Mathematical Reasoning Mock Test 14: 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

  • Algebraic Substitutions: Replacing variables and evaluating expressions.
  • Inverse Operations: Working backwards from a result to find an unknown.
  • Order of Operations: Applying brackets, indices, and operation priority correctly.
  • Number Sequences: Identifying rules and next terms in patterns.
  • Prime Numbers: Divisibility, factors, and prime-related reasoning.
  • Multi-step Word Problems: Breaking down scenarios into equations and checking reasonableness.

Sample Questions from Test 14

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

Mathematical Reasoning

Alice and Sophie were both tasked to type a document with the same number of words. Alice typed 40 words per …

Question 1 · Multiple choice

Question

Alice and Sophie were both tasked to type a document with the same number of words. Alice typed 40 words per minute on average. After Sophie typed 80 words, Alice started typing. After 16 minutes, they both finished the task simultaneously. How many words did Sophie type per minute on average?

Options

  • A.30 words per minute
  • B.32 words per minute
  • C.33 words per minute
  • D.35 words per minute
  • E.40 words per minute

Correct answer

D.35 words per minute

Explanation

Step 1: Find the total number of words in the document

After Alice starts, they both type for exactly 16 minutes and finish together.

Alice types at 40 words per minute for 16 minutes:

Total words = 40 × 16 = 640 words

Step 2: Find how many words Sophie still needed to type when Alice started

Sophie had already typed 80 words before Alice started. After that, Sophie typed for the same 16 minutes.

Words remaining for Sophie = 640 − 80 = 560 words

Step 3: Find Sophie's typing speed

Sophie typed 560 words in the 16 minutes while Alice was also typing:

Sophie's speed = 560 ÷ 16 = 35 words per minute

Check: Sophie's total = 80 + 35 × 16 = 80 + 560 = 640 words ✓

Answer: Sophie types 35 words per minute

OptionSpeedCheck (560÷speed=16?)
A30560÷30≈18.7≠16✗
B32560÷32=17.5≠16✗
C33560÷33≈17≠16✗
D35560÷35=16 ✓✓
E40640÷16=40 — divided total words by Alice's time instead of remaining words. ✗

Mathematical Reasoning

The pupils of Grades 3, 4 and 5 in Springfield Primary School are going for a spring outing in coaches. If ea…

Question 2 · Multiple choice

Question

The pupils of Grades 3, 4 and 5 in Springfield Primary School are going for a spring outing in coaches. If each coach seats 45 pupils, then 20 pupils cannot get on any coach, as all the seats will be fully occupied. If each coach seats 5 more pupils, then there will be one coach left unoccupied. There are ( ) pupils in total going for the spring outing.

Options

  • A.600
  • B.650
  • C.700
  • D.720
  • E.675

Correct answer

B.650

Explanation

Step 1: Set up two expressions for the total number of pupils

Let n = the number of coaches available.

Situation 1: 45 seats per coach, all coaches are completely full AND 20 pupils are left without a seat:

Total pupils = 45n + 20

Situation 2: 50 seats per coach (5 more), pupils fill exactly (n − 1) coaches, and 1 coach is left completely empty:

Total pupils = 50 × (n − 1)

Step 2: Set the two expressions equal and solve

45n + 20 = 50(n − 1)

45n + 20 = 50n − 50

Move terms:

20 + 50 = 50n − 45n

70 = 5n

n = 14 coaches

Step 3: Find the total number of pupils

Total = 45 × 14 + 20 = 630 + 20 = 650 pupils

Check: With 50-seat coaches, 13 coaches are used (one left empty): 50 × 13 = 650 ✓

Answer: 650 pupils

OptionValueWhy it is wrong
A600Used n=13: 45×13+20=605≠600. Off-by-one. ✗
B65045×14+20=650. ✓
C700Used n=15: 45×15+20=695≠700. ✗
D720Arithmetic error with wrong n. ✗
E675Added a full coach (45) instead of the 20 leftover: 45×14+45=675. ✗

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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