Lemmara logoLemmaraWorked solution

0580/41 Oct/Nov 2021, Question 6: Reciprocal Functions

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 16 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Complete a table for y = x² − 3/(2x), plot the curve on the given grid, then use a straight-line intersection to solve an equation and find integer coefficients of a related cubic.

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 the given x-values, correct to 1 decimal place.

  1. 1x = −3: 9 − 3/(−6) = 9 + 0.5 = 9.5
  2. 2x = −2: 4 − 3/(−4) = 4.75 ≈ 4.8
  3. 3x = 3: 9 − 3/6 = 8.5

Answer9.5, 4.8 and 8.5

Part (aii) · 5 marks

Plot the graph of y = x² − 3/(2x) on the grid for −3 ≤ x ≤ −0.2 and 0.2 ≤ x ≤ 3.

  1. 1First fill the missing y-values in the table.
  2. 2x = −3: y = 9 − 3/(−6) = 9.5
  3. 3x = −2: y = 4 − 3/(−4) = 4.75 ≈ 4.8
  4. 4x = 3: y = 9 − 3/6 = 8.5
  5. 5Plot all 10 points; draw two separate smooth branches, not touching the y-axis.

Answercorrect curve

Part (b) · 4 marks

Draw a suitable straight line on the grid and use its intersections with the curve to solve x² − 3/(2x) = 24/5 − 2x.

  1. 1Rule the line y = 24/5 − 2x, through (0, 4.8) with gradient −2 (e.g. through (2, 0.8))
  2. 2Read the x-values where it crosses the curve
  3. 3Check: 10x³ + 20x² − 48x − 15 = 0 gives x ≈ −0.28 and x ≈ 1.60 in range
  4. 4x ≈ −0.3 and x ≈ 1.6

Answer−0.4 to −0.2, 1.45 to 1.7

Part (c) · 4 marks

Rearrange the equation into the form ax³ + bx² + cx − 15 = 0 and state the integer values of a, b and c.

  1. 1Multiply x² − 3/(2x) = 24/5 − 2x by 10x
  2. 210x³ − 15 = 48x − 20x²
  3. 310x³ + 20x² − 48x − 15 = 0
  4. 4a = 10, b = 20, c = −48

Answera = 10, b = 20, c = −48

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: 0580/41/O/N/21 · 0580_w21_qp_41 · 0580 w21 41 · question 6.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.