Lemmara logoLemmaraWorked solution

0580/42 May/Jun 2026, Question 18: Equations That Become Quadratics

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 8 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Using the given triangle dimensions, show the area of ABC, equate it to the area of DEF to form a quadratic, then solve by factorising to find ABC's area.

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

Part (a) · 1 mark

Show that the area of triangle ABC, with sides 2x and x enclosing 30°, equals 1/2 x² cm².

  1. 1Area = ½ × 2x × x × sin 30°
  2. 2= x² × ½
  3. 3= ½x² cm²

Answer½ × 2x × x × sin 30 leading to ½x²

Part (b) · 3 marks

Given equal areas of ABC and DEF, show that x satisfies x² − 14x + 24 = 0.

  1. 1Area DEF = ½(2x − 6)(x − 4)
  2. 2½x² = ½(2x − 6)(x − 4)
  3. 3x² = 2x² − 8x − 6x + 24
  4. 40 = x² − 14x + 24

Answer½x² = ½(2x − 6)(x − 4) leading to x² − 14x + 24 = 0

Part (c) · 4 marks

Factorise and solve x² − 14x + 24 = 0, then use the valid x to find the area of triangle ABC.

  1. 1x² − 14x + 24 = (x − 2)(x − 12) = 0
  2. 2x = 2 or x = 12
  3. 3x = 2 gives x − 4 < 0, so x = 12
  4. 4Area = ½ × 12² = 72 cm²

Answer72

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

Practise more equations that become quadratics 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 equations that become quadratics

Also searched as: 0580/42/M/J/26 · 0580_s26_qp_42 · 0580 s26 42 · question 18.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.