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4MA1/1H Jun 2024, Question 12: Algebraic Fractions

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks

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The question, in short

Rewrite two algebra tasks: factorise the quadratic 6y² − 5y − 4, and combine two algebraic fractions over 4x and 3x into one simplified fraction.

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Part (a) · 2 marks

Write 6y² − 5y − 4 as a product of factors with no further factorisation possible.

  1. 1Find two numbers that multiply to 6 × (−4) = −24 and add to −5: −8 and 3.
  2. 2Split the middle term: 6y² − 8y + 3y − 4
  3. 3Factorise in pairs: 2y(3y − 4) + 1(3y − 4)
  4. 4= (2y + 1)(3y − 4)

Answer(2y + 1)(3y − 4)

Part (b) · 3 marks

Combine (2x + 1)/(4x) and (7 − 5x)/(3x) into one fraction, then reduce it to simplest form.

  1. 1(2x + 1)/(4x) + (7 − 5x)/(3x)
  2. 2The common denominator is 12x
  3. 3= 3(2x + 1)/(12x) + 4(7 − 5x)/(12x)
  4. 4= (6x + 3 + 28 − 20x)/(12x)
  5. 5= (31 − 14x)/(12x)

Answer(31 − 14x)/(12x)

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