Free selective test mathematical reasoning practice
The NSW Selective High School Placement Test is now taken on computer. This practice test is about half the length of the real Mathematical Reasoning section at the same pace: 18 multiple-choice questions with five options in 21 minutes, no calculator. You'll get your score by topic and a worked solution for every question.
Selective Mathematical Reasoning practice test
- Questions
- 18
- Time
- 21 min
- Calculator
- No
- ✓ 18 questions in 21 minutes: the same pace as the real section (35 questions in 40 minutes).
- ✓ Every question has five options and one correct answer.
- ✓ No calculator, as in the real test. Use paper for working out.
- ✓ There's no penalty for a wrong answer, so don't leave any blank.
Free, no account needed. Your answers stay in your browser; we only save your score.
The real test
- Format
- Computer-based, on computers provided by the NSW Department of Education, held in May
- Mathematical Reasoning
- 35 multiple-choice questions, five options each, 40 minutes
- Other sections
- Reading (17 questions, 45 minutes), Thinking Skills (40 questions, 40 minutes), Writing (1 task, 30 minutes)
- Calculators
- Not allowed in any section; students can use paper for working out
Sources: NSW Department of Education: Selective High School Placement Test · NSW Department of Education: Selective high school practice tests. Practice questions written by EagleTeach tutors; not affiliated with any exam board.
What the Mathematical Reasoning section tests
The department says the questions use the maths your child already learns at school, so there's no new content to study. What makes them hard is that most need two or three steps of reasoning, and there's just over a minute for each.
This practice test covers the main areas: number and fractions, patterns and algebra, measurement and geometry, and statistics and probability. Several questions include a tempting wrong answer, such as the number who walk instead of the number who don't, the way the real test does.
Getting used to the on-screen test
Since the tests for 2026 entry, every section has been answered on computer, so practising on screen matters: reading a question on a screen, keeping track of the countdown and working on paper at the same time all take getting used to.
Start with the department's free official practice tests, which use the same system as the real test, and use extra practice like this one to build speed.
- ✓ Do one timed section at a time before attempting all four
- ✓ Leave a question that's taking too long, flag it and come back
- ✓ Afterwards, redo every wrong answer untimed before reading the explanation
FAQs
Is this an official NSW selective practice test?＋
No. The questions were written by EagleTeach tutors in the style of the Mathematical Reasoning section. The NSW Department of Education publishes free official online practice tests, and we recommend starting with those.
How many questions are in the real Mathematical Reasoning test?＋
35 multiple-choice questions with five possible answers, in 40 minutes, according to the department's practice test page. This practice test has 18 questions in 21 minutes, about the same pace.
Can you use a calculator in the selective test?＋
No. Calculators aren't allowed in any section of the Selective High School Placement Test, so this practice test doesn't provide one.
Is the selective test still on paper?＋
No. The Selective High School and Opportunity Class placement tests moved from paper to computer-based tests for students starting in 2026, and are taken on computers provided by the department.
Does this score predict my child's selective result?＋
No. Placement is decided from the department's own marking and calculation across all the test sections, so a practice score can only show which topics need work.
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