Lemmara logoLemmaraWorked solution

0580/32 May/Jun 2022, Question 2: Reciprocal Functions

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 15 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Complete a table and draw the graph of y = −6/x, then use it to find symmetry, solve −6/x = 2.5, draw a perpendicular line through P, and find a parallel line equation.

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

Part (ai) · 3 marks

Fill in the missing y-values in the table for y = −6/x at the given x-values.

  1. 1−6 ÷ (−4) = 1.5, −6 ÷ (−1.5) = 4
  2. 2−6 ÷ 1.5 = −4, −6 ÷ 5 = −1.2
  3. 3y: 1, 1.5, 2, 3, 4, 6, −6, −4, −3, −2, −1.2, −1

Answer| x | −6 | −4 | −3 | −2 | −1.5 | −1 | 1 | 1.5 | 2 | 3 | 5 | 6 | | y | 1 | 1.5 | 2 | 3 | 4 | 6 | −6 | −4 | −3 | −2 | −1.2 | −1 |

Part (aii) · 4 marks

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

  1. 1Plot all 12 points from the table, e.g. (−6, 1), (−1, 6), (1, −6), (6, −1)
  2. 2Join each branch with a smooth curve, one for x < 0 and one for x > 0, not crossing the axes

AnswerCorrect graph drawn

Part (aiii) · 1 mark

State the order of rotational symmetry of the drawn graph.

  1. 1The graph looks the same after a half turn about (0, 0): order 2

Answer2

Part (aiv) · 2 marks

Write down the equations of all lines of symmetry of the graph.

  1. 1The curve is symmetrical in both diagonal lines through the origin
  2. 2y = x and y = −x

Answery = x and y = −x

Part (av) · 1 mark

Draw the horizontal line y = 2.5 on the grid.

  1. 1Draw a ruled horizontal line through y = 2.5 across the grid

AnswerCorrect ruled line

Part (avi) · 1 mark

Use the graph to find the x-value where −6/x = 2.5.

  1. 1The line y = 2.5 meets the curve where −6/x = 2.5
  2. 2x = −6 ÷ 2.5 = −2.4

Answer−2.4

Part (b) · 1 mark

Draw a line through point P that is perpendicular to line L.

  1. 1Place a set square along line L with its right angle at P
  2. 2Draw a ruled line through P at 90° to L

AnswerCorrect ruled line

Part (c) · 2 marks

Find the equation, in y = mx + c form, of the line parallel to y = 3x + 5 through (1, 7).

  1. 1Parallel, so gradient = 3: y = 3x + c
  2. 27 = 3 × 1 + c, so c = 4
  3. 3y = 3x + 4

Answery = 3x + 4

Stuck on a step? Read the free lesson: Reciprocal Functions

Practise more reciprocal functions questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on reciprocal functions

Also searched as: 0580/32/M/J/22 · 0580_s22_qp_32 · 0580 s22 32 · question 2.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.