OCR MEI C1 2008 June — Question 8 4 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Year2008
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeStandard binomial expansion coefficient
DifficultyModerate -0.8 This is a straightforward application of the binomial theorem requiring students to identify the correct term (r=3) and calculate using the formula. It's simpler than average as it involves direct substitution into a well-practiced formula with small numbers, though it requires careful handling of the negative sign and coefficient.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

8 Find the coefficient of \(x ^ { 3 }\) in the binomial expansion of \(( 5 - 2 x ) ^ { 5 }\).

Question 8:
AnswerMarks Guidance
\(-2000\)4 M3 for \(10 \times 5^2 \times (-2[x])^3\); or M2 for two of these elements or M1 for 10 or \((5\times4\times3)/(3\times2\times1)\); condone \(x^3\) in ans; equivs: M3 for e.g. \(5^5 \times 10 \times \left(-\frac{2}{5}[x]\right)^3\); o.e. [\(5^5\) may be outside a bracket for whole expansion of all terms], M2 for two of these elements etc; similarly for factor of 2 taken out at start
# Question 8:
| $-2000$ | 4 | M3 for $10 \times 5^2 \times (-2[x])^3$; or M2 for two of these elements or M1 for 10 or $(5\times4\times3)/(3\times2\times1)$; condone $x^3$ in ans; equivs: M3 for e.g. $5^5 \times 10 \times \left(-\frac{2}{5}[x]\right)^3$; o.e. [$5^5$ may be outside a bracket for whole expansion of all terms], M2 for two of these elements etc; similarly for factor of 2 taken out at start |

---
8 Find the coefficient of $x ^ { 3 }$ in the binomial expansion of $( 5 - 2 x ) ^ { 5 }$.

\hfill \mbox{\textit{OCR MEI C1 2008 Q8 [4]}}