CAIE P1 2018 June — Question 2 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2018
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeBinomial with negative or fractional powers of x
DifficultyModerate -0.8 This is a straightforward application of the binomial theorem requiring students to identify which term produces 1/x and calculate its coefficient. It's a single-step problem with clear methodology (find r where x^(5-r) ยท (1/x)^r = 1/x, then compute the binomial coefficient), making it easier than average but not trivial since it requires careful tracking of powers.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n
2 Find the coefficient of \(\frac { 1 } { x }\) in the expansion of \(\left( x - \frac { 2 } { x } \right) ^ { 5 }\).
Question 2:
AnswerMarks Guidance
\(_{5}C_{3}\; x^{2}\!\left(\dfrac{-2}{x}\right)^{3}\) SOIB2,1,0 \(-80\) www scores B3. Accept \(_{5}C_{2}\).
\(-80\) Accept \(\dfrac{-80}{x}\)B1 \(+80\) without clear working scores SCB1
Total: 3 marks
**Question 2:**

$_{5}C_{3}\; x^{2}\!\left(\dfrac{-2}{x}\right)^{3}$ SOI | B2,1,0 | $-80$ www scores B3. Accept $_{5}C_{2}$.

$-80$ Accept $\dfrac{-80}{x}$ | B1 | $+80$ without clear working scores SCB1

**Total: 3 marks**
2 Find the coefficient of $\frac { 1 } { x }$ in the expansion of $\left( x - \frac { 2 } { x } \right) ^ { 5 }$.\\

\hfill \mbox{\textit{CAIE P1 2018 Q2 [3]}}
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