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4MA1/2FR Jan 2021, Question 11: Substitution

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2FR (Foundation) · Calculator · 8 marks

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The question, in short

Algebra question with four parts: evaluate w = 5y² − y³ at y = −2, factorise 8p² − 2p, expand 4t(3t − 2), and expand and simplify (5x − 2)(x + 4).

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

Part (a) · 2 marks

Substitute y = −2 into w = 5y² − y³ and work out the value of w.

  1. 1Substitute y = −2: w = 5 × (−2)² − (−2)³
  2. 2(−2)² = 4 and (−2)³ = −8
  3. 3w = 20 − (−8) = 20 + 8 = 28

Answer28

Part (b) · 2 marks

Factorise 8p² − 2p completely.

  1. 1The highest common factor of 8p² and 2p is 2p
  2. 28p² ÷ 2p = 4p and 2p ÷ 2p = 1
  3. 38p² − 2p = 2p(4p − 1)

Answer2p(4p − 1)

Part (c) · 2 marks

Expand the brackets in 4t(3t − 2).

  1. 14t × 3t = 12t²
  2. 24t × (−2) = −8t
  3. 34t(3t − 2) = 12t² − 8t

Answer12t² − 8t

Part (d) · 2 marks

Expand and simplify (5x − 2)(x + 4).

  1. 15x × x = 5x² and 5x × 4 = 20x
  2. 2−2 × x = −2x and −2 × 4 = −8
  3. 3Collect terms: 5x² + 20x − 2x − 8 = 5x² + 18x − 8

Answer5x² + 18x − 8

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