Lemmara logoLemmaraWorked solution

0580/22 Feb/Mar 2025, Question 12: Algebraic Fractions

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 4 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Simplify an algebraic sum of three fractions into one fraction, then factorise a four-term expression involving x, a and y.

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

Part (a) · 3 marks

Combine x/4 + (3x)/8 − (x + 2)/12 into a single fraction in its simplest form.

  1. 1Common denominator 24
  2. 2x/4 = 6x/24, 3x/8 = 9x/24, (x + 2)/12 = 2(x + 2)/24
  3. 3(6x + 9x − 2x − 4)/24
  4. 4= (13x − 4)/24

Answer(13x − 4)/24

Part (b) · 1 mark

Factorise 3x(a + 4y) − ay − 4y².

  1. 1−ay − 4y² = −y(a + 4y)
  2. 23x(a + 4y) − y(a + 4y)
  3. 3= (3x − y)(a + 4y)

Answer(3x − y)(a + 4y)

Stuck on a step? Read the free lesson: Algebraic Fractions

Practise more algebraic fractions 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 algebraic fractions

Also searched as: 0580/22/F/M/25 · 0580_m25_qp_22 · 0580 m25 22 · question 12.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.