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A4cAlgebraic fractions

Edexcel GCSE Maths (1MA1), Higher tier · Algebra

Practise Algebraic fractions. 2 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.

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Sample questions

Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.

Question 1Easy2 marks
Simplify fully \(\frac{5x - 30}{x^{2} - 6x}\)[2]
Show the answer and mark scheme
Answer: \(\frac{5}{x}\)
  • M1 for \(5(x - 6)\) or \(x(x - 6)\)
  • A1 for \(\frac{5}{x}\)

Worked solution: \(\frac{5x - 30}{x^{2} - 6x} = \frac{5(x - 6)}{x(x - 6)} = \frac{5}{x}\)

Question 2Medium4 marks
Omar simplifies \(\frac{x + 6}{x + 2}\).
He cancels the \(x\) terms and then divides 6 by 2 to get the answer 3.
(a) Show that Omar is wrong.[1]
(b) Simplify fully \(\frac{x^2 + 4x - 12}{x^2 - 4}\).[3]
Show the answer and mark scheme
(a) Answer: E.g. \(x = 2\): \(\frac{8}{4} = 2\), not 3. (You can only cancel common factors, not terms.)
  • C1 for a correct counter-example (e.g. \(x = 2\) gives 2, not 3) or a correct explanation that only common factors of the whole numerator and denominator can be cancelled

Worked solution: When \(x = 2\), \(\frac{x + 6}{x + 2} = \frac{8}{4} = 2\), not 3. \(x\) is added, not multiplied, so it cannot be cancelled.

(b) Answer: \(\frac{x + 6}{x + 2}\)
  • M1 for \((x + 6)(x - 2)\)
  • M1 for \((x + 2)(x - 2)\)
  • A1 for \(\frac{x + 6}{x + 2}\)

Worked solution: \(\frac{x^2 + 4x - 12}{x^2 - 4} = \frac{(x + 6)(x - 2)}{(x + 2)(x - 2)} = \frac{x + 6}{x + 2}\)

Question 3Hard3 marks
Simplify fully \(\frac{9 - 3n}{n^{2} - 9n + 18}\)[3]
Show the answer and mark scheme
Answer: \(-\frac{3}{n - 6}\)
  • M1 for \(3(3 - n)\) or \(-3(n - 3)\)
  • M1 for \((n - 3)(n - 6)\)
  • A1 for \(-\frac{3}{n - 6}\) oe

Worked solution: \(9 - 3n = -3(n - 3)\) and \(n^{2} - 9n + 18 = (n - 3)(n - 6)\)
\(\frac{9 - 3n}{n^{2} - 9n + 18} = \frac{-3(n - 3)}{(n - 3)(n - 6)} = -\frac{3}{n - 6}\)

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