CAIE P1 2011 November — Question 1 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2011
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeSingle binomial expansion
DifficultyModerate -0.3 This is a straightforward binomial expansion question requiring students to identify which term has x^0 by setting up the general term and solving a simple equation. It's slightly easier than average because it's a single-step application of the binomial theorem with no additional complications, though it does require careful handling of negative powers.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

1 Find the term independent of \(x\) in the expansion of \(\left( 2 x + \frac { 1 } { x ^ { 2 } } \right) ^ { 6 }\).

Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(6C4 \times [2(x)]^4 \times \left[\frac{1}{(x^2)}\right]^2\)B2 B1 for 2/3 terms correct
\(240\)B1 [3] Identified as answer. Allow \(240x^0\)
## Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $6C4 \times [2(x)]^4 \times \left[\frac{1}{(x^2)}\right]^2$ | B2 | B1 for 2/3 terms correct |
| $240$ | B1 | [3] Identified as answer. Allow $240x^0$ |

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1 Find the term independent of $x$ in the expansion of $\left( 2 x + \frac { 1 } { x ^ { 2 } } \right) ^ { 6 }$.

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