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0580/41 May/Jun 2023, Question 7: Equations That Become Quadratics

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 18 marks

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The question, in short

Algebra question: factorise two expressions, solve an algebraic fraction equation, solve a quadratic to 2 decimal places, and rearrange a formula to make k the subject.

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

Part (ai) · 3 marks

Factorise 27y² − 3 fully.

  1. 127y² − 3 = 3(9y² − 1)
  2. 29y² − 1 = (3y)² − 1² (difference of two squares)
  3. 3= 3(3y − 1)(3y + 1)

Answer3(3y − 1)(3y + 1)

Part (aii) · 2 marks

Factorise 2m − pk + 2k − pm fully.

  1. 12m − pk + 2k − pm = 2(m + k) − p(m + k)
  2. 2= (2 − p)(m + k)

Answer(2 − p)(m + k)

Part (b) · 5 marks

Solve (x − 1)/(x + 1) − 6/(x − 1) = 1.

  1. 1Multiply by (x + 1)(x − 1): (x − 1)² − 6(x + 1) = (x + 1)(x − 1)
  2. 2x² − 2x + 1 − 6x − 6 = x² − 1
  3. 3−8x − 5 = −1
  4. 4−8x = 4
  5. 5x = −1/2

Answer−1/2

Part (c) · 4 marks

Solve 4x² − 3x − 2 = 0, showing working and giving answers to 2 decimal places.

  1. 1x = (3 ± √((−3)² − 4 × 4 × (−2)))/(2 × 4)
  2. 2x = (3 ± √41)/8
  3. 3x = (3 + 6.403…)/8 = 1.175… or x = (3 − 6.403…)/8 = −0.425…
  4. 4x = −0.43 and x = 1.18

Answer−0.43 and 1.18

Part (d) · 4 marks

Make k the subject of k/m = 4 + kp.

  1. 1k = m(4 + kp) = 4m + kpm
  2. 2k − kpm = 4m
  3. 3k(1 − pm) = 4m
  4. 4k = 4m/(1 − pm)

Answer4m/(1 − pm) or −4m/(pm − 1)

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Also searched as: 0580/41/M/J/23 · 0580_s23_qp_41 · 0580 s23 41 · question 7.
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