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0580/32 May/Jun 2021, Question 5: Reciprocal Functions

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 14 marks

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The question, in short

For y = 18/x, fill missing table values, sketch the curve on the grid over the two given intervals, state its rotational symmetry order, then work with the line through (−8, −3) and (6, 4).

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

Part (a) · 3 marks

Work out the y-values missing from the table for y = 18/x at the listed x-values.

  1. 1y = 18 ÷ x: 18 ÷ (−8) = −2.25, 18 ÷ (−4) = −4.5, 18 ÷ (−2) = −9
  2. 218 ÷ 2 = 9, 18 ÷ 4 = 4.5, 18 ÷ 8 = 2.25

Answer| x | −8 | −6 | −4 | −3 | −2 | 2 | 3 | 4 | 6 | 8 | | y | −2.25 | −3 | −4.5 | −6 | −9 | 9 | 6 | 4.5 | 3 | 2.25 |

Part (b) · 4 marks

Plot the curve y = 18/x on the grid for −8 ≤ x ≤ −2 and 2 ≤ x ≤ 8.

  1. 1Plot (−8, −2.25), (−6, −3), (−4, −4.5), (−3, −6), (−2, −9)
  2. 2Plot (2, 9), (3, 6), (4, 4.5), (6, 3), (8, 2.25)
  3. 3Join each set with a smooth curve (two separate branches, not joined across x = 0)

AnswerCorrect curve

Part (c) · 1 mark

State how many-fold rotational symmetry the graph of y = 18/x has.

  1. 1The graph looks the same after a half turn about the origin
  2. 2Order of rotational symmetry = 2

Answer2

Part (di) · 2 marks

Draw the straight line through (−8, −3) and (6, 4) on the grid.

  1. 1Plot (−8, −3) and (6, 4) and join them with a ruled line across the grid

Answer(−8, −3) and (6, 4) plotted and joined in a ruled line

Part (dii) · 2 marks

Give the x-values where that straight line meets the curve y = 18/x.

  1. 1Read the x-values where the line crosses the two branches
  2. 2x ≈ −7.1 and x ≈ 5.1

Answer−7.3 to −6.9, 4.9 to 5.3

Part (diii) · 2 marks

Determine the equation of the line through (−8, −3) and (6, 4) as y = mx + c.

  1. 1Gradient m = (4 − (−3)) ÷ (6 − (−8)) = 7/14 = 1/2
  2. 24 = 1/2 × 6 + c, so c = 1
  3. 3y = 1/2 x + 1

Answery = 1/2 x + 1

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Also searched as: 0580/32/M/J/21 · 0580_s21_qp_32 · 0580 s21 32 · question 5.
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