AOMPT-A mock exam
OMPT-A mock exam — with the answers.
The OMPT-A is 52 questions in 120 minutes: a broad algebra core, then introductory differentiation. It's the variant that economics and business programmes typically ask for — Erasmus School of Economics, Rotterdam School of Management's IBA, Utrecht, Tilburg, Groningen and others. Below: six sample questions with fully worked solutions you can read right now, no signup — and a free full-length, timed mock when you're ready to rehearse the whole sitting.
Samples: no account at all. Full mock: free account, no card.
Sample OMPT-A questions — with answers.
Six questions written to the official OMPT-A syllabus chapters, each with the fully worked solution visible below it. No signup, nothing hidden.
1Numbers
Without a calculator, write (3/4 − 2/5) ÷ 7/10 as a single fraction in lowest terms.
Worked answer
Put the bracket over a common denominator of 20: 3/4 = 15/20 and 2/5 = 8/20, so 3/4 − 2/5 = 7/20.
Dividing by 7/10 means multiplying by its reciprocal: (7/20) × (10/7) = 70/140 = 1/2.
Answer: 1/2
2Algebra
Expand and simplify (2x − 3)2 − (x − 1)(x + 5).
Worked answer
First square: (2x − 3)2 = 4x2 − 12x + 9.
Second product: (x − 1)(x + 5) = x2 + 5x − x − 5 = x2 + 4x − 5.
Subtract, flipping every sign of the second bracket: 4x2 − 12x + 9 − x2 − 4x + 5 = 3x2 − 16x + 14.
Answer: 3x2 − 16x + 14
3Systems of linear equations
Solve the system: 2x + 3y = 12 and x − y = 1.
Worked answer
From the second equation, x = y + 1. Substitute into the first: 2(y + 1) + 3y = 12, so 5y + 2 = 12, giving y = 2.
Then x = y + 1 = 3.
Check in both equations: 2(3) + 3(2) = 12 ✓ and 3 − 2 = 1 ✓.
Answer: x = 3, y = 2
4Quadratic equations
Solve 2x2 − 5x − 3 = 0.
Worked answer
Discriminant: (−5)2 − 4 · 2 · (−3) = 25 + 24 = 49, and √49 = 7.
So x = (5 ± 7) / 4, giving x = 12/4 = 3 or x = −2/4 = −1/2.
Equivalently, the quadratic factors as (2x + 1)(x − 3) — same two roots.
Answer: x = 3 or x = −1/2
5Exponentials & logarithms
Solve log2(x) + log2(x − 2) = 3.
Worked answer
Both logs must be defined, so x > 2 — note that down before you touch the algebra.
Combine: log2[x(x − 2)] = 3, so x(x − 2) = 23 = 8.
That gives x2 − 2x − 8 = 0, which factors as (x − 4)(x + 2) = 0, so x = 4 or x = −2.
Only x = 4 satisfies x > 2; x = −2 is rejected. Check: log2(4) + log2(2) = 2 + 1 = 3 ✓.
Answer: x = 4
6Differentiation
Let f(x) = x3 − 6x2 + 9x + 1. Find the stationary points of f and classify each one as a local maximum or a local minimum.
Worked answer
Differentiate: f′(x) = 3x2 − 12x + 9 = 3(x2 − 4x + 3) = 3(x − 1)(x − 3).
So f′(x) = 0 at x = 1 and x = 3. The sign of f′ is positive for x < 1, negative between 1 and 3, and positive for x > 3.
Values: f(1) = 1 − 6 + 9 + 1 = 5 and f(3) = 27 − 54 + 27 + 1 = 1.
Answer: local maximum at (1, 5), local minimum at (3, 1)
How to use these: sit them cold, no calculator, at two to three minutes each — that's the real OMPT-A pacing. If the differentiation one took you longest, that's typical: it carries 20% of the official weighting, and it's where economics and business applicants usually lose points. And note the answer style — on the real test you type your maths and a CAS checks it, so form and signs matter.
These six questions are ours, written to the chapters of the official OMPT-A syllabus — they are not leaked exam questions, and nobody outside the official test has those. What a good mock can honestly copy is the format, the pacing, the answer mechanics and the topic mix. Ours copies all four.
PDF vs interactive mock exam.
An official sample of the OMPT-A mock exam exists as a short, free PDF on omptest.org — a handful of questions with space to write your answers by hand. It's a fair first look at the question style, and copies of that same document circulate on file-sharing sites, often behind a signup wall. Don't register anywhere just to read it: the original is free at the source.
But a PDF stops there. It can't run the 120-minute clock, can't make you type answers the way the real platform's CAS expects them, can't hold you to the on-screen-calculator rule, and can't score you by topic. Those four things are most of what a first attempt gets wrong — and they're exactly what an interactive mock rehearses. The official site also sells its own practice modules; ours is simply free, full-length, and graded the moment you submit.
Use both if you like. Just make sure that before you book the real 240 € sitting, at least one rehearsal was full-length, timed and typed.