GATE 2025 Mathematics 90-Day Preparation Strategy: Syllabus, Mock Tests, Previous Papers & Recommended Books

| Updated On - Nov 8, 2024

GATE 2025 is scheduled for 1, 2, 15, and 16 February. IIT Roorkee has officially released GATE 2025 syllabus for all 30 subjects over its official website, including Mathematics.

Preparing for the GATE Mathematics 2025 requires a precise and data-driven strategy which will help the candidate master 13 major topics, from Calculus to Functional Analysis. Approximately 1,50,000 candidates appear for the GATE exam each year.

This 90-day plan divides the preparation into 13 weeks, it allocates an average of 30 hours per week, which is equal to 390 hours of focused study. Each week covers 2–3 critical subtopics, including 20+ exercises on Metric Spaces, 50+ questions on convergence theorems, and over 40 questions on Differential Equations, ensuring rigorous conceptual practice. Previous Years' Papers from 2015 to 2024 and Mock tests set comprising 65 questions are provided to help the candidates identify high-weighting areas.

For better preparation books are also recommended such as “Higher Engineering Mathematics” by B.S. Grewal for Differential Equations and “Real Analysis” by H.L. Royden. This ensures that the candidate covers all 10+ advanced topics, while mock tests add an average of 180 additional practice questions.

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GATE 2025 Mathematics 90-Day Preparation Strategy (Weeks 1–5)

Preparation Overview: Weekly and Daily Focus

This table provides a breakdown of main weekly objectives and daily activities for a systematic approach to mastering each topic.

Week	Main Topic	Weekly Focus	Daily Study Tasks	Total Weekly Hours
1	Calculus: Derivatives & Integrals	Basics of functions, continuity Partial & directional derivatives Applications in total derivatives	Days 1-2: Review functions and limits Days 3-4: Partial & directional derivatives Days 5-7: Practice total derivatives with real-world problems	30 hours
2	Calculus: Applications of Integrals	Double & triple integrals Area, volume, and surface area	Days 1-3: Double integrals practice (10+ exercises/day) Days 4-5: Triple integrals and applications Days 6-7: Review and practice integrals in mixed exercises	25 hours
3	Vector Calculus	Gradient, divergence, curl Line, surface integrals and theorems	Days 1-3: Gradient, divergence, curl Days 4-5: Line integrals Days 6-7: Practice theorems: Green’s, Gauss, Stokes	28 hours
4	Linear Algebra: Vector Spaces & Transformations	Vector spaces, linear transformations Matrix representations, rank, nullity	Days 1-3: Vector spaces concepts (50 questions) Days 4-5: Transformations & matrix rep. Days 6-7: Practice 40 exercises on rank & nullity	30 hours
5	Linear Algebra: Eigenvalues & Matrix Theory	Eigenvalues, eigenvectors Orthogonal and Hermitian matrices	Days 1-3: Focus on eigenvalues & diagonalization Days 4-5: Orthogonal matrices Days 6-7: Practice eigenvalue-based problems	28 hours

GATE Mathematics 2025 Topic-Specific Exercises for Weeks 1-5

This section details topic-specific practice goals, covering essential exercises and estimated time for each task.

Topic	Daily Exercises	Weekly Practice Goals	Estimated Time Per Week
Calculus: Derivatives	5-7 questions on derivatives	50 exercises covering partial, directional, and total derivatives	8 hours
Calculus: Integrals	10 questions on integrals	70 exercises on double/triple integrals and applications	12 hours
Vector Calculus	10 questions on vector ops	50 questions across gradient, divergence, and integrals	10 hours
Linear Algebra	8-10 questions per matrix type	60 exercises on transformations, rank, and eigenvalues	12 hours
Matrix Theory (Adv.)	5 questions on matrix types	40 questions on orthogonal, Hermitian properties	8 hours

GATE Mathematics 2025 Mock Tests and Revision Strategy for Weeks 1–5

Implementing mock tests and targeted revision will reinforce concepts covered in the first five weeks.

Week	Mock Test Focus	Number of Questions	Weekly Revision Focus	Total Hours
1	Calculus (Partial/Total Derivatives)	30	Revise functions and continuity	5 hours
2	Calculus (Applications of Integrals)	30	Review exercises on area & volume	5 hours
3	Vector Calculus	30	Focus on Green’s & Stokes’ theorems	5 hours
4	Linear Algebra Basics	30	Matrix rep. and transformation review	5 hours
5	Linear Algebra (Advanced)	30	Eigenvalues, orthogonal matrices	5 hours

GATE 2025 Mathematics 90-Day Preparation Strategy (Weeks 6–10)

GATE 2025 Mathematics Preparation Weekly and Daily Focus Tasks

Week	Main Topic	Weekly Focus	Daily Study Tasks	Total Weekly Hours
6	Real Analysis: Metric Spaces & Convergence	Metric spaces, connectedness, compactness Sequences, series of functions	Days 1-2: Metric spaces (20 exercises) Days 3-5: Compactness, connectedness (30 exercises) Days 6-7: Series and uniform convergence (50+ questions)	30 hours
7	Real Analysis: Lebesgue Integration & Convergence Theorems	Lebesgue measure, measurable functions Fatou’s Lemma, Monotone & Dominated Convergence	Days 1-3: Measure and integration basics Days 4-5: Convergence theorems practice (50 questions) Days 6-7: Mixed exercises on convergence theorems	28 hours
8	Complex Analysis Part I	Complex functions, analytic functions Harmonic functions and basic complex integration	Days 1-3: Continuity and analytic functions Days 4-5: Basic integration exercises (Cauchy’s theorem and formula) Days 6-7: 40 questions on harmonic and analytic functions	30 hours
9	Complex Analysis Part II	Taylor and Laurent series Zeros, singularities, and Residue theorem	Days 1-2: Power series, convergence (25 exercises) Days 3-5: Residue theorem applications Days 6-7: Practice evaluating real integrals using residue theory	28 hours
10	Differential Equations: Basic ODEs	First-order ODEs, existence and uniqueness Higher-order linear ODEs with constant coefficients	Days 1-3: Practice on first-order equations Days 4-5: 40 questions on higher-order linear ODEs Days 6-7: Mixed exercises with initial value problems	30 hours

GATE 2025 Mathematics Topic-Specific Exercises for Weeks 6–10

This section highlights essential practice exercises across Real Analysis, Complex Analysis, and Differential Equations.

Topic	Daily Exercises	Weekly Practice Goals	Estimated Time Per Week
Real Analysis: Metric Spaces	8-10 questions	50+ questions across metric spaces and compactness	10 hours
Lebesgue Integration	7-10 questions on measurability	30-40 questions on measurable functions and convergence	10 hours
Complex Analysis: Series	5-7 questions on Taylor series	40 questions on Taylor, Laurent, and Residue theorem	8 hours
Differential Equations	10 questions on ODEs	70 questions covering first-order, higher-order, and IVP	12 hours

GATE 2025 Mathematics Mock Tests and Revision Strategy for Weeks 6–10

Weekly mock tests and review tasks help reinforce concepts and identify areas requiring additional practice.

Week	Mock Test Focus	Number of Questions	Weekly Revision Focus	Total Hours
6	Real Analysis: Compactness & Convergence	30	Review metric space exercises	5 hours
7	Real Analysis: Lebesgue Integration	30	Focus on convergence theorems	5 hours
8	Complex Analysis Basics	30	Revise analytic and harmonic functions	5 hours
9	Complex Analysis (Advanced)	30	Power series, Laurent series, residue applications	5 hours
10	Differential Equations (ODEs)	30	Review of higher-order ODEs and initial value problems	5 hours

GATE 2025 Mathematics 90-Day Preparation Strategy (Weeks 11–13)

GATE 2025 Mathematics Weekly and Daily Focus Tasks for Preparation

Week	Main Topic	Weekly Focus	Daily Study Tasks	Total Weekly Hours
11	Differential Equations: Advanced ODEs & PDEs	Laplace transforms, Cauchy-Euler equations First-order PDEs and characteristics method	Days 1-3: Laplace and Cauchy-Euler equations Days 4-5: Practice first-order PDEs (50+ exercises) Days 6-7: Mixed exercises	30 hours
12	Algebra & Topology	Groups, subgroups, quotient groups Topology basics: bases, connectedness, compactness	Days 1-2: 40 questions on group theory Days 3-4: Homomorphisms and automorphisms Days 5-7: Topology basics and practice	28 hours
13	Functional & Numerical Analysis	Banach & Hilbert spaces, projection theorem Numerical methods for linear equations	Days 1-2: Practice 30 exercises on Banach and Hilbert spaces Days 3-5: Numerical methods (Gaussian elimination, LU decomposition) Days 6-7: Conclude with Jacobi and Gauss-Seidel methods	30 hours

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GATE 2025 Mathematics Topic-Specific Exercises for Weeks 11–13

This section emphasizes exercises for advanced differential equations, algebra, topology, and numerical analysis, providing depth for each subtopic.

Topic	Daily Exercises	Weekly Practice Goals	Estimated Time Per Week
Differential Equations (Adv.)	10-12 questions on advanced ODEs & PDEs	50 questions on PDE methods and Laplace transforms	12 hours
Group Theory	8-10 questions	50 exercises on group structures, automorphisms	8 hours
Topology	7-10 questions on bases and compactness	30 exercises across topology basics	8 hours
Numerical Analysis	8-10 questions on iterative methods	40 exercises on Gaussian, LU, Jacobi, and Gauss-Seidel	10 hours

GATE 2025 Mathematics Mock Test Strategy

The final review emphasizes testing, mock exams, and focused revision based on previous weeks’ performances.

Days	Focus Area	Daily Tasks	Total Hours
Day 1-2	Calculus & Linear Algebra	Review key exercises on integrals, derivatives, eigenvalues Mock Test: Calculus	6 hours each
Day 3-4	Real & Complex Analysis	Practice mixed questions on convergence, residue theorem Mock Test: Complex Analysis	6 hours each
Day 5-6	Differential Equations & Algebra	Focused revision on ODEs, group theory Mock Test: Differential Equations	6 hours each
Day 7-8	Functional & Numerical Analysis	Mixed exercises on Banach spaces, iterative methods Mock Test: Numerical Analysis	6 hours each
Day 9-10	Full-Length Mock Exams	Two full-length mock tests, focusing on time management and revision of weak areas	8 hours each

GATE 2025 Mathematics Recommended Books

Students’ preferences for study materials and books play a significant role in exam success. Here’s a comparison of popular resources based on user ratings and effectiveness:

Book Title	Author	Avg. Rating (out of 5)	Recommended for
Higher Engineering Mathematics	B.S. Grewal	4.7	Calculus, Algebra
Advanced Engineering Mathematics	Erwin Kreyszig	4.6	Differential Equations
Linear Algebra and Its Applications	Gilbert Strang	4.8	Linear Algebra
Real Analysis	Royden & Fitzpatrick	4.5	Real Analysis
Introductory Functional Analysis with Applications	Erwin Kreyszig	4.6	Functional Analysis

Also check: GATE 2025 Mathematics Recommended Books

GATE 2025 Mathematics Previous Years’ Papers with answer keys

Preparing for GATE 2025 Mathematics becomes so much more effective if someone utilizes the question papers for past years.

This gives an aspirant an opportunity to get familiar with an exam pattern, types of questions asked, and the problem of difficulty level. I've included all the GATE Mathematics papers from 2014 to 2024 along with answer keys to provide all kinds of practice. Use the table below to easily download PDFs by year along with session details and incorporate such useful material into your studies.

Exam DATE	Session	Question Paper PDF
2024	Afternoon Session	click here
2023	Forenoon Session	click here
2022	Forenoon Session	click here
2021	Forenoon Session	click here
2020	Forenoon Session	click here
2019	Afternoon Session	click here
2018	Afternoon Session	click here
2017	Afternoon Session	click here
2016	Afternoon Session	click here
2015	Afternoon Session	click here
2014	Forenoon Session	click here