OC Mathematical Reasoning Practice Test 6 — 2027 NSW Opportunity Class Exam

Strengthen problem solving, algebra, percentages, ratios, speed and distance, and geometry with this 35-question OC Mathematical Reasoning practice test. Matched to the 2027 NSW Opportunity Class Placement Test format and timed for real exam conditions.

Duration

40 Minutes

Format

2027 NSW Format

Questions

35 multiple-choice

Level

NSW OC Placement Test Level

Skills Covered in this Test

This practice test mirrors the official weightings of the NSW Department of Education exam.

The breakdown

  • Graphs & Means: Problem-solving and number sense under exam conditions.
  • Maps & Scale: Problem-solving and number sense under exam conditions.
  • Probability & Dice: Problem-solving and number sense under exam conditions.
  • Coordinates: Problem-solving and number sense under exam conditions.
  • Algebraic Reasoning: Problem-solving and number sense under exam conditions.
  • Mixed Problem Solving: Problem-solving and number sense under exam conditions.

Sample Questions from Test 6

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

Mathematical Reasoning

A fruit bowl has 45 pieces of fruit. 30 are oranges and the rest are apples. What is the ratio of the number …

Question 1 · Multiple choice

Question

A fruit bowl has 45 pieces of fruit. 30 are oranges and the rest are apples. What is the ratio of the number of oranges to the number of apples?

Options

  • A.1 : 2
  • B.2 : 1
  • C.3 : 2
  • D.2 : 3
  • E.5 : 3

Correct answer

B.2 : 1

Explanation

Step 1: Find the number of apples

Total fruit = 45. Oranges = 30.

Apples = 45 − 30 = 15

Step 2: Write the ratio

Oranges : Apples = 30 : 15

Step 3: Simplify

Divide both by 15 (the GCD):

30 ÷ 15 = 2

15 ÷ 15 = 1

Oranges : Apples = 2 : 1

Check: 2 + 1 = 3 parts. Oranges are 2/3 of 45 = 30 ✓

Answer: Oranges : Apples = 2 : 1

Mathematical Reasoning

Dan builds a large 2 × 2 × 2 cube by gluing together 8 identical small cubes.

Question 2 · Multiple choice

Question

Dan builds a large 2 × 2 × 2 cube by gluing together 8 identical small cubes.

He paints every outside face of the large cube red.

He then breaks the large cube apart into the 8 individual small cubes.

Options

How many faces of the small cubes are not painted red?

  • A.16
  • B.24
  • C.18
  • D.22
  • E.30

Correct answer

B.24

Explanation

Step 1: Count all faces of the 8 small cubes

Each small cube has 6 faces.

8 small cubes × 6 faces = 48 faces in total.

Step 2: Count the painted (outside) faces

When the 8 small cubes form a 2×2×2 cube, the large cube has 6 outer faces.

Each outer face of the large cube is a 2×2 grid of small faces → 4 small faces per outer face.

Painted faces = 6 outer faces × 4 small faces = 24 painted faces

Step 3: Count the unpainted faces

Unpainted = Total − Painted = 48 − 24 = 24 unpainted faces

Large 2×2×2 cube:
┌────────┐
│ ■ │ ■ │  ← outer face (4 small faces shown)
├────────┤
│ ■ │ ■ │
└────────┘
Each ■ is one small face that gets painted red.
The hidden internal faces (where cubes touch each other) stay unpainted.

Why 24 unpainted? Every inner face is shared between two small cubes touching each other. There are 12 such shared edges (4 pairs per axis × 3 axes), each contributing 2 hidden faces = 24 total.

Answer: 24 faces are not painted

Core Competencies

3D NetsAge & Rate ProblemsAlgebraic ReasoningAlgebraic SubstitutionsAngle PropertiesArea & PerimeterBefore-and-AfterCartesian CoordinatesComparing FractionsCoordinatesDecimalsFractionsFractions & RatiosGeometry & AreaGraph InterpretationGraphs & MeansInverse OperationsLogical DeductionMaps & ScaleMean, Median & ModeMental ArithmeticMixed Problem SolvingMulti-step Word ProblemsNumber PatternsNumber SequencesOrder of OperationsPercentagesPrime NumbersProbability & DiceProbability LogicProfit & LossRatiosReflection & RotationSequencesSpeed, Distance, TimeSquare & Cube NumbersSymmetryTime & CalendarsUnit ConversionsVenn DiagramsVolume & Capacity

Prepare with Precision

  • Build problem-solving speed across maths topics: percentages, ratios, algebra, and geometry.
  • Practise speed and distance, fractions, and multi-step word problems at exam pace.
  • Pinpoint the OC maths topics that need extra focus before exam day.

This public page gives students and parents a detailed look at the maths skills and question types covered in every OC Mathematical Reasoning practice test. The full 35-question timed test—with real-time scoring and detailed review—is available to enrolled members, so your child can build real confidence for the 2027 NSW Opportunity Class exam.

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