Lemmara logoLemmaraWorked solution

0580/33 Oct/Nov 2023, Question 2: Scale Drawings

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 10 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Use a 1 cm to 2 km scale drawing of Bayside and Millwater to find a real distance, locate Westbridge, and answer journey time, speed and ticket cost questions.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (ai) · 2 marks

Measure the drawing distance between Bayside and Millwater and convert it to kilometres using the scale.

  1. 1Measure BM on the scale drawing: 4.5 cm
  2. 2Actual distance = 4.5 × 2 = 9 km

Answer9 (accept 8.6 to 9.4)

Part (aii) · 2 marks

Mark Westbridge on the drawing, 17 km from Bayside on a bearing of 155°.

  1. 1Scale length = 17 ÷ 2 = 8.5 cm
  2. 2At B, measure 155° clockwise from the North line
  3. 3Mark W 8.5 cm from B along that line

AnswerW correctly placed

Part (bi) · 1 mark

Using the timetable, work out the boat's travel time from Millwater to Westbridge in hours and minutes.

  1. 111 45 to 12 45 = 1 hour; 12 45 to 13 07 = 22 minutes
  2. 2Time = 1 hour 22 minutes

Answer1 hour 22 mins

Part (bii) · 2 marks

Find the average speed for the 17 km return journey taking 1 hour 20 minutes.

  1. 11 hour 20 minutes = 1 1/3 hours = 4/3 h
  2. 2Speed = 17 ÷ 4/3 = 12.75 km/h

Answer12.75

Part (ci) · 1 mark

Work out the cost per person when a group of 15 pays $138.75.

  1. 1138.75 ÷ 15 = $9.25 per person

Answer9.25

Part (cii) · 2 marks

Find the least total cost for 24 people using the single, group of 6 and group of 15 prices.

  1. 1Per person: group of 15 = $9.25, group of 6 = 57.30 ÷ 6 = $9.55, single = $9.80
  2. 224 = 15 + 6 + 3
  3. 3Cost = 138.75 + 57.30 + 3 × 9.80 = 138.75 + 57.30 + 29.40
  4. 4= $225.45

Answer225.45

Stuck on a step? Read the free lesson: Scale Drawings

Practise more scale drawings questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on scale drawings

Also searched as: 0580/33/O/N/23 · 0580_w23_qp_33 · 0580 w23 33 · question 2.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.