Mathematical Reasoning Mock Test 10: 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

  • Fractions: Adding, comparing, and simplifying fractional quantities in context.
  • Ratios: Part-part and part-whole relationships in applied settings.
  • Percentages: Discounts, changes, and comparisons expressed as percent.
  • Decimals: Place value, rounding, and decimal operations under time pressure.
  • Multi-step Word Problems: Breaking down scenarios into equations and checking reasonableness.
  • Probability Logic: Likelihood, counting outcomes, and constraints.

Sample Questions from Test 10

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

Mathematical Reasoning

A farm has a wheat field of 2 square kilometres. A harvester machine cuts 1600 square metres of wheat per day…

Question 1 · Multiple choice

Question

A farm has a wheat field of 2 square kilometres. A harvester machine cuts 1600 square metres of wheat per day on average. The harvesting team plans to finish the harvesting in 25 days. How many such machines does the team need?

Options

  • A.50
  • B.40
  • C.60
  • D.80
  • E.25

Correct answer

A.50

Explanation

Step 1: Convert the field area to square metres

2 km² = 2 × 1 000 000 m² = 2 000 000 m²

(1 km = 1 000 m, so 1 km² = 1 000 × 1 000 = 1 000 000 m²)

Step 2: Find how much area ONE machine covers in 25 days

One machine cuts 1 600 m² per day.

In 25 days: 1 600 × 25 = 40 000 m² per machine

Step 3: Find how many machines are needed

Total area ÷ area per machine = 2 000 000 ÷ 40 000 = 50 machines

Check: 50 machines × 40 000 m² each = 2 000 000 m² ✓

Answer: 50 machines are needed

Mathematical Reasoning

Three people, A, B and C, first contributed the same amount of money to buy 5 movie tickets. Person A took 1 …

Question 2 · Multiple choice

Question

Three people, A, B and C, first contributed the same amount of money to buy 5 movie tickets. Person A took 1 ticket, and Persons B and C took two tickets each. Each ticket cost $6. How much money should each of Person B and Person C give back to Person A?

Options

  • A.$4
  • B.$6
  • C.$8
  • D.$3
  • E.$2

Correct answer

E.$2

Explanation

Step 1: Find the total cost and each person's equal contribution

Total cost = 5 tickets × $6 = $30

Each person contributed equally: $30 ÷ 3 = $10 each

Step 2: Find the actual value each person received

PersonTickets takenValue receivedPaidBalance
A11 × $6 = $6$10Overpaid by $4
B22 × $6 = $12$10Underpaid by $2
C22 × $6 = $12$10Underpaid by $2

Step 3: Work out the repayments

A overpaid by $4 total. B owes $2 and C owes $2 to A.

So each of B and C gives A $2.

Check: A receives $2 + $2 = $4 back. A's net cost = $10 − $4 = $6 = 1 ticket ✓

Answer: Each of B and C gives A $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.

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