Mathematical Reasoning Mock Test 16: 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

  • Volume & Capacity: 3D measures, unit conversion, and capacity word problems.
  • Unit Conversions: Consistent units within metric and mixed measures.
  • Area & Perimeter: Measuring and comparing plane figures in word problems.
  • Decimals: Place value, rounding, and decimal operations under time pressure.
  • Fractions: Adding, comparing, and simplifying fractional quantities in context.
  • Inverse Operations: Working backwards from a result to find an unknown.

Sample Questions from Test 16

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

Mathematical Reasoning

Mia makes a number pattern using these rules:

Question 1 · Multiple choice

Question

Mia makes a number pattern using these rules:

  • Choose the first three numbers.
  • After this, each number is the sum of the three numbers before it.

Here is Mia’s pattern with three missing numbers labelled X, Y and Z:

3, X, 1, Y, 7, Z

All the numbers are whole numbers.

Options

What number does Z represent?

  • A.11
  • B.13
  • C.12
  • D.14
  • E.15

Correct answer

B.13

Explanation

The rule in words

From the fourth number onward: each number = sum of the three numbers before it.

Sequence:    3      X      1      Y      7      Z
             │      │      │      │      │
             └──────┴──────┘      │      │
                   sums to ──────► Y     │
                          └──────┴──────┘
                                 sums to ──────► 7
                                        └──────┴──────
                                               sums to ──► Z

Step 1 — Write Y using X

The three numbers before Y are 3, X, 1:

Y = 3 + X + 1 = X + 4

Step 2 — Use the number 7

The three numbers before 7 are X, 1, Y:

7 = X + 1 + Y

Substitute Y = X + 4:

7 = X + 1 + (X + 4) = 2X + 5

2X = 2 → X = 1

Step 3 — Find Y

Y = 1 + 4 = 5

Check the row so far: 3, 1, 1, 5, 7, …

  • 3 + 1 + 1 = 5 ✓
  • 1 + 1 + 5 = 7 ✓

Step 4 — Find Z

The three numbers before Z are 1, 5, 7:

Z = 1 + 5 + 7 = 13

Answer: 13

Repeatable checklist

  1. Label the missing letters in order.

  2. Write the first missing letter using the earliest "sum of three" you can make.

  3. Use the next known number to make an equation and solve.

  4. Work forwards to any later missing letter.

  5. Check by rebuilding the next number from three before it.

Traps

  • 12 — added only 7 + 5 (two numbers, not three).
  • 14 — used 3 + 1 + 7 (skipped X and Y).
  • 15 — arithmetic slip on 2X + 5 = 7.

Mathematical Reasoning

Leo, Maya and Noah have some stickers.

Question 2 · Multiple choice

Question

Leo, Maya and Noah have some stickers.

  • Leo has 6 times as many stickers as Maya.
  • Noah has 1/2 as many stickers as Maya.

Options

Leo has [ ] times as many stickers as Noah.

What is the missing number in the sentence above?

  • A.1/12
  • B.1/3
  • C.3
  • D.6
  • E.12

Correct answer

E.12

Explanation

Use Maya as the "anchor"

Both clues compare to Maya. Picture Maya's pile as 1 unit.

Maya:  [── 1 unit ──]
Leo:   [1][1][1][1][1][1]   = 6 units
Noah:  [½]                   = ½ unit
PersonCompared to Maya
Leo6 units
Maya1 unit
Noah½ unit

Link Leo to Noah

Leo has 6 units. Noah has ½ unit.

How many of Noah's piles fit into Leo's?

6 ÷ ½ = 6 × 2 = 12

So Leo has 12 times as many stickers as Noah.

Answer: 12

Repeatable checklist

  1. Draw or write both amounts using the middle person (here Maya).

  2. Write the two amounts as numbers (or fractions) of that unit.

  3. Divide: (bigger person's amount) ÷ (smaller person's amount).

  4. Dividing by a fraction → multiply by its reciprocal (÷ ½ = × 2).

Traps

  • 6 — used 6 × ½ = 3 (multiplied instead of dividing the ratios).
  • 3 — that would be Noah's stickers if Maya had 6 (wrong person).
  • 1/12 — flipped the answer (Noah compared to Leo instead of Leo to Noah).

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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