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4MA1/2HR Jun 2024, Question 6: Solving Linear Equations

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 8 marks

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The question, in short

Four short algebra tasks: solve an equation in f, simplify a power expression, simplify a quotient of terms in a and h, and factorise an expression in x and y.

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

Part (a) · 3 marks

Solve 2f/3 = 4f − 17, showing clear algebraic working.

  1. 1Multiply both sides by 3: 2f = 3(4f − 17)
  2. 2Expand: 2f = 12f − 51
  3. 3Collect the f terms: 2f − 12f = −51, so −10f = −51
  4. 4f = 51/10 = 5.1

Answer51/10

Part (b) · 1 mark

Simplify (e + 12)⁰ given e > 0.

  1. 1Anything (other than 0) to the power 0 is 1
  2. 2So (e + 12)⁰ = 1

Answer1

Part (c) · 2 marks

Simplify fully (12a⁴h⁶)/(4ah²).

  1. 1Divide the numbers: 12 ÷ 4 = 3
  2. 2Divide the a terms: a⁴ ÷ a = a³
  3. 3Divide the h terms: h⁶ ÷ h² = h⁴
  4. 4So the answer is 3a³h⁴

Answer3a³h⁴

Part (d) · 2 marks

Factorise fully 20x⁵y + 12x³y⁴.

  1. 1The largest number dividing 20 and 12 is 4
  2. 2Both terms have at least x³ and at least one y, so the common factor is 4x³y
  3. 320x⁵y ÷ 4x³y = 5x² and 12x³y⁴ ÷ 4x³y = 3y³
  4. 4So the answer is 4x³y(5x² + 3y³)

Answer4x³y(5x² + 3y³)

Stuck on a step? Read the free lesson: Solving Linear Equations

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