Free mini-mock
Free OMPT-B mock exam: 6 timed questions
The real OMPT-B is 64 questions in 150 minutes. This is precisely a tenth of it: six questions, 14 minutes, the same 2.3-minute clock per question, scored right here in your browser.
Original questions, written by OMPT Practice. Official figures last verified 21 September 2026.
Question 1 · Differentiation
Let f(x) = 2x³ + 3x. Work out the value of the derivative at x = 1.
Question 2 · Differentiation
Differentiate f(x) = 5x^4. Give f′(x).
Question 3 · Trigonometry
In a right triangle, the side adjacent to the angle θ measures 12 and the hypotenuse measures 13. Give cos(θ) as a fraction in lowest terms.
Question 4 · Trigonometry
Convert 5π/3 radians to degrees.
Question 5 · Integration
Evaluate the integral of 6x from x = 0 to x = 5.
Question 6 · Integration
Find the exact value of the integral of 18x² taken from x = 0 to x = 6.
0 of 6 answered · unanswered questions count as wrong
What this OMPT-B mock covers
OMPT-B is the widest of the business-track tests, and the six free questions come from its back half: quadratics through integration. Differentiation is 25% of the official OMPT-B score and integration 17%, so the set leans there on purpose. If you are a strong algebra student, this is the part of the paper you have not yet been tested on.
| Question | Chapter | Official weight | Drill |
|---|---|---|---|
| 1 | Differentiation | 25% | OMPT-B differentiation rules drill |
| 2 | Differentiation | 25% | OMPT-B differentiation rules drill |
| 3 | Trigonometry | 15% | OMPT-B trig equations drill |
| 4 | Trigonometry | 15% | OMPT-B trig equations drill |
| 5 | Integration | 17% | OMPT-B integration basics drill |
| 6 | Integration | 17% | OMPT-B integration basics drill |
Official weights are from the OMPT-B learning-assessment page at omptest.org. The full chapter list with topic counts is on the OMPT-B hub.
OMPT-B format: 64 questions in 150 minutes
These are the OMPT-B figures the timer on this page copies, read from the omptest.org syllabus and pricing pages.
| Item | OMPT-B | Source |
|---|---|---|
| Questions | 64, all typed answers | omptest.org |
| Time | 150 minutes, timer starts only at Start | omptest.org |
| Pace | 2.3 minutes per question | omptest.org |
| Chapters | 10, asked in syllabus order | omptest.org |
| Answer field | Final answer; a note with working is optional and can earn partial credit. | omptest.org |
| Answer form | Exact: fractions, roots and powers unless a decimal is requested | omptest.org |
| Calculator | Only the basic on-screen calculator shared by OMPT-A, B, C and F; it does not apply order of operations | omptest.org |
| Formula sheet | None provided or allowed; special trigonometric values must be memorised | omptest.org |
| Negative marking | None; a wrong answer scores zero, not minus | omptest.org |
| Official grading | Software first, then omptest.org's mathematicians; 8 business days (4 with fast grading) | omptest.org |
| This mock | 6 original questions from the generation-1 paper, 14 minutes, scored in the browser | this site |
| Report | Score, percentage, chapters ranked weakest first, worked solution per question | this site |
How to enter answers on the OMPT-B
OMPT-B grades the typed answer, with an optional note field that can earn partial credit when the final line is wrong. That safety net only works if the note is legible and the answer is in the expected form, so the entry rules matter here too.
- Exact form
- Unless the question asks for a decimal, the answer is a fraction, a root or a power. omptest.org's help centre says a decimal where exact form is expected can lose points, and the on-screen calculator does not convert decimals back.
- Fractions
- Type a slash with no spaces and reduce it: 23/14, not 1.64 and not 46/28. A mixed number is not expected.
- Roots
- Simplify the radicand and rationalise a denominator: 2√13 rather than √52, 2√5/25 rather than 2/(5√5). Type sqrt(13) or the √ symbol; both are read.
- Powers and constants
- Use the caret: x^2, 2^(x-1). Keep π and e as symbols (pi, e), never as 3.14 or 2.72.
- Several solutions
- Give every solution the interval allows, separated by commas, smallest first when the question says so. One of two solutions is marked incomplete.
- Intervals and inequalities
- Write the two-sided inequality or the interval: -1<x<4 or (-1,4). Round brackets exclude the endpoint, square brackets include it.
- Decimal point
- When a decimal is asked for, use a point, not a comma, and give the precision the question states.
- No units
- Type the number; the field knows the unit from the question. 20 and 20 m both pass here; 20 metres does not.
- Brackets
- Close every bracket. An unclosed bracket or a doubled operator is flagged orange on the real paper and goes to manual grading, where the grader guesses at your intent.
The calculator rules are covered in detail in our note on OMPT calculator rules; the OMPT-B uses the basic on-screen calculator shared by OMPT-A, B, C and F.
What the OMPT-B score panel shows
The score panel gives six results, a percentage and the chapters in order of damage. Six questions at 2.3 minutes is 14 minutes of real OMPT-B pace; a candidate who runs out of time on question five would run out of time on question 55 of the real paper. The chapter list is more useful than the percentage: on OMPT-B it tells you whether the calculus or the trigonometry is leaking.
Free OMPT-B mock vs the official mock vs our full papers
omptest.org's OMPT-B mock is the nearest thing to the sitting: same software, same graders, one attempt. The mock on this page tests pace and finds the weak chapter. The generation papers give you the full 64 questions and 150 minutes with instant grading.
| Free OMPT-B mock | Official OMPT-B mock | Our OMPT-B generation papers | |
|---|---|---|---|
| Price | Free | €90 | €39.99 to €59.99 per paper, VAT included |
| Questions | 6, a tenth of the paper | 64 | 64 |
| Clock | 14 minutes | 150 minutes | 150 minutes |
| Grading | Instant, in the browser | Software, then omptest.org's graders; 8 business days | Instant, on submit |
| Attempts | Unlimited, same questions | One | Unlimited re-sits, same questions |
| Review | Worked solution after scoring | In the account after grading (Report, then Review) | Worked solution per question after grading |
| Note field graded | No | Optional note read for partial credit | No |
| Software | This site | Sowiso engine, the same as the real test | This site |
| Proctoring | None | None (the mock is unproctored) | None |
| Account | None needed | omptest.org account | Email login after purchase |
Official prices from omptest.org/pricing, checked 21 September 2026: practice material €95, mock €90, test attempt €240. Our four OMPT-B generation papers are listed on the plans page.
Three worked OMPT-B examples in exact-answer form
These three are not in the mock above; they show the answer form the OMPT-B field expects and the entry mistake each question invites. More are worked through in our sample questions walkthrough.
OMPT-B example 1 · Trigonometry
Give the exact value of tan(π/3) · sin(π/4).
- From the standard triangles: tan(π/3) = √3 and sin(π/4) = √2/2.
- Multiply: √3 × √2/2 = √6/2.
Answer: √6/2
Entry: Type sqrt(6)/2. No formula sheet is provided in the real sitting, so the special values must be memorised; 1.2247 is the calculator's decimal and is marked down.
OMPT-B example 2 · Integration
Evaluate the definite integral of 3√x from x = 1 to x = 4.
- Write √x as x^(1/2). An antiderivative of 3x^(1/2) is 3 × (2/3)x^(3/2) = 2x^(3/2).
- Evaluate between the limits: 2 × 4^(3/2) − 2 × 1^(3/2) = 2 × 8 − 2 × 1.
- 16 − 2 = 14.
Answer: 14
Entry: Type 14. A common slip is dividing by the old power (1/2) instead of the new one (3/2), which gives 3 × 2 × 7 = 42.
OMPT-B example 3 · Differentiation
f(x) = x² sin x. Find f′(π) in exact form.
- Product rule: f′(x) = 2x sin x + x² cos x.
- At x = π: sin π = 0 and cos π = −1.
- f′(π) = 0 + π² × (−1) = −π².
Answer: −π²
Entry: Type -pi^2. The field accepts pi as the constant; −9.87 is a rounded decimal and is not the exact value the question asks for.
After you score the OMPT-B mock
Five or six correct: you are ready for a full paper. Sit generation 1 of the OMPT-B line on the clock; it is the 64-question version of what you just did.
Three or four correct: read the chapter list. OMPT-B candidates usually lose the trigonometry or the integration item, and those two chapters are 32% of the official score. The trigonometric equations drill and the integration basics drill target exactly those.
Two or fewer: pace is the problem, not knowledge, in most cases I see. Work the differentiation rules drill untimed until the rules are reflexes, then return to this page with the timer on.
Drills by topic are on the topics page; the OMPT-B generation papers start at generation 1, which carries the 58 questions you have not seen.
Free OMPT-B mock FAQ
Is the OMPT-B mock on this page free?
The OMPT-B mock is free, with no account and no card. It serves the six free preview questions of our generation-1 OMPT-B paper, which are the only OMPT-B questions we give away; the paper itself carries 58 more.
Is this the real OMPT-B test?
No. The real OMPT-B is 64 typed-answer questions in 150 minutes under ProctorU supervision, graded by omptest.org. This page copies the pace, the exact-form answer entry and the chapter order with original questions. It is a rehearsal for the clock, not a copy of the sitting.
How long is the free OMPT-B mock?
The free OMPT-B mock runs 14 minutes for six questions, which is the official 2.3 minutes per question rounded to the set. The timer starts when you open the first question and does not pause; the real timer behaves the same after you click Start.
Can I retake the OMPT-B mock?
Yes, as many times as you like, but the OMPT-B mock uses the same six questions each time. A retake shows whether you fixed a specific error. For a new set of OMPT-B questions, generation 1 of the paid line is the next step.
Is the mock harder than the real OMPT-B?
The free OMPT-B mock comes from the harder half of our generation-1 paper, the gentlest of four. omptest.org places the real OMPT-B at the difficulty of its practice material; our generation-4 OMPT-B paper is written at that level. Treat this mock as a floor, not a ceiling.
What does the OMPT-B mock score report show?
The OMPT-B score panel shows correct answers out of six, a percentage, and every chapter ranked weakest first, with a worked solution under each question. The official OMPT-B certificate, sent by omptest.org after the real test, reports a score per topic in a similar layout.
Can I write working on the OMPT-B?
On the real OMPT-B you can add a note with your working, and omptest.org's graders may award partial credit from it. This free mock grades the typed answer only, so treat every question here as final-answer-only practice.
More on the free sets for every variant on the free OMPT practice test page.
Sources for the OMPT-B figures on this page, last checked 21 September 2026
Written by OMPT Practice. Every question above is original; none is a real OMPT item. Official prices and rules change with the class year each October.
- omptest.org: pricing (attempt, practice material, mock)
- omptest.org: practice material and mock tests
- omptest.org: calculator
- OMPT knowledge base: answer format and calculator use
- OMPT knowledge base: worked solution or final answer only
- OMPT knowledge base: how long until results
- OMPT knowledge base: formula sheet