AHSEC 2nd Year Syllabus 2024-25 Mathematics

MATHEMATICS
REVISED SYLLABUS FOR HIGHER SECONDARY COURSE
The Syllabus in the subject of Mathematics has undergone changes from time to time in accordance
with growth of the subject and emerging needs of the society. Senior Secondary stage is a launching stage
from where the students go either for higher academic education in Mathematics or for professional courses
like engineering, physical and Bioscience, commerce or computer applications. The present revised syllabus
has been designed in accordance with National Curriculum Frame work 2005 and as per guidelines given in
Focus Group on Teaching of Mathematics 2005 which is to meet the emerging needs of all categories of
students. Motivating the topics from real life situations and other subject areas, greater emphasis has been laid
on application of various concepts.
Objectives
The broad objectives of teaching Mathematics at senior school stage intend to help the pupil:
 To acquire knowledge and critical understanding, particularly by way of motivation and visualization, of
basic concepts, terms, principles, symbols and mastery of underlying processes and skills.
 To feel the flow of reasons while proving a result or solving a problem.
 To apply the knowledge and skills acquired to solve problems and wherever possible, by more than
one method.
 To develop positive attitude to think, analyze and articulate logically.
 To develop interest in the subject by participating in related competitions.
 To acquaint students with different aspects of mathematics used in daily life.
 To develop an interest in students to study mathematics as a discipline.
 To develop awareness of the need for national integration, protection of environment, observance of
small family norms, removal of social barriers, elimination of sex biases.
 To develop reverence and respect towards great Mathematicians for their contributions to the field of
Mathematics.

MATHEMATICS
SYLLABUS FOR HIGHER SECONDARY FINALYEAR COURSE
One Paper Time : Three Hours Marks 100
Unitwise Distribution of Marks and Periods :
Unit No. Title Marks Periods
Unit-I Relations and Functions 08 24
Unit-II Algebra 14 40
Unit-III Calculus 44 78
Unit-IV Vectors and Three-Dimensional Geometry 20 34
Unit-V Linear Programming 06 08
Unit-VI Probability 08 16
Total 100 200

Syllabi for H.S. Final Year
APPENDIX :

1. Proofs in Mathematics :
2. Mathematical Modelling :
Unitwise Distribution of Course contents :
Unit-I : 1. RELATIONS AND FUNCTIONS
Marks-04 Periods-12
Types of relations : Reflexive, symmetric, transitive and equivalence relations. Types of function,
composition of functions and invertible function.
2. Inverse Trigonometric Functions : Marks-04 Periods-12
Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions. Elemen-
tary properties of inverse trigonometric functions.
Unit-II : ALGEBRA
1. Matrices : Marks-06 Periods 20
Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and
skew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple proper-
ties 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, proof of uniqueness of inverse if it exist.
2. Determinants : Marks-08 Periods 20
Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, cofactors
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 example,
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 : Marks-12 Periods 20
Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigo-
nometric functions, derivative of implicit function. Concept of exponential and logarithmic functions and
their derivatives. Logarithmic differentiation. Derivative of functions expressed in parametric forms.
Second order derivatives.
2. Application of Derivatives : Marks-10 Periods 16
Applications of derivatives : Rate of change, 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 : Marks-10 Periods 20
Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by
partial fractions and by parts, Evaluation of integrals of the type.

dx dx dx dx dx ( px  q)
 x  a ,  x  a ,  a  x ,  ax  bx  c ,  ax  bx  c ,  ax  bx  c dx
2 2 2 2 2 2 2 2 2

 a  x dx,  ax  bx  c dx and  x  a dx and problems based on them.
2 2 2 2 2

 Syllabi for H.S. Final Year

Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and
evaluation of definite integrals.
4. Applications of the Integrals : Marks-04 Periods 10
Applications in finding the area under simple curves, especially lines, arcs of circles/ parabolas/ ellipses
(in standard form only),
5. Differential Equations : Marks-08 Periods 12
Definition, order and degree, general and particular solutions of a differential equation. Solution of
differential equations by method of separation of variables, solution of homogeneous differential
equations of first order and first degree. Solutions of linear differential equation of the type :
dy
 Py  Q where P and Q are functions of x.
dx
Unit-IV : VECTORS AND THREE-DIMENSIONAL GEOMETRY
1. Vectors : Marks-12 Periods 20
Vectors and scalars, magnitude and direction of a vector. Direction cosines/ ratios of vectors. 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. Scalar (dot) product of vectors, projection of a vector on
a line. Vector (cross) product of vectors.
2. Three-dimensional Geometry : Marks 08 Periods 14
Direction cosines and direction ratios of a line joining two points. Cartesian and vector equation of a
line, Angle between two lines, skew lines, shortest distance between two lines.
Unit-V : LINEAR PROGRAMMING Marks 06 Periods 08
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 solution, optimal feasible solution.
Unit-VI : PROBABILITY Marks 08 Periods 16
Multiplication theorem on probability. Conditional probability, independent events, total probability,
Baye’s theorem. Random variable and it’s probability distribution.
Appendix
1. Proofs in Mathematics :
Through a variety of examples related to mathematics and already familiar to the learner, bring out
different kinds of proofs : direct, contrapositive, by contradiction, by counter-example.
2. Mathematical Modelling :
Modelling real-life problems where many constraints may really need to be ignored (continuing from
Class XI). However, now the models concerned would use techniques/ results of matrices, calculus
and linear programming.

Recommended textbook 1. Mathematics Part-I by NCERT
2. Mathematics Part-II by NCERT
3. Ganit Pratham Khanda by AHSEC
4. Ganit Dwitiya Khanda by AHSEC

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