OC Mathematical Reasoning Practice Test 11 — 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

  • Speed, Distance, Time: Applying S=D×T and unit consistency.
  • Unit Conversions: Consistent units within metric and mixed measures.
  • Time & Calendars: Duration, timetables, and date arithmetic.
  • Inverse Operations: Working backwards from a result to find an unknown.
  • Decimals: Place value, rounding, and decimal operations under time pressure.
  • Algebraic Substitutions: Replacing variables and evaluating expressions.

Sample Questions from Test 11

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

Mathematical Reasoning

When calculating 60 ÷ (4 + 2), Lily wrote the expression as 60 ÷ 4 + 2. What is the difference between the re…

Question 1 · Multiple choice

Question

When calculating 60 ÷ (4 + 2), Lily wrote the expression as 60 ÷ 4 + 2. What is the difference between the results of the two calculations?

Options

  • A.5
  • B.6
  • C.7
  • D.8
  • E.9

Correct answer

C.7

Explanation

Step 1: Calculate the correct expression (with brackets)

60 ÷ (4 + 2)

Brackets always go first — add 4 + 2:

60 ÷ 6 = 10

Step 2: Calculate Lily's expression (without brackets)

60 ÷ 4 + 2

Without brackets, division comes before addition (this is the order of operations rule).

Divide first: 60 ÷ 4 = 15

Then add: 15 + 2 = 17

Step 3: Compare the two results

Expression      Steps           Result
─────────────────────────────────────
60 ÷ (4 + 2)   60 ÷ 6          10   ← correct
60 ÷ 4 + 2     15 + 2          17   ← Lily's version

Step 4: Find the difference

17 − 10 = 7

The brackets changed the answer by 7! This shows how important it is to place brackets correctly.

Answer: The difference is 7

OptionValueWhy it is wrong
A5Used Lily's result as 15: 15−10=5. ✗
B6Used Lily's result as 16: 16−10=6. ✗
C717−10=7. ✓
D8Used 60÷4=16 (arithmetic slip): 18−10=8. ✗
E9Used 60÷4+4=19 as Lily's result: 19−10=9. ✗

Mathematical Reasoning

A jar contains blue and green counters.

Question 2 · Multiple choice

Question

A jar contains blue and green counters.

  • There are 3 times as many blue counters as green counters.
  • When 8 blue counters are removed, there are twice as many blue as green.

How many counters were in the jar to start?

Options

  • A.24
  • B.28
  • C.30
  • D.32
  • E.36

Correct answer

D.32

Explanation

Step 1: Write the starting amounts using one variable

Let the number of green counters = g

Since there are 3 times as many blue: blue = 3g

Step 2: Apply the condition after removing 8 blue counters

After removing 8 blue counters, blue = 3g − 8

Now blue is twice as many as green:

3g − 8 = 2 × g

3g − 8 = 2g

g = 8

Step 3: Find the original total

Green = 8, Blue = 3 × 8 = 24

Total = 8 + 24 = 32 counters

Check: After removing 8 blue: blue = 16, green = 8. Is 16 = 2 × 8? Yes ✓

Answer: 32 counters were in the jar to start

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.