OCR MEI C1 — Question 17 4 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeStandard binomial expansion coefficient
DifficultyEasy -1.2 This is a straightforward two-part question requiring direct application of the binomial coefficient formula and binomial theorem. Part (a) is pure recall/calculation of 6C3 = 20, and part (b) requires identifying that the coefficient is 6C3 × (-2)³ = -160. Both are routine textbook exercises with no problem-solving or insight required, making this easier than average.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

17 Calculate \({ } ^ { 6 } \mathrm { C } _ { 3 }\).
Find the coefficient of \(x ^ { 3 }\) in the expansion of \(( 1 - 2 x ) ^ { 6 }\).

Question 17:
AnswerMarks Guidance
\(20\)2 0 for just 20 seen in second part; M1 for \(6!/(3!3!)\) or better
\(-160\) or ft for \(-8 \times\) their 202 Condone \(-160x^3\); M1 for \([-]2^3\times[\text{their}]\ 20\) seen or for \([\text{their}]\ 20\times(-2x)^3\); allow B1 for 160
## Question 17:

$20$ | **2** | 0 for just 20 seen in second part; M1 for $6!/(3!3!)$ or better

$-160$ or ft for $-8 \times$ their 20 | **2** | Condone $-160x^3$; M1 for $[-]2^3\times[\text{their}]\ 20$ seen or for $[\text{their}]\ 20\times(-2x)^3$; allow B1 for 160 | Total: **4**

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17 Calculate ${ } ^ { 6 } \mathrm { C } _ { 3 }$.\\
Find the coefficient of $x ^ { 3 }$ in the expansion of $( 1 - 2 x ) ^ { 6 }$.

\hfill \mbox{\textit{OCR MEI C1  Q17 [4]}}