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Pure Mathematics 1
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Statistics & Mechanics
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Differentiation
Integration
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Find the first 4 terms in the expansion of (2 + 3x)⁸ in ascending powers of x.
Hence find the coefficient of x³ in the expansion of (1 − x)(2 + 3x)⁸.

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Assess your work with one click
| Q | Scheme | Mark |
|---|---|---|
| 1(a) | Expands (2 + 3x)⁴ using binomial theorem | B1 |
| Correct coefficients: 4C1, 4C2, ... | M1 | |
| = 16 + 96x + 216x² + 216x³ + ... | A1 | |
| 1(b) | Substitutes x = 0.01 into expansion | M1 |
| = 19.2523... | A1 | |
| 2(a) | Uses product rule: u = x², v = sin x | M1 |
| dy/dx = 2x sin x + x² cos x | A1 | |
| 2(b) | Sets derivative equal to zero | M1 |
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