Mathematical Reasoning Mock Test 15: 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

  • Profit & Loss: Revenue, cost, and margin reasoning in scenarios.
  • 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.
  • Mental Arithmetic: Fast, accurate calculation without a calculator.
  • Ratios: Part-part and part-whole relationships in applied settings.

Sample Questions from Test 15

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

Mathematical Reasoning

A project requires writing 600 pages. Jack writes 1/4 of the pages and Sarah writes 1/3 of the remaining page…

Question 1 · Multiple choice

Question

A project requires writing 600 pages. Jack writes 1/4 of the pages and Sarah writes 1/3 of the remaining pages. How many pages are left to write?

Options

  • A. 150
  • B. 300
  • C. 450
  • D. 250
  • E. 200

Correct answer

B. 300

Explanation

The project needs 600 pages in total. Jack writes 1/4 of the pages: 1/4 x 600 = 150 pages So the number of pages left is: 600 - 150 = 450 pages Now Sarah writes 1/3 of the remaining 450 pages: 1/3 x 450 = 150 pages So the number of pages still left to write is: 450 - 150 = 300 pages So 300 pages are left to write.

Mathematical Reasoning

A population of 2,000 birds increased by 15% in the first year and then decreased by 10% in the second year. …

Question 2 · Multiple choice

Question

A population of 2,000 birds increased by 15% in the first year and then decreased by 10% in the second year. What is the final population?

Options

  • A. 2,070
  • B. 2,100
  • C. 2,300
  • D. 2,050
  • E. 2,000

Correct answer

A. 2,070

Explanation

Start with 2,000 birds. In the first year, the population increases by 15%. 15% of 2000 is: 0.15 x 2000 = 300 So after the increase: 2000 + 300 = 2300 birds In the second year, the population decreases by 10%. 10% of 2300 is: 0.10 x 2300 = 230 So the final population is: 2300 - 230 = 2070 birds So the final population is 2,070.

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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