Free GRE Subject Tests Exam Questions and Answers
GRE Subject Tests is an ETS certification exam. This page has free practice questions for it with answers and explanations, set out the way the real exam asks them, plus a timed practice test that scores you against the pass mark.
Candidates comparing GRE Subject Tests exam dumps, ExamTopics and other practice tests use this page for the answers and explanations behind each question. Download the free PDF, then sit the timed exam simulation before booking with ETS.
Last updated: October 26, 2026
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Question #1
After a stroke, a patient has intact visual fields and normal visual acuity. At meals she eats only the food on the right half of her plate, and when grooming she applies makeup only to the right side of her face. She denies that anything is wrong. Damage to which of the following brain regions is the most likely cause of these symptoms?
Correct answer: D
Explanation
Hemispatial neglect with unawareness of the deficit typically follows damage to the right posterior parietal cortex, which supports attention to both sides of space. The left hemisphere appears to attend mainly to the right side of space, so left-sided damage is usually compensated for. Damage to primary visual cortex would produce a field cut that the patient would notice and could compensate for with eye movements, and acuity and fields are stated to be normal.
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Question #2
In a visual detection task, an observer has a hit rate of .84 and a false-alarm rate of .16. The experimenter then changes the payoffs so that hits are rewarded more heavily than correct rejections. In the new condition, the observer's hit rate is .93 and the false-alarm rate is .31. Which of the following best describes the change in the observer's performance?
Correct answer: D
Explanation
Converting to z scores gives d' of about 1.99 in the first condition (0.99 + 0.99) and about 1.97 in the second (1.48 + 0.50), so sensitivity is essentially unchanged. Both hits and false alarms rose, which means the observer says "yes" more readily, a more liberal criterion. Payoff manipulations shift the criterion, not the observer's ability to discriminate signal from noise.
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Question #3
Let f be the function defined by f(x) = x^2 sin(1/x) for x ≠ 0 and f(0) = 0. Which of the following statements is true?
Correct answer: A
Explanation
The difference quotient at 0 is h sin(1/h), which tends to 0, so f'(0) = 0. For x ≠ 0, f'(x) = 2x sin(1/x) - cos(1/x), which has no limit as x approaches 0 because of the cos(1/x) term. So f' exists everywhere but is discontinuous at 0, and f''(0) cannot exist because f' is not even continuous there.
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Question #4
For x > 0, what is the derivative of f(x) = x^x?
Correct answer: C
Explanation
Write y = x^x, so ln y = x ln x. Differentiating implicitly gives y'/y = ln x + 1, hence y' = x^x (1 + ln x). The power rule gives x · x^(x-1) = x^x, which treats only the base as varying, and x^x ln x treats only the exponent as varying. The correct derivative is the sum of both contributions.
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Question #5
A person spins in place for 30 seconds with eyes closed and then stops abruptly. Immediately afterward she feels as if she is still rotating, in the direction opposite to her original spin. This sensation is best explained by which of the following?
Correct answer: B
Explanation
During sustained rotation the endolymph catches up with the canal and the cupula returns to rest. When the body stops, the fluid keeps moving by inertia and bends the cupula in the opposite direction, signaling rotation that is not occurring. The otolith organs respond to linear acceleration and head tilt, not to angular rotation.
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Question #6
A dog's conditioned salivation to a tone is extinguished by repeatedly presenting the tone without food. After a 24-hour rest period with no further training, the tone again elicits some salivation. This reappearance of the conditioned response is called
Correct answer: A
Explanation
Spontaneous recovery is the return of an extinguished conditioned response after a rest interval, which shows that extinction suppresses the response rather than erasing the original learning. Stimulus generalization concerns responding to stimuli similar to the CS. Latent inhibition concerns slower conditioning after prior exposure to the CS alone, before any pairing.
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Question #7
A soap film of thickness 300 nm and refractive index 1.33 is suspended in air and illuminated at normal incidence by white light. Which of the following wavelengths in the visible spectrum is most strongly reflected?
Correct answer: C
Explanation
Reflection at the front surface has a phase shift of π and reflection at the back surface has none, so constructive interference in reflection requires 2nt = (m + 1/2)λ. Here 2nt = 2(1.33)(300 nm) = 798 nm, so λ = 798/(m + 1/2) nm, giving 1596 nm, 532 nm, and 319 nm for m = 0, 1, 2. Only 532 nm is visible. The values 399 nm and 798 nm come from using 2nt = mλ, which is the condition for destructive interference in reflection.
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Question #8
A particle of mass 3.0 kg moves in a circle of radius 0.40 m about a fixed point with a constant angular speed of 5.0 rad/s. What is the magnitude of its angular momentum about the center of the circle, in kg·m^2/s?
Correct answer: D
Explanation
For a point mass in circular motion L = m r^2 ω = (3.0)(0.40)^2(5.0) = 2.4 kg·m^2/s. The value 6.0 comes from using m r ω, which forgets to square the radius, and 1.2 is the result of applying a solid-disk moment of inertia.
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Question #9
Let A be a 4 × 4 real matrix with A^2 = A and trace(A) = 3. What is det(A + I), where I is the 4 × 4 identity matrix?
Correct answer: E
Explanation
Since A^2 = A, A is diagonalizable with eigenvalues 0 or 1, and the trace equals the number of eigenvalues equal to 1, so the eigenvalues are 1, 1, 1, 0. Then A + I has eigenvalues 2, 2, 2, 1 and det(A + I) = 8.
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Question #10
In Sherif's Robbers Cave field study, which procedure was most effective in reducing hostility between the two groups of boys?
Correct answer: C
Explanation
Sherif found that superordinate goals, which required the groups to cooperate, reduced hostility. Mere contact such as shared meals did not reduce conflict while the groups remained in competition.
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FAQ
Learn More: https://www.ets.org/
- Q1: What is the GRE Subject Tests exam?
- A: GRE Subject Tests is a professional examination offered by ETS.
- Q2: Are there practice questions for GRE Subject Tests?
- A: Yes. The first ten are free to read with their answers and no account is needed; the rest of the bank and the practice test come with access to the exam.
- Q3: How should I prepare for GRE Subject Tests?
- A: Start from the official ETS exam objectives, which define what is actually tested, and practise against questions written to them rather than to a syllabus someone has guessed at.
- Q4: Where do I register for GRE Subject Tests?
- A: Registration is handled by the awarding body — see https://www.ets.org/ for the current fee, the testing options and the booking process.
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