1 Find the coefficient of the term in \(x ^ { 3 }\) in the expansion of \(\frac { 1 } { ( 2 + 3 x ) ^ { 2 } }\).
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Question 1:
Answer Marks
Guidance
Answer Marks
Guidance
\((2+3x)^{-2} = 2^{-2}\left(1+\frac{3x}{2}\right)^{-2}\) M1, A1
Extract 2, remaining bracket
\(=\frac{1}{4}\left(1+\frac{(-2)}{1}\left(\frac{3x}{2}\right)+\frac{(-2)(-3)}{1.2}\left(\frac{3x}{2}\right)^2+\frac{(-2)(-3)(-4)}{1.2.3}\left(\frac{3x}{2}\right)^3+...\right)\) M1
For sight of numerator and denominator and power
Coefficient is \(\frac{1}{4}\times\frac{(-2)(-3)(-4)}{1.2.3}\left(\frac{3}{2}\right)^3=\frac{1}{4}\times(-4)\times\frac{27}{8}=-\frac{27}{8}\) A1, A1
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Total: 5 marks
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## Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(2+3x)^{-2} = 2^{-2}\left(1+\frac{3x}{2}\right)^{-2}$ | M1, A1 | Extract 2, remaining bracket |
| $=\frac{1}{4}\left(1+\frac{(-2)}{1}\left(\frac{3x}{2}\right)+\frac{(-2)(-3)}{1.2}\left(\frac{3x}{2}\right)^2+\frac{(-2)(-3)(-4)}{1.2.3}\left(\frac{3x}{2}\right)^3+...\right)$ | M1 | For sight of numerator and denominator and power |
| Coefficient is $\frac{1}{4}\times\frac{(-2)(-3)(-4)}{1.2.3}\left(\frac{3}{2}\right)^3=\frac{1}{4}\times(-4)\times\frac{27}{8}=-\frac{27}{8}$ | A1, A1 | Sign |
**Total: 5 marks**
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1 Find the coefficient of the term in $x ^ { 3 }$ in the expansion of $\frac { 1 } { ( 2 + 3 x ) ^ { 2 } }$.
\hfill \mbox{\textit{OCR MEI C4 Q1 [5]}}