Mathematical Reasoning Mock Test 19: 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

  • Algebraic Substitutions: Replacing variables and evaluating expressions.
  • 3D Nets: Visualising folded and unfolded solid shapes.
  • Graph Interpretation: Reading scales, trends, and values from charts and tables.
  • Profit & Loss: Revenue, cost, and margin reasoning in scenarios.
  • Order of Operations: Applying brackets, indices, and operation priority correctly.
  • Ratios: Part-part and part-whole relationships in applied settings.
  • Mental Arithmetic: Fast, accurate calculation without a calculator.

Sample Questions from Test 19

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

Mathematical Reasoning

The sum of three consecutive whole numbers is 72. What is the product of the smallest and the largest of thes…

Question 1 · Multiple choice

Question

The sum of three consecutive whole numbers is 72. What is the product of the smallest and the largest of these three numbers?

Options

  • A. 528
  • B. 575
  • C. 576
  • D. 600
  • E. 624

Correct answer

B. 575

Explanation

Let the three consecutive whole numbers be: n - 1, n, n + 1 Their sum is 72, so: (n - 1) + n + (n + 1) = 72 3n = 72 n = 24 So the numbers are: 23, 24, 25 Now multiply the smallest and largest: 23 x 25 = 575 So the answer is 575.

Mathematical Reasoning

A large rectangle measuring 12 cm by 8 cm has a smaller square with a perimeter of 16 cm removed from its cen…

Question 2 · Multiple choice

Question

A large rectangle measuring 12 cm by 8 cm has a smaller square with a perimeter of 16 cm removed from its center. What is the remaining area of the rectangle?

Options

  • A. 64 cm²
  • B. 80 cm²
  • C. 84 cm²
  • D. 92 cm²
  • E. 96 cm²

Correct answer

B. 80 cm²

Explanation

First find the area of the large rectangle: 12 x 8 = 96 cm^2 The smaller square has perimeter 16 cm. A square has 4 equal sides, so each side is: 16 / 4 = 4 cm Now find the area of the square: 4 x 4 = 16 cm^2 Subtract the square from the rectangle: 96 - 16 = 80 cm^2 So the remaining area is 80 cm^2.

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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