OC Mathematical Reasoning Practice Test 10 — 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

  • Fractions: Adding, comparing, and simplifying fractional quantities in context.
  • Ratios: Part-part and part-whole relationships in applied settings.
  • Percentages: Discounts, changes, and comparisons expressed as percent.
  • Decimals: Place value, rounding, and decimal operations under time pressure.
  • Multi-step Word Problems: Breaking down scenarios into equations and checking reasonableness.
  • Probability Logic: Likelihood, counting outcomes, and constraints.

Sample Questions from Test 10

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

Mathematical Reasoning

Four workers can produce 100 TV parts in 5 hours. According to this, how many workers are needed to produce 6…

Question 1 · Multiple choice

Question

Four workers can produce 100 TV parts in 5 hours. According to this, how many workers are needed to produce 600 TV parts in 8 hours?

Options

  • A.10
  • B.15
  • C.20
  • D.24
  • E.30

Correct answer

B.15

Explanation

Step 1: Find the rate per worker per hour

4 workers make 100 parts in 5 hours.

Rate per worker per hour = 100 ÷ (4 × 5) = 100 ÷ 20 = 5 parts per worker per hour

Step 2: Find the number of workers needed

We need 600 parts made in 8 hours.

Total "worker-hours" needed = 600 ÷ 5 = 120 worker-hours

Number of workers = 120 ÷ 8 = 15 workers

Check: 15 workers × 5 parts/hr × 8 hours = 600 parts ✓

Answer: 15 workers are needed

Mathematical Reasoning

A sum of money is shared among Jenny, Mary and Lilian in the ratio 2 : 3 : 5. If Mary gives \$27 to Jenny, bo…

Question 2 · Multiple choice

Question

A sum of money is shared among Jenny, Mary and Lilian in the ratio 2 : 3 : 5. If Mary gives $27 to Jenny, both of them will have an equal amount of money. How much money does Lilian receive?

Options

  • A.$135
  • B.$270
  • C.$162
  • D.$216
  • E.$324

Correct answer

B.$270

Explanation

Step 1: Express each person's share using one variable

Let each "part" of the ratio = k dollars.

  • Jenny receives: 2k dollars
  • Mary receives: 3k dollars
  • Lilian receives: 5k dollars

Step 2: Work out what happens after Mary gives $27 to Jenny

Mary loses $27, Jenny gains $27:

  • Jenny now has: 2k + 27
  • Mary now has: 3k − 27

Step 3: Set them equal and solve for k

"Both will have an equal amount":

2k + 27 = 3k − 27

Add 27 to both sides:

2k + 54 = 3k

Subtract 2k from both sides:

k = 54

Step 4: Find Lilian's share

Lilian = 5k = 5 × 54 = $270

Check: After the transfer: Jenny = 2×54+27 = 135; Mary = 3×54−27 = 135. Equal! ✓

Answer: Lilian receives $270

OptionValueWhy it is wrong
A$135Used k = 27 directly without solving the equation. ✗
B$2705 × 54 = 270. ✓
C$1623 × 54 = 162 — Mary's share, not Lilian's. ✗
D$2164 × 54 — used wrong ratio part. ✗
E$3246 × 54 — over-counted the ratio. ✗

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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