Mathematical Reasoning Mock Test 9: 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

  • Venn Diagrams: Overlaps, unions, and logical counts from sets.
  • Ratios: Part-part and part-whole relationships in applied settings.
  • Speed, Distance, Time: Applying S=D×T and unit consistency.
  • Profit & Loss: Revenue, cost, and margin reasoning in scenarios.
  • Logical Deduction: Using given constraints to eliminate impossible answers.
  • Graph Interpretation: Reading scales, trends, and values from charts and tables.
  • Decimals: Place value, rounding, and decimal operations under time pressure.

Sample Questions from Test 9

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

Mathematical Reasoning

A bag holds red and yellow beads.

Question 1 · Multiple choice

Question

A bag holds red and yellow beads.

  • There are 4 times as many yellow beads as red beads.
  • When 6 yellow beads are removed, there are twice as many yellow beads as red beads.

Options

How many beads were in the bag to start?

  • A.10
  • B.12
  • C.15
  • D.18
  • E.20

Correct answer

C.15

Explanation

Step 1: Set up expressions using one variable

Let the number of red beads = r.

Yellow beads = 4r (four times as many yellow as red).

Step 2: Use the second clue (remove 6 yellow beads)

After removing 6 yellow beads:

  • Yellow left = 4r − 6
  • Red stays at r

Now Tom has twice as many yellow as red:

4r − 6 = 2 × r

Step 3: Solve the equation

4r − 6 = 2r

4r − 2r = 6

2r = 6

r = 3 (there are 3 red beads)

Step 4: Find the total number of beads

Yellow beads = 4r = 4 × 3 = 12

Total beads = red + yellow = 3 + 12 = 15

Check: After removing 6 yellow: 12 − 6 = 6 yellow, 3 red. Is 6 = 2 × 3? Yes ✓

Answer: 15 beads in total

Mathematical Reasoning

In play money:

Question 2 · Multiple choice

Question

In play money:

  • 6 winks = 4 zots
  • 2 zots = 5 flips

How many winks are worth the same as 20 flips?

Options

  • A.9 winks
  • B.10 winks
  • C.15 winks
  • D.18 winks
  • E.12 winks

Correct answer

E.12 winks

Explanation

What we know:

  • 6 winks = 4 zots
  • 2 zots = 5 flips

Step 1: Convert 20 flips → zots

2 zots = 5 flips, so 1 flip = 2/5 of a zot.

20 flips = 20 × (2/5) = 40/5 = 8 zots

Step 2: Convert 8 zots → winks

6 winks = 4 zots, so 1 zot = 6/4 = 1.5 winks.

8 zots = 8 × 1.5 = 12 winks

20 flips
  ↓ (×2/5)
  8 zots
  ↓ (×1.5)
 12 winks

Check: 12 winks = 8 zots (÷1.5) ✓. 8 zots = 20 flips (×5/2) ✓.

Answer: 12 winks

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.

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