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0580/42 Feb/Mar 2022, Question 2: Plotting Curves from a Table of Values

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 8 marks

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The question, in short

Table of y = x² − 1/(3x) with two missing values; complete it, plot the curve for −2 ≤ x ≤ −0.1, then use a line to solve x² − 1/(3x) + 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 two missing y-values in the table for x = −0.75 and x = −0.5, rounded to 1 decimal place.

  1. 1x = −0.75: (−0.75)² − 1/(3 × −0.75) = 0.5625 + 0.444… = 1.0
  2. 2x = −0.5: (−0.5)² − 1/(3 × −0.5) = 0.25 + 0.666… = 0.9

Answer| x | −0.75 | −0.5 | | y | 1.0 | 0.9 |

Part (b) · 4 marks

Plot the curve y = x² − 1/(3x) on the grid for −2 ≤ x ≤ −0.1, using your completed table values.

  1. 1Plot (−2, 4.2), (−1.5, 2.5), (−1, 1.3), (−0.75, 1.0), (−0.5, 0.9), (−0.25, 1.4), (−0.1, 3.3)
  2. 2Join with a smooth curve: it dips to a minimum near x = −0.5 and rises steeply as x approaches 0

Answercorrect curve

Part (c) · 2 marks

Draw a suitable straight line on the grid and use it to find the solutions of x² − 1/(3x) + 1 = 0.

  1. 1x² − 1/(3x) + 1 = 0 means x² − 1/(3x) = −1
  2. 2Draw the line y = −1
  3. 3Where the line meets the x > 0 branch of the curve: x ≈ 0.305

Answer0.3 to 0.32

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Also searched as: 0580/42/F/M/22 · 0580_m22_qp_42 · 0580 m22 42 · question 2.
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