FFree OMPT-F mock exam
OMPT-F mock exam — with the answers in view.
The OMPT-F is the maths placement test some economics and business programmes ask for — several Radboud tracks accept OMPT-A or OMPT-F. It runs algebra through applied differentiation, with no trigonometry and no integration. On this page: the exact format, six sample questions with fully worked answers you can read right now, no signup — and a free full-length mock at the real length and clock.
21 questions · 180 minutesOpen-ended, application-level
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The OMPT-F format, exactly.
Fewer questions than any other variant except OMPT-D, and the most time per question — because each question is a multi-step application, not a drill.
| What | On the OMPT-F |
|---|
| Questions | 21, all open-ended — you type your answer, no multiple choice |
| Time limit | 180 minutes — about 8–9 minutes per question |
| Calculator | Your own is banned; a basic on-screen calculator is provided |
| Syllabus | 149 topics across six chapters — no trigonometry, no integration |
| Recommended prep | Around 80 hours, less if your algebra base is solid |
| Proctoring | Live remote proctoring (ProctorU) |
| Languages | English and Dutch |
| Results | Within 8 working days of submitting |
An official OMPT-F attempt costs €270, and depending on your programme you get between 1 and 3 attempts, each purchased separately. That price is the whole argument for rehearsing free first — the mock below costs nothing.
Sample OMPT-F questions — with answers.
Six questions, one per chapter of the OMPT-F syllabus, at the open-ended, application level the real test uses. Every solution is fully worked and visible right here — nothing to download, nothing to sign up for. Try each one on paper first, then read down.
1Algebra
Write (x3 · √x) / x2 as a single power of x.
Worked solution
- Rewrite the root as a power: √x = x1/2.
- Multiply the powers in the numerator by adding exponents: x3 · x1/2 = x3 + 1/2 = x7/2.
- Divide by x2 by subtracting exponents: x7/2 − 2 = x7/2 − 4/2 = x3/2.
Answer: x3/2 (equivalently x√x). Typed answer: x^(3/2). On the real test your answer is checked symbolically, so an unsimplified form like x7/2/x2 may be refused where the simplified power is expected — practise finishing the simplification.
2Linear formulas & equations
Town A has 12,400 residents and loses 250 residents per year. Town B has 8,200 residents and gains 100 per year. Assuming both trends stay linear, after how many years do the towns have the same population?
Worked solution
- Model each population after t years: A(t) = 12,400 − 250t and B(t) = 8,200 + 100t.
- Set them equal: 12,400 − 250t = 8,200 + 100t.
- Collect terms: 12,400 − 8,200 = 100t + 250t, so 4,200 = 350t.
- Solve: t = 4,200 / 350 = 12.
Answer: after 12 years — both towns then hold 9,400 residents (12,400 − 3,000 = 9,400 and 8,200 + 1,200 = 9,400, which is the check the real test expects you to be able to do). Typed answer: 12.
3Quadratic equations
Solve 2x2 − 5x − 3 = 0. Give all solutions exactly.
Worked solution
- Compute the discriminant: D = b2 − 4ac = (−5)2 − 4 · 2 · (−3) = 25 + 24 = 49.
- D = 49 > 0, so there are two real solutions, and √49 = 7.
- Apply the quadratic formula: x = (5 ± 7) / (2 · 2) = (5 ± 7) / 4.
- So x = 12/4 = 3 or x = −2/4 = −1/2.
Answer: x = 3 or x = −1/2. Typed answer: x=3 or x=-1/2. Factoring works too — 2x2 − 5x − 3 = (2x + 1)(x − 3) — but keep the exact fraction −1/2: a rounded decimal is not the same answer to a symbolic checker.
4Functions
Let f(x) = 2x + 3 and g(x) = x2. Compute g(f(1)), and find the inverse function f−1(x).
Worked solution
- Inside first: f(1) = 2 · 1 + 3 = 5.
- Then apply g: g(5) = 52 = 25. So g(f(1)) = 25.
- For the inverse, write y = 2x + 3 and solve for x: y − 3 = 2x, so x = (y − 3)/2.
- Swap the variable name: f−1(x) = (x − 3)/2.
Answer: g(f(1)) = 25 and f−1(x) = (x − 3)/2. Typed answers: 25 and (x-3)/2. Quick check: f−1(25) = 11 and f(11) = 25 — composing a function with its inverse must return the input.
5Exponentials & logarithms
Solve log2(x) + log2(x − 6) = 4.
Worked solution
- Domain first: both arguments must be positive, so x > 0 and x − 6 > 0, i.e. x > 6.
- Combine the logs: log2(x(x − 6)) = 4.
- Rewrite in exponential form: x(x − 6) = 24 = 16.
- Expand and solve: x2 − 6x − 16 = 0, which factors as (x − 8)(x + 2) = 0, so x = 8 or x = −2.
- Apply the domain: x = −2 is outside x > 6, so it is rejected.
Answer: x = 8. Typed answer: x=8. Check: log2(8) + log2(2) = 3 + 1 = 4. Forgetting to reject the negative root is one of the most common ways to lose a full question on log equations.
6Differentiation
A farmer has 60 m of fence and builds a rectangular enclosure against a straight wall, so only three sides need fencing: two widths and one length. What width maximises the enclosed area, and what is that maximum area?
Worked solution
- Let the width be x. The fencing constraint gives the length: 2x + L = 60, so L = 60 − 2x.
- Write the area as a function of one variable: A(x) = x(60 − 2x) = 60x − 2x2.
- Differentiate: A′(x) = 60 − 4x.
- Set A′(x) = 0: 60 − 4x = 0, so x = 15.
- Confirm it is a maximum: A″(x) = −4 < 0, so x = 15 gives the peak.
- Compute the area: L = 60 − 30 = 30, so A = 15 · 30 = 450.
Answer: width 15 m, maximum area 450 m². Typed answers: 15 and 450. This is the OMPT-F pattern in miniature: translate a situation into a function, differentiate, optimise, and justify the extremum.
The chapters are not equal. In the official weighting omptest.org publishes for the OMPT-F, differentiation alone is 40% of the exam — by far the largest chapter. If question 6 was the one that hurt, that is the chapter to drill first; the free test below will tell you whether it was a one-off or a pattern.
PDF vs interactive mock exam.
Most "OMPT mock exam PDF" results are the same free document re-uploaded on different sites: a Sample of the OMPT-A Mock Exam — a handful of questions to answer by hand. It is a fair first look at the question style. But it is a sample of the OMPT-A, not the OMPT-F: a different syllabus (the OMPT-F skips trigonometry and integration but goes deeper into applied differentiation) and a very different rhythm.
The official omptest.org also sells its own practice modules and a mock test — that is the official route, and it is a reasonable one. What no PDF can do, official or not: run the clock, check a typed answer symbolically, enforce the on-screen-calculator constraint, or hand you a per-topic score the moment you finish. Our mock does all four, at the OMPT-F's real length, for free.
Whatever materials you choose, do at least one full-length, timed run before booking. Three hours of sustained multi-step work is a skill of its own, and paper cannot rehearse it.