Selective School Maths Test: Topics, Question Types & Tips

The Mathematical Reasoning section of the 2026 SHSPT contains 35 multiple-choice questions, each with 5 options, to be completed in 40 minutes. No calculator is allowed — students may use scratch paper for working out.

This section contributes 25% of the overall placement score. Importantly, it's called "Mathematical Reasoning" — the emphasis is on applying mathematical understanding to solve problems, not recalling memorised procedures. Students who rely on rote computation without conceptual understanding will struggle.

The section draws from Stage 2–3 (Year 4–6) curriculum content across seven major topic areas:

1. Number and arithmetic

• Operations with whole numbers (addition, subtraction, multiplication, division, mixed operations)
• Multi-step word problems involving money, time, or measurement
• Estimation and reasonableness checks

2. Fractions, decimals, and percentages

• Comparing and ordering fractions and decimals
• Converting between fractions, decimals, and percentages
• Percentage of a quantity, percentage increase/decrease
• Fraction-of-amount problems in real contexts (sharing, discounts, recipes)

3. Patterns and sequences

• Number patterns with additive, multiplicative, or mixed rules
• Completing tables or sequences, including patterns in shapes or grids
• Identifying the nth term or applying a rule to find a missing element

4. Pre-algebra (algebraic reasoning)

• Using simple algebra notation or unknowns in equations
• Solving for unknowns in balance equations or worded relationships
• Understanding equalities/inequalities and maintaining balance

5. Measurement and geometry

• Perimeter, area, and volume of basic and composite shapes
• Angle properties (straight lines, right angles, angle sums)
• Units and conversions for length, mass, capacity, and time
• Reading and using scales (rulers, thermometers, speedometers)

6. Data and chance (statistics and probability)

• Reading and interpreting tables, bar graphs, line graphs, and pie charts
• Calculating totals, differences, and simple averages from data displays
• Basic probability in equally likely cases (dice, spinners, simple selection)

7. Multi-step problem-solving and puzzle-style questions

• Problems combining multiple topic areas (geometry + fractions, time + arithmetic)
• Logical numeric puzzles requiring deduction from constraints

The difficulty in Mathematical Reasoning doesn't come from advanced maths — it comes from how standard concepts are applied in unfamiliar ways:

• Multi-step problems: Most questions require 2–4 steps to solve, and the challenge is figuring out which steps to take, not just executing them
• Unfamiliar contexts: Questions wrap familiar maths in novel scenarios — students who've only drilled textbook problems may not recognise the underlying concept
• Distractor options: With 5 answer choices, common mistakes are designed into the options. Students who rush or skip steps will find a plausible-looking wrong answer waiting for them
• No calculator: Arithmetic errors under time pressure are a significant source of lost marks. Mental maths fluency is essential
• Time pressure: At roughly 1 minute 9 seconds per question, there's no time for slow, written-out methods on every problem

With 35 questions in 40 minutes, efficient time use is critical:

• Quick wins first: Scan each question — if you can solve it in under a minute, do it immediately. Skip harder questions and come back.
• Don't get stuck: If a question takes more than 90 seconds, flag it and move on. One hard question isn't worth three easier ones.
• Use scratch paper strategically: Write down key numbers and intermediate results. Trying to hold everything in your head causes errors.
• Estimate before calculating: Rough estimation can eliminate 2–3 wrong answers immediately, saving time and reducing error risk.
• Check your work on easy questions: Losing marks on questions you can solve is more costly than not solving the hardest ones.
• Attempt every question: There's no negative marking. If time is running out, make educated guesses on remaining questions.

Certain mistakes appear over and over in maths reasoning tests:

• Unit conversion errors: Mixing up cm and m, grams and kg, or minutes and hours. Always check that your answer is in the right unit.
• Reading the question wrong: The question asks for the remaining amount, but the student calculates the total. Read what's being asked twice.
• Fraction/decimal confusion: Students who aren't fluent at converting between fractions, decimals, and percentages lose time and make errors.
• Forgetting order of operations: BODMAS/BIDMAS mistakes are common under time pressure.
• Misinterpreting graphs: Reading the wrong axis, misunderstanding scale intervals, or confusing "increase" with "total".
• Choosing the first plausible answer: With 5 options, the first reasonable-looking answer may be a deliberate trap. Verify before selecting.

Effective maths preparation builds both conceptual understanding and speed:

Master the fundamentals:

• Ensure the entire Year 5–6 maths curriculum is solid — no gaps in understanding fractions, decimals, percentages, area, perimeter, or data interpretation
• Focus on understanding concepts, not just memorising methods. Can your child explain why a method works?

Build mental arithmetic speed:

• Practise times tables until they're instant (not just recitable)
• Daily mental maths challenges: quick multiplication, division, fraction conversions
• Speed is built through regular short sessions, not occasional marathon drills

Practise multi-step word problems:

• Work through problems that require identifying what to do, not just doing it
• Practise translating worded problems into mathematical operations
• Focus on problems with multiple solution steps — this is where the real challenge lies

Review every mistake:

• After each practice session, review every wrong answer and understand why it was wrong
• Categorise mistakes: was it a careless arithmetic error, a conceptual gap, or a time-pressure issue?
• Target the category causing the most errors

SelectiveExams includes Mathematical Reasoning in every monthly mock exam — 35 questions under strict 40-minute timing with instant scoring and detailed worked solutions for every question.

Create your free account and start practising today.