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4024/22 May/Jun 2024, Question 7: Expanding Two Brackets

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 8 marks

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The question, in short

Solve two linear equations, factorise a quadratic expression, and find constants a, b and c in an identity involving a squared binomial.

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

Part (a) · 1 mark

Solve x/3 = 7 for x.

  1. 1x = 7 × 3 = 21

Answer21

Part (b) · 2 marks

Solve 6x − 5 = 2(x + 3) for x.

  1. 16x − 5 = 2x + 6
  2. 26x − 2x = 5 + 6, so 4x = 11
  3. 3x = 11/4 = 2 3/4

Answer2 3/4

Part (c) · 2 marks

Factorise 3x² − 2x − 8.

  1. 13x² − 2x − 8 = 3x² − 6x + 4x − 8
  2. 2= 3x(x − 2) + 4(x − 2)
  3. 3= (3x + 4)(x − 2)

Answer(3x + 4)(x − 2)

Part (d) · 3 marks

Given (ax + b)² = 4x² − 12x + c and a > 0, find a, b and c.

  1. 1(ax + b)² = a²x² + 2abx + b²
  2. 2a² = 4, a > 0, so a = 2
  3. 32 × 2 × b = −12, so b = −3
  4. 4c = b² = 9: a = 2, b = −3, c = 9

Answera = 2, b = −3, c = 9

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Also searched as: 4024/22/M/J/24 · 4024_s24_qp_22 · 4024 s24 22 · question 7.
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