Lemmara logoLemmaraWorked solution

0580/31 May/Jun 2021, Question 5: Reciprocal Functions

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 10 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Using a decreasing curve y = k/x for 1 ≤ x ≤ 8, find a coordinate, establish k, evaluate the formula, tabulate and draw negative-x values, then sketch and state symmetry lines.

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

Part (a) · 1 mark

Read off the x-coordinate on the curve where the y-value is 4.

  1. 1Read across from y = 4 to the curve and down to the x-axis
  2. 2x = 2

Answer2

Part (bi) · 1 mark

Substitute the given point (2, 4) into y = k/x to demonstrate that k equals 8.

  1. 1The curve passes through (2, 4)
  2. 24 = k/2
  3. 3k = 4 × 2 = 8

Answere.g. 4 = k/2 leading to k = 8

Part (bii) · 1 mark

With y = 8/x, work out y when x is 250.

  1. 1y = 8/250
  2. 2= 0.032

Answer0.032

Part (ci) · 2 marks

Fill in the four missing y-values in the table for x = −8, −4, −2, −1 using y = 8/x.

  1. 18 ÷ −8 = −1, 8 ÷ −4 = −2
  2. 28 ÷ −2 = −4, 8 ÷ −1 = −8
  3. 3y values: −1, −2, −4, −8

Answer| x | −8 | −4 | −2 | −1 | | y | −1 | −2 | −4 | −8 |

Part (cii) · 3 marks

Plot the curve y = 8/x on the grid across the interval from −8 to −1.

  1. 1Plot (−8, −1), (−4, −2), (−2, −4) and (−1, −8).
  2. 2Join them with a smooth curve (not straight lines) in the third quadrant.

AnswerCorrect curve

Part (d) · 2 marks

Draw a rough sketch of y = 8/x for −8 ≤ x ≤ −1 and give the equations of all its lines of symmetry.

  1. 1The two branches are symmetrical about the diagonal lines through the origin.
  2. 2y = x and y = −x

Answery = x, y = −x

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: 0580/31/M/J/21 · 0580_s21_qp_31 · 0580 s21 31 · question 5.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.