Mathematical Reasoning Mock Test 8: 2027 NSW Selective Format

Build fluency with multi-step problems, diagrams, and data interpretation in our 35-question mock test—aligned to the Janison-style NSW Selective Mathematical Reasoning paper.

Duration

40 Minutes

Format

2027 NSW Format

Questions

35 multiple-choice

Level

Official Selective Test Level

Skills Covered in this Test

This mock 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 sports drink is made by mixing water and concentrate in the ratio 5 : 2.

Question 1 · Multiple choice

Question

A sports drink is made by mixing water and concentrate in the ratio 5 : 2 . How much concentrate is needed to make 3.5 litres of drink?

Options

A. $750 mL$
B. $800 mL$
C. $900 mL$
D. $1000 mL$
E. $1200 mL$

Correct answer

1000 mL

Explanation

Step 1: Understand the ratio Water : Concentrate = 5 : 2 This means for every 7 parts of drink (5 + 2), there are 2 parts of concentrate. Step 2: Find the value of one part Total drink = 3.5 litres = 3500 mL Total parts = 5 + 2 = 7 parts Value of 1 part = 3500 \div 7 = 500 mL per part Step 3: Find the amount of concentrate Concentrate = 2 parts \times 500 mL = 1000 mL Check: Water = 5 \times 500 = 2500 mL. Total = 2500 + 1000 = 3500 mL ✓ Answer: 1000 mL of concentrate

Mathematical Reasoning

A regular octagon (all sides equal) is placed beside a square, sharing one full edge. Both shapes have a side…

Question 2 · Multiple choice

Question

A regular octagon (all sides equal) is placed beside a square, sharing one full edge. Both shapes have a side length of 4 cm. What is the perimeter of the combined shape?

Options

A. $36 cm$
B. $38 cm$
C. $44 cm$
D. $48 cm$
E. $40 cm$

Correct answer

40 cm

Explanation

Step 1: Find each shape's perimeter separately Both shapes have side length 4 cm. Regular octagon (8 sides): 8 \times 4 = 32 cm Square (4 sides): 4 \times 4 = 16 cm Step 2: Subtract the shared edge When the two shapes are placed side by side sharing one edge (4 cm), that edge disappears from the outer boundary of BOTH shapes — it's hidden inside. Combined perimeter = 32 + 16 - 4 - 4 = 40 cm Answer: 40 cm

Core Competencies

3D NetsAlgebraic SubstitutionsAngle PropertiesArea & PerimeterCartesian CoordinatesDecimalsFractionsGraph InterpretationInverse OperationsLogical DeductionMean, Median & ModeMental ArithmeticMulti-step Word ProblemsNumber SequencesOrder of OperationsPercentagesPrime NumbersProbability LogicProfit & LossRatiosReflection & RotationSpeed, Distance, TimeSquare & Cube NumbersSymmetryTime & CalendarsUnit ConversionsVenn DiagramsVolume & Capacity

Prepare with Precision

Sharpen accuracy on multi-step and diagram-based items.
Get comfortable with the Janison-style interface.
Identify topics to revisit before exam day.

This public page is designed so students and parents get rich, accurate information about the test structure and skills assessed. The full timed mock—including the rest of the 35 questions, scoring, and detailed review—is available to enrolled members after sign-in, matching how premium preparation platforms balance discoverability with protected content.

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