Edudel Syllabus Class 12 Maths

ANNUAL SYLLABUS
CLASS XII
SUBJECT: MATHEMATICS (041)
SESSION (2023-24)

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, chainrule, 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 ,∫ ,∫ 2 dx
2
x ±a √x ±a
2 2
√ a −x 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 15TH SEPTEMBER 2023
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 15 th December 2023
Preparation for Pre Board Examination (2023-24)
Pre Board Examination
BOARD EXAM 2023-24

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

https://cbseacademic.nic.in/web_material/CurriculumMain23/SrSec/Maths_SrSec_2022-23.pdf