50%
Calculus
- Limits & continuity
- Derivatives & applications
- Integrals & techniques
- Sequences & series
- Multivariable calculus
Largest section — but many questions depend on clean algebra and trig.
Guide
How to Prepare for the GRE Math Subject Test
A practical guide to what the test covers, where most people get stuck, and how to build a study plan that actually raises your score.
66 questions · 170 minutes
How the test breaks down by weight
Calculus
~33 questions
~33 questions
Algebra
~17 questions
~17 questions
Additional
~16 questions
~16 questions
Most calculus errors trace back to weak algebra or trig — the real starting point is usually earlier than you think.
What the test covers
Know what you're facing before you start studying.
The GRE Math Subject Test covers a wide range of undergraduate mathematics. Here's roughly how the 66 questions break down.
25%
Algebra
- Linear algebra & eigenvalues
- Abstract algebra & groups
- Number theory
- Modular arithmetic
Includes both concrete computation and proof-style reasoning.
25%
Additional Topics
- Combinatorics & probability
- Logic & set theory
- Topology basics
- Real analysis concepts
These vary from test to test — high-value if you can pick up easy points.
Don't study in exam-outline order.
The exam outline lists calculus, algebra, and additional topics as separate categories. But studying them in that order usually backfires. Here's why:
- 1Shaky algebra or trig makes calculus practice wasted effort.
- 2One weak foundation can silently break 5–10 later topics.
- 3Start with your weakest prerequisite, not the hardest topic.
Study in prerequisite order instead.
A smarter study plan works backward from what's blocking you:
- 1Shore up expression fluency — fractions, factoring, exponents, sign rules.
- 2Rebuild trig and graph reading — stop them from slowing down calculus.
- 3Then tackle calculus — limits, derivatives, integrals click faster now.
- 4Layer in algebra and additional topics — linear algebra, number theory, combinatorics.
Public topic pages
Free topic guides for every major area.
Pick a topic below to start reviewing. Each guide covers key concepts, common mistakes, and practice problems.
GRE Math Subject Test topic guides: start with the topics that unlock the most progress.
High-impact GRE Mathematics Subject Test topic guides built from the Math GRE Studio concept graph.
Simplify $$\frac{x^2-9}{x^2-3x}$$ and state all excluded values.
Algebra review
Simplify multi-step expressions without introducing sign or domain errors.
Let $$f(x)=x^2+1$$ and $$g(x)=3x-2$$. Find $$(f\circ g)(x)$$.
Functions review
Read and use function notation comfortably.
For $$f(x)=\frac{x-1}{x+2}$$, identify the x-intercept, vertical asymptote, and horizontal asymptote.
Graph behavior review
Recognize major graph families and their signature behavior.
Find $$\sin(5\pi/6)$$.
Trigonometry review
Use the unit circle and reference-angle logic fluently.
Evaluate $$\lim_{x\to 3} \frac{x^2-9}{x-3}$$.
Limits and continuity
Interpret limits numerically, graphically, and algebraically.
Differentiate $$f(x)=(3x^2-1)^5$$.
Derivatives review
Interpret the derivative as rate of change and slope.
Evaluate $$\int_0^2 (3x^2+1)\,dx$$.
Integrals review
Interpret integrals as accumulation and signed area.
Does $$\sum_{n=0}^{\infty}\left(\frac12\right)^n$$ converge, and if so to what?
Sequences and series
Choose convergence tools and distinguish sequence behavior from series behavior.
Solve $$x+y=3$$ and $$x-y=1$$.
Linear algebra review
Represent and solve linear systems using matrix language.
Does $$(2,3)$$ lie in the span of $$(1,1)$$ and $$(1,2)$$?
Span, basis, dimension
Decide whether a vector lies in the span of a set.
For $$A=\begin{bmatrix}2&1\\1&3\end{bmatrix}$$, compute the determinant and interpret it.
Determinants review
Interpret a matrix as a transformation, not just a table of numbers.
Find the eigenvalues of $$\begin{bmatrix}2&0\\0&5\end{bmatrix}$$.
Eigenvalues and eigenvectors
Find eigenvalues and eigenvectors for manageable matrices.