Kerala PSC HSA Maths Online Coaching

Module I (Renaissance & Freedom Movement): Social reform movements in Kerala, major socio-religious reformers,anti-colonial struggles, and important events in modern Indian and Kerala history.

Module II (General Knowledge & Current Affairs): Important national and international events, awards, sports,politics, science, and technology updates.

Module III (Methodology of Teaching Mathematics):

• Nature & Scope: History, conceptual development, and real-life applications of mathematics.
• Aims & Objectives: Taxonomy of Educational Objectives (Bloom's Taxonomy - old and revised versions).
• Pedagogy & Planning: Pedagogic analysis, lesson planning, unit plans, and instruction design at the secondary school level.
• Teacher Competencies: Qualities of a teacher, essential teaching skills, microteaching, and action research.

Module 1: Elementary Mathematics, Algebra & Geometry

• Set Theory: Relations, partial order, equivalence relations, functions, bijections, composition, and inverse functions.
• Algebra: Quadratic equations (relations between roots and coefficients), mathematical induction, permutations, and combinations.
• Trigonometry: Trigonometric identities, solution of triangles, heights, and distances.
• Geometry & Mensuration: Length, perimeter, and area of polygons and circles; surface area and volume of 3D solids; Euler’s formula.

Module 2: Matrices & Linear Algebra

• Matrix Operations: Addition, multiplication, transpose, determinants, inverse, and singular matrices.
• Matrix Types & Reduction: Symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal matrices; normal form, row echelon form, and rank of a matrix.
• Linear Systems: Solutions to systems of linear equations, eigenvalues, eigenvectors, and the Cayley-Hamilton Theorem.

Module 3: Calculus & Analytical Geometry

• Calculus: Limits, continuity, differentiation, integration techniques, definite integrals, and properties.
• Applications of Calculus: Area under/between curves, volume and surface area of revolution, double and triple integrals.
• Conic Sections: Standard equations, properties, parametric, Cartesian, and polar forms of parabolas, ellipses, and hyperbolas.

Module 4: Real & Complex Analysis

• Real Analysis: Bounded sets, infimum, supremum, neighborhood, open/closed sets, limit points, Bolzano-Weierstrass theorem, sequences (convergence, divergence, monotonic, subsequences), continuity, uniform continuity, and Riemann integration.
• Complex Analysis: Complex numbers, modulus, polar form, nn-th roots of complex numbers, analytic functions,Cauchy-Riemann equations, Taylor series, and Laurent series.

Module 5: Vector Calculus

• Vector Differentiation: Unit tangent/normal vectors, curvature, torsion, scalar and vector fields, gradient,divergence, curl, and directional derivatives.
• Vector Integration: Line integrals, conservative fields, Green's theorem, surface integrals, Stokes' theorem, and the Divergence theorem.

Module 6: Statistics & Probability

• Descriptive Statistics: Measures of central tendency (Mean, Median, Mode, GM, HM), measures of dispersion (Range, Quartile Deviation, Standard Deviation, Variance, Coefficient of Variation), moments, skewness, and kurtosis.
• Probability & Distributions: Random variables, joint/marginal distributions, moment-generating functions, and standard distributions (Uniform, Binomial, Poisson, Normal).
• Statistical Inference: Point estimation (unbiasedness, consistency, sufficiency, efficiency) and testing of hypotheses (Null/Alternative hypotheses, Type I & Type II errors, level of significance, power of a test).