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0580/12 Feb/Mar 2025, Question 18: Reciprocal Functions

Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Non-calculator · 9 marks

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The question, in short

Complete a table for y = 12/x, plot the curve on a grid for −6 ≤ x ≤ −1 and 1 ≤ x ≤ 6, draw y = −9, and use the graph to solve 12/x = −9.

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 given x values.

  1. 1x = −6: 12 ÷ −6 = −2
  2. 2x = −3: −4; x = −1: −12
  3. 3x = 1: 12; x = 3: 4; x = 6: 2

Answer−2, −4, −12, 12, 4, 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
  2. 2Join (−6, −2) to (−1, −12) with a smooth curve
  3. 3Join (1, 12) to (6, 2) with a separate smooth curve
  4. 4Do not join the two branches across x = 0

AnswerCorrect curve through (−6, −2), (−4, −3), (−3, −4), (−2, −6), (−1, −12) and (1, 12), (2, 6), (3, 4), (4, 3), (6, 2)

Part (c) · 1 mark

Draw the horizontal line y = −9 on the same grid.

  1. 1Rule a horizontal line through y = −9 across the grid

Answery = −9 correctly drawn, ruled

Part (d) · 1 mark

Use the graph to find the x value where 12/x = −9.

  1. 1Read the x-value where y = −9 meets the curve
  2. 212/x = −9 gives x = −12/9 ≈ −1.3
  3. 3x = −1.3

Answer−1.4 to −1.2

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Also searched as: 0580/12/F/M/25 · 0580_m25_qp_12 · 0580 m25 12 · question 18.
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