RAJASTHAN PUBLIC SERVICE COMMISSION, AJMER
SYLLABUS FOR EXAMINATION FOR THE POST OF
SECONDARY EDUCATION DEPARTMENT
PAPER - II
Part - (i) 180 marks
(Secondary and Senior Secondary standard)
Number system : Irrational numbers, real numbers and their decimal expansions, operation on real numbers,
Laws of exponents for real number, Fundamental theorem of Arithmetic.
Plane Geometry : Angles and lines at a point, Angles made by a transversal with two lines, classification of
triangles on the basis of sides and angles, Rectilinear figures, congruence of triangles, inequalities of triangles,
similar triangles, Area of plane figures, Circles, Arcs and Angles subtended by them, Tangents to a circle.
Algebra : Linear Equations (in two variables), Polynomials in one variable, zeroes of a polynomial,
Remainder theorem, Factorization of polynomials, algebraic identifies, Mathematical induction, Binomial
theorem, Quadratic equations, nature of roots, linear inequalities, finite and infinite sequences, Arithmetic
progression, Geometric Progression, Harmonic Progression, Permutations, Combinations, Matrix,
Determinants of order two and three, Inverse matrix, solution of simultaneous linear equations of two and
three unknowns, Sets, Relations and Functions, Complex numbers, its elementary properties, Argand plane
and polar representation of complex numbers, square root of a complex number.
Surface Area and Volume : Cube, Cuboids, Cone, Cylinder and Sphere, Conversion of solid from one
shape to another, frustum of a Cone.
Trigonometry : Angles and their measurements, Trigonometric ratios of acute angles, Angles and lengths of
arc, trigonometric functions, compound multiple angles, solutions of trigonometric equations, inverse
trigonometric functions, properties of triangles.
1 Differential Calculus - Limits, differentiability, continuity, derivative of Sum and Difference,
derivative of product of functions, Composite functions, implicit functions, trigonometric functions,
parametric functions, Second order derivative, Rolle’s and Lagrange’s mean value theorem,
applications of derivatives, Increasing/decreasing function, tangents and normals, maxima and minima
of one variable.
2 Integral Calculus - Indefinite integrals, definite integrals, definite integral as a limit of sum,
Applications of definite integral in finding the area under simple curves, arc of circles,
lines/parabola/ellipse, area between the two above said curves.
Co-ordinate Geometry :
1 Two Dimensional Geometry - Distance between two points, Sections formula, area of triangle, locus,
equations of straight line, pair of straight lines, circles, parabola, ellipse, hyperbola, their equations,
general properties, tangent, normal, chord of contact, pair of tangents.
2 Co-ordinate Geometry in 3 - dimensions – Co-ordinate axes and co-ordinate planes in three
dimensions, co-ordinates of a point, distance between two points and section formula, direction
cosines/ratios of a line joining two points, Cartesian and vector equation of a line, coplaner 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.
Statistics : Mean, Mode, Median, Quartiles, Deciles, Percentiles, Measure of dispersion, Probability - Laws of
probability, addition and multiplications law, conditional probability, Random variable and probability
distributions, repeated independent (Bernoulli) trials and Bionomial distribution.
Vector - Dot product, Cross product, their properties, Scalar triple product, Vector triple product and related
Part - (ii) 80 marks
1 Abstract Algebra - Group, Normal subgroup, permutation group, Quotient group, Homomorphism &
groups, Isomorphism theorems, Calay and Lagrange's theorems, Automorphism.
2 Calculus - Partial derivatives, Maxima and Minima of functions of two variables, Asymptotes, double
and triple integrals, Beta and Gamma functions. Mean Value Theorems.
3 Real Analysis - Real numbers as a complete ordered field, linear sets, lower and upper bounds, limit
points, closed and open sets, Real sequence, limit and convergence of a sequence, Riemann
integration, convergence of series, absolute convergence, uniform convergence of sequence and series
4 Vector Analysis - Differentiation of a vector functions of scalar variable, Gradient, divergence and
curl (rectangular co-ordinates), vector identities, Gauss's Stoke's and Green's theorems.
5 Differential Equations - Ordinary differential equations of first order and first degree, differential
equations of first order but not of first degree, Clairaut's equations, general and singular solutions,
linear differential equations with constant coefficients, homogeneous differential equation, second
order linear differential equations, simultaneous linear differential equations of first order.
6 Statics and Dynamics : Composition and resolution of co-planer forces, component of a force in two
given directions, equilibrium of concurrent forces, parallel forces and moment, velocity and
acceleration, simple linear motion under constant acceleration, Laws of motion, projectile.
7 Linear Programming - Graphical method of solution of linear programming in two variables, convex
sets and their properties, simplex method, Assignment problems, Transportation problems.
8 Numerical Analysis and Difference Equation - Polynomial interpolation with equal or unequal
stepsize, Lagrange's interpolation formula, Truncation error, Numerical differentiation, Numerical
integration, Newton-Cotes quadrature formula, Gauss's quadrature formulae, convergence, Estimation
of errors, Transcendental and polynomical equations, bisection method, Regula-falsi method, method
of interation, Newton - Raphson method, Convergence, First and higher order homogeneous linear
difference equations, non homogenous linear difference equations, Complementary functions,
Part - (iii) 40 marks
- Meaning and Nature of Mathematics.
- Aims & Objectives of Mathematics Teaching.
- Methods of Mathematics Teaching (analytic, synthetic, inductive, deductive, heuristic, Project &
- Using various techniques of teaching mathematics viz - Oral, written, drill, assignment, supervised - study &
- Arousing and maintaining interest in learning of Mathematics.
- Importance & meaning of planning, Preparing Lesson Plan, Unit Plan, Yearly Plan, Short Lesson Plan.
- Preparing low cost improvised teaching aids, Audio-Visual aids in Mathematics.
- Transfer of mathematics learning to various subjects and actual life situation.
- Planning & equipments of Mathematics laboratory.
- The mathematics teacher academic & professional - preparation.
- Principle of curriculum & qualities of a good text book.
- Process of obtaining feed-back and evaluation in Mathematics in terms of Cognitive, Affective and Psycho-
- Preparation and use of tests for evaluation such as achievement test & diagnostic test.
- Diagnostic, Remedial and enrichment programmes with respect to syllabus at Secondary and Senior Secondary
- Mathematics for gifted and retarded children.
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For the competitive examination for the post of senior teacher :-
1 The question paper will carry maximum 300 marks.
2 Duration of question paper will be Two Hours Thirty Minutes.
3 The question paper will carry 150 questions of multiple choices.
4 Paper shall include following subjects carrying the number of marks as shown against them :-
(i) Knowledge of Secondary and Sr. Secondary Standard
about relevant subject matter. 180 Marks
(ii) Knowledge of Graduation Standard about
relevant subject matter. 80 Marks
(iii) Teaching Methods of relevant subject. 40 Marks
Total 300 Marks
5 All questions carry equal marks.
6 There will be Negative Marking.
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