Free OMPT-B mock exam

A free OMPT-B mock exam. Answers included.

The OMPT-B is the longest OMPT sitting there is — 64 questions in 150 minutes, everything in OMPT-A plus trigonometry and integration. It's the maths-intensive variant: applied engineering and IT programmes, econometrics tracks, and several technical universities ask for it. Below: the exact format, six sample OMPT-B questions with fully worked answers you can read right now, and a free full-length interactive mock at the real length and the real clock.

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The mock needs a free account — takes a minute, no card. The sample questions below need nothing at all.

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The real OMPT-B vs this mock.

Same format, same rules, same weighting — the only differences are the price and how fast you're scored.

Real OMPT-BThis free mock
Format64 questions · 150 minutesIdentical — same question count, same countdown
SyllabusEverything in OMPT-A, plus trigonometry and integrationSame chapters, drawn at the official weighting
Answer entryTyped maths, checked by a CAS — form and signs matterSame: a maths keyboard, answers checked symbolically
CalculatorYour own is banned; a basic calculator is provided on screenSame rule — the basic on-screen calculator, nothing else
ScoringCertificate with per-topic scores, up to 8 working daysInstant — score by topic the moment you submit
Price€240 per attemptFree, with a free account — no card
The real exam is remotely proctored via ProctorU (webcam, photo ID, room scan), must be booked at least 72 hours ahead, and your programme may allow as few as one attempt — between 1 and 3, depending on the university. Pass cutoffs are set per programme; published thresholds range from about 50% up to 75%. All the more reason to rehearse the full sitting before you pay for one: see the complete OMPT-B guide for the syllabus and pass-mark details.

Sample OMPT-B questions — with answers.

Six questions matched to the official OMPT-B syllabus. By the official weighting, differentiation (25%), integration (17%) and trigonometry (15%) are the three heaviest chapters — 57% of the exam between them — so they're all here. Every solution is fully worked and fully visible. No signup, no PDF hunt.

1 Algebra · 10% of the exam

Solve for x:  3⁄(x − 2) = 5⁄(x + 4).

Full solution

  1. Note the domain first: x ≠ 2 and x ≠ −4, or a denominator is zero.
  2. Cross-multiply: 3(x + 4) = 5(x − 2).
  3. Expand: 3x + 12 = 5x − 10.
  4. Collect terms: 22 = 2x, so x = 11.
  5. Check: 3⁄(11 − 2) = 3⁄9 = 1⁄3 and 5⁄(11 + 4) = 5⁄15 = 1⁄3. Both sides agree, and 11 is in the domain.

Answer to enter: x = 11

2 Quadratic equations & functions · 10%

Let f(x) = 2x² − 12x + 7. Write f in vertex form and give the minimum value of f.

Full solution

  1. Factor the leading coefficient out of the x-terms: f(x) = 2(x² − 6x) + 7.
  2. Complete the square: x² − 6x = (x − 3)² − 9.
  3. Substitute back: f(x) = 2((x − 3)² − 9) + 7 = 2(x − 3)² − 18 + 7 = 2(x − 3)² − 11.
  4. Since the coefficient 2 is positive, the parabola opens upwards, so the vertex is a minimum: at x = 3 the squared term vanishes and f(3) = −11.

Answer to enter: f(x) = 2(x − 3)² − 11 — minimum value −11, reached at x = 3.

3 Exponentials & logarithms · 10%

Solve:  log2(x) + log2(x − 6) = 4.

Full solution

  1. Domain: both arguments must be positive, so x > 0 and x > 6 — that is, x > 6.
  2. Combine the logs: log2(x(x − 6)) = 4.
  3. Rewrite in exponential form: x(x − 6) = 2⁴ = 16.
  4. Expand and solve: x² − 6x − 16 = 0, which factors as (x − 8)(x + 2) = 0, so x = 8 or x = −2.
  5. Only x = 8 satisfies x > 6; reject x = −2. Check: log2(8) + log2(2) = 3 + 1 = 4. ✓

Answer to enter: x = 8 — the tempting second root fails the domain check, which is exactly the kind of detail the CAS grading will not forgive.

4 Trigonometry · 15%

Solve sin(2x) = ½ for 0 ≤ x < π. Give exact answers.

Full solution

  1. Substitute u = 2x. As x runs over [0, π), u runs over [0, 2π).
  2. Solve sin(u) = ½ on [0, 2π): the sine of an angle is ½ at u = π⁄6 and at u = π − π⁄6 = 5π⁄6.
  3. Adding 2π to either value leaves the interval [0, 2π), so those are the only two solutions for u.
  4. Return to x: x = u⁄2, giving x = π⁄12 and x = 5π⁄12 — both inside [0, π).

Answer to enter: x = π/12 and x = 5π/12 — exact form, not decimals. Miss the second solution and you lose the question.

5 Differentiation · 25% — the heaviest chapter

Let f(x) = (2x − 1)³. Find f ′(x), and give the equation of the tangent line to the graph of f at x = 1.

Full solution

  1. Chain rule: the outer function is u³, the inner is u = 2x − 1, so f ′(x) = 3(2x − 1)² · 2 = 6(2x − 1)².
  2. Point of tangency: f(1) = (2 · 1 − 1)³ = 1³ = 1, so the point is (1, 1).
  3. Slope there: f ′(1) = 6(2 · 1 − 1)² = 6 · 1 = 6.
  4. Tangent line through (1, 1) with slope 6: y = 1 + 6(x − 1) = 6x − 5.

Answer to enter: f'(x) = 6(2x − 1)² and tangent y = 6x − 5. Forgetting the inner factor 2 — writing 3(2x − 1)² — is the classic chain-rule slip.

6 Integration · 17%

Evaluate the definite integral  ∫0π sin(x) dx.

Full solution

  1. An antiderivative of sin(x) is −cos(x), since the derivative of −cos(x) is sin(x).
  2. Apply the fundamental theorem of calculus: ∫0π sin(x) dx = [−cos(x)] from 0 to π = (−cos π) − (−cos 0).
  3. Evaluate: cos π = −1 and cos 0 = 1, so this is (−(−1)) − (−1) = 1 + 1 = 2.

Answer to enter: 2 — the area under one full arch of the sine curve. A sign slip on −cos(x) gives −2 or 0; the check is that sin(x) ≥ 0 on [0, π], so the integral must be positive.

Felt comfortable? Then the question is pacing: on the real OMPT-B you get a little over two minutes per question, for 150 minutes straight, typing every answer with no calculator of your own. That's what the full-length mock rehearses — or start smaller with 10 free questions scored instantly, with OMPT-B selectable in the test.

Looking for an OMPT-B mock exam PDF?

Fair warning about what's out there: the free sample PDF that circulates online — re-uploaded across various sites — is the official Sample of the OMPT-A Mock Exam. It's 8 questions over 3 pages, answered by hand, and it samples the OMPT-A: no trigonometry, no integration. Those two chapters are what set OMPT-B apart — 32% of your paper — so as a rehearsal for OMPT-B specifically, it can only take you so far. As a free first look at the question style, though, it's perfectly decent; use it.

What no static PDF can do is rehearse the sitting itself: no 150-minute countdown, no typed maths entry (on the real test you type your answers, checked by a CAS — you don't write them), no basic-calculator constraint, no per-topic score at the end. The official omptest.org sells its own practice material and mock test; this one is simply free, full-length at the OMPT-B format, and corrected the moment you submit.

Whatever mix of materials you use, sit at least one full-length, timed run before booking the real €240 attempt. Pacing over 150 minutes is a skill of its own, and paper can't train it.

Rehearse the full 150 minutes.

The real OMPT-B length, a real countdown, typed answers, and a score by topic the moment you finish. Free account — no card.

Start the full OMPT-B mock → Try 10 free questions first →

FAQ

Is there a free OMPT-B mock exam with answers?

Yes. The six sample questions on this page come with fully worked solutions you can read without signing up for anything. The full-length interactive mock — the same 64-question, 150-minute format as the real OMPT-B — is also free; it just needs a free account, no card.

How many questions does the OMPT-B mock exam have?

The OMPT-B has 64 questions in 150 minutes, and the mock uses exactly that: the same question count, the same clock and the same official chapter weighting. It is the most extensive OMPT variant — around 226 syllabus topics, with roughly 100 hours of preparation recommended.

Can I download an OMPT-B mock exam PDF with answers?

The free sample PDF that circulates online is the official Sample of the OMPT-A Mock Exam — 8 questions over 3 pages, with no trigonometry and no integration, the two chapters that set OMPT-B apart. It is a fair look at the question style, but it is not an OMPT-B paper. The sample questions on this page are matched to the OMPT-B syllabus, and the interactive mock rehearses the full sitting.

What topics does an OMPT-B mock exam cover?

The official OMPT-B syllabus: numbers, algebra, linear formulas and equations, quadratic equations and functions, exponential functions and logarithms, trigonometry, differentiation and integration. By the official weighting, differentiation (25%), integration (17%) and trigonometry (15%) are the three heaviest chapters — 57% of the exam between them. See the full OMPT-B guide for the chapter-by-chapter breakdown.

Will the mock exam predict my real OMPT-B score?

No — and be wary of anything that claims it can. A mock tells you your score on the questions you sat today, broken down by topic, so you can see which chapters are solid and which are costing you points. That is what makes it useful; the rest is up to your preparation.

Keep reading.

Know the test, then know the process.

OMPT-B guide: format, topics & pass marks Mock exams for every OMPT variant Which OMPT do I need? How to book the OMPT