1. Which number rounds to 60 when rounded to the nearest ten?
Free OC and Selective Mathematical Reasoning practice
Thirty-five questions in 40 minutes, with no calculator, at both levels. In the Department's practice tests, each question has five options to choose from, not four.
Last updated: 5 October 2026
What it covers
School maths, used to solve problems. The content stops at the NSW curriculum for Year 4 at OC level and Year 6 at selective level. The difficulty is in seeing which piece of it a question needs, not in the arithmetic.
In the Department's practice tests, number work carries the largest share, then measurement. Space, algebra, statistics and probability make up the rest.
Where marks go
- Questions that read like a puzzle. The maths is familiar, but nothing says which operation to use. Writing down what is known and what is wanted comes before any working.
- Answers that fit the working but not the question. Checking an answer against what was asked, not just against the working, catches many of them.
- Time. Forty minutes for 35 questions is just over a minute each. A question that has taken three minutes is worth leaving and coming back to.
Sample questions
Try each one first, then open the answer and worked solution under it.
Answer and worked solution
Correct answer: B
A number rounds to 60 if it is closer to 60 than to any other ten — that means 55 up to 64.
Check each: 53 → 50, 58 → 60, 66 → 70, 72 → 70.
Only 58 lands on 60.
58 rounds to 60.
2. Which of these decimals is CLOSEST to 1?
Answer and worked solution
Correct answer: C
Work out how far each one sits from 1.
0.9 is 0.1 away, 1.2 is 0.2 away, and 0.09 is more than 0.9 away.
0.95 is only 0.05 away, which is the smallest gap.
0.95 is closest to 1, being only 0.05 away.
3. Mia has 3 times as many stickers as Ben. Together they have 24 stickers. How many stickers does MIA have?
Answer and worked solution
Correct answer: C
Think in equal shares: Ben has 1 share and Mia has 3 shares — 4 shares altogether.
4 shares make 24, so one share is 24 ÷ 4 = 6.
Mia has 3 shares: 3 × 6 = 18.
Check: Mia 18 + Ben 6 = 24. ✓
Mia has 18 stickers.
How our practice works
Our Mathematical Reasoning papers are 35 questions in 40 minutes, with no calculator, at OC and selective level. The worked solution under each question shows the working, so a wrong answer shows where the thinking went off.
Common questions
Can my child use a calculator?
No. The section is sat without one at both levels.
Is it harder than school maths?
The content is school content up to Year 4 or Year 6. What makes it harder is that the questions are problems to work out rather than exercises to complete.
Also in the test: Reading · Thinking Skills
Practise free, no account needed. Every paper is marked the moment your child finishes, with a worked solution on every question.
Free practice draws from a limited set of questions, so some will repeat. Subscribers get the full question bank and fewer repeats.
Free OC Mathematical Reasoning paperFree Selective Mathematical Reasoning paperOC and Selective practice
Question counts, timings and test dates can change from year to year. The NSW Department of Education publishes the current year's details.
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