0580/32 Feb/Mar 2024, Question 6: Speed, Distance and Time
Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 11 marks
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The question, in short
Scale drawing of town S from R, timing a 44 km cycle, finding a drawing scale, and using bearings and distances between three towns to show a right angle and find a side.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (ai) · 2 marks
Using 1 cm to 8 km, mark S at 44 km from R on bearing 117°.
- 1Distance on map = 44 ÷ 8 = 5.5 cm
- 2Measure 117° clockwise from North at R
- 3Mark S 5.5 cm from R along this line
AnswerS marked 5.5 cm from R on a bearing of 117°
Part (aii) · 3 marks
Anvi leaves R at 13 15 cycling 44 km at 12 km/h; find her arrival time.
- 1Time = 44 ÷ 12 = 3.666… h
- 20.666… h = 40 min, so 3 h 40 min
- 313 15 + 3 h 40 min = 16 55
Answer16 55
Part (b) · 2 marks
Tower 16 m drawn as 20 cm; find the scale as 1 : n.
- 116 m = 1600 cm
- 220 : 1600
- 3= 1 : 80
Answer80
Part (ci) · 2 marks
Using bearings 288° and 018° from Y, show angle XYZ equals 90°.
- 1Angle between North and YX = 360 − 288 = 72°
- 2Angle between North and YZ = 18°
- 3Angle XYZ = 72 + 18 = 90°
Answer360 − 288 + 18 = 90
Part (cii) · 2 marks
With XY = 6 km and YZ = 9.7 km, calculate the length XZ.
- 1XZ² = 6² + 9.7²
- 2= 36 + 94.09 = 130.09
- 3XZ = √130.09 = 11.40…
- 4= 11.4 km
Answer11.4 or 11.40 to 11.41
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