4024/12 Oct/Nov 2025, Question 15: Plotting Curves from a Table of Values
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 10 marks
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The question, in short
For the cubic y = x³ − 4x² + 12, fill in a missing table value, plot the curve from x = −2 to 4, and use graphs to locate solutions of two related equations.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 1 mark
Work out the y value when x = 4 for y = x³ − 4x² + 12 and write it in the table.
- 1y = 4³ − 4 × 4² + 12 = 64 − 64 + 12 = 12
Answer12
Part (b) · 4 marks
Plot the points from the table and join them with a smooth curve for −2 ≤ x ≤ 4 on the grid.
- 1Plot (−2, −12), (−1, 7), (0, 12), (1, 9), (2, 4), (3, 3), (4, 12)
- 2Join with a smooth curve (turning points near x = 0 and x = 2.7)
AnswerCorrect smooth curve
Part (c) · 1 mark
From your drawn curve, state the x value where y = 0.
- 1Solutions are where the curve crosses y = 0 (the x-axis)
- 2x ≈ −1.5
Answer−1.7 to −1.3
Part (d) · 4 marks
Add a straight line to the grid and use where it meets the curve to find the roots of x³ − 4x² + x + 4 = 0.
- 1x³ − 4x² + x + 4 = 0 → x³ − 4x² + 12 = 8 − x
- 2Draw the line y = 8 − x (through (0, 8) and (4, 4))
- 3Read the x-coordinates where the line meets the curve
- 4x ≈ −0.8, x ≈ 1.5, x ≈ 3.3
Answer−0.9 to −0.7, 1.4 to 1.6, 3.2 to 3.5
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