CAIE P1 2015 November — Question 2 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2015
SessionNovember
Marks4
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Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeBinomial with negative or fractional powers of x
DifficultyStandard +0.3 This is a straightforward binomial expansion question requiring identification of the correct term where powers of x sum to give x^1. Students must apply the binomial theorem systematically and combine powers, which is slightly above routine practice but involves no novel insight—just careful algebraic manipulation of a standard technique.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n
2 Find the coefficient of \(x\) in the expansion of \(\left( \frac { x } { 3 } + \frac { 9 } { x ^ { 2 } } \right) ^ { 7 }\).
Question 2:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\([7C2] \times \left[\left(\frac{x}{3}\right)^5\right] \times \left[\left(\frac{9}{x^2}\right)^2\right]\) soiB2,1,0 Seen
\(21 \times \frac{1}{3^5}(x^5) \times 81\left(\frac{1}{x^4}\right)\) soiB1 Identified as required term
\(7\)B1 Accept \(7x\)
[4] 
## Question 2:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $[7C2] \times \left[\left(\frac{x}{3}\right)^5\right] \times \left[\left(\frac{9}{x^2}\right)^2\right]$ soi | B2,1,0 | Seen |
| $21 \times \frac{1}{3^5}(x^5) \times 81\left(\frac{1}{x^4}\right)$ soi | B1 | Identified as required term |
| $7$ | B1 | Accept $7x$ |
| **[4]** | | |

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2 Find the coefficient of $x$ in the expansion of $\left( \frac { x } { 3 } + \frac { 9 } { x ^ { 2 } } \right) ^ { 7 }$.

\hfill \mbox{\textit{CAIE P1 2015 Q2 [4]}}
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Q1 3 Q2 4 Q3 6 Q4 7 Q5 7 Q6 8 Q7 8 Q8 9 Q9 11 Q10 12