Mathematical Reasoning Mock Test 6: 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

  • 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

The ratio of Adam's savings to John's savings was 9 : 4. After Adam spent \$63, the ratio became 3 : 2. How m…

Question 1 · Multiple choice

Question

The ratio of Adam's savings to John's savings was 9 : 4. After Adam spent $63, the ratio became 3 : 2. How much savings did John have?

Options

  • A.$56
  • B.$63
  • C.$72
  • D.$84
  • E.$126

Correct answer

D.$84

Explanation

Step 1: Express both savings using one variable

Original ratio Adam : John = 9 : 4.

Let Adam's savings = 9k and John's savings = 4k.

Step 2: Set up the equation for the new ratio

John's savings are unchanged (he doesn't spend anything).

After Adam spends $63:

  • Adam has: 9k − 63
  • John still has: 4k

The new ratio is 3 : 2:

(9k − 63) : 4k = 3 : 2

Step 3: Solve for k

Cross-multiply (means × extremes):

2 × (9k − 63) = 3 × 4k

18k − 126 = 12k

18k − 12k = 126

6k = 126

k = 126 ÷ 6 = 21

Step 4: Find John's savings

John = 4k = 4 × 21 = $84

Check:

  • Adam originally: 9 × 21 = $189
  • After spending: $189 − $63 = $126
  • New ratio: $126 : $84 = 3 : 2 ✓

Answer: John has $84

OptionValueWhy it is wrong
A$56Used k = 14 — solved the equation incorrectly. ✗
B$63Confused Adam's spend with John's savings. ✗
C$72Used k = 18 — arithmetic slip. ✗
D$844 × 21 = 84. ✓
E$126Found 6k = 126 but gave that as the answer instead of 4k. ✗

Mathematical Reasoning

Some coins are used to form a pentagon. Each side of the pentagon is made up of 8 coins. How many coins are u…

Question 2 · Multiple choice

Question

Some coins are used to form a pentagon. Each side of the pentagon is made up of 8 coins. How many coins are used altogether?

Options

  • A.40
  • B.30
  • C.35
  • D.38
  • E.45

Correct answer

C.35

Explanation

Step 1: Understand the problem

Coins form the outline of a pentagon (5 sides), with 8 coins per side. The tricky part is that the corner coins are shared between two sides — they get counted twice if we just multiply.

Step 2: Count naively first (then correct)

If each side had 8 completely separate coins:

5 sides × 8 coins = 40 coins

But each of the 5 corner coins belongs to two sides. When we counted 40, we counted each corner coin twice — once for each of its two sides.

Coins overcounted = 5 corners (each counted one extra time)

Step 3: Subtract the overcount

Total = 40 − 5 = 35 coins

Alternative method: Count each side but skip the last coin of each side (which becomes the corner of the next side):

Each side contributes (8 − 1) = 7 unique coins

5 × 7 = 35 coins ✓

Answer: 35 coins

OptionValueWhy it is wrong
A40Counted 5 × 8 without adjusting for shared corners. ✗
B30Used (8 − 2) × 5 = 30, subtracted both corners per side. ✗
C355 × 8 − 5 = 35, or 5 × 7 = 35. ✓
D38Arithmetic error. ✗
E45Added extra coins per side. ✗

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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