Kerala HSS Mathematics Teacher PSC Question Paper and Answer Key in PDF Format

• Total Questions: 100
• Total Exam Time : 75 Minutes
• Medium of Exam: Malayalam/ English
• Difficulty Level: Same as the Original PSC Test

Notification Number	Name of the Post	Department
720/2025	Higher Secondary School Teacher (Junior) Mathematics	Kerala Higher Secondary Education

Students can download the HSST (Junior) Mathematics questions and answers in the PDF format from here.

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Part / Module	Subject Area	Key Topics & Details	Marks
Module I	Linear Algebra	Vector spaces, subspaces, linear independence, basis, dimension. Matrices, rank, determinant, eigenvalues, Cayley-Hamilton theorem. Jordan forms, inner product spaces, and quadratic forms.	7
Module II	Real Analysis I	Sequences and series, convergence, Bolzano-Weierstrass theorem, Heine-Borel theorem. Continuity, differentiability, Mean Value Theorem, and Riemann integrals.	7
Module III	Real Analysis II	Lebesgue measure and integral. Functions of several variables, inverse and implicit function theorems. Fourier series, Beta and Gamma functions.	7
Module IV	Abstract Algebra I	Groups, subgroups, normal subgroups, homomorphisms, isomorphisms, cyclic groups. Sylow theorems and the Fundamental theorem for abelian groups.	7
Module V	Abstract Algebra II	Rings, ideals, quotient rings, UFD, PID, Euclidean domains. Polynomial rings, field extensions, and Galois theory.	7
Module VI	Topology	Metric spaces, topological spaces, base/subbase, countability. Separation axioms, compactness, connectedness, and product topology.	7
Module VII	Complex Analysis	Analytic functions, Cauchy-Riemann equations, Conformal mappings. Mobius transformation, Cauchy's theorem, and Residue calculus.	7
Module VIII	Functional Analysis	Normed linear spaces, Banach spaces, Hahn-Banach theorem. Open mapping theorem, Hilbert spaces, and self-adjoint operators.	7
Module IX	Differential Equations	Existence/uniqueness of ODEs. General theory of homogeneous linear ODEs. Lagrange and Charpit methods for PDEs, Heat and Wave equations.	7
Module X	Theory of Numbers	Divisibility, congruences, Chinese Remainder Theorem. Euler's totient function, Fermat's, Wilson's, and Euler's theorems. Primitive roots.	7
Part II	Research & Teaching Aptitude	Teaching objectives and methods, learner characteristics, research types, ethics, and thesis writing format.	10
Part III	Constitution & Renaissance	Fundamental Rights, Directive Principles, Legislature, Judiciary. Kerala Renaissance leaders and social reform movements.	10
Part IV	GK & Current Affairs	General Knowledge and latest national and international current events.	10
Total Marks			100

Department	Kerala Higher Secondary Education
Name of Post	Higher Secondary School Teacher (Junior) Mathematics
Monthly Salary of an HSST Mathematics Teacher	45,600 - 95,600/- Indian Rupees
Number of HSST Mathematics vacancies	Anticipated Vacancies
Last Date To Apply	04-02-2026
Written Test Date of HSST Mathematics
Date Of Downloading Hall Tickets
HSST Mathematics PSC Exam Cut-Off Mark
Date Of Publishing Rank List of HSST Mathematics

To prepare for the PSC Degree Level Common Preliminary examination, visit this link.

1. Master's Degree in the Mathematics with not less than 50% marks from any of the Universities in Kerala or a qualification recognized as equivalent thereto in the respective subject by a University in Kerala

2. (1) B.Ed in the Mathematics acquired after a regular course of study from any of the Universities in Kerala or a qualification recognized as equivalent thereto by a University in Kerala.

   (2) In the absence of persons with B.Ed. Degree in the Mathematics subject, B.Ed Degree acquired in the concerned faculty as specified in the Acts and Statutes of any of the Universities in Kerala.

   (3) In the absence of persons with B.Ed. Degree as specified in items (1) and (2) above, persons with B.Ed. Degree in any subject acquired after a regular course of study from any of the Universities in Kerala or a qualification recognized as equivalent thereto by any of the Universities in Kerala.

3. Must have passed the State Eligibility Test (SET) for the post of Higher Secondary School Teacher conducted by Government of Kerala or by the agency authorized by the State Government.

The age limit for a general category applicant is 20 to 40. Refer to the table below for the upper age relaxation for OBC and SC/ST applicants.

S.NO.	CATEGORIES	EXTENT OF AGE CONCESSION
1	General Category	0 years
2	OBC	3 years
3	SC/ST	5 years

Students can check the complete list of Kerala PSC Exam Mock Test and Study Materials from this link.

1. https://www.keralapsc.gov.in/sites/default/files/2026-01/noti-716-721-25.pdf
2. https://www.hseportal.kerala.gov.in/hse/public/institutions
3. https://thulasi.psc.kerala.gov.in/thulasi/
4. https://www.keralapsc.gov.in/shortlists
5. https://www.keralapsc.gov.in/sites/default/files/inline-files/HSST-Mathematics.pdf