GRE Subject Test in Mathematics
GRE Mathematics Subject Test
Calculus, algebra and the rest of undergraduate mathematics as the Subject Test asks it, with original problems.
AI-drafted · awaiting expert reviewGRE Mathematics Test as described by ETS for the 2026–27 testing year (policies in effect July 1, 2026 to June 30, 2027): computer-delivered, approximately 66 multiple-choice questions in 2 hours 50 minutes, content specifications from ETS's Mathematics Test fact sheet and practice book.
A complete course for the GRE Subject Test in Mathematics, organized by ETS's content specifications: calculus of one and several variables with differential equations (about half the test), elementary, linear and abstract algebra with number theory (about a quarter), and the additional topics ETS lists (introductory real analysis, discrete mathematics, general topology, geometry, complex variables, probability and statistics, and numerical analysis). Each lesson teaches the mathematics rigorously, then the fast, reliable techniques and classic traps that matter when there are about 66 five-choice questions and no calculator. Every lesson and problem is original, with full explanations, and a full-length 66-question practice exam is weighted like the specification.
About the exam
- The Mathematics Test consists of approximately 66 multiple-choice questions drawn from standard undergraduate courses. The total testing time is 2 hours and 50 minutes, and the test is not divided into separately timed sections.GRE Subject Test Content and Structure · Practice Book for the GRE Subject Test in Mathematics
- Content weights are about 50% calculus (differential and integral calculus of one and several variables, with applications and connections to coordinate geometry, trigonometry and differential equations), about 25% algebra (elementary, linear and abstract algebra, and number theory) and about 25% additional topics (introductory real analysis; discrete mathematics; and other topics: general topology, geometry, complex variables, probability and statistics, numerical analysis). ETS says these percentages are estimates that vary somewhat from one edition to another.The GRE Mathematics Test (fact sheet with the content specifications) · Practice Book for the GRE Subject Test in Mathematics
- Each question has five answer choices. In the practice book's directions, a logarithm with no base shown is the natural logarithm, and Z, Q, R and C denote the integers, rationals, reals and complex numbers.Practice Book for the GRE Subject Test in Mathematics
- The score is based on the number of questions answered correctly; nothing is subtracted for wrong answers, so it pays to answer every question. All questions carry equal weight.Strategies and Tips for the GRE Subject Tests · Practice Book for the GRE Subject Test in Mathematics
- The number correct is converted to a total scaled score reported on a 200–990 scale in 10-point increments, equated so that equal scaled scores mean essentially equal performance across editions. ETS describes content-area subscores only for the Physics and Psychology Tests, so a Mathematics Test result is the single total score. Scores are reportable for 5 years.Understanding Your GRE Subject Test Scores · Getting Your GRE Subject Test Scores · GRE Subject Tests (information for score users)
- The GRE Subject Tests are computer-delivered at test centers worldwide, and can also be taken at home on select dates within the testing windows.GRE Subject Test Content and Structure · Register for the GRE: Test Dates and Registration (frequently asked questions) · Taking a GRE Subject Test At Home
- No onscreen calculator is available for the Subject Tests, and personal calculators are not permitted unless approved as an accommodation. There is no break during a Subject Test. Test centers supply scratch paper; at home you use one small whiteboard or one sheet in a transparent sleeve with an erasable marker.GRE Information Bulletin 2026–27 · Strategies and Tips for the GRE Subject Tests
- For the 2026–27 testing year the Subject Test windows are September 14–27, 2026 (scores reported October 5, 2026), October 19–November 1, 2026 (scores reported November 9, 2026) and April 19–May 2, 2027 (scores reported May 10, 2027). A Subject Test may be taken once every 14 days.GRE Subject Tests (information for score users) · Getting Your GRE Subject Test Scores · Register for the GRE: Test Dates and Registration (frequently asked questions)
- The registration fee for a GRE Subject Test is 199 U.S. dollars worldwide; fee reductions may be available to eligible test takers.Register for the GRE: Test Dates and Registration (frequently asked questions)
Syllabus
21 lessons, 208 practice questions and 1 timed practice exam.
Getting started
The test and how to work it
What ETS says the Mathematics Test contains, how it is timed and scored, and the multiple-choice techniques that save minutes on every page.
- The Mathematics Test and how to work itFree sample35 min
Calculus (about 50%)
Limits, derivatives and their uses
Limits and continuity, the derivative and its rules, and the mean value theorem, optimization, related rates and curve behaviour built on them.
- Limits and continuityFree sample45 min
- Derivatives and their applications(included with the course)50 min
Integrals and series
The fundamental theorem, every standard technique of integration, improper integrals, areas, volumes and lengths, and infinite series with Taylor expansions.
- Techniques of integration(included with the course)55 min
- Applications of integration, parametric and polar curves(included with the course)50 min
- Sequences, series and Taylor expansions(included with the course)55 min
Multivariable calculus
Vectors, lines and planes, partial derivatives, gradients and constrained extrema, multiple integrals in any coordinate system, and the theorems of Green, Stokes and Gauss.
- Vectors, partial derivatives and optimization in several variables(included with the course)55 min
- Multiple integrals and vector calculus(included with the course)60 min
Differential equations
First-order equations, linear equations with constant coefficients, systems, and the qualitative facts the test likes to probe.
- Differential equations(included with the course)55 min
Algebra (about 25%)
Elementary algebra
Polynomials and their roots, inequalities, exponents and logarithms, trigonometric identities and finite sums: the precalculus that ETS warns can be among the hardest questions.
- Elementary algebra and precalculus(included with the course)50 min
Linear algebra
Systems of equations, vector spaces, rank and nullity, determinants, linear transformations, characteristic polynomials, eigenvalues and eigenvectors.
- Linear systems, vector spaces and determinants(included with the course)55 min
- Characteristic polynomials, eigenvalues and eigenvectors(included with the course)55 min
Abstract algebra and number theory
Groups, rings, modules and fields at the level of a first course, and the number theory of divisibility and congruences.
- Group theory(included with the course)60 min
- Rings, fields and modules(included with the course)55 min
- Number theory(included with the course)50 min
Additional topics (about 25%)
Real analysis and topology
Sequences and series of numbers and functions, continuity, differentiability and integrability, the topology of the real line and of ℝⁿ, and general topology.
- Introductory real analysis(included with the course)60 min
- Topology of the real line, metric spaces and general topology(included with the course)55 min
Discrete mathematics
Logic, set theory, combinatorics, graph theory and reading algorithms.
- Discrete mathematics(included with the course)60 min
Complex variables, probability, geometry and numerical analysis
Analytic functions and residues, probability and statistics, Euclidean and analytic geometry, and the basic numerical methods.
- Complex variables(included with the course)60 min
- Probability and statistics(included with the course)55 min
- Geometry and numerical analysis(included with the course)55 min
Practice exams
- Full-length practice exam 166 questions · 170 minutesIncluded with the course
Free official resources
Use these alongside the course. They are free, and they are the final word.
- Practice Book for the GRE Subject Test in Mathematics (free PDF)ETS's free full-length practice test with answer key and score conversion. Take it under timed conditions (2 hours 50 minutes) once you have worked through the course.
- GRE Mathematics Test fact sheet (content specifications)The official list of topics and their approximate weights.
- GRE Subject Test Content and StructureETS's overview of the Mathematics Test's length, timing and content areas.
- Strategies and Tips for the GRE Subject TestsHow the mark-and-review screen works, scoring, timing and note-taking materials.
- GRE Information Bulletin 2026–27 (PDF)Registration, test-day rules (including the calculator policy), score reporting and dates.
- Getting Your GRE Subject Test ScoresScore scale, reporting dates for each window, and what score reports contain.
GRE is a registered trademark of ETS, which is not affiliated with and does not endorse Lumenary Prep. Every lesson and question here is original; use ETS's free official practice book alongside it. Every source this course cites.