CAIE P1 2014 June — Question 1 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2014
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 requiring identification of the correct term where powers of x sum to 1. It's slightly easier than average as it's a single-step problem with clear method (general term formula), though students must be careful with negative powers and signs.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n
1 Find the coefficient of \(x\) in the expansion of \(\left( x ^ { 2 } - \frac { 2 } { x } \right) ^ { 5 }\).
AnswerMarks Guidance
\(\left(x^2 - \frac{2}{x}\right)^5\)
Term in \(x\) is \(10 \times (x^2)^2 \times \left(\frac{-2}{x}\right)^3\)B1 B1 B1 10 or \(^5C_2\) or \(^5C_3\), B1 \(\frac{(-2)^3}{x}\)
Coefficient \(= -80(x)\)B1 co Must be identified
[3] 
$\left(x^2 - \frac{2}{x}\right)^5$ | | |
Term in $x$ is $10 \times (x^2)^2 \times \left(\frac{-2}{x}\right)^3$ | B1 B1 | B1 10 or $^5C_2$ or $^5C_3$, B1 $\frac{(-2)^3}{x}$ |
Coefficient $= -80(x)$ | B1 | co Must be identified |
| | [3] |
1 Find the coefficient of $x$ in the expansion of $\left( x ^ { 2 } - \frac { 2 } { x } \right) ^ { 5 }$.

\hfill \mbox{\textit{CAIE P1 2014 Q1 [3]}}
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