OCR MEI C1 2007 June — Question 6 4 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Year2007
SessionJune
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 direct formula application with small numbers and no algebraic manipulation beyond the expansion itself.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n
6 Find the coefficient of \(x ^ { 3 }\) in the expansion of \(( 3 - 2 x ) ^ { 5 }\).
Question 6:
AnswerMarks Guidance
Binomial expansion of \((3-2x)^5\):
\(\binom{5}{2}(3)^2(-2x)^3\)M1 Correct term identified
\(= 10 \times 9 \times (-8x^3)\)M1 Correct binomial coefficient and powers
\(= -720\)A1 A1 Coefficient of \(x^3\) is \(-720\) 
## Question 6:
Binomial expansion of $(3-2x)^5$: | |
$\binom{5}{2}(3)^2(-2x)^3$ | M1 | Correct term identified
$= 10 \times 9 \times (-8x^3)$ | M1 | Correct binomial coefficient and powers
$= -720$ | A1 A1 | Coefficient of $x^3$ is $-720$

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

\hfill \mbox{\textit{OCR MEI C1 2007 Q6 [4]}}
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Q1 3 Q2 3 Q3 2 Q4 3 Q5 4 Q6 4 Q7 3 Q8 5 Q9 4 Q10 5 Q11 12 Q12 12 Q13 12