Mathematical Reasoning Mock Test 10: 2026 NSW Selective Format

Build fluency with multi-step problems, diagrams, and data interpretation in our 35-question mock test—aligned to the Janison-style NSW Selective Mathematical Reasoning paper.

Duration

40 Minutes

Format

2026 NSW Format

Questions

35 multiple-choice

Level

Official Selective Test Level

Skills Covered in this Test

This mock test mirrors the official weightings of the NSW Department of Education exam.

The breakdown

  • Fractions: Adding, comparing, and simplifying fractional quantities in context.
  • Ratios: Part-part and part-whole relationships in applied settings.
  • Percentages: Discounts, changes, and comparisons expressed as percent.
  • Decimals: Place value, rounding, and decimal operations under time pressure.
  • Multi-step Word Problems: Breaking down scenarios into equations and checking reasonableness.
  • Probability Logic: Likelihood, counting outcomes, and constraints.

Sample Questions from Test 10

The first two questions of this mock test (same order and wording as the timed exam).

Mathematical Reasoning

A smoothie recipe mixes banana and yogurt in the ratio 2 cups of banana to 3 cups of yogurt. If you use 27 cu…

Question 1 · Multiple choice

Question

A smoothie recipe mixes banana and yogurt in the ratio 2 cups of banana to 3 cups of yogurt. If you use 27 cups of yogurt, how many cups of banana do you need?

Options

  • A. 12
  • B. 15
  • C. 18
  • D. 21
  • E. 24

Correct answer

C. 18

Explanation

The ratio of banana to yogurt is 2 : 3. That means: for every 2 parts of banana, there are 3 parts of yogurt. We are told the yogurt amount is 27 cups. Yogurt is the 3-part amount, so: 3 parts = 27 cups Now find 1 part: 27 / 3 = 9 cups Banana is 2 parts, so: 2 x 9 = 18 cups So the banana amount is 18 cups.

Mathematical Reasoning

A fair spinner has 36 equal sectors numbered from 1 to 36. What is the probability that the spinner stops on …

Question 2 · Multiple choice

Question

A fair spinner has 36 equal sectors numbered from 1 to 36. What is the probability that the spinner stops on a number that is a multiple of 12?

Options

  • A. 1/12
  • B. 1/6
  • C. 1/9
  • D. 1/18
  • E. 1/4

Correct answer

A. 1/12

Explanation

We need numbers from 1 to 36 that are multiples of 12. The multiples of 12 are: 12, 24, 36 That is 3 successful numbers. There are 36 numbers altogether from 1 to 36. So the probability is: 3/36 Simplify by dividing top and bottom by 3: 3/36 = 1/12 So the answer is 1/12.

Core Competencies

3D NetsAlgebraic SubstitutionsAngle PropertiesArea & PerimeterCartesian CoordinatesDecimalsFractionsGraph InterpretationInverse OperationsLogical DeductionMean, Median & ModeMental ArithmeticMulti-step Word ProblemsNumber SequencesOrder of OperationsPercentagesPrime NumbersProbability LogicProfit & LossRatiosReflection & RotationSpeed, Distance, TimeSquare & Cube NumbersSymmetryTime & CalendarsUnit ConversionsVenn DiagramsVolume & Capacity

Prepare with Precision

  • Sharpen accuracy on multi-step and diagram-based items.
  • Get comfortable with the Janison-style interface.
  • Identify topics to revisit before exam day.

This public page is designed so students and parents get rich, accurate information about the test structure and skills assessed. The full timed mock—including the rest of the 35 questions, scoring, and detailed review—is available to enrolled members after sign-in, matching how premium preparation platforms balance discoverability with protected content.

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