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0580/42 May/Jun 2022, Question 8: Equations That Become Quadratics

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 18 marks

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The question, in short

Solve five algebra tasks: a linear equation in p, rearrange a formula for m, a rational equation in x, simultaneous equations with a quadratic, and expand a triple product.

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

Part (a) · 2 marks

Solve 10 − 3p = 3 + 11p for p.

  1. 110 − 3 = 11p + 3p
  2. 27 = 14p
  3. 3p = 1/2

Answer1/2 or 0.5

Part (b) · 3 marks

Rearrange mc² − 2k = mg to make m the subject.

  1. 1mc² − mg = 2k
  2. 2m(c² − g) = 2k
  3. 3m = 2k/(c² − g)

Answer2k/(c² − g)

Part (c) · 5 marks

Solve 1/(x − 3) + 4/(2x + 3) = 1 for x.

  1. 1Multiply by (x − 3)(2x + 3): (2x + 3) + 4(x − 3) = (x − 3)(2x + 3)
  2. 26x − 9 = 2x² − 3x − 9
  3. 32x² − 9x = 0
  4. 4x(2x − 9) = 0
  5. 5x = 0 or x = 4.5

Answer0 or 4.5

Part (d) · 5 marks

Solve x + 2y = 12 and 5x + y² = 39 simultaneously, showing all working.

  1. 1x = 12 − 2y, so 5(12 − 2y) + y² = 39
  2. 2y² − 10y + 21 = 0
  3. 3(y − 3)(y − 7) = 0, so y = 3 or y = 7
  4. 4y = 3: x = 12 − 6 = 6; y = 7: x = 12 − 14 = −2
  5. 5x = −2, y = 7 and x = 6, y = 3

Answerx = −2, y = 7 and x = 6, y = 3

Part (e) · 3 marks

Expand and simplify (2x − 3)(x + 6)(x − 4).

  1. 1(2x − 3)(x + 6) = 2x² + 12x − 3x − 18 = 2x² + 9x − 18
  2. 2(2x² + 9x − 18)(x − 4) = 2x³ − 8x² + 9x² − 36x − 18x + 72
  3. 3= 2x³ + x² − 54x + 72

Answer2x³ + x² − 54x + 72

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Also searched as: 0580/42/M/J/22 · 0580_s22_qp_42 · 0580 s22 42 · question 8.
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