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0580/41 Oct/Nov 2021, Question 2: Calculating with Bounds

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 15 marks

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The question, in short

Compare three runners' race times and charity money using ratios and percentages, then bound stride counts from rounded measurements and grow a total by 2.4% yearly for 5 years.

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

Part (ai) · 1 mark

Express Chao's run time as a percentage of Mei's, given the ratio 4 : 5 : 7.

  1. 15/7 × 100 = 71.42… ≈ 71.4%

Answer71.4 or 71.42 to 71.43

Part (aii) · 3 marks

Bob's time is 55 minutes 40 seconds; use the ratio to find Mei's time in minutes and seconds.

  1. 155 min 40 s = 3340 s
  2. 2Mei = 3340 ÷ 4 × 7 = 5845 s
  3. 35845 ÷ 60 = 97 remainder 25
  4. 497 min 25 s

Answer97 min 25 s

Part (bi) · 2 marks

Chao raises $47.50; work out Bob's total, which is 28% larger.

  1. 147.50 × (1 + 28/100) = 47.50 × 1.28
  2. 2= $60.80

Answer60.80

Part (bii) · 3 marks

Chao's total is 60% below Mei's; find how much extra Mei raised compared with Chao.

  1. 1Mei × (1 − 60/100) = 47.50, so Mei = 47.50 ÷ 0.4 = $118.75
  2. 2118.75 − 47.50 = $71.25

Answer71.25

Part (c) · 4 marks

Stride 70 cm to nearest 5 cm, distance 11.2 km to nearest 0.1 km; find the smallest possible number of strides.

  1. 1Minimum distance = 11.15 km = 1 115 000 cm
  2. 2Maximum stride = 70 + 2.5 = 72.5 cm
  3. 31 115 000 ÷ 72.5 = 15 379.3…
  4. 4Minimum number of strides = 15 380

Answer15 380

Part (d) · 2 marks

Starting from $1.6 million in 2015, find the 2020 total after 2.4% yearly exponential growth over 5 years.

  1. 11.6 × (1 + 2.4/100)⁵ = 1.6 × 1.024⁵
  2. 2= 1.801… ≈ $1.80 million

Answer1.80 or 1.801 to 1.802 (million)

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Also searched as: 0580/41/O/N/21 · 0580_w21_qp_41 · 0580 w21 41 · question 2.
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