OC Mathematical Reasoning Practice Test 5 — 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

Volume & Capacity: 3D measures, unit conversion, and capacity word problems.
Comparing Fractions: Problem-solving and number sense under exam conditions.
Decimals: Place value, rounding, and decimal operations under time pressure.
Before-and-After: Problem-solving and number sense under exam conditions.
Percentages: Discounts, changes, and comparisons expressed as percent.
Number Patterns: Problem-solving and number sense under exam conditions.

Sample Questions from Test 5

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

Mathematical Reasoning

In a jar of sweets, 9/13 of the sweets are mints. The rest are toffees. What is the ratio of the number of to…

Question 1 · Multiple choice

Question

In a jar of sweets, 9/13 of the sweets are mints. The rest are toffees. What is the ratio of the number of toffees to the number of mints?

Options

A. $9 : 4$
B. $4 : 9$
C. $9 : 13$
D. $4 : 13$
E. $13 : 9$

Correct answer

4 : 9

Explanation

Step 1: Find the fraction of toffees Mints = 9/13 of all sweets. Toffees = 1 − 9/13 = 13/13 − 9/13 = 4/13 Step 2: Write the ratio Toffees : Mints = 4/13 : 9/13 Since both fractions have the same denominator, just compare the numerators: Toffees : Mints = 4 : 9 Check: 4 + 9 = 13, and mints are 9/13 of 13 = 9 ✓ Answer: Toffees : Mints = 4 : 9

Mathematical Reasoning

A fruit shop has 516 kilograms of apples and 372 kilograms of pears. If the weight of the fruit in each box i…

Question 2 · Multiple choice

Question

A fruit shop has 516 kilograms of apples and 372 kilograms of pears. If the weight of the fruit in each box is 12 kilograms, then how many more boxes of apples than pears does the shop have?

Options

A. $43$
B. $31$
C. $74$
D. $24$
E. $12$

Correct answer

12

Explanation

Step 1: Find the number of apple boxes Apple boxes = 516 \div 12 = 43 boxes Step 2: Find the number of pear boxes Pear boxes = 372 \div 12 = 31 boxes Step 3: Find the difference Extra apple boxes = 43 - 31 = 12 more apple boxes Check: 43 \times 12 = 516 ✓ and 31 \times 12 = 372 ✓ Answer: There are 12 more boxes of apples

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.

Get Started — Full OC Practice Tests