Free OMPT-D mock exam: 2 timed problems

What this OMPT-D mock covers

Two problems is a tenth of the 21-question OMPT-D, and both come from the paper's back half: one on functions, one on integration. Functions, equations and inequalities are 30% of the official OMPT-D score and integration 15%. The first four chapters of the syllabus are marked prerequisite by omptest.org and carry no weight of their own, which is why none appears here.

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

OMPT-D format: 21 questions in 180 minutes

The OMPT-D figures the timer copies, read from the syllabus and pricing pages at omptest.org. Note the note-field rule; it changes how you should practise.

How to enter answers on the OMPT-D

OMPT-D is one of two variants (with F) where the final answer is not enough: omptest.org expects your calculations in the note field, and two graders score each step against a rubric. This free mock grades the typed answer only, so write your working on paper as you go and compare it with the solution afterwards; that is the habit the real paper rewards.

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-D uses the extended on-screen calculator shared by OMPT-D and G.

What the OMPT-D score panel shows

The panel scores two problems, so the percentage is 0, 50 or 100 and means little on its own. What matters is the time: 17 minutes for two problems is the official 8.6 minutes each, and OMPT-D candidates who finish with time to spare are rare. Note how long each took you; the worked solutions show which steps you can shorten.

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

The official OMPT-D mock costs €110, more than the other variants, and it is the only practice that gets your notes read by a human grader. Our free mock checks the pace on two problems. The generation papers give all 21 problems and the 180-minute clock, 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-D generation papers are listed on the plans page.

Three worked OMPT-D examples in exact-answer form

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

1. OMPT-D example 1 · Functions

   Solve |2x − 3| < 5. Give the solution as an interval.

   1. An absolute value below 5 means the inside lies between −5 and 5: −5 < 2x − 3 < 5.
   2. Add 3 throughout: −2 < 2x < 8.
   3. Divide by 2: −1 < x < 4.

   Answer: −1 < x < 4, the open interval (−1, 4)

   Entry: Type -1<x<4 or (-1,4). On OMPT-D the note field must show the two-sided inequality, not just the answer; a closed interval [−1, 4] is wrong because the original inequality is strict.

2. OMPT-D example 2 · Differentiation

   Find the equation of the tangent to y = x·eˣ at x = 1.

   1. Product rule: y′ = eˣ + x·eˣ = eˣ(1 + x).
   2. At x = 1 the gradient is 2e and the point is (1, e).
   3. Tangent: y − e = 2e(x − 1), so y = 2ex − e.

   Answer: y = 2ex − e

   Entry: Type 2*e*x-e. Leave e as the constant; 5.44x − 2.72 is a rounded decimal and loses the exact-form mark. The rubric awards a step for the derivative even if the final line slips.

3. OMPT-D example 3 · Integration

   Evaluate the integral of sin(3x) from x = 0 to x = π/3.

   1. An antiderivative of sin(3x) is −cos(3x)/3.
   2. Upper limit: −cos(π)/3 = −(−1)/3 = 1/3. Lower limit: −cos(0)/3 = −1/3.
   3. 1/3 − (−1/3) = 2/3.

   Answer: 2/3

   Entry: Type 2/3. Dropping the minus on the antiderivative gives −2/3, and forgetting the 1/3 factor gives 2; both are visible in the note and cost a rubric step each.

After you score the OMPT-D mock

Both correct within time: sit the generation-1 OMPT-D paper in one three-hour block. The point is stamina; OMPT-D candidates who score well on short sets often fade after problem 15.

One correct: the problem you missed names the chapter. The applications of derivatives drill and the integration techniques drill cover the two most common OMPT-D losses, and our OMPT-D survival guide walks through the multi-step format.

Neither correct: do not start with a full paper. Work the trigonometric equations drill and the inverse and composite functions drill untimed, then the limits drill, and return here.

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

Free OMPT-D mock FAQ

More on the free sets for every variant on the free OMPT practice test page.

Sources for the OMPT-D 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