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4024/21 Oct/Nov 2022, Question 3: Plotting Curves from a Table of Values

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 8 marks

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The question, in short

For y = x³/2 − 3x + 2, complete a table, plot the curve for −3 ≤ x ≤ 3, then use the graph to find a minimum point and solve an equation.

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

Part (a) · 1 mark

Find the missing y-value in the table for x = 3 using y = x³/2 − 3x + 2.

  1. 1y = 3³/2 − 3 × 3 + 2
  2. 2= 13.5 − 9 + 2 = 6.5

Answer6.5

Part (b) · 3 marks

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

  1. 1Plot (−3, −2.5), (−2, 4), (−1, 4.5), (0, 2), (1, −0.5), (2, 0), (3, 6.5)
  2. 2Join with a smooth curve through all the points

AnswerCorrect smooth curve

Part (c) · 2 marks

State the coordinates of the minimum point on the graph where x > 0.

  1. 1The lowest point of the curve for x > 0 lies between x = 1 and x = 2
  2. 2Minimum ≈ (1.4, −0.8)

Answer(1.3 to 1.5, −0.9 to −0.7)

Part (d) · 2 marks

Use the drawn graph to solve x³/2 − 3x + 2 = 0.

  1. 1Read where the curve crosses the x-axis (y = 0)
  2. 2x ≈ −2.7, x ≈ 0.7, x = 2

Answer−2.8 to −2.7, 0.7 to 0.8, 2

Stuck on a step? Read the free lesson: Plotting Curves from a Table of Values

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Also searched as: 4024/21/O/N/22 · 4024_w22_qp_21 · 4024 w22 21 · question 3.
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