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0580/31 May/Jun 2024, Question 7: Scale Drawings

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 14 marks

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The question, in short

Scale drawing and bearings problem: mark a house position from a walk, find reverse bearing and distance bounds, model scale, similar rectangles, and cylinder curved surface area.

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

Part (a) · 3 marks

Using scale 1 cm to 2 km, mark H after walking 4.8 km/h for 3 hours on bearing 236° from C.

  1. 1Distance = 4.8 × 3 = 14.4 km
  2. 2On the drawing: 14.4 ÷ 2 = 7.2 cm
  3. 3Measure 236° clockwise from North at C
  4. 4Mark H 7.2 cm from C along that line

AnswerH correctly marked 7.2 cm from C on bearing 236°

Part (bi) · 2 marks

Find the bearing of C from R given R is on bearing 083° from C.

  1. 1Back bearing = 83 + 180
  2. 2= 263°

Answer263

Part (bii) · 2 marks

Given d is 5 km to nearest km, complete the inequality bounds for d.

  1. 1Nearest kilometre: half of 1 km = 0.5
  2. 2Lower bound 5 − 0.5 = 4.5
  3. 3Upper bound 5 + 0.5 = 5.5

Answer4.5 ≤ d < 5.5

Part (c) · 2 marks

Model wall 5 cm represents actual 90 m; find scale in form 1 : n.

  1. 190 m = 9000 cm
  2. 25 : 9000
  3. 3= 1 : 1800

Answer1 : 1800

Part (d) · 2 marks

Rectangles ABCD and EFGH are similar with AB=5.6 m, AD=8.4 m, EF=9.2 m; calculate x=EH.

  1. 1Scale factor = 9.2 ÷ 5.6
  2. 2x = 8.4 × 9.2 ÷ 5.6
  3. 3x = 13.8

Answer13.8

Part (e) · 3 marks

Cylinder radius 2.4 m, height 25 m; calculate curved surface area and give units.

  1. 1Curved surface area = 2πrh
  2. 2= 2 × π × 2.4 × 25
  3. 3= 120π = 376.99…
  4. 4≈ 377 m²

Answer377 or 376.9 to 377.04 m²

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Also searched as: 0580/31/M/J/24 · 0580_s24_qp_31 · 0580 s24 31 · question 7.
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