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4MA1/2F Jun 2022, Question 11: Constructing Equations

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2F (Foundation) · Calculator · 7 marks

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The question, in short

Simplify algebraic products and sums, expand and factorise expressions, then form a formula for T, the total marbles from m small bags of 15 and p large bags of 40.

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

Part (a) · 1 mark

Write c multiplied by itself six times as a single power.

  1. 1c × c × c × c × c × c = c⁶

Answerc⁶

Part (b) · 1 mark

Combine the three like terms in h³ into one term.

  1. 12h³ + 5h³ − h³ = (2 + 5 − 1)h³ = 6h³

Answer6h³

Part (c) · 1 mark

Multiply out the bracket by distributing x over x + 5.

  1. 1x(x + 5) = x × x + x × 5 = x² + 5x

Answerx² + 5x

Part (d) · 1 mark

Write 9y − 12 as a product of a common factor and a bracket.

  1. 19y − 12 = 3 × 3y − 3 × 4 = 3(3y − 4)

Answer3(3y − 4)

Part (e) · 3 marks

Give T as an expression using m and p, with 15 and 40 marbles per bag.

  1. 1Each small bag has 15 marbles, so m small bags give 15m marbles
  2. 2Each large bag has 40 marbles, so p large bags give 40p marbles
  3. 3Total marbles T = 15m + 40p

AnswerT = 15m + 40p

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