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0580/31 May/Jun 2022, Question 6: Constructing Equations

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 15 marks

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The question, in short

Algebra question set: form a points expression, build and solve an equation for three teams' scores, simplify two expressions, and solve simultaneous equations showing working.

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

Part (a) · 2 marks

Write an expression in w and d for total points, with 3 points per win and 1 per draw.

  1. 13 points per win: 3w; 1 point per draw: d
  2. 2Total = 3w + d

Answer3w + d

Part (b) · 5 marks

Using x for Athletic, write an equation from the three teams' scores totalling 121, then solve to find each team's score.

  1. 1Rovers = x + 12, United = 2x − 3
  2. 2x + x + 12 + 2x − 3 = 121
  3. 34x + 9 = 121, so 4x = 112, x = 28
  4. 4Athletic 28, Rovers 28 + 12 = 40, United 2 × 28 − 3 = 53

AnswerAthletic 28, Rovers 40, United 53

Part (ci) · 2 marks

Simplify 4a − 3b + 5a + 6b by collecting like terms.

  1. 14a + 5a = 9a, −3b + 6b = 3b
  2. 2= 9a + 3b

Answer9a + 3b

Part (cii) · 2 marks

Simplify 6(2x + 1) − 5(x − 2) by expanding and collecting like terms.

  1. 112x + 6 − 5x + 10
  2. 2= 7x + 16

Answer7x + 16

Part (d) · 4 marks

Solve 3x + 5y = 11 and 2x − 3y = 20 simultaneously, showing all working.

  1. 1× 2: 6x + 10y = 22; × 3: 6x − 9y = 60
  2. 2Subtract: 19y = −38, so y = −2
  3. 33x + 5(−2) = 11, so 3x = 21, x = 7
  4. 4x = 7, y = −2

Answerx = 7, y = −2

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