Mathematical Reasoning practice questions for the 2027 Selective and OC tests
The OC Mathematical Reasoning section is 35 multiple-choice questions in 40 minutes. The OC questions for this page are being checked before they go up. Until then, the full papers are free: sit a whole Mathematical Reasoning paper, marked on the same test screen.
Questions being prepared
We publish a question here only after a person has checked it, its answer and its explanation. The OC set is not ready yet.
Free OC papers: the Department's sample tests and our free online sets.
Mathematical Reasoning question types
- Word problems: turning words into working
- Fractions, ratio and percentage questions
- Rates, speed and work problems
- Area, perimeter and geometry traps
- Time, timetables and elapsed time
- Counting, combinations and chance
- Number patterns and sequences
- Bar models and other visual methods
Sit the full paper free
A whole OC Mathematical Reasoning paper under the real time limit, then every question explained.
Questions families ask
What is in the Mathematical Reasoning test?
Multiple-choice problems that ask a child to apply primary maths rather than recall it: word problems, fractions, ratio and percentages, rates, measurement and geometry, time, counting and chance, and number patterns. Most questions take more than one step.
How long is the Mathematical Reasoning test?
35 questions in 40 minutes, in both the Selective and the OC test. That is a little over a minute a question, so a child needs quick, reliable methods, not just the ability to get there eventually.
Can my child use a calculator?
No. Working is done by hand, which is why the explanations here write every step out in full, one operation per line.
Does my child need high-school maths for the Selective test?
The questions are built on primary-school content, but they combine ideas in unfamiliar ways. Strong reasoning with Year 5 and 6 content matters more than learning new topics early.
How should my child use these questions?
Answer each one without help first, then check it and read the worked explanation, even when the answer was right: it shows the quickest method, and speed decides this section as much as getting answers right.
Where can my child sit a full Mathematical Reasoning paper?
The free papers page has the Department's sample tests and our free online sets, which are marked for you on the same test screen as these questions.