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0580/32 Oct/Nov 2021, Question 8: Pythagoras' Theorem

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 12 marks

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The question, in short

Similar right-angled triangles, two tiles forming a rectangle with a 84.5 cm diagonal, and a scale drawing of two towns using bearings.

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

Part (ai) · 2 marks

Use the scale factor between the similar triangles to find EF.

  1. 1Scale factor = 74.9 ÷ 21.4 = 3.5
  2. 2EF = 14.8 × 3.5 = 51.8 cm

Answer51.8

Part (aii) · 2 marks

Find angle BCA with trigonometry.

  1. 1cos BCA = 14.8/21.4
  2. 2Angle BCA = 46.24… ≈ 46.2°

Answer46.2 or 46.24…

Part (b) · 4 marks

Width 32.5 cm and diagonal 84.5 cm: find the length of one tile.

  1. 1Long side² + 32.5² = 84.5²
  2. 2Long side = √(84.5² − 32.5²) = √6084 = 78 cm
  3. 3Each tile = 78 ÷ 2 = 39 cm

Answer39

Part (ci) · 3 marks

Draw B 72 km on 058° from A, then C 60 km east of B, at 1 cm to 12 km.

  1. 1AB = 72 ÷ 12 = 6 cm; BC = 60 ÷ 12 = 5 cm
  2. 2At A measure 58° clockwise from North and draw AB 6 cm; mark B
  3. 3From B draw a line 5 cm due east (perpendicular to North); mark C

AnswerAccurate scale drawing

Part (cii) · 1 mark

Measure the bearing of C from A on the drawing.

  1. 1Join AC and measure the angle clockwise from North at A
  2. 2Accurate drawing gives about 072° (by calculation 72.5°)

Answer72.5 (accept 71 to 74)

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Also searched as: 0580/32/O/N/21 · 0580_w21_qp_32 · 0580 w21 32 · question 8.
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