Mathematical Reasoning Mock Test 7: 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

  • Number Sequences: Identifying rules and next terms in patterns.
  • Prime Numbers: Divisibility, factors, and prime-related reasoning.
  • Square & Cube Numbers: Powers, roots, and number patterns.
  • Algebraic Substitutions: Replacing variables and evaluating expressions.
  • Multi-step Word Problems: Breaking down scenarios into equations and checking reasonableness.
  • Mental Arithmetic: Fast, accurate calculation without a calculator.

Sample Questions from Test 7

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

Mathematical Reasoning

20 students are queuing for their favourite food. Andy is the third in the queue. Ashley is the fifth from th…

Question 1 · Multiple choice

Question

20 students are queuing for their favourite food. Andy is the third in the queue. Ashley is the fifth from the end of the queue. How many students are queuing between the two of them?

Options

  • A.12
  • B.13
  • C.11
  • D.14
  • E.10

Correct answer

A.12

Explanation

Step 1: Find each person's position from the front

There are 20 students total.

  • Andy: 3rd from the front (position 3)

  • Ashley: 5th from the end → convert to position from front:

    Position from front = Total − Position from end + 1 = 20 − 5 + 1 = position 16

Step 2: Visualise the queue

Front → 1  2  [3]  4  5  6  7  8  9  10  11  12  13  14  15  [16]  17  18  19  20 ← Back
               Andy                                              Ashley
               ←──────────── 12 students between ────────────→

Step 3: Count students between them

"Between" means not counting Andy or Ashley themselves.

Students between = (Ashley's position) − (Andy's position) − 1

= 16 − 3 − 1 = 12 students

Verify: Positions 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 → count them: 12 ✓

Answer: 12 students

OptionValueWhy it is wrong
A1216 − 3 − 1 = 12. ✓
B13Forgot to subtract 1 for Andy himself. ✗
C11Off-by-one error. ✗
D14Miscalculated Ashley's position. ✗
E10Used 15 − 3 − 2 incorrectly. ✗

Mathematical Reasoning

Oliver starts at point X. He follows these steps:

Question 2 · Multiple choice

Question

Oliver starts at point X. He follows these steps:

  1. Walk 9 m east.

  2. Walk 6 m north.

  3. Walk 9 m west.

  4. Walk 15 m south.

After this, how far south of his starting position is Oliver?

Options

  • A.6 m
  • B.9 m
  • C.12 m
  • D.15 m
  • E.18 m

Correct answer

B.9 m

Explanation

Step 1: Understand that opposite directions cancel

Oliver's journey has four steps. East and West are opposites; North and South are opposites.

Let's track East/West and North/South separately.

Step 2: Track East/West

← West          East →
         X ──────────── 9 m east
         └──────────── 9 m west (back)
         Net East/West = 0
  • Walk 9 m East: +9
  • Walk 9 m West: −9
  • Net = 0 (back to the same column as X)

Step 3: Track North/South

    ↑ North
    │
    6 m north
    │
    X  ← starting point
    │
    15 m south
    ↓ South
  • Walk 6 m North: +6
  • Walk 15 m South: −15
  • Net = 6 − 15 = −9 m (9 m south of X)

Answer: Oliver is 9 m south of his starting position

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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