0580/31 Oct/Nov 2023, Question 8: Reciprocal Functions
Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 11 marks
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The question, in short
From a given straight line L on a coordinate grid, find its equation, draw y = x, locate their intersection, complete a table for y = 8/x, and sketch that curve.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 2 marks
Find the equation of the straight line L shown on the grid, giving it as y = mx + c.
- 1L crosses the y-axis at (0, −5), so c = −5
- 2L passes through (3, 1): gradient = (1 − (−5))/(3 − 0) = 2
- 3y = 2x − 5
Answery = 2x − 5
Part (bi) · 1 mark
On the grid, draw the straight line y = x.
- 1Rule a line through (0, 0), (2, 2) and (5, 5)
AnswerCorrect ruled line
Part (bii) · 1 mark
State the coordinates where the line y = x crosses line L.
- 1x = 2x − 5 gives x = 5
- 2(5, 5)
Answer(5, 5)
Part (ci) · 3 marks
Fill in the missing y-values in the table for y = 8/x at the given x-values.
- 1y = 8/x: 8 ÷ (−4) = −2, 8 ÷ (−2) = −4, 8 ÷ (−1) = −8
- 28 ÷ 1 = 8, 8 ÷ 2 = 4, 8 ÷ 4 = 2
Answer| x | −4 | −2 | −1 | 1 | 2 | 4 | | y | −2 | −4 | −8 | 8 | 4 | 2 |
Part (cii) · 4 marks
Draw the graph of y = 8/x on the grid for −5 ≤ x ≤ −1 and 1 ≤ x ≤ 5.
- 1Plot (−5, −1.6), (−4, −2), (−3, −2.7), (−2, −4), (−1, −8) and (1, 8), (2, 4), (3, 2.7), (4, 2), (5, 1.6)
- 2Join each set with a smooth curve; two separate branches, not joined across x = 0
AnswerCorrect curve
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Also searched as: 0580/31/O/N/23 · 0580_w23_qp_31 · 0580 w23 31 · question 8.
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