CAIE P1 2016 November — Question 2 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2016
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeSingle binomial expansion
DifficultyModerate -0.3 This is a standard binomial expansion question requiring students to identify which term has x^0 by setting up the general term and solving for r. It's slightly easier than average because it's a single-step application of a well-practiced technique with no additional complications, though it does require careful algebraic manipulation of powers.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

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

Question 2:
AnswerMarks Guidance
\(8C6(2x)^6\left(\frac{1}{2x^3}\right)^2\) soiB1 May be seen within a number of terms
\(28 \times 64 \times \frac{1}{4}\) oe (powers and factorials evaluated)B2,1,0 May be seen within a number of terms
\(448\)B1 [4] Identified as answer
## Question 2:
$8C6(2x)^6\left(\frac{1}{2x^3}\right)^2$ soi | **B1** | May be seen within a number of terms
$28 \times 64 \times \frac{1}{4}$ oe (powers and factorials evaluated) | **B2,1,0** | May be seen within a number of terms
$448$ | **B1** [4] | Identified as answer

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

\hfill \mbox{\textit{CAIE P1 2016 Q2 [4]}}