Free OMPT-F mock exam: 2 timed problems

What this OMPT-F mock covers

Two problems make a tenth of the 21-problem OMPT-F, and both come from the back half of the paper: quadratic equations and differentiation. Differentiation is 40% of the official OMPT-F score, the heaviest single weight on any variant except OMPT-C's numbers chapter, and equations and inequalities are another 30%.

Official weights are from the OMPT-F learning-assessment page at omptest.org. The full chapter list with topic counts is on the OMPT-F hub.

OMPT-F format: 21 questions in 180 minutes

The OMPT-F figures the timer copies, from the syllabus and pricing pages at omptest.org. OMPT-F shares OMPT-D's note-field rule and its higher prices.

How to enter answers on the OMPT-F

OMPT-F, like OMPT-D, expects your calculations in the note field, and two graders score each step. The final answer still has to be in exact form. This free mock grades only the typed answer, so write the method on paper during the mock and check it against the worked solution; the real paper pays for every correct step.

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-F uses the basic on-screen calculator shared by OMPT-A, B, C and F.

What the OMPT-F score panel shows

Two problems score 0, 50 or 100, so the number is not the point. The pace is: 17 minutes for two problems is the official 8.6 minutes each, and a problem that takes you twelve minutes here would sink the real paper. The worked solutions after scoring show the shortest route, which is usually two steps shorter than the one candidates take.

Free OMPT-F mock vs the official mock vs our full papers

The official OMPT-F mock costs €110 and it is the only practice where a grader reads your note field. Our free mock checks the pace on two problems. The generation papers give all 21 problems and 180 minutes, graded on the final answer.

Official prices from omptest.org/pricing, checked 21 September 2026: practice material €95, mock €110, test attempt €270. Our four OMPT-F generation papers are listed on the plans page.

Three worked OMPT-F examples in exact-answer form

These three are not in the mock above; they show the answer form the OMPT-F field expects and the entry mistake each question invites. More are worked through in our sample questions walkthrough.

1. OMPT-F example 1 · Quadratic equations

   Solve x⁴ − 5x² + 4 = 0.

   1. Substitute u = x²: u² − 5u + 4 = 0.
   2. Factor: (u − 1)(u − 4) = 0, so u = 1 or u = 4.
   3. Back-substitute: x² = 1 gives x = ±1; x² = 4 gives x = ±2.

   Answer: x = −2, −1, 1, 2

   Entry: Type -2,-1,1,2. Stopping at u = 1, 4 is the most common incomplete answer; on OMPT-F the note must show the substitution, and the rubric pays for it separately.

2. OMPT-F example 2 · Functions

   f(x) = (2x + 1)/(x − 3). Find the inverse function f⁻¹(x).

   1. Write y = (2x + 1)/(x − 3) and clear the fraction: y(x − 3) = 2x + 1, so xy − 3y = 2x + 1.
   2. Collect the x-terms: xy − 2x = 3y + 1, so x(y − 2) = 3y + 1 and x = (3y + 1)/(y − 2).
   3. Swap the letters: f⁻¹(x) = (3x + 1)/(x − 2), defined for x ≠ 2.

   Answer: f⁻¹(x) = (3x + 1)/(x − 2)

   Entry: Type (3x+1)/(x-2) with both brackets. Writing 1/f(x) = (x − 3)/(2x + 1) is the reciprocal, not the inverse, and scores nothing.

3. OMPT-F example 3 · Differentiation

   f(x) = x³ − 3x² − 9x + 5 on the interval [−2, 4]. Find the maximum and minimum values of f.

   1. f′(x) = 3x² − 6x − 9 = 3(x − 3)(x + 1), zero at x = −1 and x = 3, both inside the interval.
   2. Evaluate at the critical points and the endpoints: f(−1) = 10, f(3) = −22, f(−2) = 3, f(4) = −15.
   3. Largest is 10 at x = −1; smallest is −22 at x = 3.

   Answer: maximum 10, minimum −22

   Entry: Enter 10 and -22 in the fields asked for. Skipping the endpoints is the classic omission; here they do not win, but the rubric still expects them in the note.

After you score the OMPT-F mock

Both correct within time: sit the generation-1 OMPT-F paper in one three-hour block to test stamina. Most OMPT-F candidates who fail do so on problems 16 to 21.

One correct: the panel names the chapter. The applications of derivatives drill covers the extreme-value and tangent problems that dominate the 40% differentiation weight; the inequalities drill covers the sign-table work under equations and inequalities.

Neither correct: work the rational functions drill and the inverse and composite functions drill untimed first, then the differentiation rules drill, and return to this page.

Drills by topic are on the topics page; the OMPT-F generation papers start at generation 1, which carries the 19 questions you have not seen.

Free OMPT-F mock FAQ

More on the free sets for every variant 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.

• 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