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4MA1/1F Jun 2020, Question 20: Solving Linear Equations

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1F (Foundation) · Calculator · 8 marks

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The question, in short

Solve a linear equation showing algebraic working, factorise two expressions fully, and use a given factorisation to solve a quadratic equation.

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

Part (a) · 3 marks

Solve 5(4 − x) = 7 − 3x, showing clear algebraic working.

  1. 1Expand: 20 − 5x = 7 − 3x
  2. 220 − 7 = 5x − 3x
  3. 313 = 2x
  4. 4x = 6.5

Answer6.5

Part (b) · 2 marks

Factorise fully 16m³g³ + 24m²g⁵.

  1. 1HCF of 16 and 24 is 8; lowest powers are m² and g³.
  2. 2So the common factor is 8m²g³.
  3. 316m³g³ ÷ 8m²g³ = 2m and 24m²g⁵ ÷ 8m²g³ = 3g²
  4. 4Answer: 8m²g³(2m + 3g²)

Answer8m²g³(2m + 3g²)

Part (ci) · 2 marks

Factorise the quadratic expression y² − 2y − 48.

  1. 1Find two numbers that multiply to −48 and add to −2.
  2. 2−8 × 6 = −48 and −8 + 6 = −2
  3. 3Answer: (y − 8)(y + 6)

Answer(y − 8)(y + 6)

Part (cii) · 1 mark

Using the given factorisation (y − 8)(y + 6), solve y² − 2y − 48 = 0.

  1. 1Factorise: (y − 8)(y + 6) = 0
  2. 2y − 8 = 0 or y + 6 = 0
  3. 3y = 8, −6

Answer8, −6

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