OC Mathematical Reasoning Practice Test 9 — 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

Venn Diagrams: Overlaps, unions, and logical counts from sets.
Ratios: Part-part and part-whole relationships in applied settings.
Speed, Distance, Time: Applying S=D×T and unit consistency.
Profit & Loss: Revenue, cost, and margin reasoning in scenarios.
Logical Deduction: Using given constraints to eliminate impossible answers.
Graph Interpretation: Reading scales, trends, and values from charts and tables.
Decimals: Place value, rounding, and decimal operations under time pressure.

Sample Questions from Test 9

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

Mathematical Reasoning

Mr Brown made 840 spare parts in 12 hours. At this pace, how many hours will he need to make 3150 spare parts?

Question 1 · Multiple choice

Question

Mr Brown made 840 spare parts in 12 hours. At this pace, how many hours will he need to make 3150 spare parts?

Options

A. $35$
B. $40$
C. $45$
D. $50$
E. $55$

Correct answer

45

Explanation

Step 1: Find Mr Brown's rate 840 parts in 12 hours. Rate = 840 \div 12 = 70 parts per hour Step 2: Find the time for 3 150 parts Time = Total parts \div Rate = 3 150 \div 70 = 45 hours (70 \times 40 = 2 800; 3 150 - 2 800 = 350; 350 \div 70 = 5; total = 40 + 5 = 45) Check: 70 \times 45 = 3 150 ✓ Answer: Mr Brown needs 45 hours

Mathematical Reasoning

11/20 of the total number of beads in a bag are red. The others are blue. What is the ratio of the number of …

Question 2 · Multiple choice

Question

11/20 of the total number of beads in a bag are red. The others are blue. What is the ratio of the number of blue beads to the number of red beads?

Options

A. $9 : 11$
B. $11 : 9$
C. $9 : 20$
D. $11 : 20$
E. $1 : 2$

Correct answer

9 : 11

Explanation

Step 1: Find the fraction of blue beads Red = 11/20 of all beads. Blue = 1 − 11/20 = 9/20 of all beads. Step 2: Write the ratio Blue : Red = 9/20 : 11/20 Since both fractions have the same denominator (20), we can just compare the numerators: Blue : Red = 9 : 11 Check: 9 + 11 = 20, and red is 11/20 ✓ Answer: Blue : Red = 9 : 11

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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