Lemmara logoLemmaraWorked solution

4024/11 Oct/Nov 2023, Question 21: Algebraic Fractions

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 5 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Factorise two expressions and simplify an algebraic fraction, showing each result in simplest form.

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

Part (a) · 1 mark

Factorise 6a − 9 by taking out the common factor.

  1. 16a − 9 = 3(2a − 3)

Answer3(2a − 3)

Part (b) · 1 mark

Factorise 4b² − 25 as a difference of two squares.

  1. 14b² − 25 = (2b)² − 5²
  2. 2= (2b + 5)(2b − 5)

Answer(2b + 5)(2b − 5)

Part (c) · 3 marks

Simplify the fraction (2c² − 8c)/(2c² − 5c − 12) by factorising numerator and denominator.

  1. 12c² − 8c = 2c(c − 4)
  2. 22c² − 5c − 12 = (2c + 3)(c − 4)
  3. 32c(c − 4)/((2c + 3)(c − 4)) = 2c/(2c + 3)

Answer2c/(2c + 3)

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

Practise more algebraic fractions questions

Real 4024 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: 4024/11/O/N/23 · 4024_w23_qp_11 · 4024 w23 11 · question 21.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.