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4024/22 Oct/Nov 2023, Question 9: Choosing Between Sine and Cosine Rules

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 11 marks

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The question, in short

Use a rectangular field with A north of C, AB = 450 m, BC = 210 m, to work out walking time and a bearing.

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

Part (ai) · 3 marks

Calculate the time to walk the whole perimeter at 5.2 km/h, giving minutes to the nearest minute.

  1. 1Perimeter = 2 × 450 + 2 × 210 = 1320 m = 1.32 km
  2. 2Time = 1.32 ÷ 5.2 = 0.2538… h
  3. 3× 60 = 15.2… ≈ 15 minutes

Answer15

Part (aii) · 3 marks

Show the bearing of D from A equals 245°, correct to 3 significant figures.

  1. 1In triangle ACD: DC = 450, AD = 210
  2. 2tan DAC = 450/210 so angle DAC = 64.98…°
  3. 3C is due south, so bearing = 180 + 64.98… = 244.98… ≈ 245°

Answer244.98…

Part (b) · 5 marks

Calculate QS in triangle PQR using PS = 10.3 cm, QR = 12.6 cm, angle QPS = 42°, angle QRS = 35°.

  1. 1Angle PQR = 180 − 42 − 35 = 103°
  2. 2PQ/sin 35° = 12.6/sin 42° so PQ = 10.80…
  3. 3QS² = 10.80…² + 10.3² − 2 × 10.80… × 10.3 × cos 42° = 57.39…
  4. 4QS = 7.576… ≈ 7.58 cm

Answer7.58 or 7.575 to 7.577

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Also searched as: 4024/22/O/N/23 · 4024_w23_qp_22 · 4024 w23 22 · question 9.
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