OC Mathematical Reasoning Practice Test 2 — 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

3D Nets: Visualising folded and unfolded solid shapes.
Number Sequences: Identifying rules and next terms in patterns.
Area & Perimeter: Measuring and comparing plane figures in word problems.
Symmetry: Recognising reflection and rotational symmetry in diagrams.
Angle Properties: Using angles on lines, triangles, and parallel lines.
Multi-step Word Problems: Breaking down scenarios into equations and checking reasonableness.

Sample Questions from Test 2

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

Mathematical Reasoning

There are 56 motorcycles in a car park. This is 25 more than the number of SUVs. The number of cars there is …

Question 1 · Multiple choice

Question

There are 56 motorcycles in a car park. This is 25 more than the number of SUVs. The number of cars there is 10 more than the total number of motorcycles and SUVs. How many cars are there in the car park?

Options

A. $87$
B. $92$
C. $97$
D. $102$
E. $107$

Correct answer

97

Explanation

Step 1 — Find the number of SUVs. Motorcycles = 56. SUVs are 25 fewer: SUVs = 56 - 25 = 31 Step 2 — Find the total of motorcycles and SUVs. 56 + 31 = 87 Step 3 — Find the number of cars. Cars = 87 + 10 = 97 Check: 56 motorcycles + 31 SUVs + 97 cars = 184 total. And 97 - 87 = 10 ✔

Mathematical Reasoning

A bag holds red and blue marbles in the ratio 3 : 7.

Question 2 · Multiple choice

Question

A bag holds red and blue marbles in the ratio 3 : 7 . There are 42 blue marbles. How many red marbles are there?

Options

A. $18$
B. $12$
C. $21$
D. $14$
E. $24$

Correct answer

18

Explanation

Step 1: Understand the ratio Red : Blue = 3 : 7 This means for every 3 red marbles, there are 7 blue marbles. Step 2: Find the value of one "part" Blue marbles = 42, which represents 7 parts of the ratio. Value of 1 part = 42 \div 7 = 6 marbles Step 3: Find the number of red marbles Red marbles = 3 parts \times 6 = 18 marbles Check: Red = 18, Blue = 42. Ratio = 18:42 = 3:7 ✓ Answer: 18 red marbles

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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