Selective Mathematical Reasoning — Question Types & How to Practise (2026)

1. What Mathematical Reasoning really tests

Selective Mathematical Reasoning tests whether students can use school mathematics to solve unfamiliar problems under time pressure. It is not mainly a memory test. A student may know the curriculum content but still struggle if they cannot translate the wording, choose a strategy and calculate efficiently.

Core skills being assessed

• Word problem translation: turning language like “three times as many”, “shared equally”, “difference”, “remaining” or “per cent of” into mathematical operations
• Foundational fluency: quick recall of times tables, fraction-decimal-percentage equivalents, mental arithmetic and common measurement conversions
• Mathematical reasoning: deciding which information matters, which operation is needed and whether an answer is reasonable
• Multi-step problem solving: holding several pieces of information in mind and avoiding early mistakes that flow through the whole solution
• Efficient checking: using estimation, answer options and number sense to catch impossible answers

The strongest students are not always the ones who know the most advanced procedures. They are often the students who can set up a familiar-looking but slightly twisted problem quickly, then keep their working neat enough to avoid careless errors.

2. Core question patterns

Selective-style practice is the best way to build pattern recognition. Topic lists are useful, but students need repeated exposure to the way these ideas appear inside timed problem-solving questions.

Number, operations, fractions and percentages

• Multi-step arithmetic in realistic contexts
• Fractions of quantities, equivalent fractions and fraction comparisons
• Decimals and percentages, especially discounts, increases and comparisons
• Ratios, rates and proportional reasoning
• Number patterns, sequences and missing values

Measurement and geometry

• Area, perimeter and volume questions
• Composite shapes and diagrams that require careful visualisation
• Angles, symmetry and transformations
• Time, distance, speed and elapsed-time problems
• Metric unit conversions

Data, chance and problem solving

• Reading tables, charts and graphs accurately
• Comparing datasets and identifying trends
• Mean, median, mode and range
• Probability expressed as fractions, decimals or percentages
• Problems where answer options can be tested efficiently

3. Timing & pacing cues

Students have 40 minutes for 35 questions, so the average pace is a little over one minute per question. In practice, some questions should take far less than that, so there is enough time for the more complex problems.

Target timing

• Quick questions: 30–60 seconds for straightforward calculations, direct graph reading or familiar patterns
• Standard questions: 1–2 minutes for multi-step word problems or fraction/percentage reasoning
• Hard questions: 2–3 minutes for complex spatial, proportional or multi-condition problems
• Danger zone: if a question has not been translated into a clear method after about 30–45 seconds, it may be better to flag it and move on

Use answer options intelligently

• Estimate before calculating so obviously unreasonable options can be ignored
• Work backwards from the answer choices when the algebra or setup feels messy
• Check whether the question asks for the total, the difference, one person’s amount or what is left over
• Make an educated guess rather than leaving anything blank

4. Mistakes to avoid

• Doing calculations before understanding the question: students should identify what is being asked before writing numbers down.
• Ignoring units: metres vs centimetres, hours vs minutes, grams vs kilograms and dollars vs cents can completely change the answer.
• Using long methods when a shortcut is available: estimation, answer-option testing and friendly numbers often save time.
• Losing track in multi-step questions: neat working on paper matters because the test is on screen but the reasoning still happens off screen.
• Spending too long on one hard question: every multiple-choice question is worth one response, so protecting time matters.

5. Practise the right way

Good selective maths practice should develop both mathematical strength and test behaviour. A child who can solve a problem slowly at the kitchen table may still need practice solving similar problems quickly on screen.

Build fluency first

Times tables, common fractions, decimal conversions, percentages and mental arithmetic should become automatic. When these basics are slow, harder reasoning feels much more difficult than it needs to.

Use targeted mini-tests

Short topic-based sessions help identify whether the real issue is fractions, data, geometry, word problem translation or speed.

Use full section practice

A 40-minute Mathematical Reasoning section helps students learn pacing, flagging and stamina. This should be followed by careful review, not just a score check.

Review mistakes properly

• Classify the mistake: reading, setup, calculation, concept, timing or guessing
• Redo the question: solve it again without looking at the answer
• Find the pattern: repeated error types should drive the next practice session
• Explain the method: if the student can explain it clearly, the learning is much more likely to stick

• How much time should my child spend on each Selective Mathematical Reasoning question?

  Aim for about 1.1 minutes per question on average. Some questions should be much quicker, while harder questions may need two or three minutes. If a question is taking too long, students should make an educated guess, flag it if the interface allows, and move on.
• Are calculators allowed in Selective Mathematical Reasoning?

  No. Students cannot use a calculator, but they can use paper for working out. This makes mental maths fluency and neat working especially important.
• Is Selective Mathematical Reasoning just Year 6 maths?

  The questions draw on school mathematics, but they test application and reasoning rather than simple recall. Students need to apply familiar ideas in unfamiliar problem-solving contexts.
• What topics should my child prioritise?

  Prioritise fractions, decimals, percentages, ratios, multi-step word problems, measurement, geometry, data and probability. Just as importantly, practise translating word problems into clear mathematical steps.
• How often should my child do a full maths section?

  During steady preparation, occasional full 40-minute sections are useful. Closer to the test, they can be used more often, but every full section should be followed by careful review.

Sources & acknowledgements

• NSW Department of Education — Selective high school practice tests and section timing: education.nsw.gov.au/.../selective-high-school-practice-tests
• NSW Department of Education — Get ready for the Selective High School Placement Test: education.nsw.gov.au/.../get-ready-for-the-selective-high-school-placement-test
• NSW Education Standards Authority — Mathematics K–10 Syllabus: curriculum.nsw.edu.au/.../mathematics-k-10-2022