Lemmara logoLemmaraWorked solution

0580/41 Oct/Nov 2025, Question 24: Forming and solving a quadratic

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 11 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Martha walks 10 km at x km/h, then runs 5 km at (x + 4) km/h. The whole journey takes 3.5 hours. Form and solve a quadratic, then compare the two times.

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

Part (a) · 1 mark

Write an expression for the time Martha spends walking.

  1. 1Time = distance ÷ speed = 10/x

Answer10/x

Part (b) · 4 marks

Show that 7x² − 2x − 80 = 0.

  1. 110/x + 5/(x + 4) = 3.5
  2. 2Multiply by x(x + 4): 10(x + 4) + 5x = 3.5x(x + 4)
  3. 310x + 40 + 5x = 3.5x² + 14x
  4. 40 = 3.5x² − x − 40
  5. 5Multiply by 2: 7x² − 2x − 80 = 0

AnswerLeading to 7x² − 2x − 80 = 0

Part (c) · 3 marks

Solve 7x² − 2x − 80 = 0, giving answers to 2 decimal places.

  1. 1x = (2 ± √((−2)² − 4 × 7 × (−80)))/(2 × 7)
  2. 2= (2 ± √2244)/14
  3. 3x = −3.24 or x = 3.53

Answer−3.24 and 3.53

Part (d) · 3 marks

Find the difference between her walking time and running time, to the nearest minute.

  1. 1Walking time = 10 ÷ 3.526… = 2.835… h
  2. 2Running time = 5 ÷ 7.526… = 0.664… h
  3. 3Difference = 2.171… h = 2 h 10.28… min
  4. 4= 2 h 10 min

Answer2h 10min

Stuck on a step? Read the free lesson: Equations That Become Quadratics

Practise more forming and solving a quadratic 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 forming and solving a quadratic

Also searched as: 0580/41/O/N/25 · 0580_w25_qp_41 · 0580 w25 41 · question 24.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.