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4MA1/2H Jun 2021, Question 15: Plotting Curves from a Table of Values

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 4 marks

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The question, in short

Complete a table of values for y = (1/x)(x² + 4) at given x values, then draw its graph on the grid for 0.25 ≤ x ≤ 8.

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Part (a) · 2 marks

Fill in the missing y values in the table for y = (1/x)(x² + 4) at x = 0.5, 1, 2 and 4.

  1. 1y = x + 4/x, so substitute each missing x value.
  2. 2When x = 0.5, y = 0.5 + 4 ÷ 0.5 = 0.5 + 8 = 8.5
  3. 3When x = 1, y = 1 + 4 ÷ 1 = 1 + 4 = 5
  4. 4When x = 2, y = 2 + 4 ÷ 2 = 2 + 2 = 4
  5. 5When x = 4, y = 4 + 4 ÷ 4 = 4 + 1 = 5
  6. 6The missing values are 8.5, 5, 4, 5

Answer8.5, 5, 4, 5

Part (b) · 2 marks

Plot the graph of y = (1/x)(x² + 4) on the grid for x from 0.25 to 8.

  1. 1The completed table is x = 0.25, 0.5, 1, 2, 4, 8 with y = 16.25, 8.5, 5, 4, 5, 8.5
  2. 2Plot (0.25, 16.25), (0.5, 8.5), (1, 5), (2, 4), (4, 5) and (8, 8.5)
  3. 3Join them with a single smooth curve from x = 0.25 to x = 8
  4. 4The curve falls steeply, reaches its lowest point at (2, 4), then rises again

AnswerA smooth curve through (0.25, 16.25), (0.5, 8.5), (1, 5), (2, 4), (4, 5) and (8, 8.5), falling to a lowest point at (2, 4) then rising

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