OCR MEI C1 — Question 15 4 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeStandard binomial expansion coefficient
DifficultyModerate -0.8 This is a straightforward application of the binomial theorem requiring identification of the correct term and calculation of one coefficient. It's easier than average as it involves only substitution into the binomial formula with small numbers and no algebraic manipulation beyond the expansion itself.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

15 Find the coefficient of \(x ^ { 3 }\) in the expansion of \(( 3 - 2 x ) ^ { 5 }\).

Question 15:
AnswerMarks Guidance
\(-720\ [x^3]\)4 B3 for 720; M1 for each of \(3^2\) and \(\pm2^3\) or \((-2x)^3\) or \((2x)^3\), and M1 for 10 or \((5\times4\times3)/(3\times2\times1)\) or for 1 5 10 10 5 1 seen but not for \(^5C_3\)
## Question 15:

$-720\ [x^3]$ | **4** | B3 for 720; M1 for each of $3^2$ and $\pm2^3$ or $(-2x)^3$ or $(2x)^3$, and M1 for 10 or $(5\times4\times3)/(3\times2\times1)$ or for 1 5 10 10 5 1 seen but not for $^5C_3$ | Total: **4**

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15 Find the coefficient of $x ^ { 3 }$ in the expansion of $( 3 - 2 x ) ^ { 5 }$.

\hfill \mbox{\textit{OCR MEI C1  Q15 [4]}}