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0580/31 May/Jun 2022, Question 9: Reciprocal Functions

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 9 marks

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The question, in short

Complete a table for y = 12/x, plot the curve on the grid for the given x ranges, add the line y = 5, and use the graph to solve 12/x = 5.

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 = 12/x at the listed x-values.

  1. 1y = 12 ÷ x: 12 ÷ (−6) = −2, 12 ÷ (−3) = −4, 12 ÷ (−1) = −12
  2. 212 ÷ 1 = 12, 12 ÷ 3 = 4, 12 ÷ 6 = 2
  3. 3y: −2, −3, −4, −6, −12, 12, 6, 4, 3, 2

Answer| x | −6 | −4 | −3 | −2 | −1 | 1 | 2 | 3 | 4 | 6 | | y | −2 | −3 | −4 | −6 | −12 | 12 | 6 | 4 | 3 | 2 |

Part (b) · 4 marks

Draw the graph of y = 12/x on the grid for −6 ≤ x ≤ −1 and 1 ≤ x ≤ 6.

  1. 1Plot the 10 points from the table, e.g. (−6, −2), (−1, −12), (1, 12), (6, 2)
  2. 2Join each branch with a smooth curve: one for −6 ≤ x ≤ −1, one for 1 ≤ x ≤ 6, not crossing the y-axis

AnswerCorrect curve

Part (c) · 1 mark

Draw the horizontal line y = 5 on the same grid.

  1. 1Draw a ruled horizontal line through y = 5 across the grid

AnswerCorrect ruled line drawn

Part (d) · 1 mark

Use your graph to find the x-value where 12/x = 5.

  1. 1The line y = 5 meets the curve where 12/x = 5
  2. 2x = 12 ÷ 5 = 2.4

Answer2.4

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