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0580/41 May/Jun 2025, Question 14: Plotting Curves from a Table of Values

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 11 marks

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The question, in short

Complete a table of values for y = 5x² − x³ − 4, plot the curve for −2 ≤ x ≤ 5, then use a straight line to solve x³ − 5x² − x + 14 = 0.

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

Part (a) · 3 marks

Fill in the missing y-values in the table for y = 5x² − x³ − 4 at the given x-values.

  1. 1x = −1: y = 5 × 1 − (−1) − 4 = 2
  2. 2x = 1: y = 5 − 1 − 4 = 0
  3. 3x = 4: y = 5 × 16 − 64 − 4 = 12

Answer2, 0, 12

Part (b) · 4 marks

Plot the graph of y = 5x² − x³ − 4 on the grid for x from −2 to 5.

  1. 1Plot (−2, 24), (−1, 2), (0, −4), (1, 0), (2, 8), (3, 14), (4, 12), (5, −4)
  2. 2Join with a smooth curve from x = −2 to x = 5

AnswerCorrect curve

Part (c) · 4 marks

Draw a suitable straight line on the grid and use it to solve x³ − 5x² − x + 14 = 0.

  1. 1x³ − 5x² − x + 14 = 0 gives 5x² − x³ = 14 − x
  2. 2So 5x² − x³ − 4 = 10 − x: draw the line y = 10 − x
  3. 3Read off the x-values where the line meets the curve
  4. 4x ≈ −1.5, x = 2, x ≈ 4.5

Answer−1.7 to −1.4, 1.9 to 2.1, 4.4 to 4.7

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Also searched as: 0580/41/M/J/25 · 0580_s25_qp_41 · 0580 s25 41 · question 14.
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