Sample Questions from Test 5

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

Mathematical Reasoning

The perimeter of an isosceles trapezium is 30 cm, the length of one lateral side is 5 cm and the height is 4 …

Question 1 · Multiple choice

Question

The perimeter of an isosceles trapezium is 30 cm, the length of one lateral side is 5 cm and the height is 4 cm. Find its area.

Options

A. $40 cm²$
B. $50 cm²$
C. $60 cm²$
D. $80 cm²$
E. $36 cm²$

Correct answer

A.

40 cm²

Explanation

Step 1: Understand the shape An isosceles trapezium has two parallel sides (top and bottom) and two equal slanted sides (the lateral sides). ←─── a ───→ ┌───────────┐ 5 / ↕ 4 \ 5 / \ └─────────────────┘ ←── b ──→ Perimeter = a + b + 5 + 5 = 30 cm Step 2: Find the sum of the two parallel sides Using the perimeter formula: Perimeter = top + bottom + 2 × lateral side 30 = (top + bottom) + 2 × 5 30 = (top + bottom) + 10 top + bottom = 30 − 10 = 20 cm Step 3: Apply the trapezium area formula Area = ½ × (top + bottom) × height = ½ × 20 × 4 = 40 cm² Answer: 40 cm² OptionValueWhy it is wrongA40 cm²½×20×4=40. ✓B50 cm²Subtracted only one lateral side: (30−5)×4÷2=50. ✗C60 cm²Used full perimeter as sum of bases: ½×30×4=60. ✗D80 cm²Forgot the ½: 20×4=80. ✗E36 cm²Misread height as 3.6 instead of 4: ½×20×3.6=36. ✗

Mathematical Reasoning

Four identical cubes are put together to form a cuboid. The sum of the lengths of all the edges of the cuboid…

Question 2 · Multiple choice

Question

Four identical cubes are put together to form a cuboid. The sum of the lengths of all the edges of the cuboid is 120 centimetres. How many cubic centimetres is the volume of each cube?

Options

A. $64 cm³$
B. $125 cm³$
C. $216 cm³$
D. $343 cm³$
E. $512 cm³$

Correct answer

B.

125 cm³

Explanation

Step 1: Picture the cuboid formed by 4 identical cubes When 4 cubes (each with edge s) are placed in a row, they form a cuboid: ┌────┬────┬────┬────┐ │ │ │ │ │ height = s └────┴────┴────┴────┘ \leftarrow────── 4s ──────\to length=4s, width=s, height=s Step 2: Count all the edges of the cuboid A cuboid has 12 edges in three groups of 4: 4 long edges of length 4s 4 width edges of length s 4 height edges of length s Step 3: Set up and solve the equation Sum of all edges = 4(4s) + 4(s) + 4(s) = 24s 24s = 120 s = 120 \div 24 = 5 cm Step 4: Find the volume of each cube Volume = s³ = 5³ = 5 \times 5 \times 5 = 125 cm³ Answer: 125 cm³ Option Volume Why it is wrong A 64 cm³ s=4 (used wrong edge count). ✗ B 125 cm³ s=5; 5³=125. ✓ C 216 cm³ s=6 (used \div20 instead of \div24). ✗ D 343 cm³ s=7 (wrong method). ✗ E 512 cm³ s=8 (divided 120 by 15 instead of 24). ✗

Prepare with Precision

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Mathematical Reasoning Mock Test 5: 2027 NSW Selective Format

Skills Covered in this Test

Sample Questions from Test 5

Core Competencies

Prepare with Precision

Option	Value	Why it is wrong
A	40 cm²	½×20×4=40. ✓
B	50 cm²	Subtracted only one lateral side: (30−5)×4÷2=50. ✗
C	60 cm²	Used full perimeter as sum of bases: ½×30×4=60. ✗
D	80 cm²	Forgot the ½: 20×4=80. ✗
E	36 cm²	Misread height as 3.6 instead of 4: ½×20×3.6=36. ✗

Option	Volume	Why it is wrong
A	64 cm³	s=4 (used wrong edge count). ✗
B	125 cm³	s=5; 5³=125. ✓
C	216 cm³	s=6 (used ÷20 instead of ÷24). ✗
D	343 cm³	s=7 (wrong method). ✗
E	512 cm³	s=8 (divided 120 by 15 instead of 24). ✗