Edudel Syllabus 2025 Class 12 Math

ANNUAL SYLLABUS
CLASS XII
SUBJECT: MATHEMATICS (041)
SESSION (2024-25)
CONTENT

Unit-I: Relations and Functions
1.Relations and Functions
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one
and onto functions.
2. Inverse Trigonometric Functions
Definition, range, domain, principal value branch. Graphs of inverse trigonometric
functions.

Unit-II: Algebra
1.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. On- 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
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
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.

2.Applications of Derivatives
Applications of derivatives: rate of change of q u a n t i t i e s , 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
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 dx dx dx dx px+q
.∫ 2 ,∫ 2 ,∫ 2 ,∫ ,∫ ,∫ 2 dx
2
x ±a √x ±a
2
√ a −x
2 2
ax +bx+c √ ax +bx+c ax +bx+c
2

∫ px+q dx , ∫ √ a2 ± x 2 dx , ∫ √ x 2−a 2 dx ,∫ √ ax 2 +bx+c dx
√ ax +bx +c
2

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
Solutions of linear differential equation of the type:
dy
+ py=q , where p and q are functions of x or constants
dx
dx
+ px=q ,where p and q are functions of y or constants.
dy

COMPLETION OF MID TERM SYLLABUS BY 13TH SEPTEMBER 2024
REVISION
Mid Term Exam
Discussion of Mid Term Question Paper
Unit-IV: Vectors and Three-Dimensional Geometry
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, 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
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
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
Conditional probability, multiplication theorem on probability, independent events, total
probability, Bayes’ theorem, Random variable and its probability distribution, mean of
random variable.
Note- Syllabus must be completed by 13 th December 2024
Preparation for Pre Board Examination (2024-25)
Pre Board Examination
CBSE BOARD EXAM (2024-25)

For further Information kindly refer to CBSE guidelines https://cbseacademic.nic.in/