OMPT-F full mock exam, generation 4: 21 problems in 180 minutes
The top of the line, written at the difficulty of the sitting itself. I tell students to keep this one sealed until exam week and sit it once, on the clock, as the dress rehearsal.
Original problems, written by OMPT Practice. Official figures last verified 21 September 2026.
You type every answer and the grader checks it the way the real sitting does. There is no multiple choice to lean on.
The rest of the paper
All 21 questions unlock with purchase
The full set runs in chapter order under the real 180-minute clock, graded instantly, with a worked solution behind every question, including the ones you got right.
OMPT-F exam format this mock reproduces: 21 problems in 180 minutes
This OMPT-F paper follows the format below: 21 long-form problems in 180 minutes across six chapters, with no numbers chapter and no trigonometry. Official rows are from omptest.org; the last two describe this paper and its limitation.
Item
OMPT-F
Source
Questions
21, all typed answers
omptest.org
Time
180 minutes, timer starts only at Start
omptest.org
Pace
8.6 minutes per question
omptest.org
Chapters
6, asked in syllabus order
omptest.org
Answer field
Final answer plus your calculations in the note field; two graders score each step with a rubric.
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 paper
21 original questions, 180-minute clock, exam-level tier, graded on submit
this site
Report
Score, percentage, every chapter ranked weakest first, worked solution per question
this site
Official rows are read from the OMPT-F syllabus, the pricing page and the OMPT knowledge base at omptest.org, checked 21 September 2026. The OMPT-F hub lists every chapter with its topic count.
What an OMPT-F generation 4 sitting is like
Generation 4 is written at the difficulty of the OMPT-F sitting as omptest.org describes it: application and analysis items; omptest.org says the real test is harder than the practice material. The 21 questions keep the official chapter order and quota, and the hardest items sit late in each chapter, the way the real paper builds.
Keep it sealed until exam week and sit it once, on the clock, as the dress rehearsal, then spend the remaining days on the chapters it ranks lowest. Two graders will read your notes on the real paper; write this one as if they were reading.
Chapter mix of OMPT-F generation 4
The chapter quota is the same across the four OMPT-F generations. What climbs is the depth: a generation-1 differentiation item asks for one derivative, a generation-4 item asks for the extreme values on an interval with the endpoints checked and the answer justified. Differentiation is 40% of the official OMPT-F score, so that is where the generations differ most.
Official weights are from the OMPT-F learning-assessment page at omptest.org. Each drill link opens a free topic page with its own ten-problem set; the full list is on the topics page.
How to enter answers on the OMPT-F paper
On the real OMPT-F the note field earns partial credit step by step, and the final answer still has to be exact. This paper grades only the answer field, so keep paper beside you and mark your own method against the worked solution.
Fractions and decimals
A fraction question wants a reduced fraction (7/16), a decimal question wants a decimal point, and swapping them costs the mark. The real calculator shows decimals only, so keep the fraction arithmetic on paper.
Roots and constants
Reduce the root and clear the denominator: 3+sqrt(5), 8pi, 2sqrt(5)/25. Numeric approximations of π, e and roots are wrong where exact form is asked.
Powers
x^2 and x² are read the same; so are cm^2 and cm². A negative exponent stays a power or becomes a fraction, never a decimal.
Multiple answers
List all solutions, comma-separated, in the order the question asks. A missing second root or angle is an incomplete answer, not a half-right one.
Intervals
Give inequalities as -5<=x<-2 or as [-5,-2). The bracket type carries meaning: round excludes the endpoint, square includes it.
Units and prefixes
Type the bare number; a unit the question named is stripped on grading. Do not add words such as metres or joules.
Working
On OMPT-D and OMPT-F the real paper scores your note field step by step; on B and G a note is optional; on A, C and E there is none. This paper grades the answer field only on every variant.
Invalid input
A half-filled template or an unclosed bracket on the real paper is flagged orange, stored and graded by hand. Here it is simply marked wrong, so check the syntax before you move on.
The OMPT-F uses the basic on-screen calculator shared by OMPT-A, B, C and F. What it can and cannot do is in our note on OMPT calculator rules.
Three worked OMPT-F examples in the answer form this paper grades
None of these three is in the paper; they show the exact-form answer the OMPT-F field expects and the entry error each question invites. Three more, from other chapters, are on the free OMPT-F mock page, and a longer set is in our sample questions walkthrough.
OMPT-F example 1 · Linear formulas and equations
Solve the inequality (x − 1)/(x + 2) ≥ 2.
Do not multiply by (x + 2), whose sign is unknown. Move 2 across: (x − 1)/(x + 2) − 2 ≥ 0.
Sign table with the points −5 and −2: the quotient is negative or zero between them, and x = −2 is excluded because it makes the denominator zero.
Answer: −5 ≤ x < −2, the interval [−5, −2)
Entry: Type -5<=x<-2 or [-5,-2). Multiplying through by x + 2 gives x ≤ −5, wrong for every candidate who did it; the sign-table step is where the rubric marks are.
OMPT-F example 2 · Functions
Give all asymptotes of f(x) = (3x² − 2)/(x² − 4).
Vertical asymptotes where the denominator is zero and the numerator is not: x² − 4 = 0 gives x = −2 and x = 2; the numerator is 10 at both.
Degrees of top and bottom are equal, so the horizontal asymptote is the ratio of leading coefficients: y = 3/1.
There is no slant asymptote because the degrees match.
Answer: x = −2, x = 2 and y = 3
Entry: Enter all three; two out of three is marked incomplete. Writing y = 0 for the horizontal asymptote is the usual error, carried over from cases where the top has lower degree.
OMPT-F example 3 · Differentiation
Find the equation of the tangent to f(x) = ln(x)/x at x = e.
At x = e: ln e = 1, so f′(e) = 0. The tangent is horizontal.
f(e) = 1/e, so the tangent is y = 1/e.
Answer: y = 1/e
Entry: Type 1/e, not 0.368. Candidates who compute f′(e) = 0 and then write the tangent as y = 0 confuse the gradient with the value; the note should show both numbers.
How OMPT-F generation 4 compares with the official OMPT-F
Copied from the official OMPT-F: 21 problems, 180 minutes, chapter order, exact-form typed answers, no negative marking and no formula sheet. Not copied: the note field that two omptest.org graders score with a step rubric (this paper grades the final answer only), the Sowiso engine, ProctorU and randomised values. omptest.org describes the real OMPT-F as open-ended and harder than its practice material; our generation-4 OMPT-F paper is written to that description.
Free OMPT-F mock
Official OMPT-F mock
OMPT-F generation 4 (€59.99)
Price
Free
€110
€59.99 once, VAT included
Questions
2, a tenth of the paper
21
21
Clock
17 minutes
180 minutes
180 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
Yes, by two graders
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, OMPT-F mock €110, test attempt €270. The official mock and the practice material expire with the class year at the end of September.
What the OMPT-F score report shows after you submit
Submit and the OMPT-F paper is graded instantly on the 21 final answers, each with a stepwise worked solution, and the six chapters ranked weakest first. Sit it in a single three-hour block. The paper stays in your account for re-sitting, with earlier scores kept. Prices include VAT. Refunds within 14 days of purchase, by email, to the original payment method.
The refund and access wording in full is on the terms page. Bundles that pair this paper with another generation are on the plans page.
The ladder
Other OMPT-F generations
Generations climb toward the real sitting. Work them in order; each OMPT-F set uses entirely different questions.
No. The OMPT-F generation 4 paper is original, written to the six-chapter OMPT-F syllabus at omptest.org: algebra, equations and inequalities, functions, exponentials and logarithms, differentiation. Real OMPT-F problems are never published.
›Can I re-sit OMPT-F generation 4?
Yes. One purchase of €59.99 keeps the OMPT-F generation 4 paper in your account for re-sitting under the 180-minute clock. The 21 problems stay the same, so a re-sit is for timing the ones you left unfinished.
›Can I sit the OMPT-F paper on a phone?
The OMPT-F paper runs in a phone browser, but its long-form problems need paper for working, and the real OMPT-F is taken on a computer with a webcam under the Guardian browser with up to three A4 scratch sheets. Rehearse on a laptop.
›How is the OMPT-F paper graded?
The OMPT-F paper is graded instantly on the typed final answer in exact form. The real OMPT-F is graded by two omptest.org mathematicians who score your note field step by step, with results in eight business days. Our worked solutions show the rubric-style steps so you can mark your own method.
›What if an OMPT-F problem contains an error?
Report it with the button under the OMPT-F problem. Reports are checked against the script that re-derives generated answers, the paper is corrected, and you get a reply. The curated long-form problems were re-derived by hand before release.
›Is OMPT-F generation 4 as hard as the real OMPT-F?
Generation 4 is our OMPT-F paper written to the open-ended level omptest.org describes for the sitting, which it says is harder than its own practice material. Keep a margin above your programme's cutoff even after a good generation-4 score.
›Does the OMPT-F paper expire?
No. A purchased OMPT-F paper has no end date. omptest.org's OMPT-F products (practice €95, mock €110, attempt €270) expire with the class year at the end of September.
Booking, proctoring and retake questions are answered on the help page; what the free sets cover for every variant is on the free OMPT practice test page.
Sources for the OMPT-F 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.