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4MA1/2H Jan 2023, Question 9: Index Laws with Letters

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 7 marks

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The question, in short

Answer four short algebra questions: evaluate a zero power, simplify a cubed product, factorise an expression fully, and find the equation of a straight line from a grid diagram.

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

Part (a) · 1 mark

State the value of (m + 2)⁰ for a positive integer m.

  1. 1Any number to the power of 0 is 1, so (m + 2)⁰ = 1

Answer1

Part (b) · 2 marks

Simplify (3a²b⁴)³.

  1. 1Cube each part: 3³ = 27, (a²)³ = a⁶, (b⁴)³ = b¹²
  2. 2(3a²b⁴)³ = 27a⁶b¹²

Answer27a⁶b¹²

Part (c) · 2 marks

Factorise 14x²y⁴ + 21x³y² completely.

  1. 1HCF of the two terms is 7x²y²
  2. 214x²y⁴ ÷ 7x²y² = 2y² and 21x³y² ÷ 7x²y² = 3x
  3. 314x²y⁴ + 21x³y² = 7x²y²(2y² + 3x)

Answer7x²y²(2y² + 3x)

Part (d) · 2 marks

Using the grid diagram, write down an equation for the straight line shown.

  1. 1The line crosses the y-axis at 4, so y-intercept is 4
  2. 2Gradient = rise/run = (0 − 4)/(2 − 0) = −4/2 = −2
  3. 3So equation is y = −2x + 4

Answery = −2x + 4

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