| Date | May 2009 | Marks available | 1 | Reference code | 09M.1.sl.TZ2.3 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Write down | Question number | 3 | Adapted from | N/A |
Question
The fifth term in the expansion of the binomial \({(a + b)^n}\) is given by \(\left( {\begin{array}{*{20}{c}}
{10}\\
4
\end{array}} \right){p^6}{(2q)^4}\) .
Write down the value of \(n\).
[1]
a.
Write down a and b, in terms of p and/or q.
[2]
b.
Write down an expression for the sixth term in the expansion.
[3]
c.
Markscheme
\(n = 10\) A1 N1
[1 mark]
a.
\(a = p\) , \(b = 2q\) (or \(a = 2q\) , \(b = p\) ) A1A1 N1N1
[2 marks]
b.
\(\left( {\begin{array}{*{20}{c}}
{10}\\
5
\end{array}} \right){p^5}{(2q)^5}\) A1A1A1 N3
[3 marks]
c.
Examiners report
[N/A]
a.
[N/A]
b.
The most common error was in (c) where many candidates interpreted the "sixth" term as using \(\left( {\begin{array}{*{20}{c}}
{10}\\
6
\end{array}} \right)\) , with accompanying powers of 4 and 6 in the expression.
c.
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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