CAIE P1 2014 June — Question 3 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2014
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeSingle binomial expansion
DifficultyModerate -0.8 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 a standard textbook exercise testing routine application of the binomial theorem with no problem-solving insight required, making it easier than average.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

3 Find the term independent of \(x\) in the expansion of \(\left( 4 x ^ { 3 } + \frac { 1 } { 2 x } \right) ^ { 8 }\).

AnswerMarks Guidance
\([^8C_8 \text{ or } 28] \times [16 \text{ or } 4^2](x^6) \times \left[\frac{1}{(64 \text{ or } 2^6)(x^6)}\right]\)B1B1B1 [4] Seen in expansion ok. Allow \(^6C_2\); Identified as answer
\(7\)
$[^8C_8 \text{ or } 28] \times [16 \text{ or } 4^2](x^6) \times \left[\frac{1}{(64 \text{ or } 2^6)(x^6)}\right]$ | B1B1B1 [4] | Seen in expansion ok. Allow $^6C_2$; Identified as answer

$7$
3 Find the term independent of $x$ in the expansion of $\left( 4 x ^ { 3 } + \frac { 1 } { 2 x } \right) ^ { 8 }$.

\hfill \mbox{\textit{CAIE P1 2014 Q3 [4]}}