0606/23 May/Jun 2026, Question 4: Turning Curves into Straight Lines
Cambridge IGCSE Additional Mathematics 0606 · Paper 23 (Calculator) · Calculator · 6 marks
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The question, in short
Given data for x and y linked by y = Px⁴ + Q, plot y against x⁴, then use the line to find P and Q and estimate y at x = 1.05.
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Part (a) · 2 marks
Plot the given y values against x⁴ on the axes and draw a straight line of best fit.
- 1x⁴ values: 0.053, 0.815, 2.005, 3.224, 3.842
- 2Plot (x⁴, y): (0.053, 0.23), (0.815, 0.61), (2.005, 1.20), (3.224, 1.81), (3.842, 2.12)
- 3Draw a ruled straight line through the points
AnswerPoints (0.053, 0.23), (0.815, 0.61), (2.005, 1.20), (3.224, 1.81), (3.842, 2.12) plotted with a ruled straight line of best fit
Part (b) · 3 marks
Use the gradient and intercept of your line to estimate the constants P and Q.
- 1Gradient = P, y-intercept = Q
- 2Gradient ≈ (2.12 − 0.23)/(3.842 − 0.053) ≈ 0.50
- 3So P ≈ 0.5
- 4Q = 0.23 − 0.5 × 0.053 ≈ 0.2
AnswerP = 0.47 to 0.53, Q = 0.15 to 0.25
Part (c) · 1 mark
From your graph, estimate the value of y when x = 1.05.
- 1x = 1.05 ⇒ x⁴ = 1.216
- 2Read from the line (or use y = 0.5x⁴ + 0.2): y ≈ 0.5 × 1.216 + 0.2 ≈ 0.81
Answer0.78 to 0.84
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