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4MA1/1FR Jun 2024, Question 22: Linear Inequalities

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1FR (Foundation) · Calculator · 9 marks

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The question, in short

Simplify an index division, expand a product, factorise and solve a quadratic, and solve a linear inequality.

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

Part (a) · 1 mark

Simplify g⁹ ÷ g².

  1. 1When dividing powers of g, subtract the indices: 9 − 2 = 7.
  2. 2g⁹ ÷ g² = g⁷

Answerg⁷

Part (b) · 2 marks

Expand 5k²(k³ + 4).

  1. 15k²(k³ + 4) = 5k² × k³ + 5k² × 4
  2. 25k² × k³ = 5k²⁺³ = 5k⁵
  3. 35k² × 4 = 20k²
  4. 45k⁵ + 20k²

Answer5k⁵ + 20k²

Part (ci) · 2 marks

Factorise x² − 2x − 63.

  1. 1x² − 2x − 63
  2. 2Find two numbers that multiply to −63 and add to −2: 7 and −9
  3. 3(x + 7)(x − 9)

Answer(x + 7)(x − 9)

Part (cii) · 1 mark

Using your factorisation, solve x² − 2x − 63 = 0.

  1. 1(x + 7)(x − 9) = 0
  2. 2x + 7 = 0 or x − 9 = 0
  3. 3x = −7 or x = 9

Answer−7, 9

Part (d) · 3 marks

Solve the inequality 7 − 2y < 3y − 12.

  1. 17 − 2y < 3y − 12
  2. 27 + 12 < 3y + 2y
  3. 319 < 5y
  4. 45y > 19
  5. 5y > 19/5

Answery > 19/5

Stuck on a step? Read the free lesson: Linear Inequalities

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