 1 1 - 1 - -
14
3D-Geometry 2. 3-Dimensional Geometry 1 - - 1 - 1
V. Linear Progra- 1. Linear Programming - - - - - 1 05
mming
VI. Probability 1. Probability 1 1 1 - 1 - 08
Total Marks (Nos. of questions) 1x10 1x10 2x5 3x4 4x7 5x2 80
(10 Nos) (10 Nos) (5 Nos) (4 Nos) (7 Nos) (2 Nos) (38 Nos)

Internal Assessment - 20