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0580/32 Feb/Mar 2022, Question 9: Area of a Parallelogram and Trapezium

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 13 marks

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The question, in short

Use the given triangle measurements and angles to prove a right angle, find the quadrilateral's area, work with rounded mass bounds, verify a percentage increase, and calculate a corn amount after successive percentage changes.

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

Part (ai) · 2 marks

Use the side lengths of triangle PQR to show that angle PRQ equals 90 degrees.

  1. 1PR² + QR² = 126² + 120² = 15876 + 14400 = 30276
  2. 2PQ² = 174² = 30276
  3. 3PR² + QR² = PQ², so by the converse of Pythagoras angle PRQ = 90°

AnswerComplete method shown and evaluated

Part (aii) · 5 marks

Find the total area of quadrilateral PQRS, giving the answer to 4 significant figures.

  1. 1PS = 126 × tan 53° = 167.2… m
  2. 2Area PRS = 1/2 × 126 × 167.2… = 10534.08… m²
  3. 3Area PQR = 1/2 × 120 × 126 = 7560 m²
  4. 4Total = 7560 + 10534.08… = 18094.08…
  5. 5= 18090 m² (4 s.f.)

Answer18090

Part (bi) · 2 marks

Complete the inequality showing the lower and upper bounds of m, given 4.3 tonnes to 1 decimal place.

  1. 1Half of 0.1 is 0.05: 4.3 − 0.05 and 4.3 + 0.05
  2. 24.25 ≤ m < 4.35

Answer4.25 ≤ m < 4.35

Part (bii) · 1 mark

Show that barley production rising from 2.6 to 3.25 tonnes is a 25% increase.

  1. 1Increase = 3.25 − 2.6 = 0.65
  2. 20.65/2.6 × 100 = 25%

AnswerComplete method seen

Part (biii) · 3 marks

Starting from 2.4 tonnes of corn in 2019, apply a 20% increase then a 20% decrease to find the 2021 amount.

  1. 12020: 2.4 × 1.2 = 2.88 tonnes
  2. 22021: 2.88 × 0.8 = 2.304 tonnes

Answer2.304

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Also searched as: 0580/32/F/M/22 · 0580_m22_qp_32 · 0580 m22 32 · question 9.
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