Lemmara logoLemmaraWorked solution

0580/41 Oct/Nov 2021, Question 4: The Quadratic Formula and Completing the Square

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

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Solve two equations for x, factorise two expressions completely, and solve a cubic equation showing working with answers to 2 decimal places.

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

Part (ai) · 3 marks

Solve 6(7 − 2x) = 3x − 8 for x.

  1. 142 − 12x = 3x − 8
  2. 250 = 15x
  3. 3x = 10/3

Answer10/3 or 3 1/3 or 3.333…

Part (aii) · 3 marks

Solve 2x/(x − 5) = 2/3 for x.

  1. 13 × 2x = 2(x − 5)
  2. 26x = 2x − 10, 4x = −10
  3. 3x = −2.5

Answer−2.5 or −2 1/2 or −5/2

Part (bi) · 3 marks

Factorise 2x² − 288y² completely.

  1. 12(x² − 144y²)
  2. 2= 2(x + 12y)(x − 12y)

Answer2(x + 12y)(x − 12y)

Part (bii) · 2 marks

Factorise 5x² + 17x − 40 completely.

  1. 15x² + 25x − 8x − 40 = 5x(x + 5) − 8(x + 5)
  2. 2= (5x − 8)(x + 5)

Answer(5x − 8)(x + 5)

Part (c) · 5 marks

Solve x³ + 4x² − 17x = x³ − 9, showing all working and giving answers to 2 decimal places.

  1. 14x² − 17x + 9 = 0
  2. 2x = (17 ± √(17² − 4 × 4 × 9))/(2 × 4) = (17 ± √145)/8
  3. 3x = 0.619… or 3.630…
  4. 4x = 0.62 and 3.63

Answer0.62 and 3.63

Stuck on a step? Read the free lesson: The Quadratic Formula and Completing the Square

Practise more the quadratic formula and completing the square 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 the quadratic formula and completing the square

Also searched as: 0580/41/O/N/21 · 0580_w21_qp_41 · 0580 w21 41 · question 4.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.