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4MA1/1HR Jan 2022, Question 12: Algebraic Fractions

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

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The question, in short

Two algebra tasks: multiply out and simplify a product of three factors, then combine three algebraic fractions into one simplified fraction.

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

Part (a) · 2 marks

Multiply out and simplify the product n(n − 4)(3n + 5).

  1. 1Expand the two brackets first: (n − 4)(3n + 5) = 3n² + 5n − 12n − 20
  2. 2(n − 4)(3n + 5) = 3n² − 7n − 20
  3. 3Now multiply by n: n(3n² − 7n − 20) = 3n³ − 7n² − 20n
  4. 4n(n − 4)(3n + 5) = 3n³ − 7n² − 20n

Answer3n³ − 7n² − 20n

Part (b) · 3 marks

Write 3/x + (x + 2)/(2x) + 1/4 as one fraction in its simplest form.

  1. 1The lowest common denominator of x, 2x and 4 is 4x.
  2. 23/x = 12/(4x)
  3. 3(x + 2)/(2x) = (2x + 4)/(4x)
  4. 41/4 = x/(4x)
  5. 512/(4x) + (2x + 4)/(4x) + x/(4x) = (12 + 2x + 4 + x)/(4x)
  6. 6= (3x + 16)/(4x)

Answer(3x + 16)/(4x)

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