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4024/21 May/Jun 2022, Question 3: Upper and Lower Bounds

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 8 marks

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The question, in short

Use a cost-length graph for fabric, then share 10 m in the ratio 6 : 8 : 11, and find d from an upper-bound area of 8.8125 m² with width 2.3 m.

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

Part (ai) · 1 mark

Read from the graph the cost of 3.8 m of fabric.

  1. 1The line passes through (5, 37), so fabric costs 37 ÷ 5 = $7.40 per metre
  2. 2Read up from t = 3.8: cost = 3.8 × 7.40
  3. 3≈ $28.1

Answer27.80 to 28.40

Part (aii) · 2 marks

Samira pays with $20 and gets $1.50 change; use the graph to find k, the metres bought.

  1. 1Amount paid = 20 − 1.50 = $18.50
  2. 2Read across from $18.50 to the line: t = 18.50 ÷ 7.40
  3. 3k = 2.5

Answer2.45 to 2.55

Part (b) · 2 marks

10 m of fabric is divided in the ratio 6 : 8 : 11; find the dress length.

  1. 1Total parts = 6 + 8 + 11 = 25
  2. 2Dress = 11/25 × 10
  3. 3= 4.4 m

Answer4.4

Part (c) · 3 marks

Area upper bound 8.8125 m², width 2.3 m to nearest 0.1 m; find d, length to nearest 0.1 m.

  1. 1Upper bound of width = 2.35 m
  2. 2Upper bound of length = 8.8125 ÷ 2.35 = 3.75 m
  3. 3d + 0.05 = 3.75
  4. 4d = 3.7

Answer3.7

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Also searched as: 4024/21/M/J/22 · 4024_s22_qp_21 · 4024 s22 21 · question 3.
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