HIMACHAL PRADESH BOARD OF SCHOOL EDUCATION.
Syllabus of plus two (12th) examination
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
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.
The broad objectives of teaching Mathematics at senior school stage
intend to help the pupil :
c to acquire knowledge and critical understanding particularly by way of
motivation of visualization of basic facts, concepts, terms, principles and
symbols and mastery of underlying processes and skills.
c to feel the flow of reasons while proving a result or solving a problem.
c to apply the knowledge and skills acquired to solve problems and
wherever possible, by more than one method.
c to develop positive attitude to think, analyze and articulate logically.
c to develop interest in the subject by participating in related competitions.
c to acquaint students with different aspects of mathematics used in daily
c to develop an interest in students to study mathematics as a discipline.
c 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.
c to develop reverence and respect towards great Mathematicians for their
contribution to the field of Mathematics.
ONE PAPER THREE HOURS M.M. 85
I. RELATIONS AND FUNCTIONS 8
II. ALGEBRA 11
III. CALCULUS 38
IV. VECTORS AND THREE-DIMENSION GEOMETRY 15
V. LINEAR PROGRAMMING 5
VI. PROBABILITY 8
UNIT I. RELATIONS AND FUNCTIONS
1. Relations and Functions : (10) Periods
Types of relations: reflexive, symmetric, transitive and equivalence
relations. One to one and onto functions, composite functions,
inverse of a function. Binary operations.
2. Inverse Trigonometric Functions : (12) Periods
Definition, range, domain, principal value branches. Graphs of
inverse trigonometric functions. Elementary propoerties of inverse
UNIT II. ALGEBRA
1. Matrices : (18) Periods
Concept, notation, order, equality, types of matrices, zero matrix,
transpose of a matrix, symmetric and skew symmetric matrices.
Addition, multiplication and scalar multipliocation of matrices, simple
properties of addition, multiplication and scalar multiplication. Noncommutativity
of multiplication of matrices and existence of non-zero
matrices whose product is the zero matrix (restrict to square
matrices of order 2). Concept of elementary row and column
operations. Invertible matrices and proof of the uniqueness of
inverse, if it exists; (Here all matrices will have real entries).
2. Determinants : (20) Periods
Determinant of a square matrix (up to 3 x 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 examples, solving system of linear equations in
two or three variables (having unique solution) using inverse of a
UNIT III. CALCULUS
1. Continuity and Differentiability : (18) Periods
Continuity and differentiability, derivative of composite functions,
chain rule. derivatives of inverse trigonometric functions, derivative
of implicit function. Concept of exponential and logarithmic functions
and their derivative. Logarithmic differentiation. Derivative of
functions expressed in parametric forms. Second order derivatives.
Rolle’s and Lagrange’s Mean Value Theorems (without proof) and
their geometric interpretations.
2. Applications of Derivatives : (10) Periods
Applications of derivatives : rate of change, increasing/decreasing
functions, tangents & normals, approximation, 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
3. Integrals : (20) Periods)
Integration as inverse process of differentiation. Integration of a
variety of functions by substitution, by partial fractions and by parts,
only simple integrals of the type
2 2 2 2 2 2 2 2 2
dx , dx , dx , dx , dx
x a x a a – x ax bx c ax bx c
to be evaluated.
Definite integrals as a limit of a sum, Fundamental Theorem of
Calculus (without proof). Basic properties of definite integrals and
evaluation of definite integrals.
4. Applications of the Integrals : (10) Periods
Applications in finding the area under simple curves, especially lines,
areas of circles/parabolas/ellipses (in standard form only), area
between the two above said curves (the region should be clearly
5. Differential Equations : (10) Periods
Definition, order and degree, general and particular solutions of a
differential equation, Formation of differential, equation whose
general solution is given, Solution of differential equations by method
of separation of variables, homogenous differential equations of first
order and first degree. Solutions of linear differential equation of the
+ p(x) y = q(x), where p(x) and q(x) are functions of x,
UNIT IV. VECTORS AND THREE-DIMENSIONAL GEOMETRY
1. Vectors : (12) Periods
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 : (12) Periods
Direction cosines/ratios of a line joining two points. Cartesian and
vector equation of a line, coplanar and skew lines, shortest distance
between two lines. Cartesian and vector equation of a plane. Angle
between (i) two lines, (ii) two planes. (iii) a line and a plane. Distance
of a point from a plane.
UNIT V. LINEAR PROGRAMMING
1. Linear Programming : (12) Periods
Introduction, definition of related terminology such as constraints,
objective function, optimization, different types of linear programming
(L.P.) problems, mathematical formulation of L.P. problems,
graphical method of solution for problems in two variables, feasible
and infeasible regions, feasible and infeasible solutions, optional
feasible solutions (up to three non-trivial constraints).
UNIT VI. PROBABILITY
1. Probability : (18) Periods
Multiplication theorem on probability. Conditional probability,
independent events, total probability, Baye’s theorem, Random
variable and its probability distribution, mean and variance of
haphazard variable. Repeated independent (Bernoulli) trials and
PRESCRIBED BOOKS :
1. Mathematics Part-I Published by H.P. Board of School Education
2. Mathematics Part-II Published by H.P. Board of School Education
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