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0580/41 Oct/Nov 2021, Question 9: Arc Length

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 14 marks

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The question, in short

Three separate shapes each have perimeter 20 cm: a rectangle, a rhombus and a circle sector. Work out x, then y, then z.

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

Part (a) · 3 marks

A rectangle has sides x cm and x + 3 cm and perimeter 20 cm. Determine x.

  1. 12(x + x + 3) = 20
  2. 24x + 6 = 20, 4x = 14
  3. 3x = 3.5

Answer3.5

Part (b) · 5 marks

A rhombus with perimeter 20 cm has M as midpoint of a side; a line from the opposite vertex makes 20° with a side. Find obtuse angle y.

  1. 1Side = 20 ÷ 4 = 5 cm, half side = 2.5 cm
  2. 2In the triangle: sin p/5 = sin 20°/2.5, where p is the angle at M
  3. 3sin p = 2 sin 20° = 0.684…, p = 43.16…°
  4. 4y = 180 − (20 + 43.16…) = 116.83… ≈ 116.8°

Answer116.8 or 116.83 to 116.85

Part (c) · 6 marks

A sector with radius r cm and angle 40° has perimeter 20 cm. A chord of length z cm spans the arc. Determine z.

  1. 1r + r + 40/360 × 2 × π × r = 20
  2. 2r(2 + 0.698…) = 20, r = 7.412…
  3. 3z = 2 × 7.412… × sin 20°
  4. 4z = 5.070… ≈ 5.07

Answer5.07 or 5.068 to 5.071

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Also searched as: 0580/41/O/N/21 · 0580_w21_qp_41 · 0580 w21 41 · question 9.
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