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Date May 2009 Marks available 2 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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