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Kerala PSC HSA Maths examination updated Syllabus 2014
Kerala PSC HSA Mathematics updated Syllabus
Kerala Public Service Commissions ( KPSC ) Recruitment Exam for selection towards the posts of High School Assistants (HSA) in Maths now has a revised Syllabus. Exams will be conduted as 2 parts. ie, PART A and PART B. Details of the Syllabus are given below:
HSA MATHEMATICS EXAM LATEST SYLLABUS
PART A
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 (Co
primes), Fundamental Theorem of Arithmetic, congruences, solution of linear congruences, Fermat’s
Theorem.Matrices – Addition, Multiplication, Transpose,
Determinants, singular matrices, inverse,
symmetric, skewsymmetric, hermitian, skewhermitian, 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 ∑1/n p .
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, n th 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 nonhomogeneous equations, solutions by undetermined coefficients.
Module VI
Data Representation: Raw Data, Classification and tabulation of data, 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 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 Nonsampling 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.
Kerala PSC website has updated the Syllabus for HSA recruitment in following subjects, Please check the given website for more info
SANSKRIT, ARABIC, URDU, PHYSICAL SCIENCE, MATHEMATICS, SOCIAL SCIENCE, ENGLISH, KANNADA, NATURAL SCIENCE , HINDI, MALAYALAM, TAMIL
For more details, please visit Kerala PSC website and check the
keralapsc.gov.in >> Examination >> Syllabus section .
Related topic
Visit keralapsc.gov.in >> Examination >> Syllabus section
Please read the advertisement document carefully and make sure you are eligibile as per the eligibility criteria mentioned in the document.
Please visit the recruiter's official website to confirm the recruitment information, read the official job notification carefully and make sure that you are eligible for the respective post and then apply. It is applicants responsibility to confirm the validity of Job opening.
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Kerala PSC HSA Maths examination updated Syllabus 2014
Kerala Public Service Commissions ( KPSC ) Recruitment Exam for selection towards the posts of High School Assistants (HSA) in Maths now has a revised Syllabus. Exams will be conduted as 2 parts. ie, PART A and PART B. Details of the Syllabus are given below:
HSA MATHEMATICS EXAM LATEST SYLLABUS
PART A
 Module I : Renaissance and freedom movement
 Module II: General Knowledge and current affairs
 Module III: Methodology of teaching the subject
 Methods and Strategies of teaching the subject Models of Teaching, Techniques ofindividualising instruction.
 Curriculum  Definition, Principles, Modern trends and organizational approaches,Curriculum reforms  NCF/KCF.
 Teacher  Qualities and Competencies  different roles  Personal Qualities  Essential teaching skills  Microteaching  Action research.
 Aims, Objectives, and Values of Teaching  Taxonomy of Educational Objectives  Oldand revised
 Pedagogic analysis Need, Significance and Principles.
 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.
 Instructional resources Laboratory, Library, Club, Museum Visual and AudioVisual
 aids  Community based resources  eresources  Text book, Work book and Hand book.
 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.
 History/conceptual development. Need and Significance, Meaning Nature and Scope of the Subject.
 Correlation with other subjects and life situations.
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 (Co
primes), Fundamental Theorem of Arithmetic, congruences, solution of linear congruences, Fermat’s
Theorem.Matrices – Addition, Multiplication, Transpose,
Determinants, singular matrices, inverse,
symmetric, skewsymmetric, hermitian, skewhermitian, 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 ∑1/n p .
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, n th 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 nonhomogeneous equations, solutions by undetermined coefficients.
Module VI
Data Representation: Raw Data, Classification and tabulation of data, 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 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 Nonsampling 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.
Kerala PSC website has updated the Syllabus for HSA recruitment in following subjects, Please check the given website for more info
SANSKRIT, ARABIC, URDU, PHYSICAL SCIENCE, MATHEMATICS, SOCIAL SCIENCE, ENGLISH, KANNADA, NATURAL SCIENCE , HINDI, MALAYALAM, TAMIL
For more details, please visit Kerala PSC website and check the
keralapsc.gov.in >> Examination >> Syllabus section .
Related topic
 Kerala PSC HSA HINDI Recruitment Examination updated Syllabus
 New Syllabus for Kerala PSC HSA MALAYALAM Recruitment Exam
 Latest topics for Kerala PSC HSA TAMIL Recruitment Examination
 PSC HSA MATHS Recruitment Exam New updated Syllabus
 PSC HSA NATURAL SCIENCE Exam updated Syllabus
 Updated topics for HSA KANNADA Recruitment Exam by Kerala PSC
 KPSC HSA PHYSICAL SCIENCE Examination revised Syllabus
 PSC HSA SANSKRIT Recruitment Examination updated Syllabus
 KPSC HSA ARABIC Recruitment Exam latest Syllabus
 Kerala PSC HSA URDU Recruitment Exam revised Syllabus
 Kerala PSC HSA ENGLISH Exam updated Syllabus
Visit keralapsc.gov.in >> Examination >> Syllabus section
Please read the advertisement document carefully and make sure you are eligibile as per the eligibility criteria mentioned in the document.
Please visit the recruiter's official website to confirm the recruitment information, read the official job notification carefully and make sure that you are eligible for the respective post and then apply. It is applicants responsibility to confirm the validity of Job opening.
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