OCR MEI C1 2006 June — Question 8 4 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Year2006
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeStandard binomial expansion coefficient
DifficultyEasy -1.2 This is a straightforward application of basic binomial theorem formulas requiring only recall and simple arithmetic. Calculating ⁶C₃ is direct substitution into the combination formula, and finding the coefficient requires one application of the binomial theorem with r=3. Both parts are routine textbook exercises with no problem-solving element, making this easier than average.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

Calculate \(^6C_3\). Find the coefficient of \(x^3\) in the expansion of \((1 - 2x)^6\). [4]

AnswerMarks Guidance
\(20\)2 marks 0 for just \(20\) seen in second part; M1 for \(\frac{6!}{3!(3!)}\) or better
\(-160\) or ft for \(-8 \times\) their \(20\)2 marks condone \(-160x^2\); M1 for \([-]2^2 \times\) [their] \(20\) seen or for [their] \(20 \times (-2x)^3\); allow B1 for \(160\)
4 marks
$20$ | 2 marks | 0 for just $20$ seen in second part; M1 for $\frac{6!}{3!(3!)}$ or better

$-160$ or ft for $-8 \times$ their $20$ | 2 marks | condone $-160x^2$; M1 for $[-]2^2 \times$ [their] $20$ seen or for [their] $20 \times (-2x)^3$; allow B1 for $160$

| | 4 marks |
Calculate $^6C_3$.

Find the coefficient of $x^3$ in the expansion of $(1 - 2x)^6$. [4]

\hfill \mbox{\textit{OCR MEI C1 2006 Q8 [4]}}