# Kerala PSC HSA Mathematics Exam Syllabus 2015

Kerala PSC High School Assistant [HSA] Mathematics Exam Syllabus 2015. Detailed Exam Syllabus of Kerala PSC High School Assistant [HSA Mathematics] Examination published by Kerala public service commission.

#### HSA Mathematics Detailed Exam Syllabus

PART A
Module I: Renaissance and freedom movement.
Module II: General Knowledge and current affairs.
Module III: Methodology of teaching the subject.

• History/conceptual development. Need and Significance, Meaning Nature and Scope of the Subject.
• Correlation with other subjects and life situations.
• Aims, Objectives, and Values of Teaching - Taxonomy of Educational Objectives - Old and revised
• Pedagogic analysis- Need, Significance and Principles.
• Planning of instruction at Secondary level- Need and importance. Psychological bases of Teaching the subject - Implications of Piaget, Bruner, Gagne, Vygotsky, Ausubel and Gardener - Individual difference, Motivation, Maxims of teaching.
• Methods and Strategies of teaching the subject- Models of Teaching, Techniques of individualising 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 B
Module I

Elementary Set Theory, Relations, Partial order, Equivalence relation, Functions, bijections,
Composition, inverse function, 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 circle.
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 system 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’s series, L’Hospital’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 – properties.

Fundamental theorem of calculus.
Applications of Integration – Area between curves, volume and area of revolution.
Double and Triple Integrals
Conic sections- Standard equations – Parabola, ellipse, hyperbola, Cartesian, Parametric and polar
forms.

Module IV
Bounded sets, infinum, supremum, order completeness, neighbourhood, interior, open sets, closed sets, limit points, Bolzano Weierstrass Theorem, closed sets, dense sets, countable sets, uncountable sets.
Sequences – convergence and divergence of sequences, monotonic sequences, subsequences.
Series – Convergence and divergence of series, absolute convergence, Canchy’s general principle of convergence of series. The series Σ1/np .
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 of complex variables, Analytic functions. Taylor series, Laurent’s Series.

Module V
Vectors – Unit vector, collinear vectors, coplanar vectors, like and unlike vectors, orthogonal triads (i, j, k) Dot product, 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, Stoke’s Theorem, Divergence Theorem.

Differential Equations – Order and degree of differential equations. First order differential
equations- solution of Linear equations, separable equations and exact equations.
Second order differential equations- Solution of homogeneous equations with constant coefficients – various types non-homogeneous equations, solutions by undetermined coefficients.

Module VI
Data Representation: Raw Data, Classification and tabulation of data, Frequency tables, Contingency tables; Diagrams – Bar diagrams, sub-divided bar diagrams, Pie diagrams, Graphs – Frequency polygon, frequency curve, Ogives.

Descriptive Statistics: Percentiles, Deciles, Quartiles, Arithmetic Mean, Median, Mode, Geometric Mean and Harmonic Mean; Range, Mean deviation, Variance, Standard deviation, Quartile deviation; Relative measures of dispersion – Coefficient of variation; Moments, Skewness and Kurtosis – Measures of Skewness and Kurtosis.

Probability: Random Experiment, Sample space, Events, Type of Events, Independence of events; Definitions of probability, Addition theorem, Conditional probability, Multiplication theorem, Baye’s theorem.

Module VII
Random variables and probability distributions: Random variables, Mathematical Expectation, Definitions and properties of probability mass function, probability density function and distribution function. Independence of random variables; Moment generating function; Standard distributions – Uniform, Binomial, Poisson and Normal distribution.

Bivariate distribution: Joint distribution of two random variables, marginal and conditional
distributions.
Correlation and regression: Scatter Diagram, Karl Pearson’s Correlation Coefficient, Spearman’s rank correlation coefficient. Principle of least squares – curve fitting – Simple linear regression.

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 of estimate – Unbiasedness, consistency, sufficiency and efficiency.

Testing of hypothesis (basic concepts only) - Simple and composite hypotheses, null and alternate hypotheses, Type I error, Type II error, Level of significance, Power of a test.