CAIE P1 2019 November — Question 1 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2019
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeSingle binomial expansion
DifficultyModerate -0.3 This is a standard binomial expansion question requiring identification of the term where powers of x cancel. Students must apply the binomial theorem formula, set up the general term, and solve a simple equation for the power. It's slightly easier than average as it's a single-step application with straightforward arithmetic, though it does require careful handling of the x^(-2) term.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n
1 Find the term independent of \(x\) in the expansion of \(\left( 2 x + \frac { 1 } { 4 x ^ { 2 } } \right) ^ { 6 }\).
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
\(6C2 \times (2x)^4 \times \frac{1}{(4x^2)^2}\)B1 SOI; SC: Condone errors in \((4^{-1})^2\) evaluation or interpretation for B1 only
\(15 \times 2^4 \times \frac{1}{4^2}\)B1 Identified as required term
\(15\)B1
Total: 3 
**Question 1:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| $6C2 \times (2x)^4 \times \frac{1}{(4x^2)^2}$ | B1 | SOI; SC: Condone errors in $(4^{-1})^2$ evaluation or interpretation for B1 only |
| $15 \times 2^4 \times \frac{1}{4^2}$ | B1 | Identified as required term |
| $15$ | B1 | |
| **Total: 3** | | |

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1 Find the term independent of $x$ in the expansion of $\left( 2 x + \frac { 1 } { 4 x ^ { 2 } } \right) ^ { 6 }$.\\

\hfill \mbox{\textit{CAIE P1 2019 Q1 [3]}}
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