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0580/32 May/Jun 2022, Question 8: Speed, Distance and Time

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 14 marks

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The question, in short

Regular octagon questions: prove an exterior angle, find an interior angle, use bearings and a triangle, then work out race time and judge a scale choice.

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

Part (ai) · 1 mark

Demonstrate that a regular octagon's exterior angle equals 45°.

  1. 1Exterior angles of a polygon add to 360°
  2. 2Exterior angle = 360 ÷ 8 = 45°

Answer360/8 = 45 or 180 − ((8 − 2) × 180)/8 = 45

Part (aii) · 1 mark

Determine the size of the interior angle of a regular octagon.

  1. 1Interior angle = 180 − 45 = 135°

Answer135

Part (bi) · 1 mark

Using the diagram, state the bearing of B measured from A.

  1. 1AH points due west (270°); angle HAB = 135°
  2. 2Bearing of B from A = 270 − 135 = 135°

Answer135

Part (bii) · 1 mark

Fill the gap so the bearing of C from D matches another bearing.

  1. 1DC is parallel to HG and in the same direction
  2. 2The bearing of C from D is the same as the bearing of H from G

AnswerH, G or B, E or A, F

Part (biiia) · 1 mark

Give the mathematical name for triangle ABH.

  1. 1AB = AH (sides of a regular octagon): isosceles

AnswerIsosceles

Part (biiib) · 2 marks

Find the size of angle ABH.

  1. 1Angle ABH = (180 − 135) ÷ 2
  2. 2= 22.5°

Answer22.5

Part (biiic) · 2 marks

Work out the bearing of H as seen from B.

  1. 1Bearing of H from B = 360 − (45 + 22.5)
  2. 2= 292.5°

Answer292.5

Part (c) · 3 marks

With each side 1.35 km and average speed 45 km/h, find the race time in minutes.

  1. 1Total distance = 8 × 1.35 = 10.8 km
  2. 2Time = 10.8 ÷ 45 = 0.24 h
  3. 30.24 × 60 = 14.4 minutes

Answer14.4

Part (d) · 2 marks

Decide whether 1 : 500 000 suits a scale drawing of the route, showing working and explaining your choice.

  1. 11 : 500 000 means 1 cm represents 500 000 cm = 5 km
  2. 2Each side 1.35 km would be 1.35 ÷ 5 = 0.27 cm
  3. 3No: the drawing would be too small

AnswerNo because the scale drawing is too small, e.g. 1 cm is 5 km or 0.27 cm is 1.35 km or 2.16 cm is 10.8 km

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Also searched as: 0580/32/M/J/22 · 0580_s22_qp_32 · 0580 s22 32 · question 8.
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