OC Mathematical Reasoning Practice Test 8 — 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.
  • Symmetry: Recognising reflection and rotational symmetry in diagrams.
  • Reflection & Rotation: Transformations and image positions on grids.
  • Area & Perimeter: Measuring and comparing plane figures in word problems.
  • Angle Properties: Using angles on lines, triangles, and parallel lines.
  • Volume & Capacity: 3D measures, unit conversion, and capacity word problems.

Sample Questions from Test 8

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

Mathematical Reasoning

A rectangle has a perimeter of 40 cm.

Question 1 · Multiple choice

Question

A rectangle has a perimeter of 40 cm.

Its length is 4 times its width.

Options

What is the area of the rectangle?

  • A.24 cm²
  • B.64 cm²
  • C.40 cm²
  • D.48 cm²
  • E.96 cm²

Correct answer

B.64 cm²

Explanation

Step 1: Set up the dimensions using one variable

Let the width = w cm.

The length is 4 times the width: length = 4w cm.

┌──────────────────────────┐
│                          │ w
│         length = 4w      │
└──────────────────────────┘
←──────── 4w ────────────→

Step 2: Use the perimeter formula

Perimeter = 2 × (length + width)

40 = 2 × (4w + w)

40 = 2 × 5w

40 = 10w

w = 40 ÷ 10 = 4 cm

Step 3: Find the length

Length = 4w = 4 × 4 = 16 cm

Step 4: Calculate the area

Area = length × width = 16 × 4 = 64 cm²

Check perimeter: 2 × (16 + 4) = 2 × 20 = 40 cm ✓

Answer: 64 cm²

Mathematical Reasoning

A rectangular photo measures 12 cm by 18 cm.

Question 2 · Multiple choice

Question

A rectangular photo measures 12 cm by 18 cm.

It is enlarged so that the longer side becomes 27 cm. The shorter side is enlarged by the same scale factor.

What is the new shorter side?

Options

  • A.15 cm
  • B.16 cm
  • C.17 cm
  • D.20 cm
  • E.18 cm

Correct answer

E.18 cm

Explanation

Step 1: Find the scale factor

The longer side grows from 18 cm to 27 cm.

Scale factor = new length ÷ old length = 27 ÷ 18 = 1.5

Original:          Enlarged:
length = 18 cm  →  27 cm  (× 1.5)
width  = 12 cm  →  ?  cm  (× 1.5)

Step 2: Apply the same scale factor to the shorter side

New shorter side = 12 × 1.5 = 18 cm

(12 × 1.5 = 12 × 1 + 12 × 0.5 = 12 + 6 = 18)

Answer: 18 cm

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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