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0580/31 Oct/Nov 2023, Question 7: Constructing Equations

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 13 marks

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The question, in short

Algebra question with five parts: simplify an expression, evaluate a formula, rearrange for a subject, expand brackets, and form and solve an equation from a marbles word problem.

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

Part (a) · 2 marks

Simplify 5a + 3b + 2a − 4b by collecting like terms.

  1. 15a + 2a = 7a and 3b − 4b = −b
  2. 2= 7a − b

Answer7a − b

Part (b) · 2 marks

Given P = 8x + 3y, find x when P = 21 and y = −5.

  1. 121 = 8x + 3 × (−5)
  2. 221 = 8x − 15, so 8x = 36
  3. 3x = 4.5

Answer4.5

Part (c) · 2 marks

Rearrange S = kv² to make v the subject.

  1. 1v² = S/k
  2. 2v = √(S/k)

Answer√(S/k)

Part (d) · 2 marks

Multiply out and simplify (x − 3)(x + 5).

  1. 1x² + 5x − 3x − 15
  2. 2= x² + 2x − 15

Answerx² + 2x − 15

Part (e) · 5 marks

Nasser has x marbles, Selina 15 more, Hanif 3 times Selina; total 150. Find x.

  1. 1Selina = x + 15, Hanif = 3(x + 15)
  2. 2x + (x + 15) + 3(x + 15) = 150
  3. 35x + 60 = 150
  4. 45x = 90, x = 18

Answer18

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Also searched as: 0580/31/O/N/23 · 0580_w23_qp_31 · 0580 w23 31 · question 7.
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