OCR MEI C1 2016 June — Question 6 4 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Year2016
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeStandard binomial expansion
DifficultyEasy -1.2 This is a straightforward application of the binomial theorem with a small positive integer power (n=4). It requires only direct substitution into the formula and simplification of coefficients—no problem-solving or insight needed, just mechanical execution of a standard technique taught early in C1.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

6 Find the binomial expansion of \(( 1 - 5 x ) ^ { 4 }\), expressing the terms as simply as possible.

Question 6:
AnswerMarks Guidance
\(1-20x+150x^2-500x^3+625x^4\) as final answerM3 for 4 terms correct or all coefficients correct except sign errors for binomial coefficients, \(^4C_2\) or factorial notation not sufficient; accept \(\frac{4\times3\times2\times1}{2\times1\times2\times1}\) oe etc [4]
M2 for 3 terms correct or correct expansion without correct evaluation of coefficients
M1 for \(1\ 4\ 6\ 4\ 1\) soi in Pascal's triangle or in expansion where powers of 5 ignored
# Question 6:
$1-20x+150x^2-500x^3+625x^4$ as final answer | M3 for 4 terms correct or all coefficients correct except sign errors | for binomial coefficients, $^4C_2$ or factorial notation not sufficient; accept $\frac{4\times3\times2\times1}{2\times1\times2\times1}$ oe etc [4]
| M2 for 3 terms correct or correct expansion without correct evaluation of coefficients |
| M1 for $1\ 4\ 6\ 4\ 1$ soi in Pascal's triangle or in expansion where powers of 5 ignored |

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6 Find the binomial expansion of $( 1 - 5 x ) ^ { 4 }$, expressing the terms as simply as possible.

\hfill \mbox{\textit{OCR MEI C1 2016 Q6 [4]}}