Home / iGCSE Mathematics (0580) – C4.3 Scale drawings – Exam Style Questions Paper 3

iGCSE Mathematics (0580) - C4.3 Scale drawings - Exam Style Questions Paper 3- New Syllabus

IGCSE Mathematics(0580) Practice Questions Paper 3 - All Chapters

Question

The scale drawing shows the position of ship A.
The scale is 1 centimetre represents 40 kilometres.

Ship B is 220 km from ship A on a bearing of $140^{\circ}$.
On the scale drawing, mark the position of ship B.

Most-appropriate topic codes (Cambridge IGCSE Mathematics 0580):

• C4.3 Scale drawings
▶️ Answer/Explanation

First, we convert the real-world distance to the drawing length using the given scale. Since 1 cm represents 40 km, the length on the paper is $220 \div 40 = 5.5\text{ cm}$.
Next, use a protractor to measure a bearing of $140^{\circ}$ clockwise from the North line at point A, and mark point B exactly $5.5\text{ cm}$ along that line.

✅ Answer: Point B accurately marked 5.5 cm away from A on a $140^{\circ}$ bearing.

Question

Bayside, Millwater and Westbridge are towns beside a lake.
The scale drawing shows the positions of Bayside (B) and Millwater (M).
The scale is 1 centimetre represents 2 kilometres.

(i) Find the actual distance between Bayside and Millwater.
(ii) Westbridge (W) is 17 km from Bayside on a bearing of 155°.
On the scale drawing, mark the position of Westbridge.

(b) (i) A boat travels from Bayside to Westbridge.
The table gives some information about its journey.

Work out how long the boat takes to travel from Millwater to Westbridge. Give your answer in hours and minutes.

(ii) The boat returns directly to Bayside.
It takes 1 hour 20 minutes to travel the 17 km.

Work out the average speed of this journey.

(c) Here are the ticket prices for a boat trip from Bayside to Westbridge.

(i) Calculate the cost per person for a group of 15 people.

(ii) A group of 24 people buy tickets for the boat trip from Bayside to Westbridge.

Calculate the least amount of money the group needs to pay.

▶️ Answer/Explanation
Solution

(a)(i) 9 km

Measure distance on scale drawing (4.5 cm) and multiply by scale factor (2 km/cm).

(a)(ii) W marked at correct position

Convert 17 km to 8.5 cm on drawing. Draw bearing of 155° from B and mark W.

(b)(i) 1 hour 22 minutes

Subtract departure time from Millwater (11:45) from arrival time at Westbridge (13:07).

(b)(ii) 12.75 km/h

Convert 1 hour 20 minutes to 4/3 hours. Speed = Distance/Time = 17 ÷ (4/3).

(c)(i) $9.25

Divide group cost ($138.75) by number of people (15).

(c)(ii) $225.45

Optimal combination: 1 group of 15 ($138.75), 1 group of 6 ($57.30), and 3 individuals ($29.40).

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