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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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