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4MA1/1F Jan 2020, Question 8: Solving by Substitution

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1F (Foundation) · Calculator · 7 marks

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The question, in short

Simplify an algebraic expression by collecting like terms, then use P = 2a + 3b to find P from given a and b, and to find a from given P and b.

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

Part (a) · 2 marks

Collect the m terms and the k terms in 6m − 2k + 5m − k to give a shorter expression.

  1. 16m + 5m = 11m
  2. 2−2k − k = −3k
  3. 311m − 3k

Answer11m − 3k

Part (b) · 2 marks

Substitute a = 5 and b = 8 into P = 2a + 3b and calculate the resulting number.

  1. 1P = 2a + 3b
  2. 2a = 5, b = 8
  3. 32 × 5 = 10
  4. 43 × 8 = 24
  5. 510 + 24 = 34

Answer34

Part (c) · 3 marks

With P = 16 and b = 20, solve P = 2a + 3b to determine the number a.

  1. 1Substitute: 16 = 2a + 3 × 20
  2. 216 = 2a + 60
  3. 32a = 16 − 60 = −44
  4. 4a = −44 ÷ 2 = −22

Answer−22

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