Sample Questions from Test 4

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

Mathematical Reasoning

A hexagon has 6 sides.

Question 1 · Multiple choice

Question

A hexagon has 6 sides. How many diagonals can be drawn inside a hexagon?

Options

A. $9$
B. $10$
C. $12$
D. $15$
E. $18$

Correct answer

A.

9

Explanation

Step 1: Understand what a diagonal is A diagonal is a line segment connecting two non-adjacent vertices of a polygon. It goes through the inside of the shape (NOT along the sides). Step 2: Count diagonals from one vertex A hexagon has 6 vertices. From any one vertex, you can draw a line to: 5 other vertices total Subtract 2 adjacent vertices (connected by sides, not diagonals) Diagonals from one vertex = 6 - 1 (itself) - 2 (adjacent) = 3 diagonals Step 3: Calculate the total 6 vertices \times 3 diagonals each = 18 But each diagonal is counted twice (once from each end), so divide by 2: Total diagonals = 18 \div 2 = 9 Alternative formula: n(n - 3) \div 2 = 6 \times 3 \div 2 = 9 Answer: 9 diagonals Option Value Why it is wrong A 9 6 \times (6 - 3) \div 2 = 9. ✓ B 10 Off-by-one error. ✗ C 12 Forgot to divide by 2 (each diagonal counted twice). ✗ D 15 Counted all pairs of vertices including sides: C(6,2)=15 — but sides are not diagonals. ✗ E 18 6 \times 3 = 18 — forgot to divide by 2. ✗

Mathematical Reasoning

In play money:

Question 2 · Multiple choice

Question

In play money: 6 winks = 4 zots 2 zots = 5 flips How many winks are worth the same as 20 flips ?

Options

A. $9 winks$
B. $10 winks$
C. $15 winks$
D. $18 winks$
E. $12 winks$

Correct answer

E.

12 winks

Explanation

What we know: 6 winks = 4 zots 2 zots = 5 flips Step 1: Convert 20 flips \to zots 2 zots = 5 flips, so 1 flip = 2/5 of a zot. 20 flips = 20 \times (2/5) = 40/5 = 8 zots Step 2: Convert 8 zots \to winks 6 winks = 4 zots, so 1 zot = 6/4 = 1.5 winks. 8 zots = 8 \times 1.5 = 12 winks 20 flips ↓ (\times2/5) 8 zots ↓ (\times1.5) 12 winks Check: 12 winks = 8 zots (\div1.5) ✓. 8 zots = 20 flips (\times5/2) ✓. Answer: 12 winks

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OC Mathematical Reasoning Practice Test 4 — 2027 NSW Opportunity Class Exam

Skills Covered in this Test

Sample Questions from Test 4

Core Competencies

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Option	Value	Why it is wrong
A	9	6 × (6 − 3) ÷ 2 = 9. ✓
B	10	Off-by-one error. ✗
C	12	Forgot to divide by 2 (each diagonal counted twice). ✗
D	15	Counted all pairs of vertices including sides: C(6,2)=15 — but sides are not diagonals. ✗
E	18	6 × 3 = 18 — forgot to divide by 2. ✗