Skills assessed
Problem solving
Turning a worded situation into a plan and a calculation.
Multi-step reasoning
Holding several steps together to reach a final answer.
Number sense
Fractions, decimals, percentages, ratios and proportion.
Patterns & measurement
Sequences, relationships, measurement and data.
Common question types
Word problems
Real-world scenarios that must be translated into maths.
Patterns & sequences
Finding the rule and extending or completing it.
Measurement & geometry
Length, area, time, shape and spatial reasoning.
Data & graphs
Reading tables and charts to answer questions.
Why Mathematical Reasoning matters
This section separates students who have memorised procedures from those who genuinely reason. Questions are often short on numbers but long on thinking — the challenge is choosing the right approach quickly.
Because time is tight, recognising the type of problem at a glance is as valuable as the arithmetic itself.
One example question
A single representative question, to show what this section looks like — not a practice set. The full sets live on the free practice questions page below.
A jug holds 1.5 litres. If 3 glasses each hold 250 mL are poured from a full jug, how much is left?
- 250 mL
- 500 mL
- 750 mL ✓
- 1 litre
Answer & explanation
750 mL. 3 × 250 mL = 750 mL poured. 1.5 L = 1500 mL, so 1500 − 750 = 750 mL remains. The trick is converting litres and millilitres before subtracting.
Want more? Try a set of free practice questions across all four subjects.
How to prepare at home
What helps between now and the test. Technique for the test itself — pacing, elimination, checking your reasoning — is a separate job, and has its own guide.
- ✓Sharpen mental maths and times tables until arithmetic is automatic.
- ✓Ask for the working, not just the answer — that is where reasoning shows.
- ✓Talk through everyday maths: change, timings, distances, doubling a recipe.
For technique in the test itself, read how to improve at Mathematical Reasoning.
Ready to practise Mathematical Reasoning?
Sit a free, full-length sample test and practise Mathematical Reasoning under real exam conditions.