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4024/22 May/Jun 2025, Question 19: Plotting Curves from a Table of Values

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 8 marks

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The question, in short

Complete a table for y = x³ − 5x + 4, plot its graph for −3 ≤ x ≤ 3, then use a straight line to solve x³ − 5x − 3 = 0.

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Part (a) · 1 mark

Fill in the missing y value in the table for y = x³ − 5x + 4 at the given x values.

  1. 1x = −3: y = (−3)³ − 5 × (−3) + 4
  2. 2= −27 + 15 + 4 = −8

Answer−8

Part (b) · 4 marks

Plot the graph of y = x³ − 5x + 4 on the grid for x from −3 to 3.

  1. 1Plot (−3, −8), (−2, 6), (−1, 8), (0, 4), (1, 0), (2, 2), (3, 16)
  2. 2Join with a smooth curve: maximum near (−1.3, 8.3), minimum near (1.3, −0.3)

AnswerCorrect smooth curve

Part (c) · 3 marks

Sketch the curve, add a suitable straight line, and use it to find the solutions of x³ − 5x − 3 = 0.

  1. 1x³ − 5x − 3 = 0 ⇔ x³ − 5x + 4 = 7
  2. 2Draw the line y = 7
  3. 3Read off where it crosses the curve
  4. 4x ≈ −1.8, x ≈ −0.7, x ≈ 2.5

Answer−1.95 to −1.7, −0.8 to −0.5, 2.3 to 2.6

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Also searched as: 4024/22/M/J/25 · 4024_s25_qp_22 · 4024 s25 22 · question 19.
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