Mathematical Reasoning Mock Test 6: 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

  • Probability Logic: Likelihood, counting outcomes, and constraints.
  • Cartesian Coordinates: Plotting, distance, and reading coordinates from grids.
  • Graph Interpretation: Reading scales, trends, and values from charts and tables.
  • Fractions: Adding, comparing, and simplifying fractional quantities in context.
  • Ratios: Part-part and part-whole relationships in applied settings.
  • Logical Deduction: Using given constraints to eliminate impossible answers.

Sample Questions from Test 6

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

Mathematical Reasoning

Three apples and two oranges cost $4.80. Two apples and three oranges cost $4.70. What is the cost of one app…

Question 1 · Multiple choice

Question

Three apples and two oranges cost $4.80. Two apples and three oranges cost $4.70. What is the cost of one apple?

Options

  • A. $0.90
  • B. $0.95
  • C. $1.00
  • D. $0.85
  • E. $0.80

Correct answer

C. $1.00

Explanation

Let the price of one apple be A and the price of one orange be O. We are told: 3A + 2O = 4.80 2A + 3O = 4.70 Method 1: Add the equations. (3A + 2O) + (2A + 3O) = 4.80 + 4.70 5A + 5O = 9.50 Now divide both sides by 5: A + O = 1.90 Method 2: Subtract the second equation from the first: (3A + 2O) - (2A + 3O) = 4.80 - 4.70 A - O = 0.10 Now we have: A + O = 1.90 A - O = 0.10 Add these two equations: 2A = 2.00 A = 1.00 So one apple costs $1.00.

Mathematical Reasoning

A bag contains 5 red, 7 blue, and 8 green marbles. If you pick one marble, what is the probability it is NOT …

Question 2 · Multiple choice

Question

A bag contains 5 red, 7 blue, and 8 green marbles. If you pick one marble, what is the probability it is NOT blue?

Options

  • A. 7/20
  • B. 13/20
  • C. 3/5
  • D. 1/2
  • E. 12/20

Correct answer

B. 13/20

Explanation

There are 20 counters altogether. We are told 7 are blue. So the number that are not blue is: 20 - 7 = 13 The probability of picking a counter that is not blue is: 13 / 20 So the answer is 13/20.

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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