Edexcel C2 2005 January — Question 1 4 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2005
SessionJanuary
Marks4
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Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeExpansion up to x^2 term
DifficultyEasy -1.2 This is a straightforward application of the binomial theorem requiring only direct substitution into the formula for the first three terms of (a+b)^n with n=5. It's purely procedural with no problem-solving element, making it easier than average, though slightly more involved than basic index law recall due to the arithmetic required.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

Find the first three terms, in ascending powers of \(x\), of the binomial expansion of \(( 3 + 2 x ) ^ { 5 }\), giving each term in its simplest form.
(4)

AnswerMarks Guidance
\((3+2x)^5 = (3)^5 + \binom{5}{1}3^4 \cdot (2x) + \binom{5}{2}3^3(2x)^2 + \cdots = 243+810x+1080x^2\)M1, B1, A1, A1 (4 marks)
$(3+2x)^5 = (3)^5 + \binom{5}{1}3^4 \cdot (2x) + \binom{5}{2}3^3(2x)^2 + \cdots = 243+810x+1080x^2$ | M1, B1, A1, A1 | (4 marks) | M1: Use of binomial leading to correct expression for $x$ or $x^2$ term; can be implied. $\binom{n}{r}$ notation is acceptable.
Find the first three terms, in ascending powers of $x$, of the binomial expansion of $( 3 + 2 x ) ^ { 5 }$, giving each term in its simplest form.\\
(4)\\

\hfill \mbox{\textit{Edexcel C2 2005 Q1 [4]}}