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0606/21 May/Jun 2026, Question 4: Turning Curves into Straight Lines

Cambridge IGCSE Additional Mathematics 0606 · Paper 21 (Calculator) · Calculator · 9 marks

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The question, in short

Given a straight line from plotting ln 3y against x² through (4.64, 12.24) and (6.84, 8.94), show y = k e^(ax²), then find y at x = 3 and x when y = 10.

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Part (a) · 6 marks

Use the two points to find the gradient and intercept of the line, then rearrange to show y = k e^(ax²) with exact k and a.

  1. 1ln 3y = mx² + c
  2. 2m = (12.24 − 8.94)/(4.64 − 6.84) = −1.5
  3. 312.24 = −1.5(4.64) + c, so c = 19.2
  4. 4ln 3y = 19.2 − 1.5x², so 3y = e^(19.2 − 1.5x²)
  5. 5y = (e^19.2/3) e^(−1.5x²)

Answery = (e^19.2/3) e^(−1.5x²) shown (k = e^19.2/3, a = −3/2)

Part (b) · 1 mark

Substitute x = 3 into the equation to calculate y.

  1. 1y = (1/3)e^(19.2 − 1.5 × 9)
  2. 2= (1/3)e^5.7
  3. 3= 99.6

Answer99.6 (99.622…)

Part (c) · 2 marks

Set y = 10 in the equation and solve for the values of x.

  1. 110 = (1/3)e^(19.2 − 1.5x²)
  2. 2ln 30 = 19.2 − 1.5x²
  3. 3x² = (19.2 − ln 30)/1.5 = 10.53…
  4. 4x = ±3.25

Answerx = ±3.25 (±3.245…)

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Also searched as: 0606/21/M/J/26 · 0606_s26_qp_21 · 0606 s26 21 · question 4.
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