OCR MEI C1 — Question 16 3 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Marks3
PaperDownload PDF ↗
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) × 5² = 15 × 25 = 375. It's a single-step calculation with no problem-solving required, making it easier than average but not trivial since students must recall and correctly apply the binomial coefficient formula.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

16 Calculate the coefficient of \(x ^ { 4 }\) in the expansion of \(( x + 5 ) ^ { 6 }\).

Question 16:
AnswerMarks Guidance
\(375\)3 Allow \(375x^4\); M1 for \(5^2\) or 25 used or seen with \(x^4\) and M1 for 15 or \(\frac{6\times5}{2}\) oe e.g. \(\frac{6!}{4!2!}\) or 1 6 15 … seen [\(^6C_4\) not sufficient]
## Question 16:

$375$ | **3** | Allow $375x^4$; M1 for $5^2$ or 25 used or seen with $x^4$ and M1 for 15 or $\frac{6\times5}{2}$ oe e.g. $\frac{6!}{4!2!}$ or 1 6 15 … seen [$^6C_4$ not sufficient] | Total: **3**

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16 Calculate the coefficient of $x ^ { 4 }$ in the expansion of $( x + 5 ) ^ { 6 }$.

\hfill \mbox{\textit{OCR MEI C1  Q16 [3]}}