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RPSC 2nd Grade Mathematics

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RPSC 2nd Grade Mathematics

RAJASTHAN PUBLIC SERVICE COMMISSION, AJMER
 
SYLLABUS FOR EXAMINATION FOR THE POST OF  
SR.TEACHER (GRADE-II), 
SECONDARY EDUCATION DEPARTMENT
 
PAPER - II
 
MATHEMATICS 
 
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. 
 
Calculus : 
 
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
problems. 
 
Part - (ii)                                                                           80  marks  
 
(Graduation Standard)
 
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
of functions. 
 
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,
Particular integral. 
 
Part - (iii)                                                                         40  marks  
 
(Teaching Methods) 
 
 
-  Meaning and Nature of Mathematics. 
-  Aims & Objectives of Mathematics Teaching.
-  Methods  of  Mathematics  Teaching  (analytic,  synthetic,  inductive,  deductive,  heuristic,  Project  &
Laboratory).  
-  Using various  techniques of  teaching mathematics  viz  - Oral, written, drill, assignment,  supervised  -  study &
programmed Learning. 
-  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-
motor Development. 
-  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
stages. 
-  Mathematics for gifted and retarded children. 
 
* * * * *
 
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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