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4024/11 Oct/Nov 2025, Question 22: Plotting Curves from a Table of Values

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 10 marks

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The question, in short

Table of values for y = x³ − 3x + 2; complete it, plot the curve for −3 ≤ x ≤ 3, then use a line to solve x³ − 7x + 1 = 0.

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

Part (a) · 2 marks

Fill in the missing y-values in the table for y = x³ − 3x + 2 at the given x-values.

  1. 1x = −2: (−2)³ − 3(−2) + 2 = −8 + 6 + 2 = 0
  2. 2x = 2: 8 − 6 + 2 = 4

Answer| x | −2 | 2 | | y | 0 | 4 |

Part (b) · 4 marks

Plot the graph of y = x³ − 3x + 2 on the grid for x from −3 to 3.

  1. 1Plot (−3, −16), (−2, 0), (−1, 4), (0, 2), (1, 0), (2, 4), (3, 20)
  2. 2Join with a smooth curve: maximum at (−1, 4), minimum at (1, 0)

AnswerCorrect curve

Part (c) · 4 marks

Sketch the curve, draw a suitable straight line, and use it to find the solutions of x³ − 7x + 1 = 0.

  1. 1x³ − 7x + 1 = 0 gives x³ − 3x + 2 = 4x + 1
  2. 2Draw y = 4x + 1, e.g. through (−3, −11), (0, 1) and (3, 13)
  3. 3Read the x-coordinates where the line meets the curve
  4. 4x ≈ −2.7, x ≈ 0.14, x ≈ 2.6

Answer−2.8 to −2.6, 0.1 to 0.2, 2.4 to 2.7

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Also searched as: 4024/11/O/N/25 · 4024_w25_qp_11 · 4024 w25 11 · question 22.
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