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0580/43 Oct/Nov 2023, Question 11: Solving Quadratics by Factorising

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 9 marks

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The question, in short

Using the sketched curve y = 18 + 5x − 2x² with intercepts A, B, C, find the intercept coordinates, the derivative, and where the gradient equals 17.

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

Part (a) · 4 marks

Work out the coordinates of the three intercepts A, B and C of the curve.

  1. 1At B, x = 0: y = 18, so B (0, 18)
  2. 218 + 5x − 2x² = 0 → 2x² − 5x − 18 = 0
  3. 3(2x − 9)(x + 2) = 0 → x = −2 or x = 4.5
  4. 4A (−2, 0), B (0, 18), C (4.5, 0)

AnswerA (−2, 0), B (0, 18), C (4.5, 0)

Part (b) · 2 marks

Work out the derivative of 18 + 5x − 2x² with respect to x.

  1. 1Multiply by the power, then take 1 off the power: axⁿ → naxⁿ⁻¹
  2. 218 → 0
  3. 35x → 5
  4. 4−2x² → 2 × (−2)x = −4x
  5. 5dy/dx = 5 − 4x

Answer5 − 4x

Part (c) · 3 marks

Determine the coordinates of the curve point whose gradient is 17.

  1. 15 − 4x = 17 → −4x = 12 → x = −3
  2. 2y = 18 + 5 × (−3) − 2 × (−3)² = 18 − 15 − 18 = −15
  3. 3Point (−3, −15)

Answer(−3, −15)

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Also searched as: 0580/43/O/N/23 · 0580_w23_qp_43 · 0580 w23 43 · question 11.
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