Selective School Maths Test: Mathematical Reasoning
The NSW Selective Mathematical Reasoning test asks students to use maths to solve problems. Understanding the conditions of a problem is as important as carrying out the calculation.
This guide offers original questions with worked solutions, alongside ways to organise information and check an answer. The examples are free to read and review without signing in.
Selective Mathematical Reasoning format
The section contains 35 questions in 40 minutes, answered on a computer. Each question has five answer options. Calculators and rulers are not permitted.
The department describes the maths as drawing on concepts learned at school up to Year 6. Preparation can focus on using familiar knowledge in unfamiliar situations. The practice topics in this guide are teaching examples, not a prediction of the next paper.
Turn the words into a useful representation
First say what the answer must describe: a cost, an amount left, a distance or a number of arrangements. Write down the relevant quantities with their units. Then decide whether a sketch, table, number line or short calculation will make the relationships clearer.
For a problem with two kinds of objects, start with a simple case in which every object is the same kind. Work out what changes when one is replaced. This often exposes the structure without needing formal algebra.
- Keep the whole clear. A fraction may refer to the starting amount or to what remains after an earlier step.
- Track units. Convert minutes and hours, or centimetres and metres, before combining them.
- Use the options carefully. Substitute a candidate into every condition, including any limit on the number or size of objects.
Manage the time without rushing the reading
The average allowance is just over a minute per question, but an average is not a deadline for every item. A short calculation can leave time for a longer reasoning problem.
During timed practice, note which questions absorb time because you have no clear method. After the session, solve those untimed and compare two possible approaches. Use the official online practice interface to learn its navigation before test day.
Check the method as well as the answer
- Estimate first. Decide whether the result should be small or large before calculating precisely.
- Check all conditions. A number that fits the total may still violate a condition about equal groups or whole objects.
- Name the error. Separate calculation slips from choosing the wrong operation or answering an intermediate step.
- Try a changed version. Alter one number after reviewing a solution and solve again. This checks whether the method makes sense beyond the original answer.
Example questions (written by iClass)
A tank starts three-quarters full. After 28 litres are used, it is two-fifths full.
What is the tank's capacity?
- A.40 litres
- B.60 litres
- C.70 litres
- D.80 litres
- E.100 litres
The 28 litres represent the difference between three-quarters and two-fifths of the same tank. In twentieths, that is 15/20 - 8/20 = 7/20. One twentieth is 28 ÷ 7 = 4 litres, so the full capacity is 20 × 4 = 80 litres. Check: 60 litres at the start minus 28 litres leaves 32 litres, which is two-fifths of 80.
A bus leaves at 9:18 am. It takes 27 minutes to reach the interchange. Maya needs 8 minutes to walk to the train platform. Trains leave at 9:40 am and every 12 minutes after that.
What is the earliest train Maya can catch?
- A.9:45 am
- B.9:52 am
- C.9:53 am
- D.10:00 am
- E.10:04 am
The bus arrives at 9:45 am, and Maya reaches the platform at 9:53 am. The trains leave at 9:40, 9:52 and 10:04. She misses the 9:52 train by one minute, so the earliest she can catch is 10:04 am. The platform arrival time is not itself a departure time.
A group buys 14 tickets. Adult tickets cost $18 each and child tickets cost $11 each. The total cost is $196.
How many adult tickets did the group buy?
- A.4
- B.5
- C.6
- D.7
- E.8
Fourteen child tickets would cost 14 × $11 = $154. The actual cost is $42 more. Replacing one child ticket with an adult ticket adds $7, so there are $42 ÷ $7 = 6 adult tickets. Check: 6 × $18 + 8 × $11 = $196.
Common questions
Mathematical Reasoning has 35 questions in 40 minutes. Each question has five choices.
The department describes the content as based on school concepts up to Year 6. Start by checking whether your child can explain and apply those concepts to unfamiliar problems.
Identify the exact step that went wrong, then redo the problem with written units and an estimate. If the method was sound, practise accuracy; if the setup was wrong, revisit how the quantities relate.
Other NSW Selective School Test sections
Next steps
- NSW Selective School Test guide: format, dates and how placement works.
- Selective test practice books: full practice papers with worked solutions.
Sources
- NSW Department of Education: Selective test format and student guide
- NSW Department of Education: Selective practice tests
Last reviewed 16 October 2026