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4024/22 May/Jun 2020, Question 2: Solving Linear Equations

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 6 marks

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The question, in short

Rectangle width w, length 6 cm longer, perimeter 37 cm: write an equation in w and solve for the width. Then find the upper bound of a shaded area after a 20 by 8 rectangle is removed from a 28 by 15 rectangle, all to nearest cm.

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Part (a) · 3 marks

Using w for the width and a length 6 cm greater, express the perimeter as 37 cm, then solve for w.

  1. 1Length = w + 6
  2. 22w + 2(w + 6) = 37
  3. 34w + 12 = 37
  4. 44w = 25, w = 6.25

Answer6.25

Part (b) · 3 marks

With all sides rounded to the nearest centimetre, work out the largest possible area left after the inner 20 cm by 8 cm rectangle is removed.

  1. 1Upper bounds: 28.5 and 15.5; lower bounds of the cut-out: 19.5 and 7.5
  2. 2Upper bound area = 28.5 × 15.5 − 19.5 × 7.5
  3. 3= 441.75 − 146.25 = 295.5 cm²

Answer295.5

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