CAIE P1 2010 November — Question 1 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2010
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 \(\left( x - \frac { 1 } { x ^ { 2 } } \right) ^ { 9 }\).

Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(^9C_6\) or \(^9C_3\) usedM1
\(\left(\frac{1}{x^2}\right)^3\) seenB1
\(-84\)A1 Correct answer only \(\Rightarrow\) 3 marks
[3]
## Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $^9C_6$ or $^9C_3$ used | M1 | |
| $\left(\frac{1}{x^2}\right)^3$ seen | B1 | |
| $-84$ | A1 | Correct answer only $\Rightarrow$ 3 marks |
| **[3]** | | |

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1 Find the term independent of $x$ in the expansion of $\left( x - \frac { 1 } { x ^ { 2 } } \right) ^ { 9 }$.

\hfill \mbox{\textit{CAIE P1 2010 Q1 [3]}}