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Math Pass Syllabus of West Bengal School Service
Commission Math
Hons/P.G. Math Pass Other
Subjects If this website helps you in any way email
at sscmath10@gmail.com Click Here to Download PDF file of the WBSSC Pure Science
Syllabus Syllabus of
Mathematics (Pass) for West Bengal School Service Commission Examination: MATHEMATICS A. Classical Algebra: 1. Complex number: Definition on the basis of ordered
pairs of real numbers. Algebra of complex numbers, modulus amplitude,
conjugate, Argand diagram. Demovire s Theorem and its applications.
Exponential, Sine, Cosine and Logarithm of a complex number. Definition of az
(a 0). Inverse Circular and Hyperbolic functions. 2. Polynomial, Synthetic division. Remainder theorem:
Fundamental theorem of Classical Algebra (statement only). Polynomials with
real coefficients; the nth degree polynomial equation has exactly n roots. Nature
of roots of an equation (surd or complex roots occur in pairs). Statement of
Descrte s Rule of signs and its applications. General properties of
equations. Multiple roots. Rolle s theorem and its application Relation
between roots and co-efficeints, symmetric functions of roots. Transformation
of equations. Cardan s method of solution of a cubic. 3. Determinants upto the third order. Definition of a
determinant,Properties, Minors and cofactors. Product of two determinants.
Adjoint,Symmetric, and Skew-symmetric determinants. Solutions of linear equations
with not more than three variables by Cramer s Rule 4. Matrices of Real Numbers: Definition, Equality of
matrices. Addition of matrices, Multiplication of a matrix by a scalar.
Multiplication of matrices.Scaler matrix, identity matrix. Inverse of a
non-singular square matrix. Elementary operations on matrices, Rank of a
matrix;determination of rank either by considering minors or by Sweepout process.
Consistency and solution of a system of linear equations with not more than
three variables by matrix method. B. Modern Algebra: 1. Basic concepts: Sets, Subsets, Equality sets,
Operations on Sets. Union, Intersection and Complement. Verification of the
laws of algebra of set and De Morgan s Laws. Cartesian product of two sets.
Mappings One to one and onto mapping composition of mappings Identity and
inverse mappings. 2. Introduction to Group Theory. Group Definition an
examples taken from different branches (examples from number system, roots of
unity 2 x 2 real matrices, non-singular real matrices of fixed order).
Elementary properties using definition of group. Definition and example of
subgroup. 3. Definitions and examples of Ring. Field, Sub-ring,
Sub-field. 4. Concept of Vector Space over a field: Examples,
Concepts of linear combinations Linear dependence and independence of finite
set of finite set of vectors. Subspace, concepts of Generators and Basis of a
finite dimensional vector space. 5. Real quadratic form involving not more than three
variables - Problem only. 6. Characteristic equation of square Matrix of order not
more than three. Determination of Eigen values and Eigen vectors Problems
only. Statement and illustration of Cayley Hamilton theorem. II GEOMETRY A. ANALYTICAL GEOMETRY OF TWO DIMENSIONS. 1. Transformation of Rectangular axes. Translation,
Rotation and their combinations. Invariants. 2. General Equation of second degree in x and y. Reduction
to canonical forms classification of Conic. 3. Pair of straight lines: Condition that the general
equation of second degree in x and y may represent two straight lines. Point
of intersection of two intersecting straight lines. Angle between two lines
given by ax2 + 2hxy+ by2 = 0. Equation of Bisectors.
Equation of two lines joining the origin to the points which a line meets a
conic. 4. Equation of pair of tangents from an external point,
chord of contact, poles and polars of ellipse and hyperbola. 5. Polar equations of straight lines and circles, polar
equation of conic referred to a focus a pole. Equation of chord joining two
points. Equations oftengents and normals. B. ANALYTICAL GEOMETRY OF THREE DIMENSIONS: 1. Rectangular Cartesian co-ordinate. Distance between two
points. Division of a line segment in a given ratio. Direction cosines and
Direction ratios of a straight line. Projection of a line segment on another
straight line. Angle between two straight lines. 2. Equation of a plane: General Form, Intercept and Normal
Form. Angle between two planes. Signed distance of a point from a plane.
Bisectors of angles between two intersection planes. 3. Equation of straight lines. General and symmetric form.
Distance of a point from a line. Co planarity of two straight lines. Shortest
distance between two skew-lines. III DIFFERENT CALCULUS 1. Rational numbers Geometrical representation. Irrational
numbers. Real numbers represented as points on a line Linear continuum.
Acquaintance with basic properties of real numbers (No deduction of Proof is
included)2. Sequence: Definition of bounds of a sequence and Monotone
sequence. Limit of a sequence. Statement of theorems. Concept of convergence
and divergence of monotone sequences applications of the theorems, in particular,
definition of e. Statement of Cauchy s general principle of convergence and
its applications. 3. Infinite series of constant terms. Convergence and
divergence (definitions). Cauchy s principle as applied to Infinite series
(application only). Series of positive terms. Statements of comparison test,
D Alembert s Ratio test. Cauchy s root test Applications Alternating series:
Statement of Leibnitz test and its applications. 4. Real valued functions defined on an interval: Limit of
a function (Cauchy s definition). Algebra of limits. Continuity of a function
at a point and in an interval. Acquaintances (no proof) with the important
properties of continuous functions on closed intervals. Statement on
existence of inverse function on a strictly monotone function and its
continuity. 5. Derivative. Its geometrical and physical
interpretation. Sign of derivative Monotonic increasing and decreasing
functions. Relation between continuity and derivability. Differential
application in finding approximatuer. Successive derivative Leibnitz s
theorem and its application. 6. Statement of Rolle s Theorem and its geometrical
interpretation. Mean value Theorems of Langrance and indeterminate Forms. L.
Hospital s Rules Application of the Principle of Maximum and Minimum for a
function of single variables in geometrical physical and other problems. 7. Functions of two variables. Their geometrical
representations. Limit and continuity (definitions only) for functions of two
variables partial derivatives. Knowledge and use of chair rule.
Differentiation of implicit functions of two variables (existence being
assumed). Function of two variable successive partial derivatives Statement
of Schwarz s Theorem on commutative property of mixed derivatives. Statement
of Euler s Theorem on homogeneous function of two variables. Maxima and
minima of functions of two variables. 8. Applications of Differential calculus: Tangent and
normal. Envelope of family of curves (problems only) IV INTERGRAL CALCULUS 1.
Integrations of the form ---- 1/(a+bcosx), (lsinx+mcos)/(nsinx+pcosx), and integration of rational functions. 2. Evaluation of definite Integrals. 3. Integration as the Limit of a sum (with equally spaced
intervals). 4. Reduction formula of +"Sinm x conn x dx ,+" sinmx/sinnx
dx +"
tannx
dx and associated probles (m and n are non-negative integers) 5. Working knowledge of Double Integral 6. Rectification. Quadrature, volume and surface areas of
solids formed by revolution of plane curves and areas. IV INTERGRAL CALCULUS 1. Order, degree and solution of an ordinary differential
equation (ODE) in presence of arbitrary constants. Formation of ODE, First
order equations. (i) Variables separable. (ii) Homogeneous equations and equations reducible to
homogeneous forms. (iii) Euler s and Bermoulli s Equations (Linear) (iv) Clairaut s Equation: General and Singular solutions. 2. Second order linear equations: Second order linear
differential equations with constant coefficients. Euler s Homogeneous
equations. V VECTOR ALGEBRA Definition of vector and scalar. Addition of vectors.
Multiplication of vector by a scalar. Collinear and coplanar vectors, Scalar
and vector products of two and three vectors. Simple applications to problems
of Geometry. VI ANALYTICAL DYNAMICS 1. Velocity and Acceleration of a particle. Expressions
for velocity and acceleration in rectangular Cartesian and polar coordinates
for a particle moving in a plane. Tangential and Normal components of
velocity and acceleration of a particle moving along a plane curve. 2. Concept of Force: Statement and explanation of Newton s
laws of motion. Work, power and energy Principles of conservation of Energy
and Momentum. Motion under impulsive forces. Equations of motion of a particle
moving in a straight ling. 3. Study of motion of a particle in a straight line order
(i) constant forces (ii)variable forces (SHM, Inverse square law. Forced and
Damped oscillation. Motion in an elastic string) Equation of energy.
Conservative forces. 4. Motion in tow dimensions: Projectiles in vacuo and in
a medium with resistance varying linearly with velocity. Motion under forces
varying as distance from a fixed point. 5. Central orbit. VII LINEAR PROGRAMMING Motivation of Linear Programming problem. Statements of
L.P.P. Formulation of L.P.P. L.P.P. in matrix forms. Convex Set, Hyper plane,
Extreme points. Convex Poly hedron. Basic solutions and Basic Feasible
solutions (B.F.S.) The set of all feasible solutions of an L.P.P. in a convex
set. The objective Function of an L.P.P. assumes its optimal value at an
extreme point of the convex set of feasible solutions. Fundamental Theorem of
L.P.P. (Statement only) Reduction of a feasible solution to a B. F.S.
Standard form of an L.P.P. Solution by graphical method (for two variables)
by simplex method (not more than four variables). Feasibility and optimality
condition. Method of penalty concept of duality. Duality Theory. The dual of
the dual is the primal. Relation between the objective values of dual and the
primal problems. Dual problems with almost one unrestricted. Variable, one constraint
of equality. Transportation and Assignment problem and their optimal solutions. VIII NUMERICAL METHODS 1. Approximate numbers, significant figures, rounding-off
numbers. Error : - absolute, relative and percentage 2. Operator D, N and E (Definition
and some relations among them). 3. Interpolations: --- The problem of interpolation,
Simple problems regarding difference table, Newton s forward and backward
interpolation formula. 4. Numerical Integration: Simple problems using
trapezoidal and Simpon s 1/3 rule. 5. Solution of Equations: Location of root (tabular
method)Bisection Method, Newton Raphson Method Numerical problems. IX ELEMENTS OF PROBABILITY THEORY AND STATISTICS 1. Introduction: Variables, Statistics, Population &
sample. Discrete and continuous variables. Frequency distributions. 2. Measure of Central tendencies: A.M. Medina, Mode. 3. Measures of Dispersions: Range, mean deviation,
Standard deviation, variance. 4. Elements of Probability Theory: Concept of sample
spaces. Event and random variables. Classical definition of Probability.
Total probability,compound probability, conditional Probability. Bayes
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