GRE Subject Test · Mathematics

Free GRE Subject Test Mathematics Practice, Organised Into 10 Focused Sections

Build a disciplined GRE preparation pathway across calculus, algebra, linear algebra, number theory, analysis, geometry, probability, and undergraduate mathematical reasoning. Begin with free topic-based practice, diagnose weak areas, and move to premium timed and explanation-rich practice when you need greater depth.

Page at a glance
Free accessNo code needed
Sections10
PremiumExpanded bank
PreparationTimed + explained
CalculusAlgebraAnalysisProbability
Free Mathematics Subject Test Practice

Start With Focused GRE Mathematics Subject Test Practice

Use the free pathway to begin immediately, work through one domain at a time, identify recurring weaknesses, and strengthen the knowledge and reasoning patterns tested in GRE Mathematics Subject Test.

  • No access code needed
  • Ten focused GRE sections
  • Targeted revision pathway
  • Direct topic-practice links
Premium Mathematics Subject Test Practice

Move From Topic Revision to Exam-Ready Practice

10domains reinforced through an expanded premium practice pathway

Use premium practice when you need higher-volume questions, worked explanations, broader reinforcement, and timed exam-style preparation across the full pathway.

  • Expanded GRE question bank
  • Worked explanations and error review
  • Timed exam-style practice
  • Reinforcement across all ten domains

Use free practice to diagnose weaknesses, then use premium practice for depth, repetition, explanations, and timed preparation.

GRE exam coverage

What the GRE Subject Test Mathematics Practice Covers

Use the ten sections as a revision map. Review the scope of each domain, then open its corresponding free practice in a new tab.

01 Cross-Cutting Skills and Mathematical ThinkingBuild the flexible mathematical thinking that supports the entire GRE Subject Test in Mathematics, including symbolic fluency, logical precision, fast recognition of standard forms, and the habit of testing edge cases.
  • Algebraic manipulation under time pressure, including factoring, completing the square, simplifying radicals, rationalising, and partial fractions
  • Quantifier logic in definitions and statements involving for all, there exists, infinitely many, and limiting language
  • Constructing counterexamples and checking boundary cases such as 0, 1, -1, endpoints, and equality conditions
  • Moving between symbolic, graphical, geometric, and matrix-based representations of the same idea
  • Recognising standard forms quickly, including Taylor patterns, eigenvalue facts, common integrals, and trigonometric identities
Start Section 1 Free →
02 Single-Variable Differential CalculusStrengthen the differential calculus core of the exam by mastering limits, continuity, derivatives, theorem-based reasoning, and the qualitative interpretation of single-variable functions.
  • Limit laws, one-sided limits, indeterminate forms, and the distinction between removable, jump, and infinite discontinuities
  • Continuity, differentiability, and the meaning of derivative from its definition
  • Product, quotient, chain, implicit, inverse-function, and logarithmic differentiation techniques
  • Mean Value Theorem, Rolle theorem, and consequences for monotonicity and function behaviour
  • Critical points, concavity, inflection, asymptotes, optimisation, graph sketching, and L Hopital rule
  • Taylor and Maclaurin polynomials together with local approximation and error awareness
Start Section 2 Free →
03 Integral Calculus and Infinite SeriesDevelop the integral and series fluency needed for antiderivatives, definite integrals, applications of accumulation, improper integrals, convergence testing, and power series analysis.
  • Antiderivatives, substitution, integration by parts, trigonometric methods, and partial fractions
  • Fundamental Theorem of Calculus, variable limits, and accumulation functions
  • Areas, volumes, average value, and other standard applications of integration
  • Improper integrals over infinite intervals or unbounded integrands and how convergence is judged
  • Comparison, ratio, root, alternating, and integral tests for infinite series
  • Power series, radius and interval of convergence, and term-by-term differentiation or integration
Start Section 3 Free →
04 Multivariable Calculus, Vector Calculus, and Analytic GeometryPrepare for several-variable and geometric reasoning by working with partial derivatives, gradients, multiple integrals, coordinate changes, and major undergraduate vector-calculus ideas.
  • Lines and planes in three dimensions, distances, angles, projections, and recognition of quadrics
  • Partial derivatives, mixed partials, directional derivatives, gradients, tangent planes, and linearisation
  • Double and triple integrals, iterated integrals, changing order, and region description
  • Jacobian-based changes of variables in polar, cylindrical, and spherical coordinates
  • Line integrals, conservative vector fields, potential functions, and interpretation of curl and divergence
  • Green theorem, Stokes theorem, and the Divergence theorem at standard undergraduate usage level
Start Section 4 Free →
05 Differential Equations and Calculus-Based ModelingReview the differential-equation methods that commonly arise through calculus, with emphasis on setup, standard solution forms, qualitative behaviour, and interpretation of mathematical models.
  • Separable first-order equations, linear first-order equations, integrating factors, and recognition of exact equations
  • Slope fields, equilibrium solutions, qualitative behaviour, and stability ideas
  • Second-order linear equations with constant coefficients, including real, repeated, and complex roots
  • Particular solutions for polynomial, exponential, and trigonometric forcing terms
  • Initial value problems, basic boundary-value awareness, and power-series solution concepts
  • Exponential growth and decay, logistic models, and simple harmonic motion interpretations
Start Section 5 Free →
06 Elementary Algebra, Functions, and Complex NumbersSharpen the algebra and function-analysis skills that often feel elementary on paper but become demanding under GRE timing and multiple-choice pressure.
  • Factoring strategies, polynomial identities, rational expressions, inequalities, exponents, and logarithms
  • Domain, range, inverses, composition, monotonicity, symmetry, periodicity, and graph transformations
  • Functional equations and parameter-based reasoning that require clever constraint use
  • Linear and quadratic systems, counting the number of solutions, and discriminant-style interpretation
  • Asymptotic comparison and high-speed symbolic simplification
  • Complex numbers in rectangular and polar form, De Moivre theorem, and roots of unity
Start Section 6 Free →
07 Linear AlgebraBuild command of one of the most important algebra blocks on the exam by revising matrices, vector spaces, linear transformations, and eigenvalue-based reasoning.
  • Matrix operations, inverses, determinants, rank, row reduction, and reduced row-echelon form
  • Consistency, uniqueness, homogeneous versus nonhomogeneous systems, and parametric solution sets
  • Span, linear independence, basis, dimension, and subspaces such as null space and column space
  • Linear transformations, kernel, image, matrix representation, and change of basis
  • Rank-nullity theorem and how dimensions of related spaces connect
  • Characteristic polynomials, eigenvalues, eigenvectors, diagonalisation, and special matrix types
Start Section 7 Free →
08 Abstract Algebra and Proof IdeasPrepare for the abstract-algebra portion by revising essential definitions, theorem consequences, structural relationships, and the proof habits that support group, ring, field, and module questions.
  • Groups, subgroups, cyclic groups, orders of elements, and standard consequences of Lagrange theorem
  • Homomorphisms, isomorphisms, kernels, quotient-group recognition, and permutation-cycle reasoning
  • Rings, integral domains, units, zero divisors, ideals, and ring homomorphisms
  • Polynomial rings and irreducibility over the rational, real, and complex numbers
  • Field extensions, degree ideas, and elementary recognition of finite fields
  • Modules as a generalisation of vector spaces together with core proof-style reasoning
Start Section 8 Free →
09 Number Theory and Modular ReasoningStrengthen the number-theory toolkit used for divisibility, congruences, Diophantine equations, modular inverses, and theorem-based arithmetic shortcuts.
  • Divisibility, greatest common divisor, Euclidean algorithm, Bezout identity, and lcm-gcd relationships
  • Prime factorisation, valuation-style thinking, and structural arithmetic arguments
  • Congruences, modular inverses, linear congruences, and Chinese Remainder Theorem applications
  • Fermat little theorem, Euler totient theorem, and orders modulo n
  • Linear Diophantine equations, solution existence, parameterisation, and impossibility proofs via modular constraints
  • Arithmetic functions such as tau, sigma, and phi in standard GRE-style use
Start Section 9 Free →
10 Additional Topics in Analysis, Discrete Mathematics, Geometry, Probability, and Numerical MethodsCover the additional-topic families that round out the GRE Subject Test in Mathematics, especially analysis, topology, combinatorics, geometry, complex variables, probability, and numerical approximation.
  • Sequences, convergence, continuity, uniform continuity, differentiability, integrability, compactness, and connectedness in introductory analysis
  • Logic, proof methods, set theory, combinatorics, graph theory, and elementary algorithmic ideas
  • Euclidean geometry, coordinate geometry, conic sections, and transformation-based reasoning
  • Complex arithmetic, modulus-argument form, roots of unity, and introductory complex-variable recognition
  • Discrete and continuous probability, expectation, variance, independence, conditional probability, and Bayes rule
  • Numerical methods such as bisection, Newton method, error analysis, and basic numerical integration concepts
Start Section 10 Free →
GRE preparation overview

Why the Free and Premium Mathematics Subject Test Pathways Work Together

“Structured preparation makes it easier to identify what to study next and where more practice is needed.”

This page is designed specifically for GRE Subject Test Mathematics preparation. Its ten sections organise calculus, algebra, linear algebra, number theory, analysis, geometry, probability, and undergraduate mathematical reasoning into manageable domains so candidates can revise deliberately rather than practise at random.

The free pathway is useful for diagnosis and focused revision. The premium pathway adds greater practice depth, worked explanations, repetition, and timed exam-style preparation when you are ready to move beyond isolated topic review.

Candidates building a broader GRE study plan can return to the GRE practice hub or continue with GRE Verbal Reasoning, GRE Quantitative Reasoning, GRE Physics Subject Test, GRE Psychology Subject Test.

Better diagnosisTopic separation makes weak GRE domains easier to identify, revisit, and track.
Efficient revision flowMove between concept review, reasoning, application, and timed practice in a deliberate sequence.
Stronger GRE readinessFocused repetition supports accuracy, speed, confidence, and disciplined decision-making.
Have questions?

GRE Subject Test Mathematics Frequently Asked Questions

Ten targeted answers about using this specific GRE Mathematics Subject Test preparation pathway effectively.

What does this Mathematics Subject Test page cover?

The page organises calculus, algebra, linear algebra, number theory, analysis, geometry, probability, and undergraduate mathematical reasoning into ten focused GRE practice sections so you can revise the tested knowledge and reasoning skills systematically.

Are the ten Mathematics Subject Test practice sections free?

Yes. The ten topic-based practice sections can be opened without an access code. They are designed for diagnosis, focused revision, and repeated practice before moving to the premium pathway.

What is included in premium Mathematics Subject Test practice?

The premium pathway provides a larger GRE Mathematics Subject Test question bank, worked explanations, timed exam-style practice, and broader reinforcement across the ten domains on this page.

How should I use the ten Mathematics Subject Test sections?

Start with the domain where your accuracy is weakest, complete focused practice, review errors carefully, and then rotate through the remaining sections so preparation becomes balanced rather than concentrated in one area.

Can I use this page for timed GRE Mathematics Subject Test preparation?

Yes. Use the free sections first for topic control and error diagnosis, then use the premium pathway for higher-volume and timed exam-style practice when you are ready to train under greater pressure.

How do I identify weak areas in Mathematics Subject Test?

Compare your accuracy and confidence across the ten sections, especially across calculus, algebra, linear algebra, number theory, analysis, geometry, probability, and undergraduate mathematical reasoning. Repeated errors in one section indicate where additional concept review and practice are needed.

Does the Mathematics Subject Test page include worked explanations?

The premium pathway is designed to include worked explanations so that mistakes can be reviewed systematically. The free pathway is primarily organised for immediate topic-based practice and diagnosis.

Should I complete the Mathematics Subject Test sections in numerical order?

Not necessarily. The numbered structure gives you a clear revision map, but you can begin with the section that needs the most attention and return to other sections as your preparation develops.

How should I move from free to premium Mathematics Subject Test practice?

Use the free sections to establish your baseline and identify recurring weaknesses. Move to premium when you need a larger question bank, worked explanations, broader reinforcement, and timed practice for exam readiness.

Can this page be used as part of a complete GRE study plan?

Yes. Combine this Mathematics Subject Test pathway with the other GRE practice areas available from the GRE hub, while allocating more revision time to the domains where your results show the greatest need.