CAIE P1 2008 November — Question 1 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2008
SessionNovember
Marks3
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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 term containing x² using the general term formula. While it involves fractional powers and requires careful algebraic manipulation to simplify (x/2)^r · (2/x)^(6-r), it's a standard textbook exercise with a clear method and no conceptual challenges beyond routine application of the binomial theorem.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n
1 Find the value of the coefficient of \(x ^ { 2 }\) in the expansion of \(\left( \frac { x } { 2 } + \frac { 2 } { x } \right) ^ { 6 }\).
AnswerMarks Guidance
\(\text{Term in } x^2: \left(\frac{x}{2}\right)^4 \left(\frac{2}{x}\right)^2 \times 15\)M1, A1 Correct term – needs powers 4 and 2. For × 15
\(\text{Coeff} = \frac{15}{4} \text{ or } 3.75\)A1 Ignore inclusion of \(x^2\) 
$\text{Term in } x^2: \left(\frac{x}{2}\right)^4 \left(\frac{2}{x}\right)^2 \times 15$ | M1, A1 | Correct term – needs powers 4 and 2. For × 15

$\text{Coeff} = \frac{15}{4} \text{ or } 3.75$ | A1 | Ignore inclusion of $x^2$

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

\hfill \mbox{\textit{CAIE P1 2008 Q1 [3]}}
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Q1 3 Q2 4 Q3 4 Q4 7 Q5 8 Q6 8 Q7 8 Q8 9 Q9 12 Q10 12