Mathematics

This is a complete, free study companion for Mathematics — built around what the exam actually asks. The topics examiners repeat most are Eigenvalues, Eigenvectors, Eigenspaces, Algebraic and Geometric Multiplicity, Definite Integral Evaluation Using Symmetry and Substitution, and Convergence Tests for Infinite Series. The syllabus runs to 9 chapters. Below you'll find the full topic-frequency ranking, the exam paper pattern, every chapter, a step-by-step study plan, and the official downloads — everything in one place.

Everything here is free. We're an independent student resource, not the official GATE body, so always confirm the current syllabus and exam dates on the official GATE website before you rely on them.

Key information

Level: MA
Programme: Mathematics
Exam: GATE Mathematics Exam (MA)
Conducted by: IISc and IIT

Most frequently examined topics

#	Topic	Times asked
1	Eigenvalues, Eigenvectors, Eigenspaces, Algebraic and Geometric Multiplicity	7
2	Definite Integral Evaluation Using Symmetry and Substitution	6
3	Convergence Tests for Infinite Series	6
4	Basis and Dimension of Vector Subspaces	6
5	Kernel, Image, Rank and Nullity of Linear Transformations	6
6	Diagonalization of Matrices over R or C	6
7	Standard Limits and Algebra of Limits	5
8	Ordinary Derivatives of Composite, Implicit and Inverse Functions	5
9	Taylor and Maclaurin Expansion with Remainder or Coefficients	5
10	Local Extrema and Saddle Points	5
11	Improper Integral Convergence	5
12	Double Integrals and Change of Order	5

Counted across the official previous-year question papers we have analysed for this subject. It shows what has been asked before — it does not predict what will appear in your exam. Always confirm the current syllabus on the official portal.

What you will study (chapters)

Chapter 1: Limits and Continuity
Chapter 2: Differentiation
Chapter 3: Applications of Derivatives
Chapter 4: Techniques of Integration
Chapter 5: Definite Integrals and Applications
Chapter 6: Sequences and Series
Chapter 7: Vectors, Vector Spaces, and Linear Transformations
Chapter 8: Matrices, Systems of Linear Equations, and Eigenvalues
Chapter 9: Ordinary Differential Equations and Applications

How to study Mathematics and score well

Start with the highest-frequency topics — In Mathematics, Eigenvalues, Eigenvectors, Eigenspaces, Algebraic and Geometric Multiplicity, Definite Integral Evaluation Using Symmetry and Substitution, Convergence Tests for Infinite Series, and Basis and Dimension of Vector Subspaces appear again and again in past papers. Master these first — they return the most marks for the time you put in.
Practise with previous-year papers — Solve the last 5–10 years of GATE Mathematics papers under timed, exam-like conditions. Past papers show exactly which topics repeat and how questions are worded.
Revise actively, not passively — Write a one-page summary for each of the 9 chapters — key definitions, formulas and the points examiners reward — then re-test yourself instead of re-reading.
Mark your answers with the official scheme — After each practice paper, score yourself against the official marking scheme. It shows how marks are awarded step-by-step, so you learn to present answers the way examiners expect.

Exam tips: how to score higher in Mathematics

Where students lose marks: attempting questions they have not truly eliminated options for, spending too long on one hard question, and rushing the sections they know best. Read the whole paper first, bank the marks you are sure of, and come back to the rest.

Manage your time and guess carefully: split your time in proportion to the marks each section carries and keep a few minutes at the end to check. This paper carries negative marking, so attempt a question only when you can rule out at least one or two options — a blind guess costs you marks. Confirm the exact marking scheme for your session on the official portal.

Frequently asked questions

What are the most important topics in Mathematics?

Based on past papers, the most frequently asked topics include Eigenvalues, Eigenvectors, Eigenspaces, Algebraic and Geometric Multiplicity, Definite Integral Evaluation Using Symmetry and Substitution, Convergence Tests for Infinite Series. The full ranked list with how often each appears is in the "Most important topics" section above.

Where can I download Mathematics previous-year question papers?

Official GATE previous-year question papers are available on the official GATE website. Open the Question Papers section for the direct link, plus the exam pattern and the topics that repeat most.

How can I prepare for Mathematics faster?

Start with the highest-frequency topics, learn the exam pattern so you know how each section is marked, and practise with past papers. A subject-aware study tutor can quiz you on exactly these topics.

A Gyani AI tutor trained on the Mathematics syllabus and past papers can quiz you on the most-asked topics and show you exactly what to revise.