OMPT practice worksheets
The OMPT is the online mathematics placement test set by more than forty European universities. These are practice sheets for every level from OMPT-A to OMPT-G — one sheet per chapter of each syllabus — 21 sheets, 630 questions, every one with a full worked answer and the common mistakes named. Free to print.
The seven levels are different SUBJECT LISTS, not seven difficulties of the same paper: OMPT-B adds trigonometry and integration to OMPT-A, while OMPT-E drops the calculus entirely and adds statistics, probability and counting. Practising the wrong one is wasted work, so start from the level your programme names.
You choose how long each sheet is. Every sheet carries 30 questions and a control at the top sets it to 10, 20 or all of them — for a five-minute drill or a full period. The answers follow your choice, and it is remembered across the sheets.
The OMPT is open-answer: you type the answer rather than choosing one. So instead of explaining wrong options, each answer names the mistakes students actually make and shows the value each one leads to — if your answer matches one of them, you can see immediately where it went wrong.
OMPT-A
Numbers, algebra, linear formulas, systems, quadratics, functions, exponentials and logarithms, differentiation. Typically set for economics, business and the social sciences.
270 questions across 9 sheets
- 1. Exact fraction arithmeticAdding, subtracting, multiplying and dividing fractions without a calculator, leaving every answer exact.30 questions
- 2. Algebraic fractionsSimplifying and combining fractions whose numerators and denominators are expressions.30 questions
- 3. Straight linesThe gradient of the line through two points, and the equation that follows from it.30 questions
- 4. Systems of two equationsSolving two linear equations in two unknowns.30 questions
- 5. QuadraticsSolving quadratic equations by factorisation, by formula, and finding turning points.30 questions
- 6. FunctionsAsymptotes, composites, and equations with the unknown underneath.30 questions
- 7. LogarithmsCombining logarithms into one, and solving logarithmic and exponential equations.30 questions
- 8. DifferentiationThe product, quotient and chain rules, and finding stationary points.30 questions
- OMPT-A mixed paperEvery OMPT-A topic together.30 questions
OMPT-B
Everything in OMPT-A, plus trigonometry and integration. Typically set for engineering, computer science, natural sciences and mathematics.
330 questions across 11 sheets
- 1. Exact fraction arithmeticAdding, subtracting, multiplying and dividing fractions without a calculator, leaving every answer exact.30 questions
- 2. Algebraic fractionsSimplifying and combining fractions whose numerators and denominators are expressions.30 questions
- 3. Straight linesThe gradient of the line through two points, and the equation that follows from it.30 questions
- 4. Systems of two equationsSolving two linear equations in two unknowns.30 questions
- 5. QuadraticsSolving quadratic equations by factorisation, by formula, and finding turning points.30 questions
- 6. FunctionsAsymptotes, composites, and equations with the unknown underneath.30 questions
- 7. LogarithmsCombining logarithms into one, and solving logarithmic and exponential equations.30 questions
- 8. DifferentiationThe product, quotient and chain rules, and finding stationary points.30 questions
- 9. TrigonometryExact values, identities and trigonometric equations.30 questions
- 10. IntegrationAntiderivatives and definite integrals.30 questions
- OMPT-B mixed paperEvery OMPT-B topic together.30 questions
OMPT-C
Numbers, algebra, linear formulas and basic geometry. No quadratics, no functions and no calculus — the shortest of the seven. Typically set for general admission where a basic numeracy standard is required.
150 questions across 5 sheets
- 1. Exact fraction arithmeticAdding, subtracting, multiplying and dividing fractions without a calculator, leaving every answer exact.30 questions
- 2. Algebraic fractionsSimplifying and combining fractions whose numerators and denominators are expressions.30 questions
- 3. Straight linesThe gradient of the line through two points, and the equation that follows from it.30 questions
- 13. GeometryAngles, triangles, polygons, circles, Pythagoras and distances.30 questions
- OMPT-C mixed paperEvery OMPT-C topic together.30 questions
OMPT-D
Everything in OMPT-B, plus geometry. The most demanding of the seven: 21 questions in 180 minutes. Typically set for advanced engineering, physics, pure mathematics and theoretical computer science.
360 questions across 12 sheets
- 1. Exact fraction arithmeticAdding, subtracting, multiplying and dividing fractions without a calculator, leaving every answer exact.30 questions
- 2. Algebraic fractionsSimplifying and combining fractions whose numerators and denominators are expressions.30 questions
- 3. Straight linesThe gradient of the line through two points, and the equation that follows from it.30 questions
- 4. Systems of two equationsSolving two linear equations in two unknowns.30 questions
- 5. QuadraticsSolving quadratic equations by factorisation, by formula, and finding turning points.30 questions
- 6. FunctionsAsymptotes, composites, and equations with the unknown underneath.30 questions
- 7. LogarithmsCombining logarithms into one, and solving logarithmic and exponential equations.30 questions
- 8. DifferentiationThe product, quotient and chain rules, and finding stationary points.30 questions
- 9. TrigonometryExact values, identities and trigonometric equations.30 questions
- 10. IntegrationAntiderivatives and definite integrals.30 questions
- 13. GeometryAngles, triangles, polygons, circles, Pythagoras and distances.30 questions
- OMPT-D mixed paperEvery OMPT-D topic together.30 questions
OMPT-E
OMPT-A without the calculus, plus descriptive statistics, probability, combinatorics and distributions. Typically set for statistics, econometrics, data programmes and psychology.
300 questions across 10 sheets
- 1. Exact fraction arithmeticAdding, subtracting, multiplying and dividing fractions without a calculator, leaving every answer exact.30 questions
- 2. Algebraic fractionsSimplifying and combining fractions whose numerators and denominators are expressions.30 questions
- 3. Straight linesThe gradient of the line through two points, and the equation that follows from it.30 questions
- 4. Systems of two equationsSolving two linear equations in two unknowns.30 questions
- 5. QuadraticsSolving quadratic equations by factorisation, by formula, and finding turning points.30 questions
- 6. FunctionsAsymptotes, composites, and equations with the unknown underneath.30 questions
- 7. LogarithmsCombining logarithms into one, and solving logarithmic and exponential equations.30 questions
- 11. Descriptive statisticsMean, median and the spread of a data set.30 questions
- 12. Probability and countingSample spaces, permutations, combinations and binomial probabilities.30 questions
- OMPT-E mixed paperEvery OMPT-E topic together.30 questions
OMPT-F
Algebra, linear formulas, quadratics, functions, logarithms and differentiation. No numbers chapter and no systems chapter. Typically set for biology, earth sciences and the other natural sciences.
210 questions across 7 sheets
- 2. Algebraic fractionsSimplifying and combining fractions whose numerators and denominators are expressions.30 questions
- 3. Straight linesThe gradient of the line through two points, and the equation that follows from it.30 questions
- 5. QuadraticsSolving quadratic equations by factorisation, by formula, and finding turning points.30 questions
- 6. FunctionsAsymptotes, composites, and equations with the unknown underneath.30 questions
- 7. LogarithmsCombining logarithms into one, and solving logarithmic and exponential equations.30 questions
- 8. DifferentiationThe product, quotient and chain rules, and finding stationary points.30 questions
- OMPT-F mixed paperEvery OMPT-F topic together.30 questions
OMPT-G
Linear formulas through logarithms, plus sequences and series, trigonometry and geometry. Typically set for stem programmes that also test physics and chemistry.
270 questions across 9 sheets
Not here: OMPT-G also has a physics module and a chemistry module, 4 topics each. Those are not mathematics and are not on this site — the sheets below cover its nine mathematics chapters.
- 3. Straight linesThe gradient of the line through two points, and the equation that follows from it.30 questions
- 4. Systems of two equationsSolving two linear equations in two unknowns.30 questions
- 5. QuadraticsSolving quadratic equations by factorisation, by formula, and finding turning points.30 questions
- 6. FunctionsAsymptotes, composites, and equations with the unknown underneath.30 questions
- 7. LogarithmsCombining logarithms into one, and solving logarithmic and exponential equations.30 questions
- 9. TrigonometryExact values, identities and trigonometric equations.30 questions
- 13. GeometryAngles, triangles, polygons, circles, Pythagoras and distances.30 questions
- 14. Sequences and seriesArithmetic and geometric sequences, and the sum of a series.30 questions
- OMPT-G mixed paperEvery OMPT-G topic together.30 questions
Which OMPT are you sitting?
OMPT is not one test. There are seven, and they differ in SYLLABUS as well as in difficulty, so practising the wrong one is wasted work. Your university names the level it wants and sets its own pass mark — check your programme page before you start.
| Test | What it covers | On this site |
|---|---|---|
| OMPT-A | Numbers, algebra, linear formulas, systems, quadratics, functions, exponentials and logarithms, differentiation. | 9 sheets, 270 questions |
| OMPT-B | Everything in OMPT-A, plus trigonometry and integration. | 11 sheets, 330 questions |
| OMPT-C | Numbers, algebra, linear formulas and basic geometry. No quadratics, no functions and no calculus — the shortest of the seven. | 5 sheets, 150 questions |
| OMPT-D | Everything in OMPT-B, plus geometry. The most demanding of the seven: 21 questions in 180 minutes. | 12 sheets, 360 questions |
| OMPT-E | OMPT-A without the calculus, plus descriptive statistics, probability, combinatorics and distributions. | 10 sheets, 300 questions |
| OMPT-F | Algebra, linear formulas, quadratics, functions, logarithms and differentiation. No numbers chapter and no systems chapter. | 7 sheets, 210 questions |
| OMPT-G | Linear formulas through logarithms, plus sequences and series, trigonometry and geometry. Its physics and chemistry modules are not here. | 9 sheets, 270 questions |
Every answer on these pages was re-derived by an independent method before the page was built. Nothing here is published on the strength of the code that produced it.