CAIE P3 2010 November — Question 1 3 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2010
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicGeneralised Binomial Theorem
TypeForm (1+bx)^n expansion
DifficultyEasy -1.2 This is a straightforward application of the binomial expansion formula for negative indices, requiring only substitution of n=-3 and b=2, then simplifying three coefficients. It's a routine drill exercise with no problem-solving element, making it easier than average but not trivial since students must handle negative indices and fractional arithmetic correctly.
Spec1.04c Extend binomial expansion: rational n, |x|<1
1 Expand \(( 1 + 2 x ) ^ { - 3 }\) in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\), simplifying the coefficients.
AnswerMarks Guidance
Obtain \(1 - 6x\)B1
State correct unsimplified \(x^2\) term. Binomial coefficients must be expanded.M1
Obtain \(\ldots + 24x^2\)A1 [3] 
Obtain $1 - 6x$ | B1 | 
State correct unsimplified $x^2$ term. Binomial coefficients must be expanded. | M1 |
Obtain $\ldots + 24x^2$ | A1 | [3]
1 Expand $( 1 + 2 x ) ^ { - 3 }$ in ascending powers of $x$, up to and including the term in $x ^ { 2 }$, simplifying the coefficients.

\hfill \mbox{\textit{CAIE P3 2010 Q1 [3]}}
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