Master Selective Test Maths
The NSW selective maths test doesn't reward memorising formulas—it rewards reasoning. Students who practise by thinking through problems, not just drilling procedures, consistently outperform those who don't. These guides show you how.
The ARIS Maths Pyramid
Fifteen skills across three tiers, organised by how the NSW selective test actually distributes difficulty. Master the base, reason through the middle, and attack the problem-solving tier where the top marks live.
Problem Solving
Work it out step by step
The skills that win selective test marks—multi-step, unfamiliar problems where you must reason, not just recall. These questions are disproportionately where top scores are built.
Reasoning
Think it through
Apply number sense to structured domains: measurement, data, spatial thinking, chance, and ratio. These skills appear in roughly 35% of selective test questions.
Number Sense
Get the numbers right
The foundation of all maths. Strong number sense lets you estimate, check, and reason with confidence—without a calculator.
Why Three Tiers?
Number Sense first. Roughly 40% of selective test questions draw on these foundations. You can't reason well with numbers you don't understand deeply.
Reasoning in the middle. Around 35% of questions apply number sense to structured domains—measurement, data, geometry, probability.
Problem Solving at the top. The remaining 25% are multi-step, unfamiliar problems. Disproportionately where top scores are built.
The Research Behind Our Method
Every exercise format in our Maths Gym applies a specific, evidence-based learning principle. These aren't theories—they're findings with measurable effect sizes from peer-reviewed studies.
Worked Examples
Showing a step-by-step solution before asking students to solve dramatically accelerates learning for novices.
Fill the Gap & Spot the Error exercisesInterleaved Practice
Mixing different problem types across a session beats blocked practice by 30%. Forces students to identify which skill applies—exactly what the NSW test demands.
Mixed-skill sessionsProductive Failure
Students who attempt a problem before seeing the method learn the method more deeply. Struggling first builds better understanding.
Solve exercisesVariation Theory
Learning accelerates when students contrast correct examples with near-miss incorrect ones. The difference between right and wrong reveals the concept itself.
Identify & Rank exercises6 Maths Exercise Formats
Unlike writing drills, maths exercises need different evaluation for different tasks. Multiple choice gets instant feedback. Shown working gets thoughtful AI coaching. Every format is designed for a specific cognitive purpose.
Identify
Multiple choice — pick the correct answer, approach, or example.
Rank
Order solutions by quality, correctness, or efficiency.
Spot the Error
Find and fix the mistake in a worked solution.
Solve
Show your working and give the answer.
Explain
Write why a method works or why an answer is wrong.
Fill the Gap
Complete the missing step in a worked solution.
Every Skill the Test Actually Assesses
Each skill has a full guide explaining the concept, worked examples showing the wrong and correct approach, common mistakes, and a practice challenge.
Number Sense
— Get the numbers rightPlace Value
Know exactly what each digit is worth.
Read guideFractions
See fractions as one number, not two.
Read guideOperations
Choose the right calculation, then check it.
Read guidePercentages
Percentages are just fractions in disguise.
Read guidePatterns
Find the rule, then use it.
Read guideReasoning
— Think it throughMeasurement
Convert and calculate without losing track of units.
Read guideReading Data
Find the story hiding in numbers.
Read guideSpatial Reasoning
See the shape in your mind before you draw it.
Read guideProbability
Count what could happen, count what you want.
Read guideRatio & Proportion
If one part changes, all parts change together.
Read guideProblem Solving
— Work it out step by stepWord Problems
Turn words into maths, then solve.
Read guideWorking Backwards
Unwind the problem from the answer.
Read guideLogical Deduction
Eliminate what cannot be true.
Read guideAlgebra Thinking
Let the unknown be a box—what's inside?
Read guideMulti-Step Problems
Break it into steps, solve one at a time.
Read guideReady to Practice These Skills?
Reading about techniques is just the start. Our Maths Gym lets you practise each skill with instant feedback across 6 exercise formats, tracking your progress as you improve.