Mathematical Reasoning Mock Test 18: 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

  • Time & Calendars: Duration, timetables, and date arithmetic.
  • Speed, Distance, Time: Applying S=D×T and unit consistency.
  • Unit Conversions: Consistent units within metric and mixed measures.
  • Inverse Operations: Working backwards from a result to find an unknown.
  • Multi-step Word Problems: Breaking down scenarios into equations and checking reasonableness.
  • Ratios: Part-part and part-whole relationships in applied settings.

Sample Questions from Test 18

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

Mathematical Reasoning

A rectangle has a perimeter of 40 cm. If its length is 4 cm longer than its width, what is the area of the re…

Question 1 · Multiple choice

Question

A rectangle has a perimeter of 40 cm. If its length is 4 cm longer than its width, what is the area of the rectangle?

Options

  • A. 84 cm²
  • B. 96 cm²
  • C. 100 cm²
  • D. 80 cm²
  • E. 144 cm²

Correct answer

B. 96 cm²

Explanation

The rectangle has perimeter 40 cm. Use the perimeter formula: 2(length + width) = 40 Divide both sides by 2: length + width = 20 We are told the length is 4 cm longer than the width. So let width = w. Then length = w + 4. Substitute: w + (w + 4) = 20 2w + 4 = 20 2w = 16 w = 8 So the width is 8 cm and the length is: 8 + 4 = 12 cm Now find the area: 12 x 8 = 96 cm^2 So the area is 96 cm^2.

Mathematical Reasoning

In a group of 40 students, 25 play tennis, 15 play cricket, and 10 play both. How many students play neither …

Question 2 · Multiple choice

Question

In a group of 40 students, 25 play tennis, 15 play cricket, and 10 play both. How many students play neither sport?

Options

  • A. 0
  • B. 5
  • C. 10
  • D. 15
  • E. 20

Correct answer

C. 10

Explanation

To find how many students play neither sport, first find how many play at least one sport. Use: Tennis + Cricket - Both So: 25 + 15 - 10 = 30 That means 30 students play at least one of the two sports. There are 40 students altogether. So the number who play neither is: 40 - 30 = 10 So the answer is 10.

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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