The Kerala PSC High School Assistant (HSA) Mathematics exam is designed to assess a candidate’s subject knowledge, teaching aptitude, and overall suitability for a teaching position in government high schools. A thorough understanding of the syllabus is crucial for focused and effective preparation. The syllabus covers a wide range of mathematical concepts along with pedagogical principles, aiming to evaluate both academic proficiency and the ability to teach the subject efficiently. To achieve this Read carefully Below syllabus:

PART I (15 Marks)
Module I: Renaissance and Freedom Movement
Module II: General Knowledge and Current Affairs

PART II (5 Marks)
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.

PART III (80 Marks)

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)