OC Mathematical Reasoning Practice Test 3 — 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

  • Graph Interpretation: Reading scales, trends, and values from charts and tables.
  • Ratios: Part-part and part-whole relationships in applied settings.
  • Percentages: Discounts, changes, and comparisons expressed as percent.
  • Mean, Median & Mode: Choosing and computing the right average for the data.
  • Venn Diagrams: Overlaps, unions, and logical counts from sets.
  • Logical Deduction: Using given constraints to eliminate impossible answers.

Sample Questions from Test 3

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

Mathematical Reasoning

Matthew has 2½ times as many stickers as Shirley. Find the ratio of Matthew's stickers to Shirley's stickers.

Question 1 · Multiple choice

Question

Matthew has 2½ times as many stickers as Shirley. Find the ratio of Matthew's stickers to Shirley's stickers.

Options

  • A.5 : 2
  • B.2 : 5
  • C.3 : 2
  • D.5 : 3
  • E.7 : 2

Correct answer

A.5 : 2

Explanation

Step 1: Convert "2½ times" into a fraction

"Matthew has 2½ times as many stickers as Shirley."

2½ as a fraction = 5/2

So: Matthew = (5/2) × Shirley

Step 2: Write the ratio

Matthew : Shirley = (5/2) × Shirley : Shirley

= 5/2 : 1

Step 3: Remove the fraction by multiplying both parts by 2

= (5/2 × 2) : (1 × 2)

= 5 : 2

A helpful way to picture it: if Shirley has 2 stickers, Matthew has 5 stickers.

Answer: Matthew : Shirley = 5 : 2

OptionValueWhy it is wrong
A5 : 22½ = 5/2, so Matthew : Shirley = 5 : 2. ✓
B2 : 5Reversed the ratio — Shirley : Matthew. ✗
C3 : 2Confused 2½ with 1½ (= 3/2). ✗
D5 : 3Used the wrong denominator when converting 2½. ✗
E7 : 2Used 3½ instead of 2½. ✗

Mathematical Reasoning

Chloe glues together 5 identical cubes in a T-shape as shown.

Question 2 · Multiple choice

Question

Chloe glues together 5 identical cubes in a T-shape as shown.

T-shaped solid made from 5 identical cubes: 3 in a row, 2 stacked on top of the middle cube.

How many faces of the small cubes are visible (exposed)?

Options

  • A.18
  • B.20
  • C.22
  • D.24
  • E.26

Correct answer

C.22

Explanation

Step 1: Count the total faces if cubes were separate

There are 5 cubes. Each cube has 6 faces.

Total faces = 5 × 6 = 30 faces

Step 2: Find how many faces are hidden by joins

From the T-shape (3 cubes across the top, 2 cubes hanging below the middle cube):

[A][B][C]   ← top row: 3 cubes
   [D]      ← below B
   [E]      ← below D

Joins (where cubes touch each other):

  • A ↔ B: 1 join
  • B ↔ C: 1 join
  • B ↔ D: 1 join
  • D ↔ E: 1 join

Total joins = 4. Each join hides 2 faces (one on each cube touching).

Faces hidden = 4 × 2 = 8 faces

Step 3: Calculate visible faces

Visible = 30 − 8 = 22 faces

Answer: 22 visible faces

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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