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4MA1/1H Jun 2023, Question 6: Index Laws with Letters

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

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The question, in short

Simplify a cubed product of powers, evaluate an expression with a zero index, factorise two expressions fully, and factorise then solve a quadratic.

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

Part (a) · 2 marks

Simplify (2c⁴d⁷)³, giving the result in its simplest index form.

  1. 1Cube each part: 2³ = 8
  2. 2(c⁴)³ = c¹² and (d⁷)³ = d²¹ (multiply the powers)
  3. 38c¹²d²¹

Answer8c¹²d²¹

Part (b) · 1 mark

Work out the value of 5y⁰ given that y is greater than 0.

  1. 1Any non-zero number to the power 0 is 1, so y⁰ = 1
  2. 25 × 1 = 5

Answer5

Part (c) · 2 marks

Factorise 16a²b³ + 20a³b completely.

  1. 1Find common factor: 4a²b
  2. 216a²b³ ÷ 4a²b = 4b²
  3. 320a³b ÷ 4a²b = 5a
  4. 44a²b(4b² + 5a)

Answer4a²b(4b² + 5a)

Part (di) · 2 marks

Factorise the quadratic expression x² + 9x − 22.

  1. 1Look for two numbers that multiply to −22 and add to 9: 11 and −2
  2. 2(x + 11)(x − 2)

Answer(x + 11)(x − 2)

Part (dii) · 1 mark

Using your factorisation, solve x² + 9x − 22 = 0.

  1. 1(x + 11)(x − 2) = 0
  2. 2x + 11 = 0 → x = −11
  3. 3x − 2 = 0 → x = 2
  4. 4−11, 2

Answer−11, 2

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