OC Mathematical Reasoning Practice Test 15 — 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

  • Profit & Loss: Revenue, cost, and margin reasoning in scenarios.
  • 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.
  • Mental Arithmetic: Fast, accurate calculation without a calculator.
  • Ratios: Part-part and part-whole relationships in applied settings.

Sample Questions from Test 15

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

Mathematical Reasoning

Three friends share a \$400 prize in the ratio 2 : 3 : 5.

Question 1 · Multiple choice

Question

Three friends share a $400 prize in the ratio 2 : 3 : 5.

How much does the person with the largest share receive?

Options

  • A.$120
  • B.$200
  • C.$150
  • D.$180
  • E.$240

Correct answer

B.$200

Explanation

Step 1: Find the total number of parts

Ratio = 2 : 3 : 5

Total parts = 2 + 3 + 5 = 10 parts

Step 2: Find the value of one part

$400 ÷ 10 = $40 per part

Step 3: Calculate each person's share

SharePartsAmount
Smallest2 parts2 × $40 = $80
Middle3 parts3 × $40 = $120
Largest5 parts5 × $40 = $200

Check: $80 + $120 + $200 = $400 ✓

Answer: The largest share is $200

Mathematical Reasoning

Tom is 3 times as old as his sister.

Question 2 · Multiple choice

Question

Tom is 3 times as old as his sister.

In 8 years, he will be twice as old as his sister.

How old is Tom now?

Options

  • A.18
  • B.20
  • C.21
  • D.22
  • E.24

Correct answer

E.24

Explanation

Step 1: Set up expressions for their ages now

Let the sister's current age = S years.

Tom is 3 times as old: Tom's age = 3S years.

Step 2: Write expressions for their ages in 8 years

In 8 years:

  • Tom's age = 3S + 8
  • Sister's age = S + 8

Step 3: Use the future relationship (Tom will be twice as old)

3S + 8 = 2 × (S + 8)

3S + 8 = 2S + 16

3S − 2S = 16 − 8

S = 8 (sister is currently 8 years old)

Step 4: Find Tom's current age

Tom = 3 × S = 3 × 8 = 24 years old

Check: In 8 years, Tom = 32, sister = 16. Is 32 = 2 × 16? Yes ✓

Answer: Tom is 24 years old

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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