RPSC 2nd Grade Eligibility

The Mathematics syllabus covers topics from both school-level and graduation-level concepts, along with teaching methodology.
Part I: Secondary & Senior Secondary Level
1. Number Systems Rational numbers, irrational numbers, real numbers, decimal expansions, laws of exponents, Euclid’s division lemma, Fundamental Theorem of Arithmetic.
2. Geometry Lines and angles, triangles (properties, congruence, similarity), quadrilaterals, circles (chords, arcs, tangents, cyclic quadrilaterals).
3. Mensuration Areas of plane figures, surface areas and volumes of solids, problems involving conversions and mixed figures.
4. Algebra Polynomials, quadratic equations, inequalities, complex numbers, sequences and series, permutations and combinations, binomial theorem.
5. Matrices and Determinants Types of matrices, operations, determinants, adjoint, inverse, solving linear equations.
6. Sets, Relations and Functions Set operations, relations, functions, types of functions, composition, special functions.
7. Trigonometry Angles, trigonometric functions, identities, equations, inverse trigonometry, heights and distances.
8. Analytical Geometry Straight lines, circles, conic sections, locus, three-dimensional geometry including planes and lines.
9. Calculus Limits, continuity, differentiation, applications of derivatives, integration, definite integrals, area under curves.
10. Vector Algebra Vector operations, scalar and vector products, projections.
11. Statistics and Probability Measures of central tendency, standard deviation, probability, Bayes theorem, binomial distribution.



Part II: Graduation Level
1. Abstract Algebra Groups, subgroups, permutations, homomorphisms, isomorphisms, quotient groups.
2. Real Analysis Sequences, series, convergence, uniform convergence.
3. Complex Analysis Analytic functions, Cauchy-Riemann equations, harmonic functions.
4. Advanced Calculus Partial differentiation, maxima and minima, curvature, multiple integrals, Beta and Gamma functions.
5. Differential Equations First and second order equations, simultaneous equations.
6. Vector Calculus Gradient, divergence, curl, integral theorems (Green, Gauss, Stokes).
7. 3D Geometry Sphere, cone, cylinder, tangent planes.
8. Statics and Dynamics Forces, equilibrium, motion, laws of motion.
9. Linear Programming Formulation, graphical method, simplex method, duality.
10. Numerical Analysis Interpolation, numerical differentiation, integration, solution of equations, difference equations.



Part III: Teaching Methods
Nature and objectives of Mathematics teaching
Bloom’s taxonomy
Teaching methods (inductive, deductive, project method, etc.)
Lesson planning and unit planning
Use of teaching aids and technology (TPCK)
Evaluation methods (unit tests, diagnostic tests)
360-degree assessment