CAIE P1 2011 June — Question 1 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2011
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeBinomial with negative or fractional powers of x
DifficultyModerate -0.3 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 because it's a single-step problem with clear method (general term formula), though students must be careful with the negative power arithmetic.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

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

AnswerMarks Guidance
\(^7C_3 x^3 \left(\frac{2}{x^2}\right)^2\) SOI and leading to final answerB2 B1 for 2/3 parts correct leading to ans.
84 or 84x as final answerB1 If no answer; 84x seen scores B2, else \(^7C_3 x^5 \left(\frac{2}{x^2}\right)\) scores SCB1 only
$^7C_3 x^3 \left(\frac{2}{x^2}\right)^2$ SOI and leading to final answer | B2 | B1 for 2/3 parts correct leading to ans.
84 or 84x as final answer | B1 | If no answer; 84x seen scores B2, else $^7C_3 x^5 \left(\frac{2}{x^2}\right)$ scores SCB1 only

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

\hfill \mbox{\textit{CAIE P1 2011 Q1 [3]}}