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Key Facts: GRE Math Subject Test Exam

~66 questions

Exam Length

ETS GRE Subject Test Content & Structure

2 hrs 50 min

Time Limit

ETS GRE Subject Test Overview

200–990

Score Scale

ETS GRE Score Reporting

~50% Calculus

Largest Content Area

ETS GRE Mathematics Content Outline

$199

Registration Fee (Worldwide)

ETS GRE Subject Test Fees (effective August 1, 2026)

3× per year

Test Dates

ETS GRE Subject Test Schedule (Sept, Oct, Apr)

The GRE Mathematics Subject Test contains approximately 66 five-choice questions and lasts 2 hours 50 minutes, with scores reported on a 200–990 scale. Calculus accounts for roughly 50% of questions, algebra (including linear, abstract, and number theory) for ~25%, and additional topics for ~25%. ETS administers the computer-delivered test during September, October, and April windows at test centers and, where available, at home. ETS sets no passing score; applicants should check each graduate program's current requirements and interpret scores with ETS percentile data.

Sample GRE Math Subject Test Practice Questions

Try these sample questions to review concepts for the GRE Math Subject Test exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Find the derivative of f(x) = x³ ln(x).
A.3x² ln(x) + x²
B.3x² ln(x) + x
C.x² ln(x) + x²
D.3x ln(x) + x²
Explanation: By the product rule, f'(x) = 3x² · ln(x) + x³ · (1/x) = 3x² ln(x) + x². The product rule states (uv)' = u'v + uv'.
2Evaluate ∫₀¹ x·eˣ dx.
A.1
B.e − 1
C.e + 1
D.2e − 2
Explanation: Integration by parts with u = x, dv = eˣ dx gives uv − ∫v du = x·eˣ − ∫eˣ dx = x·eˣ − eˣ. Evaluating from 0 to 1: (e − e) − (0 − 1) = 0 + 1 = 1.
3Let f(x) = (x² − 4)/(x − 2). What is lim_{x→2} f(x)?
A.0
B.2
C.4
D.undefined
Explanation: Factor the numerator: x² − 4 = (x−2)(x+2). So f(x) = x+2 for x ≠ 2. The limit as x→2 is 2+2 = 4.
4If f(x) = arctan(x), find f'(x).
A.1/(1 + x²)
B.1/√(1 − x²)
C.−1/(1 + x²)
D.1/(1 − x²)
Explanation: The standard derivative formula is d/dx[arctan(x)] = 1/(1 + x²). This follows from implicit differentiation of tan(y) = x.
5Find the area enclosed between y = x² and y = x over [0, 1].
A.1/6
B.1/3
C.1/2
D.1/4
Explanation: On [0,1], x ≥ x², so the area = ∫₀¹ (x − x²) dx = [x²/2 − x³/3]₀¹ = 1/2 − 1/3 = 1/6.
6Which of the following is the general solution to the ODE dy/dx = 2xy?
A.y = Ce^(x²)
B.y = Ce^(2x)
C.y = C·x²·e^x
D.y = Ce^(x² + C)
Explanation: Separating variables: dy/y = 2x dx. Integrating: ln|y| = x² + K, so y = Ce^(x²) where C = ±e^K is an arbitrary constant.
7For the series Σ_{n=1}^{∞} 1/n², which of the following is true?
A.It diverges by the comparison test
B.It converges to π²/6
C.It converges to 1
D.It converges but its sum cannot be determined
Explanation: The series Σ 1/n² is a p-series with p = 2 > 1, so it converges. By the Basel problem (Euler), the sum equals π²/6 ≈ 1.645.
8Find ∂f/∂y for f(x, y) = x³y² + sin(xy).
A.2x³y + x·cos(xy)
B.3x²y² + y·cos(xy)
C.2xy + x·cos(xy)
D.3x²y² + cos(xy)
Explanation: ∂f/∂y = x³·(2y) + cos(xy)·(x) = 2x³y + x·cos(xy). Treat x as a constant when differentiating with respect to y.
9Determine all critical points of f(x) = x³ − 3x + 1.
A.x = 1 only
B.x = −1 only
C.x = ±1
D.x = 0 only
Explanation: f'(x) = 3x² − 3 = 3(x²−1) = 3(x−1)(x+1). Setting f'(x) = 0 gives x = 1 and x = −1. Both are critical points.
10What is the radius of convergence of the power series Σ_{n=0}^{∞} nˣⁿ / n!?
A.0
B.1
C.e
D.∞
Explanation: By the ratio test: |a_{n+1}/a_n| = |(n+1)x^{n+1}/((n+1)!) · n!/nxⁿ| = |x|/(n+1) → 0 for all finite x. Since the limit is 0 < 1 for every x, the radius of convergence is ∞.

About the GRE Math Subject Test Exam

The GRE Mathematics Subject Test is a computer-delivered exam of approximately 66 multiple-choice questions designed to assess undergraduate mathematics knowledge. It is offered in September, October, and April each year. The test covers calculus (~50%), algebra (~25%), and additional topics such as real analysis, topology, complex variables, and probability (~25%). ETS describes it as intended for test takers who majored in mathematics or have an extensive mathematics background.

Exam sponsor: Educational Testing Service (ETS). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Questions

66 questions

Time Limit

2 hours 50 minutes

Passing Score

Scored 200–990 (no universal passing score; programs set their own cutoffs)

Exam / Certification Fees

$199 worldwide

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

~50%

Calculus and Applications

Single-variable calculus (limits, derivatives, integrals, arc length, optimization), multivariable calculus (partial derivatives, gradients, double/triple integrals, Jacobians, Green's/Stokes' theorems), differential equations (separable, linear first-order, second-order linear with constant coefficients, Bernoulli equations), and sequences and series (convergence tests, Taylor/Maclaurin series, power series, radius of convergence).

~25%

Algebra

Elementary algebra; linear algebra (vector spaces, subspaces, rank-nullity theorem, eigenvalues and eigenvectors, determinants, diagonalization, and characteristic polynomials); abstract algebra (groups, rings, ideals, modules, and fields); and number theory.

~25%

Additional Topics

Real analysis (sequences and series of numbers and functions, continuity, differentiability, integrability, and elementary topology of R and R^n); logic, set theory, combinatorics, graph theory, and algorithms; plus general topology, geometry, complex variables, probability and statistics, and numerical analysis.

Preparing for the GRE Math Subject Test Exam

What You Need to Know

  • Passing score: Scored 200–990 (no universal passing score; programs set their own cutoffs)
  • Exam length: 66 questions
  • Time limit: 2 hours 50 minutes
  • Exam / certification fees: $199 worldwide Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

GRE Math Subject Test: Suggested Study Strategy

1Master the fundamental theorems: IVT, MVT, Heine-Borel, Cauchy-Riemann, Lagrange's theorem — expect questions that ask you to identify which theorem applies.
2Drill convergence tests for series: ratio test, root test, comparison, integral test, and alternating series test — know which to apply and why.
3Review all standard group types (cyclic, symmetric, dihedral, quotient groups) and their orders, generators, and homomorphisms.
4Practice contour integration using Cauchy's theorem, Cauchy's integral formula, and residues so you can recognize which tool fits a given integrand and contour.
5Time yourself strictly: 66 questions in 170 minutes = about 2.5 minutes per question — learn to skip and return to hard questions.

Frequently Asked Questions

Who should take the GRE Mathematics Subject Test?

ETS describes the test as intended for students who majored in mathematics or have an extensive mathematics background. Whether to submit it is program-specific, so consult each graduate department's current admissions requirements.

What score do I need on the GRE Math Subject Test?

There is no universal passing or target score. ETS reports a scaled score and percentile rank; compare those data with the current requirements or recommendations published by each graduate program.

How is the GRE Math Subject Test scored?

Scores are reported on a 200–990 scale in 10-point increments. The raw score (number of correct answers) is converted to a scaled score, and there is no penalty for incorrect answers, so test takers should answer every question.

When is the GRE Mathematics Subject Test offered?

ETS offers the Mathematics Subject Test three times per year: September, October, and April. The test is computer-delivered at Prometric test centers and via at-home testing. Register several weeks in advance to secure a preferred date and location.

What undergraduate topics should I review?

Prioritize single and multivariable calculus (the largest section), then real analysis, linear algebra, abstract algebra, and differential equations. Spend secondary effort on complex variables, topology, number theory, probability, and discrete mathematics.

How long should I study for the GRE Math Subject Test?

Study time depends on your undergraduate preparation and diagnostic results. Start with the ETS official practice book, map missed questions to the published content outline, and schedule enough review to cover all three weighted domains plus timed practice.