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0580/31 Oct/Nov 2022, Question 7: Constructing Equations

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

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The question, in short

Algebra revision question: simplify an expression, evaluate a formula, factorise, solve an equation, work with indices, and form and solve an age equation.

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

Part (a) · 2 marks

Simplify 5g − 3h − 7g + 6h by collecting like terms.

  1. 15g − 7g = −2g
  2. 2−3h + 6h = 3h
  3. 3= −2g + 3h

Answer−2g + 3h

Part (b) · 2 marks

Use j = 4k + 7m with k = −5 and m = 6 to find j.

  1. 1j = 4(−5) + 7(6)
  2. 2= −20 + 42
  3. 3= 22

Answer22

Part (c) · 2 marks

Factorise 14x³ + 49x completely.

  1. 1HCF of 14x³ and 49x is 7x
  2. 214x³ + 49x = 7x(2x² + 7)

Answer7x(2x² + 7)

Part (d) · 3 marks

Solve 8(3t − 9) = 108 for t.

  1. 124t − 72 = 108
  2. 224t = 180
  3. 3t = 7.5

Answer7.5

Part (ei) · 1 mark

Given 9²⁴ ÷ 9ʷ = 9⁵, find the value of w.

  1. 19²⁴ ÷ 9ʷ = 9²⁴⁻ʷ
  2. 224 − w = 5
  3. 3w = 19

Answer19

Part (eii) · 1 mark

Solve 4x² = 256 to find the value of x.

  1. 1x² = 256 ÷ 4 = 64
  2. 2x = √64 = 8

Answer8

Part (f) · 4 marks

Ranjit is x, Suzi is 3 times Ranjit, Juan is 4 more than Suzi; total 46. Write an equation and solve for x.

  1. 1Suzi = 3x, Juan = 3x + 4
  2. 2x + 3x + 3x + 4 = 46
  3. 37x + 4 = 46
  4. 47x = 42
  5. 5x = 6

Answer6

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Also searched as: 0580/31/O/N/22 · 0580_w22_qp_31 · 0580 w22 31 · question 7.
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