EOMPT-E mock exam
A free OMPT-E mock exam. With the answers.
The OMPT-E sits 40 questions in 120 minutes — an algebra core plus statistics & probability, no calculus. This page gives you both halves of a real rehearsal: six sample OMPT-E questions with fully worked solutions you can read right now, and a full-length, timed mock at the exam's exact length and clock, scored instantly by topic.
Sample questions: no account, no signup. Full mock: free account — takes a minute, no card.
The format this mock rehearses.
The OMPT-E is the usual maths test for psychology and social-science programmes — Amsterdam University College (Social Sciences), Radboud, Erasmus Rotterdam, VU Amsterdam and Tilburg all list it for some programmes, and some have switched their requirement from OMPT-A to OMPT-E. Full details in the OMPT-E guide; if you're not sure which variant your programme wants, start with which OMPT do I need?
| OMPT-E | The real exam — and the mock |
|---|
| Length | 40 questions · 120 minutes |
| Pace | About three minutes per question, on average |
| What's on it | An algebra core and a statistics & probability half — officially weighted 50/50. No calculus. |
| Answer format | Open maths entry, typed — checked symbolically, so form and signs matter |
| Calculator | Not your own. The official platform provides a statistics digital calculator — the OMPT-E is the only variant that gets the statistics one. The mock enforces the same on-screen-only rule. |
| Delivery | Online from home, with live human proctoring; book at least 72 hours ahead |
| Results | Digital certificate with per-topic scores, generally within 8 working days — the mock scores you by topic instantly |
| Attempts | Up to 3 in general, but not every programme allows all three — never spend one "to see what it's like" |
| Languages | English and Dutch |
| Prep effort | 161 syllabus topics, ~120 hours of preparation recommended officially |
Sitting a different variant? The
OMPT mock exam page covers all seven — the mock always takes your own variant's length and clock.
Sample OMPT-E questions with answers.
Six questions aligned with the official OMPT-E syllabus chapters — three from the algebra core, three from statistics & probability, the same half-and-half the real exam draws. Every solution is fully worked and visible below its question. No signup, no PDF to download.
1
Linear formulas and equations
Solve for x: (2x − 3)/5 = (x + 1)/2.
Solution
- Multiply both sides by 10 (the least common multiple of 5 and 2): 2(2x − 3) = 5(x + 1).
- Expand both sides: 4x − 6 = 5x + 5.
- Collect the x-terms on one side: −6 − 5 = 5x − 4x, so x = −11.
- Check: left side (2·(−11) − 3)/5 = −25/5 = −5; right side (−11 + 1)/2 = −10/2 = −5. Both sides agree.
Answer to enter: x = -11. On the real test you type the value — a sign slip here costs the whole question, which is why the check step is worth its ten seconds.
2
Quadratic equations
Solve 2x² + x − 6 = 0. Give exact values.
Solution
- Compute the discriminant: D = 1² − 4·2·(−6) = 1 + 48 = 49, and √49 = 7.
- Apply the quadratic formula: x = (−1 ± 7)/(2·2) = (−1 ± 7)/4.
- The two roots: x = 6/4 = 3/2 and x = −8/4 = −2.
- Check by factoring: (2x − 3)(x + 2) = 2x² + 4x − 3x − 6 = 2x² + x − 6. Same equation, same roots.
Answer to enter: x = 3/2 or x = -2. Enter the exact fraction 3/2, not 1.5 — a symbolic checker wants the form the question asks for.
3
Exponential functions and logarithms
Solve log₂(x + 3) + log₂(x − 3) = 4.
Solution
- Domain first: both arguments must be positive, so x + 3 > 0 and x − 3 > 0, which means x > 3.
- Combine the logarithms: log₂((x + 3)(x − 3)) = log₂(x² − 9) = 4.
- Rewrite in exponential form: x² − 9 = 2⁴ = 16, so x² = 25 and x = 5 or x = −5.
- Apply the domain: x = −5 is invalid (it makes both arguments negative). Only x = 5 survives.
- Check: log₂(5 + 3) + log₂(5 − 3) = log₂ 8 + log₂ 2 = 3 + 1 = 4. Correct.
Answer to enter: x = 5. The invalid root is the classic trap in this chapter: an answer of "5 or −5" is scored wrong, because −5 is outside the domain.
4
Probability
A box contains 4 defective and 8 working light bulbs. You draw two bulbs at random, without replacement. What is the probability that exactly one of them is defective? Give your answer as a fraction in lowest terms.
Solution
- "Exactly one defective" happens along two branches: defective then working, or working then defective.
- Defective first: P = (4/12) · (8/11) = 32/132.
- Working first: P = (8/12) · (4/11) = 32/132.
- The branches are mutually exclusive, so add them: 32/132 + 32/132 = 64/132.
- Reduce: divide top and bottom by 4 to get 16/33.
Answer to enter: 16/33. Without replacement means the second draw's denominator drops to 11 — using 12 twice is the most common wrong path here.
5
Combinatorics
A committee of 3 people is to be formed from 5 women and 4 men. How many different committees contain exactly 2 women?
Solution
- Choose the 2 women from 5: C(5,2) = (5·4)/(2·1) = 10 ways.
- Choose the 1 man from 4: C(4,1) = 4 ways.
- The choices are independent, so multiply: 10 · 4 = 40 committees.
Answer to enter: 40. Combinations, not permutations — a committee has no order, so C(5,2), never 5·4 = 20 arrangements of women.
6
Common probability distributions
A fair die is rolled 3 times. What is the probability of rolling exactly two sixes? Give your answer as a fraction in lowest terms.
Solution
- Each roll is an independent trial with success probability p = 1/6 ("a six"), so the number of sixes follows a binomial distribution with n = 3.
- Binomial formula for exactly k = 2 successes: P = C(3,2) · (1/6)² · (5/6)¹.
- Compute each factor: C(3,2) = 3, (1/6)² = 1/36, and the remaining roll must not be a six: 5/6.
- Multiply: 3 · (1/36) · (5/6) = 15/216.
- Reduce: divide top and bottom by 3 to get 5/72.
Answer to enter: 5/72. Forgetting the C(3,2) factor — the two sixes can land on any two of the three rolls — gives 5/216, one third of the right answer.
These six cover half the syllabus map: the official OMPT-E spreads its 40 questions across twelve chapters, including numbers, systems of equations, functions, descriptive statistics and random variables — chapters this sample skips. The
full mock exam draws on all of them, at the official chapter weighting.
PDF vs interactive mock exam.
Search for an OMPT-E mock exam and most of what you'll find is the same free sample PDF re-uploaded across different sites — and it's a sample of the OMPT-A mock: eight questions over three pages, answered by hand. It's a fair first look at the question style, but it contains no statistics or probability at all — the half of the exam that defines the OMPT-E. The official omptest.org also sells its own practice modules and mock test.
A static PDF also can't rehearse what the OMPT-E actually tests you on: the clock, the typed maths entry (you'll type your answers on the real test, not write them), the on-screen calculator constraint, or a per-topic score at the end. This mock is simply free, OMPT-E-length, timed and corrected instantly — whatever materials you use, do at least one full-length timed run before the real session, because pacing is a skill a PDF can't train.