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0580/42 Feb/Mar 2021, Question 11: Equations That Become Quadratics

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 9 marks

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The question, in short

Gaya pays $48 for books at $x each; Myra pays $60 for books at $(x + 2) each, with Gaya having 4 more books. Form an expression, derive x² + 5x − 24 = 0, solve it, then find Myra's book count.

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

Part (a) · 1 mark

Give an expression in x for how many books Gaya gets for $48 at $x each.

  1. 1Number of books = total cost ÷ cost of one book
  2. 248/x

Answer48/x

Part (b) · 4 marks

Using Myra's $60 at $(x + 2) each and Gaya having 4 extra books, show that x² + 5x − 24 = 0.

  1. 1Myra buys 60/(x + 2) books
  2. 248/x − 60/(x + 2) = 4
  3. 348(x + 2) − 60x = 4x(x + 2)
  4. 448x + 96 − 60x = 4x² + 8x
  5. 50 = 4x² + 20x − 96
  6. 6x² + 5x − 24 = 0

Answer48x + 96 − 60x = 4x² + 8x leading to x² + 5x − 24 = 0

Part (c) · 3 marks

Find the solutions of x² + 5x − 24 = 0 using factorisation.

  1. 1Find two numbers that multiply to −24 and add to 5: 8 and −3.
  2. 2x² + 5x − 24 = (x + 8)(x − 3) = 0
  3. 3x + 8 = 0 or x − 3 = 0
  4. 4x = 3 and −8

Answer3 and −8

Part (d) · 1 mark

With x satisfying x² + 5x − 24 = 0, work out how many books Myra gets for $60 at $(x + 2) each.

  1. 1Solve x² + 5x − 24 = 0: (x + 8)(x − 3) = 0
  2. 2x = −8 or x = 3; a price cannot be negative, so x = 3
  3. 3Myra pays x + 2 = 5 dollars per book
  4. 4Myra buys 60 ÷ 5 = 12

Answer12

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Also searched as: 0580/42/F/M/21 · 0580_m21_qp_42 · 0580 m21 42 · question 11.
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