CAIE P1 2012 November — Question 1 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2012
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeStandard binomial expansion coefficient
DifficultyModerate -0.8 This is a straightforward application of the binomial theorem requiring identification of the correct term and calculation using nCr. It's a single-step problem with direct formula application, making it easier than average but not trivial since students must handle the fractional coefficient and negative sign correctly.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n
1 Find the coefficient of \(x ^ { 3 }\) in the expansion of \(\left( 2 - \frac { 1 } { 2 } x \right) ^ { 7 }\).
AnswerMarks Guidance
\(7C3 \times 2^4 \times \left(-\frac{a}{3}\right)^3\) powers 4 and 3, 35 seen or implied, -70M1, B1, A1 [3] 
$7C3 \times 2^4 \times \left(-\frac{a}{3}\right)^3$ powers 4 and 3, 35 seen or implied, -70 | M1, B1, A1 | [3]
1 Find the coefficient of $x ^ { 3 }$ in the expansion of $\left( 2 - \frac { 1 } { 2 } x \right) ^ { 7 }$.

\hfill \mbox{\textit{CAIE P1 2012 Q1 [3]}}
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Q1 3 Q2 3 Q3 4 Q4 4 Q5 5 Q6 6 Q7 8 Q8 9 Q9 10 Q10 10 Q11 13