| Date | May 2014 | Marks available | 4 | Reference code | 14M.2.sl.TZ1.2 |
| Level | SL only | Paper | 2 | Time zone | TZ1 |
| Command term | Find | Question number | 2 | Adapted from | N/A |
Question
Consider the expansion of \({(x + 3)^{10}}\).
Write down the number of terms in this expansion.
[1]
a.
Find the term containing \({x^3}\).
[4]
b.
Markscheme
11 terms A1 N1
[1 mark]
a.
evidence of binomial expansion (M1)
eg \(\left( \begin{array}{c}n\\r\end{array} \right)\) \({a^{n - r}}{b^r}\), attempt to expand
evidence of choosing correct term (A1)
eg \({8^{{\text{th}}}}{\text{ term, }}r = 7\), \(\left( \begin{array}{c}10\\7\end{array} \right)\), \({(x)^3}{(3)^7}\)
correct working (A1)
eg \(\left( \begin{array}{c}10\\7\end{array} \right)\) \({(x)^3}{(3)^7}\), \(\left( \begin{array}{c}10\\3\end{array} \right)\)\({(x)^3}{(3)^7}\),
\(262440{x^3}{\text{ (accept }}262000{x^3})\) A1 N3
[4 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
Syllabus sections
Topic 1 - Algebra » 1.3 » The binomial theorem: expansion of \({\left( {a + b} \right)^n}\), \(n \in \mathbb{N}\) .
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