Sample Questions from Test 14

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

Mathematical Reasoning

A rectangular running track has sides 9 m and 6 m.

Question 1 · Multiple choice

Question

A rectangular running track has sides 9 m and 6 m . Kimi starts at corner X and runs clockwise along the outside edge . She runs 2 complete laps of the rectangle, then runs exactly half of the perimeter one more time (still along the edge, in the same direction). How far does she run in total ?

Options

A. $75 m$
B. $65 m$
C. $70 m$
D. $80 m$
E. $85 m$

Correct answer

A.

75 m

Explanation

Step 1: Find the perimeter (one lap) of the track The rectangular track has sides 9 m and 6 m. \leftarrow── 9 m ──\to X ─────────────┐ ↑ │ │ 6 m └───────────────┘ ↓ Perimeter = 2 \times (length + width) = 2 \times (9 + 6) = 2 \times 15 = 30 m per lap Step 2: Calculate distance for 2 complete laps 2 \times 30 = 60 m Step 3: Calculate half a perimeter Half a lap = 30 \div 2 = 15 m Step 4: Add everything together Total distance = 60 + 15 = 75 m Answer: 75 m

Mathematical Reasoning

Find the value of (40 − 16) ÷ 8 + 3 × (4 + 5 × 2)

Question 2 · Multiple choice

Question

Find the value of (40 - 16) \div 8 + 3 \times (4 + 5 \times 2)

Options

A. $42$
B. $45$
C. $57$
D. $84$
E. $36$

Correct answer

B.

45

Explanation

Step 1: Work inside both brackets first (B in BODMAS) First bracket: (40 - 16) = 24 Second bracket: (4 + 5 \times 2) Inside this bracket, multiplication comes before addition: 5 \times 2 = 10, then 4 + 10 = 14 After brackets: 24 \div 8 + 3 \times 14 Step 2: Division and Multiplication (left to right) Operation Calculation Result 24 \div 8 \div 3 3 \times 14 \times 42 After this step: 3 + 42 Step 3: Addition 3 + 42 = 45 Summary of steps: (40-16) \div 8 + 3 \times (4 + 5\times2) 24 \div 8 + 3 \times 14 3 + 42 = 45 Answer: 45

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OC Mathematical Reasoning Practice Test 14 — 2027 NSW Opportunity Class Exam

Skills Covered in this Test

Sample Questions from Test 14

Core Competencies

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