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4MA1/2FR Jun 2023, Question 16: Solving Linear Equations

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2FR (Foundation) · Calculator · 9 marks

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The question, in short

Algebra question: factorise, expand, and substitute values into formulas to find r and P, then expand and simplify a product of two brackets.

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

Part (a) · 1 mark

Factorise 6y − 27.

  1. 1Factor out the highest common factor, which is 3.
  2. 26y ÷ 3 = 2y
  3. 3−27 ÷ 3 = −9
  4. 4So, 6y − 27 = 3(2y − 9)

Answer3(2y − 9)

Part (b) · 1 mark

Expand p(p − 2).

  1. 1Multiply p by p: p × p = p²
  2. 2Multiply p by −2: p × (−2) = −2p
  3. 3So, p(p − 2) = p² − 2p

Answerp² − 2p

Part (c) · 3 marks

Using T = 5g + 4r, find r when T = 46 and g = 17.

  1. 1Start with T = 5g + 4r
  2. 2Substitute T = 46 and g = 17: 46 = 5×17 + 4r
  3. 35×17 = 85, so 46 = 85 + 4r
  4. 4Rearrange: 46 − 85 = 4r
  5. 5−39 = 4r
  6. 6Divide both sides by 4: r = −39 ÷ 4
  7. 7r = −9.75

Answer−9.75

Part (d) · 2 marks

Using P = m² − 4c, find P when m = −5 and c = 3.

  1. 1Use P = m² − 4c
  2. 2Substitute m = −5 and c = 3
  3. 3(−5)² = 25
  4. 44×3 = 12
  5. 5P = 25 − 12
  6. 6P = 13

Answer13

Part (e) · 2 marks

Expand and simplify (x + 5)(x − 7).

  1. 1Expand (x + 5)(x − 7)
  2. 2x × x = x²
  3. 3x × (−7) = −7x
  4. 45 × x = 5x
  5. 55 × (−7) = −35
  6. 6Combine like terms: −7x + 5x = −2x
  7. 7So, x² − 2x − 35

Answerx² − 2x − 35

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