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0580/33 May/Jun 2024, Question 6: Constructing Equations

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 14 marks

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The question, in short

Answer six items: use a points formula with 15 wins, 7 draws and 6 bonus points; solve two equations; expand and simplify; rearrange a formula; and form and solve an equation about marbles in two bags.

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

Part (a) · 2 marks

Calculate the team's total points from 15 wins, 7 draws and 6 bonus points using the given scoring formula.

  1. 115 × 4 + 7 × 2 + 6
  2. 2= 60 + 14 + 6
  3. 3= 80

Answer80

Part (b) · 1 mark

Solve x/2 = 18 for x.

  1. 1x = 18 × 2
  2. 2x = 36

Answer36

Part (c) · 2 marks

Solve 4x + 12 = 18 for x.

  1. 14x = 18 − 12 = 6
  2. 2x = 6 ÷ 4 = 1.5

Answer1 1/2 or 1.5

Part (d) · 2 marks

Expand and simplify 6(3x − 4) + 5(x − 2).

  1. 16(3x − 4) = 18x − 24
  2. 25(x − 2) = 5x − 10
  3. 318x − 24 + 5x − 10 = 23x − 34

Answer23x − 34

Part (e) · 2 marks

Rearrange T = 5r − 6 to make r the subject.

  1. 1T + 6 = 5r
  2. 2r = (T + 6)/5

Answerr = (T + 6)/5

Part (f) · 5 marks

With x marbles in the green bag and 5 times as many in the blue, adding 6 to each gives 4 times as many in blue; write and solve an equation for x.

  1. 1Blue bag has 5x; after adding: green x + 6, blue 5x + 6
  2. 25x + 6 = 4(x + 6)
  3. 35x + 6 = 4x + 24
  4. 45x − 4x = 24 − 6
  5. 5x = 18

Answer5x + 6 = 4(x + 6); x = 18

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