OCR MEI AS Paper 2 2021 November — Question 1 3 marks

Exam BoardOCR MEI
ModuleAS Paper 2 (AS Paper 2)
Year2021
SessionNovember
Marks3
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Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeStandard binomial expansion coefficient
DifficultyEasy -1.2 This is a straightforward application of the binomial theorem requiring only substitution into the formula C(6,4) × 3^4 × 1^2. It's a single-step calculation with no problem-solving or conceptual challenge, making it easier than average but not trivial since students must recall and apply the correct formula.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n
1 Find the coefficient of \(x ^ { 4 }\) in the expansion of \(( 1 + 3 x ) ^ { 6 }\).
Question 1:
AnswerMarks Guidance
\(_{6}C_{4}\), \(^{6}C_{4}\), \(\frac{6!}{2!4!}\) or \(\binom{6}{4}\) oe or 1 6 15 20 15 6 1 soiM1 \(_{6}C_{2}\), \(^{6}C_{2}\), \(\frac{6!}{4!2!}\) or \(\binom{6}{2}\)
\(3^{4}\) seenB1 Allow for \((3x)^{4}\) seen
1215A1 Condone \(1215x^{4}\)
[3]
**Question 1:**

$_{6}C_{4}$, $^{6}C_{4}$, $\frac{6!}{2!4!}$ or $\binom{6}{4}$ oe or 1 6 15 20 15 6 1 soi | M1 | $_{6}C_{2}$, $^{6}C_{2}$, $\frac{6!}{4!2!}$ or $\binom{6}{2}$

$3^{4}$ seen | B1 | Allow for $(3x)^{4}$ seen

1215 | A1 | Condone $1215x^{4}$

**[3]**

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1 Find the coefficient of $x ^ { 4 }$ in the expansion of $( 1 + 3 x ) ^ { 6 }$.

\hfill \mbox{\textit{OCR MEI AS Paper 2 2021 Q1 [3]}}
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Q1 3 Q2 2 Q3 3 Q4 4 Q5 7 Q6 6 Q7 7 Q8 4 Q9 5 Q10 6 Q11 6 Q12 8 Q13 9