WMA12/01 Jun 2024, Question 1: The Binomial Expansion
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 5 marks
The question, in short
Expand (1 − ⅙x)⁹ up to the x³ term in simplest form, then use that result to get the x³ coefficient of (10x + 3)(1 − ⅙x)⁹.
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Part (a) · 3 marks
Write the first four terms of the expansion of (1 − ⅙x)⁹ in ascending powers of x, each simplified.
- 1(1 − ⅙x)⁹ = 1 + 9(−⅙x) + (9×8/2!)(−⅙x)² + (9×8×7/3!)(−⅙x)³ + …
- 2= 1 + 9(−x/6) + 36(x²/36) + 84(−x³/216) + …
- 3= 1 − (3/2)x + x² − (7/18)x³ + …
Answer1 − (3/2)x + x² − (7/18)x³
Part (b) · 2 marks
Using your expansion, determine the coefficient of x³ in (10x + 3)(1 − ⅙x)⁹, simplified.
- 1The x³ term comes from 10x × (x² term) and 3 × (x³ term)
- 2Coefficient = 10 × 1 + 3 × (−7/18)
- 3= 10 − 7/6 = 53/6
Answer53/6
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Also searched as: WMA12 June 2024 · WMA12/01 · wma12 jun24 · IAS Maths Pure Mathematics 2 June 2024 · question 1.
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