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4MA1/1H Jun 2019, Question 12: Solving Linear Equations

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

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The question, in short

Three algebra tasks: factorise a quadratic, solve an equation for m showing working, and rewrite a quotient of powers of y as y to a fractional power.

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

Part (a) · 2 marks

Express the quadratic 2x² − 7x + 6 as a product of two brackets.

  1. 1Look for two numbers multiplying to 2 × 6 = 12 and adding to −7
  2. 2−3 and −4 work, so 2x² − 7x + 6 = 2x² − 3x − 4x + 6
  3. 32x² − 3x − 4x + 6 = x(2x − 3) − 2(2x − 3)
  4. 4So the factorisation is (2x − 3)(x − 2)

Answer(2x − 3)(x − 2)

Part (b) · 4 marks

Find the value of m satisfying (4m + 9)/3 = 7 − 2m, showing each algebraic step.

  1. 1Multiply both sides by 3: 4m + 9 = 3(7 − 2m)
  2. 2Expand the bracket: 4m + 9 = 21 − 6m
  3. 3Collect the m terms: 4m + 6m = 21 − 9, so 10m = 12
  4. 4m = 12/10 = 6/5

Answer6/5

Part (c) · 2 marks

Express the fourth root of y divided by y as yᵇ, giving b as a fraction.

  1. 1⁴√y = y^(1/4), so the expression is y^(1/4) / y
  2. 2Dividing powers subtracts them: y^(1/4) / y¹ = y^(1/4 − 1)
  3. 31/4 − 1 = −3/4, so b = −3/4 and the answer is y^(−3/4)

Answery^(−3/4)

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

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