OC Mathematical Reasoning Practice Test 20 — 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

  • Multi-step Word Problems: Breaking down scenarios into equations and checking reasonableness.
  • Logical Deduction: Using given constraints to eliminate impossible answers.
  • Probability Logic: Likelihood, counting outcomes, and constraints.
  • 3D Nets: Visualising folded and unfolded solid shapes.
  • Algebraic Substitutions: Replacing variables and evaluating expressions.
  • Graph Interpretation: Reading scales, trends, and values from charts and tables.
  • Speed, Distance, Time: Applying S=D×T and unit consistency.

Sample Questions from Test 20

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

Mathematical Reasoning

A road maintenance team needs to repair a 4960-metre-long road. 2400 metres of the road was repaired in 15 da…

Question 1 · Multiple choice

Question

A road maintenance team needs to repair a 4960-metre-long road. 2400 metres of the road was repaired in 15 days. At this speed, how many more days are needed to complete the task?

Options

  • A.12
  • B.15
  • C.18
  • D.16
  • E.31

Correct answer

D.16

Explanation

Step 1: Find the daily repair rate

In 15 days, 2 400 metres was repaired.

Daily rate = 2 400 ÷ 15 = 160 metres per day

Step 2: Find the remaining length

Total = 4 960 m. Already repaired = 2 400 m.

Remaining = 4 960 − 2 400 = 2 560 metres

Step 3: Find the additional days needed

More days = 2 560 ÷ 160 = 16 days

Check: 15 days (done) + 16 more days = 31 total days.

160 × 31 = 4 960 m ✓

Answer: 16 more days are needed

Mathematical Reasoning

A purse costs 4 times as much as a pen. A handbag costs 5 times as much as the purse. Find the ratio of the c…

Question 2 · Multiple choice

Question

A purse costs 4 times as much as a pen. A handbag costs 5 times as much as the purse. Find the ratio of the cost of the pen to the cost of the handbag.

Options

  • A.1 : 9
  • B.1 : 20
  • C.4 : 5
  • D.1 : 25
  • E.5 : 4

Correct answer

B.1 : 20

Explanation

Step 1: Assign values using the pen as the starting point

Let the cost of the pen = 1 unit.

Then work along the chain:

Pen  ──×4──▶  Purse  ──×5──▶  Handbag
 1               4               20
  • Purse = 4 × pen = 4 × 1 = 4 units
  • Handbag = 5 × purse = 5 × 4 = 20 units

Step 2: Write the ratio pen : handbag

Pen : Handbag = 1 : 20

Answer: 1 : 20

OptionValueWhy it is wrong
A1 : 9Added 4 + 5 = 9 instead of multiplying. ✗
B1 : 204 × 5 = 20, so pen : handbag = 1 : 20. ✓
C4 : 5Gave purse : handbag ratio without converting to pen. ✗
D1 : 25Used 5 × 5 = 25 — multiplied the wrong values. ✗
E5 : 4Reversed the purse-to-handbag relationship. ✗

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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