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4024/21 Oct/Nov 2024, Question 8: Bearings with Sine and Cosine Rules

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 8 marks

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The question, in short

Calculate average speed over two legs of a quadrilateral field journey and find a bearing using given side lengths and a right angle.

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

Part (a) · 3 marks

Work out average speed for the whole trip from A to B to C, using distances 320 m and 250 m at 1.6 m/s and 2.8 m/s.

  1. 1Time A to B = 320 ÷ 1.6 = 200 s
  2. 2Time B to C = 250 ÷ 2.8 = 89.28… s
  3. 3Average speed = (320 + 250) ÷ (200 + 89.28…) = 570 ÷ 289.28…
  4. 4= 1.970… ≈ 1.97 m/s

Answer1.97 or 1.970…

Part (b) · 5 marks

Find the bearing of B from A, given bearing of D is 243°, sides 320, 250, 132, 365 and right angle at C.

  1. 1BD² = 132² + 250² = 79 924
  2. 2cos BAD = (365² + 320² − 79 924)/(2 × 365 × 320) = 155 701/233 600
  3. 3Angle BAD = 48.20…°
  4. 4Bearing of B from A = 243 − 48.20… = 194.79… ≈ 195°

Answer195 or 194.79 to 194.81

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Also searched as: 4024/21/O/N/24 · 4024_w24_qp_21 · 4024 w24 21 · question 8.
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