OC Mathematical Reasoning Practice Test 13 — 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

Mathematical Reasoning

The ratio of Adam's savings to John's savings was 9 : 4. After Adam spent \$63, the ratio became 3 : 2. How m…

Question 1 · Multiple choice

Question

The ratio of Adam's savings to John's savings was 9 : 4. After Adam spent $63, the ratio became 3 : 2. How much savings did John have?

Options

A. $$56$
B. $$63$
C. $$72$
D. $$84$
E. $$126$

Correct answer

$84

Explanation

Step 1: Express both savings using one variable Original ratio Adam : John = 9 : 4. Let Adam's savings = 9k and John's savings = 4k. Step 2: Set up the equation for the new ratio John's savings are unchanged (he doesn't spend anything). After Adam spends $63: Adam has: 9k - 63 John still has: 4k The new ratio is 3 : 2: (9k - 63) : 4k = 3 : 2 Step 3: Solve for k Cross-multiply (means \times extremes): 2 \times (9k - 63) = 3 \times 4k 18k - 126 = 12k 18k - 12k = 126 6k = 126 k = 126 \div 6 = 21 Step 4: Find John's savings John = 4k = 4 \times 21 = $84 Check: Adam originally: 9 \times 21 = $189 After spending: $189 - $63 = $126 New ratio: $126 : $84 = 3 : 2 ✓ Answer: John has $84 Option Value Why it is wrong A $56 Used k = 14 — solved the equation incorrectly. ✗ B $63 Confused Adam's spend with John's savings. ✗ C $72 Used k = 18 — arithmetic slip. ✗ D $84 4 \times 21 = 84. ✓ E $126 Found 6k = 126 but gave that as the answer instead of 4k. ✗

Mathematical Reasoning

The following solid is made of four identical cubes. Given that its volume is 32 cm³, find its total surface …

Question 2 · Multiple choice

Question

The following solid is made of four identical cubes. Given that its volume is 32 cm³, find its total surface area.

A 3-D solid made of four identical cubes arranged in an L-shape

Options

A. $72 cm²$
B. $56 cm²$
C. $64 cm²$
D. $80 cm²$
E. $96 cm²$

Correct answer

72 cm²

Explanation

Step 1: Find the size of each cube 4 identical cubes have a total volume of 32 cm³. Volume per cube = 32 \div 4 = 8 cm³ Since a cube with edge length e has volume e³: e³ = 8 \to e = 2 cm Each face area = 2 \times 2 = 4 cm² Step 2: Picture the L-shape arrangement [D] [A][B][C] Cube D sits on top of Cube A. Cubes A, B, C are in a row along the bottom. Step 3: Count exposed (visible) faces for each cube Each cube has 6 faces total. Subtract faces that are glued to another cube. Cube Touching neighbours Hidden faces Exposed faces A B (right) + D (top) 24 B A (left) + C (right) 24 C B (left) 15 D A (bottom) 15 Total exposed faces = 4 + 4 + 5 + 5 = 18 faces Step 4: Calculate the total surface area Surface area = 18 \times 4 cm² = 72 cm² Answer: 72 cm²

OC Mathematical Reasoning Practice Test 13 — 2027 NSW Opportunity Class Exam

Skills Covered in this Test

Sample Questions from Test 13

Core Competencies

Prepare with Precision

Option	Value	Why it is wrong
A	$56	Used k = 14 — solved the equation incorrectly. ✗
B	$63	Confused Adam's spend with John's savings. ✗
C	$72	Used k = 18 — arithmetic slip. ✗
D	$84	4 × 21 = 84. ✓
E	$126	Found 6k = 126 but gave that as the answer instead of 4k. ✗

Cube	Touching neighbours	Hidden faces	Exposed faces
A	B (right) + D (top)	2	4
B	A (left) + C (right)	2	4
C	B (left)	1	5
D	A (bottom)	1	5