OC Mathematical Reasoning Practice Test 17 — 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

  • Probability Logic: Likelihood, counting outcomes, and constraints.
  • Mean, Median & Mode: Choosing and computing the right average for the data.
  • Graph Interpretation: Reading scales, trends, and values from charts and tables.
  • Fractions: Adding, comparing, and simplifying fractional quantities in context.
  • Venn Diagrams: Overlaps, unions, and logical counts from sets.
  • Logical Deduction: Using given constraints to eliminate impossible answers.

Sample Questions from Test 17

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

Mathematical Reasoning

Ling can wash a van in 24 minutes working alone.

Question 1 · Multiple choice

Question

Ling can wash a van in 24 minutes working alone.

Mo can wash the same van in 40 minutes working alone.

They start together at 8:40 am and work without stopping until the van is finished.

At what time do they finish?

Options

  • A.8:52 am
  • B.8:55 am
  • C.9:00 am
  • D.9:04 am
  • E.9:10 am

Correct answer

B.8:55 am

Explanation

Step 1: Find each person's work rate

Rate = fraction of the job done per minute.

  • Ling: 1 van in 24 minutes → 1/24 van per minute
  • Mo: 1 van in 40 minutes → 1/40 van per minute

Step 2: Add their rates (combined rate)

1/24 + 1/40

Find a common denominator. LCM of 24 and 40 = 120.

= 5/120 + 3/120 = 8/120 = 1/15 van per minute

Step 3: Find the total time

If together they complete 1/15 of the van each minute, they finish the whole van in:

1 ÷ (1/15) = 15 minutes

Step 4: Find the finish time

Start: 8:40 am

8:40 am + 15 minutes = 8:55 am

Answer: They finish at 8:55 am

Mathematical Reasoning

On a map, the straight-line distance between Pria’s door and Quinn’s door measures 14 cm on the ruler.

Question 2 · Multiple choice

Question

On a map, the straight-line distance between Pria’s door and Quinn’s door measures 14 cm on the ruler.

The map scale is 1 cm on the map → 25 m in real life.

How far apart are their doors in real life?

Options

  • A.250 m
  • B.300 m
  • C.325 m
  • D.375 m
  • E.350 m

Correct answer

E.350 m

Explanation

Step 1: Understand the map scale

1 cm on the map = 25 m in real life.

Step 2: Multiply the map distance by the scale

Map distance = 14 cm

Real distance = 14 × 25

= 14 × 20 + 14 × 5

= 280 + 70

= 350 m

Map:   1 cm  →   25 m  real
       ×14        ×14
      14 cm  →  350 m  real

Answer: 350 m

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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