Mathematical Reasoning Mock Test 1: 2027 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

2027 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 rhombus and a rectangle have the same perimeter.

Question 1 · Multiple choice

Question

A rhombus and a rectangle have the same perimeter.

Each side of the rhombus is 11 cm.

The rectangle is 16 cm long.

What is the width of the rectangle?

Options

  • A.4 cm
  • B.5 cm
  • C.7 cm
  • D.8 cm
  • E.6 cm

Correct answer

E.6 cm

Explanation

Step 1: Find the perimeter of the rhombus

A rhombus has 4 equal sides.

Each side = 11 cm

Perimeter of rhombus = 4 × 11 = 44 cm

Step 2: Set up the rectangle perimeter equation

The rectangle has the same perimeter (44 cm) and a length of 16 cm.

┌──────────────────┐
│                  │ ← width = w
│   length = 16    │
└──────────────────┘

Perimeter = 2 × (length + width)

44 = 2 × (16 + w)

Step 3: Solve for the width

44 ÷ 2 = 16 + w

22 = 16 + w

w = 22 − 16 = 6 cm

Check: 2 × (16 + 6) = 2 × 22 = 44 cm ✓ Matches the rhombus perimeter.

Answer: The rectangle's width is 6 cm

Mathematical Reasoning

I am playing a card game that starts with 100 points.

Question 2 · Multiple choice

Question

I am playing a card game that starts with 100 points.

  • I play 4 rounds, scoring 47 points each round.
  • I then play 1 bonus round, losing some points.
  • I finish with 233 points.

Options

How many points did I lose in the bonus round?

  • A.45
  • B.55
  • C.75
  • D.89
  • E.267

Correct answer

B.55

Explanation

Step 1: Calculate the score after 4 regular rounds

Starting score: 100 points

Each of the 4 rounds adds 47 points:

4 × 47 = 188 points earned

Score after 4 rounds = 100 + 188 = 288 points

Step 2: Find how many points were lost in the bonus round

Final score = 233 points.

The bonus round LOST some points:

Points lost = score before bonus − final score

= 288 − 233 = 55 points

Answer: 55 points were lost in the bonus round

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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