CAIE P1 2016 June — Question 1 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2016
SessionJune
Marks3
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Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeBinomial with negative or fractional powers of x
DifficultyModerate -0.5 This is a straightforward binomial expansion with positive integer power n=5, requiring identification of the term containing x by setting up the general term and solving for the appropriate value of r. While it involves negative powers of x, the method is standard and requires only careful algebraic manipulation rather than problem-solving insight.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n
1 Find the coefficient of \(x\) in the expansion of \(\left( \frac { 1 } { x } + 3 x ^ { 2 } \right) ^ { 5 }\).
Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(5C2\left(\frac{1}{x}\right)^3(3x^2)^2\)B1 Can be seen in expansion
\(10(\times 1)\times 3^2\)B1 Identified as leading to answer
\(90(x)\)B1 [3] 
## Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $5C2\left(\frac{1}{x}\right)^3(3x^2)^2$ | B1 | Can be seen in expansion |
| $10(\times 1)\times 3^2$ | B1 | Identified as leading to answer |
| $90(x)$ | B1 [3] | |

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1 Find the coefficient of $x$ in the expansion of $\left( \frac { 1 } { x } + 3 x ^ { 2 } \right) ^ { 5 }$.

\hfill \mbox{\textit{CAIE P1 2016 Q1 [3]}}
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Q1 3 Q2 4 Q3 5 Q4 5 Q5 7 Q6 7 Q7 7 Q8 8 Q9 8 Q10 9 Q11 12