CAIE P1 2004 November — Question 1 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2004
SessionNovember
Marks4
PaperDownload PDF ↗
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 handle negative powers carefully.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

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

Question 1: \((3x - 2/x)^5\)
AnswerMarks Guidance
Answer/WorkingMarks Guidance
Required term has \(_5C_2\) or \(_5C_3 = 10\)B1 Needs 10 or implied by answers
Also has \(3^3\) and \(2^2\)B1 B1 Can be implied or in the expansion. Co. If all expansion given, gets \(\frac{3}{4}\) unless required term is isolated from expansion or ringed
\(\rightarrow 1080\)B1 [4]
## Question 1: $(3x - 2/x)^5$

| Answer/Working | Marks | Guidance |
|---|---|---|
| Required term has $_5C_2$ or $_5C_3 = 10$ | B1 | Needs 10 or implied by answers |
| Also has $3^3$ and $2^2$ | B1 B1 | Can be implied or in the expansion. Co. If all expansion given, gets $\frac{3}{4}$ unless required term is isolated from expansion or ringed |
| $\rightarrow 1080$ | B1 | [4] |

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

\hfill \mbox{\textit{CAIE P1 2004 Q1 [4]}}