Mathematical Reasoning Mock Test 1: 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

  • Multi-step Word Problems: Breaking down scenarios into equations and checking reasonableness.
  • Order of Operations: Applying brackets, indices, and operation priority correctly.
  • Fractions: Adding, comparing, and simplifying fractional quantities in context.
  • Decimals: Place value, rounding, and decimal operations under time pressure.
  • Mental Arithmetic: Fast, accurate calculation without a calculator.
  • Logical Deduction: Using given constraints to eliminate impossible answers.

Sample Questions from Test 1

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

Mathematical Reasoning

A team of three students, Alex, Blake, and Casey, are tasked with labeling 1,500 envelopes. Alex labels 25 en…

Question 1 · Multiple choice

Question

A team of three students, Alex, Blake, and Casey, are tasked with labeling 1,500 envelopes. Alex labels 25 envelopes per hour for 12 hours. Blake then labels 30 envelopes per hour for 15 hours. Casey finishes the rest. What fraction of the total envelopes did Casey label?

Options

  • A. 1/2
  • B. 11/30
  • C. 1/3
  • D. 7/15
  • E. 1/4

Correct answer

A. 1/2

Explanation

Method 1: Work out how many envelopes each person labelled. Alex labelled 25 envelopes each hour for 12 hours. 25 x 12 = 300 Blake labelled 30 envelopes each hour for 15 hours. 30 x 15 = 450 So Alex and Blake together labelled: 300 + 450 = 750 envelopes There were 1,500 envelopes altogether, so Casey labelled the rest: 1,500 - 750 = 750 envelopes Now write Casey's share as a fraction of the whole job: 750 / 1,500 Divide top and bottom by 750: 750 / 1,500 = 1 / 2 So Casey labelled 1/2 of all the envelopes.

Mathematical Reasoning

The average height of a group of six students is 152 cm. A new student joins the group, and the average heigh…

Question 2 · Multiple choice

Question

The average height of a group of six students is 152 cm. A new student joins the group, and the average height increases to 153 cm. How tall is the new student?

Options

  • A. 153 cm
  • B. 156 cm
  • C. 159 cm
  • D. 162 cm
  • E. 165 cm

Correct answer

C. 159 cm

Explanation

Average means total divided by the number of students. So first we find the total height before the new student joined. 6 students had an average of 152 cm, so their total height was: 6 x 152 = 912 cm Now there are 7 students with an average of 153 cm, so the new total height is: 7 x 153 = 1,071 cm The new student's height is the extra amount added to the total: 1,071 - 912 = 159 cm So the new student is 159 cm tall.

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.

Enroll to Start Full Mock Test