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4MA1/1F Jun 2021, Question 24: Solving Linear Equations

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1F (Foundation) · Calculator · 5 marks

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The question, in short

Two algebra tasks: rewrite a two-term expression as a product of factors, and find the value of x satisfying a squared bracket equal to a product of two brackets.

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

Part (a) · 2 marks

Write 25a⁴c⁷d + 45a⁹c³h as a product of its factors, taking out everything common.

  1. 1HCF of 25 and 45 is 5; the lowest powers are a⁴ and c³
  2. 2Take out 5a⁴c³ from both terms
  3. 325a⁴c⁷d ÷ 5a⁴c³ = 5c⁴d and 45a⁹c³h ÷ 5a⁴c³ = 9a⁵h
  4. 45a⁴c³(5c⁴d + 9a⁵h)

Answer5a⁴c³(5c⁴d + 9a⁵h)

Part (b) · 3 marks

Find x where (2x + 5)² equals (2x + 3)(2x − 1).

  1. 1Left side: (2x + 5)² = 4x² + 20x + 25
  2. 2Right side: (2x + 3)(2x − 1) = 4x² + 4x − 3
  3. 3The 4x² terms cancel: 20x + 25 = 4x − 3
  4. 416x = −28
  5. 5x = −28/16 = −1.75

Answer−1.75

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