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4PM1/02 Jun 2025, Question 5: The Cosine Rule

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 8 marks

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The question, in short

Triangle with AC 12 cm, BC 14 cm and 30° at B: use the cosine rule to get two values of x in surd form, then the difference between the two areas.

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

Part (a) · 5 marks

Form a quadratic in x and solve it in surd form.

  1. 1Cosine rule: 12² = 14² + x² − 2 × 14x cos 30°
  2. 2144 = 196 + x² − 14√3 x
  3. 3x² − 14√3 x + 52 = 0
  4. 4x = [14√3 ± √(588 − 208)]/2 = [14√3 ± √380]/2
  5. 5x = 7√3 ± √95

Answerx = 7√3 ± √95 (P = 7) shown

Part (b) · 3 marks

Difference between the two possible areas as m√n.

  1. 1Area = ½ × 14 × x × sin 30° = (7/2)x
  2. 2Difference = (7/2)[(7√3 + √95) − (7√3 − √95)]
  3. 3= (7/2) × 2√95 = 7√95

Answer7√95 cm²

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