Mathematical Reasoning 1
Free NSW Selective Mathematical Reasoning Practice Test 1
35 questions in 40 minutes, as in the Selective High School Placement Test, no calculator.
35 questions · 40 minutes
Free · no sign-up · NSW, Australia
Free NSW selective test practice: Mathematical Reasoning
Practise the Mathematical Reasoning section of the NSW Selective High School Placement Test online: 35 multiple-choice questions in 40 minutes, five options each, no calculator, just like the real section. There are two tests with different questions, and every answer is explained step by step when you finish.
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Mathematical Reasoning 2
Free NSW Selective Mathematical Reasoning Practice Test 2
A second Mathematical Reasoning test with new questions: 35 questions in 40 minutes.
35 questions · 40 minutes
How the tests work
Timed like the real test
Each module has its own countdown and ends when time is up.
No calculator
As in the real test: work things out on paper.
Flag and eliminate
Mark questions for review and cross out options you've ruled out.
Marked instantly
See your score for each module, your weakest topics and a worked explanation for every question.
The real test at a glance
- Reading
- 17 questions (38 answers) in 45 minutes
- Mathematical Reasoning
- 35 multiple-choice questions in 40 minutes, five options each
- Thinking Skills
- 40 multiple-choice questions in 40 minutes, four options each
- Writing
- One response in 30 minutes
- Weighting
- Each section counts for 25%
- Calculator
- Not allowed in any section; the test is taken on a computer
Checked against the official sources below on 27 October 2026.
What our questions cover
Number
Fractions of amounts, percentages and discounts, ratio and rates, money and best buys.
Patterns and algebra
Growing patterns, working backwards and number puzzles.
Measurement
Time and timetables, speed, area and perimeter, volume and capacity.
Geometry, statistics and chance
Angles in triangles, on lines and in polygons; the mean; chance with marbles and dice.
Tips for test day
- That's about 68 seconds a question. Skip one that's taking too long and come back to it.
- Read the question twice: many mistakes come from answering a different question ("how much is left" vs "how much was spent").
- Estimate first, then use the estimate to rule out options.
- Wrong answers don't lose marks, so answer every question.
More help: NSW selective test: a guide for parents, How to help your child with maths at home and a free mental maths game.
Questions
Are these official selective school tests?
No. They are original questions written by TutorAura to the published format of the Mathematical Reasoning section. The NSW Department of Education offers free official practice tests, including computer-based ones that use the real test software: try those too.
What maths is in the selective test?
The department says the questions use maths concepts students already learn at school, up to Year 6, applied to problems that need reasoning. There's no need to learn extra topics, but timed practice helps.
Do I get a selective test score?
No. The real test's marks are combined across the four sections, so we show the number of questions you got right, with a breakdown by topic.
Can my child use a calculator?
No. Calculators aren't allowed in any part of the test, so these practice tests don't include one. Students can work things out on paper.
Official sources
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