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0580/33 May/Jun 2022, Question 7: Reciprocal Functions

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 12 marks

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The question, in short

Complete values, plot, and analyse the reciprocal curve y = 15/x, covering symmetry and solving 15/x = −6 graphically.

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

Part (a) · 3 marks

Calculate the missing y-values in the table for y = 15/x at the listed x-values.

  1. 1y = 15/x: 15 ÷ (−15) = −1, 15 ÷ (−5) = −3, 15 ÷ (−2) = −7.5
  2. 215 ÷ 2 = 7.5, 15 ÷ 5 = 3, 15 ÷ 10 = 1.5, 15 ÷ 15 = 1
  3. 3y: −1, −1.5, −3, −5, −7.5, −15, 15, 7.5, 5, 3, 1.5, 1

Answer| x | −15 | −10 | −5 | −3 | −2 | −1 | 1 | 2 | 3 | 5 | 10 | 15 | | y | −1 | −1.5 | −3 | −5 | −7.5 | −15 | 15 | 7.5 | 5 | 3 | 1.5 | 1 |

Part (b) · 4 marks

Plot the curve y = 15/x on the grid for the two given x ranges.

  1. 1Plot (−15, −1), (−10, −1.5), (−5, −3), (−3, −5), (−2, −7.5), (−1, −15)
  2. 2Plot (1, 15), (2, 7.5), (3, 5), (5, 3), (10, 1.5), (15, 1)
  3. 3Join each set with a smooth curve (two separate branches, not crossing the axes)

AnswerCorrect curve

Part (c) · 1 mark

State the rotational symmetry order of the y = 15/x graph.

  1. 1The graph looks the same after a half turn about (0, 0)
  2. 2Order of rotational symmetry = 2

Answer2

Part (di) · 2 marks

Draw all lines of symmetry on the plotted reciprocal graph.

  1. 1Draw the line y = x (through (−16, −16) and (16, 16))
  2. 2Draw the line y = −x (through (−16, 16) and (16, −16))

AnswerLines y = x and y = −x drawn

Part (dii) · 1 mark

Give the equation of the symmetry line that misses the curve entirely.

  1. 1y = x passes through (3.87, 3.87) on the curve; y = −x never meets it
  2. 2y = −x

Answery = −x

Part (e) · 1 mark

Read off the x-value where the curve meets y = −6.

  1. 1Draw y = −6 and read x where it meets the curve
  2. 215/x = −6 gives x = 15 ÷ (−6) = −2.5

Answer−2.5 (accept −2.7 to −2.3)

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Also searched as: 0580/33/M/J/22 · 0580_s22_qp_33 · 0580 s22 33 · question 7.
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