Kerala PSC HSA Maths Online Coaching

Module I: Renaissance and Freedom Movement
Module II: General Knowledge and Current Affairs

Module III: Methodology of Teaching the Subject

• History and conceptual development: Need and significance, meaning, nature, and scope of the subject.
• Correlation with other subjects and real-life situations.
• Aims, objectives, and values of teaching: Taxonomy of Educational Objectives—both old and revised.
• Pedagogic analysis: Need, significance, and principles.
• Planning of instruction at the secondary level: Need and importance. Psychological bases of teaching the subject, including implications of Piaget, Bruner, Gagne, Vygotsky, Ausubel, and Gardner—addressing individual differences, motivation, and maxims of teaching.
• Methods and strategies for teaching the subject: Models of teaching and techniques for individualizing instruction.
• Curriculum – Definition, Principles, Modern trends and organizational approaches, Curriculum reforms – NCF/KCF.
• Instructional resources- Laboratory, Library, Club, Museum- Visual and Audio-Visual aids – Community based resources – e-resources – Text book, Work book and Hand book.
• Assessment; Evaluation- Concepts, Purpose, Types, Principles, Modern techniques – CCE and Grading- Tools and techniques – Qualities of a good test – Types of test items- Evaluation of projects, Seminars and Assignments – Achievement test, Diagnostic test – Construction, Characteristics, interpretation and remediation.
• Teacher – Qualities and Competencies – different roles – Personal Qualities – Essential teaching skills – Microteaching – Action research.

Module I

• Elementary Set Theory: Relations, Partial Order, Equivalence Relations, Functions, Bijections, Composition, Inverse Functions
• Quadratic Equations: Relation Between Roots and Coefficients
• Mathematical Induction
• Permutation and Combination
• Trigonometric Functions: Identities, Solution of Triangles, Heights, and Distances
• Geometry: Length and Area of Polygons and Circles
• Solids: Surface Area and Volume, Euler’s Formula

Module II

• Theory of Numbers: Divisibility, Division Algorithm, GCD, LCM, Relatively Prime Numbers (Coprimes), Fundamental Theorem of Arithmetic, Congruences, Solution of Linear Congruences, Fermat’s Theorem
• Matrices: Addition, Multiplication, Transpose, Determinants, Singular Matrices, Inverse, Symmetric, Skew-Symmetric, Hermitian, Skew-Hermitian, Orthogonal Matrices, Normal Form, Echelon Form, Rank of a Matrix, Solution of Systems of Linear Equations, Eigenvalues, Eigenvectors, Cayley-Hamilton Theorem

Module III

• Calculus: Limits, Continuity, Differentiability, Derivatives, Intermediate Value Theorem, Rolle’s Theorem, Mean Value Theorem, Taylor and Maclaurin Series, L’Hôpital’s Rule
• Partial Differentiation: Homogeneous Functions, Euler’s Formula
• Applications of Differentiation: Maxima and Minima, Critical Points, Concavity, Points of Inflection, Asymptotes, Tangents, and Normals
• Integration: Methods of Integration, Definite Integrals and Their Properties
• Applications of Integration: Area Between Curves, Volume, and Area of Revolution
• Double and Triple Integrals
• Conic Sections: Standard Equations of Parabola, Ellipse, Hyperbola, Cartesian, Parametric, and Polar Forms

Module IV

• Bounded Sets: Infimum, Supremum, Order Completeness, Neighborhood, Interior, Open Sets, Closed Sets, Limit Points
• Bolzano-Weierstrass Theorem: Closed Sets, Dense Sets, Countable Sets, Uncountable Sets
• Sequences: Convergence and Divergence, Monotonic Sequences, Subsequences
• Series: Convergence and Divergence, Absolute Convergence, Cauchy’s General Principle of Convergence
• Tests for Convergence of Series: Comparison Test, Root Test, Ratio Test
• Continuity and Uniform Continuity: Riemann Integrals, Properties, Integrability
• Complex Numbers: Modulus, Conjugates, Polar Form, Nth Roots of Complex Numbers
• Functions of Complex Variables: Elementary Functions, Analytic Functions, Taylor Series, Laurent Series

Module V

• Vectors: Unit Vectors, Collinear Vectors, Coplanar Vectors, Like and Unlike Vectors, Orthogonal Triads (i, j, k)
• Dot Product and Cross Product: Properties
• Vector Differentiation: Unit Tangent Vector, Unit Normal Vector, Curvature, Torsion, Vector Fields, Scalar Fields, Gradient, Divergence, Curl, Directional Derivatives
• Vector Integration: Line Integrals, Conservative Fields, Green’s Theorem, Surface Integrals, Stokes’ Theorem, Divergence Theorem

Module VI

• Data Representation: Raw Data, Classification, Tabulation, Frequency Tables, Contingency Tables
• Diagrams: Bar Diagrams, Subdivided Bar Diagrams, Pie Diagrams, Graphs (Frequency Polygon, Frequency Curve, Ogives)
• Descriptive Statistics: Percentiles, Deciles, Quartiles, Arithmetic Mean, Median, Mode, Geometric Mean, Harmonic Mean, Range, Mean Deviation, Variance, Standard Deviation, Quartile Deviation, Coefficient of Variation, Moments, Skewness, and Kurtosis

Module VII

• Probability: Random Experiment, Sample Space, Events, Types of Events, Independence of Events, Definitions of Probability, Addition Theorem, Conditional Probability, Multiplication Theorem, Bayes’ Theorem
• Random Variables and Probability Distributions: Random Variables, Mathematical Expectation, Properties of Probability Mass Function, Probability Density Function, and Distribution Function
• Independence of Random Variables: Moment Generating Function, Standard Distributions (Uniform, Binomial, Poisson, Normal Distribution)
• Bivariate Distribution: Joint Distribution of Two Random Variables, Marginal and Conditional Distributions

Module VIII

• Random Sampling Methods: Sampling and Census, Sampling and Non-Sampling Errors, Simple Random Sampling, Systematic Sampling, Stratified Sampling
• Sampling Distributions: Parameter and Statistic, Standard Error, Sampling Distributions (Normal, t, F, Chi-Square Distributions), Central Limit Theorem
• Estimates: Desirable Properties (Unbiasedness, Consistency, Sufficiency, Efficiency)
• Testing of Hypotheses: Basic Concepts (Simple and Composite Hypotheses, Null and Alternate Hypotheses, Type I Error, Type II Error, Level of Significance, Power of a Test)