OCR MEI C1 2010 January — Question 8 4 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Year2010
SessionJanuary
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeBinomial expansion with reciprocals
DifficultyEasy -1.2 This is a straightforward application of the binomial theorem with n=3 (very small power) requiring only expansion and simplification of terms involving x and 1/x. It's a routine C1 exercise with minimal steps and no problem-solving insight needed, making it easier than average.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

8 Find the binomial expansion of \(\left( x + \frac { 5 } { x } \right) ^ { 3 }\), simplifying the terms.

Question 8:
AnswerMarks Guidance
AnswerMark Guidance
\(x^3 + 15x + \dfrac{75}{x} + \dfrac{125}{x^3}\) www isw or \(x^3 + 15x + 75x^{-1} + 125x^{-3}\) www isw4 B1 for both of \(x^3\) and \(\dfrac{125}{x^3}\) or \(125x^{-3}\) isw; and M1 for 1 3 3 1 soi; A1 for each of \(15x\) and \(\dfrac{75}{x}\) or \(75x^{-1}\) isw; or SC2 for completely correct unsimplified answer
## Question 8:

| Answer | Mark | Guidance |
|--------|------|----------|
| $x^3 + 15x + \dfrac{75}{x} + \dfrac{125}{x^3}$ www isw or $x^3 + 15x + 75x^{-1} + 125x^{-3}$ www isw | 4 | B1 for **both** of $x^3$ **and** $\dfrac{125}{x^3}$ or $125x^{-3}$ isw; and M1 for 1 3 3 1 soi; A1 for **each** of $15x$ **and** $\dfrac{75}{x}$ or $75x^{-1}$ isw; **or** SC2 for completely correct unsimplified answer |
8 Find the binomial expansion of $\left( x + \frac { 5 } { x } \right) ^ { 3 }$, simplifying the terms.

\hfill \mbox{\textit{OCR MEI C1 2010 Q8 [4]}}