OC Mathematical Reasoning Practice Test 18 — 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

  • Time & Calendars: Duration, timetables, and date arithmetic.
  • Speed, Distance, Time: Applying S=D×T and unit consistency.
  • Unit Conversions: Consistent units within metric and mixed measures.
  • Inverse Operations: Working backwards from a result to find an unknown.
  • Multi-step Word Problems: Breaking down scenarios into equations and checking reasonableness.
  • Ratios: Part-part and part-whole relationships in applied settings.

Sample Questions from Test 18

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

Mathematical Reasoning

Riverside Primary School organised three groups of pupils for an outing. There were 26 pupils in Group A, 32 …

Question 1 · Multiple choice

Question

Riverside Primary School organised three groups of pupils for an outing. There were 26 pupils in Group A, 32 pupils in Group B and 30 pupils in Group C. Each group took one coach. On the way, the coach for Group C broke down, and pupils in that group needed to be transferred to the other two coaches. How many pupils should be transferred to Group A's and Group B's coaches, respectively, so that each of them would have the same number of pupils?

Options

  • A.14 and 16
  • B.16 and 14
  • C.15 and 15
  • D.18 and 12
  • E.20 and 10

Correct answer

D.18 and 12

Explanation

Step 1: Find the total number of pupils

Group A: 26 pupils

Group B: 32 pupils

Group C: 30 pupils

Total = 26 + 32 + 30 = 88 pupils

Step 2: Find the equal target for groups A and B

All 88 pupils must fit into 2 coaches (A and B) equally.

Target per coach = 88 ÷ 2 = 44 pupils each

Step 3: Find how many pupils to move to each coach

Pupils to move to Coach A = Target − Current = 44 − 26 = 18 pupils

Pupils to move to Coach B = Target − Current = 44 − 32 = 12 pupils

Check: 18 + 12 = 30 (all of Group C) ✓

After transfer: A = 44, B = 44 ✓

Answer: 18 pupils should go to Coach A and 12 to Coach B

Mathematical Reasoning

Katie had 4 times as many beads as Emma. After Katie gave 30 beads to Emma, they had equal numbers of beads. …

Question 2 · Multiple choice

Question

Katie had 4 times as many beads as Emma. After Katie gave 30 beads to Emma, they had equal numbers of beads. How many beads did Emma have at first?

Options

  • A.14
  • B.16
  • C.18
  • D.20
  • E.22

Correct answer

D.20

Explanation

Step 1: Set up variables

Let Emma's beads at first = E

Katie's beads = 4E (four times Emma's)

Step 2: Apply the transfer (Katie gives 30 to Emma)

After giving 30:

  • Emma has: E + 30
  • Katie has: 4E − 30

Step 3: Use the equal condition

"They had equal numbers of beads":

4E − 30 = E + 30

3E = 60

E = 20

Step 4: Verify

Katie at first = 4 × 20 = 80

After: Emma = 50, Katie = 50. Equal ✓

Answer: Emma had 20 beads at first

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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