Write down the number of terms in the expansion.

Find the term in ${x^4}$ .

10 terms     A1     N1

[1 mark]

evidence of binomial expansion     (M1)

e.g. ${a^9}{b^0} + \left( \begin{array}{l} 9\\ 1 \end{array} \right){a^8}b + \left( \begin{array}{l} 9\\ 2 \end{array} \right){a^7}{b^2} + \ldots$, $\left( \begin{array}{l} 9\\ r \end{array} \right){(a)^{n - r}}{(b)^r}$ , Pascal’s triangle

evidence of correct term     (A1)

e.g. 8th term, $r = 7$ , $\left( \begin{array}{l} 9\\ 7 \end{array} \right)$ , ${(3{x^2})^2}{2^7}$

correct expression of complete term     (A1)

e.g. $\left( \begin{array}{l} 9\\ 7 \end{array} \right){(3{x^2})^2}{(2)^7}$ , $_2^9C{(3{x^2})^2}{(2)^7}$ , $36 \times 9 \times 128$

$41472{x^4}$ (accept $41500{x^4}$ )     A1     N2

[4 marks]

Many candidates were familiar with the binomial expansion, although some expanded entirely which at times led to careless errors. Others attempted to use Pascal's Triangle. Common errors included misidentifying the binomial coefficient corresponding to this term and not squaring the 3 in ($3{x^2}$) . 

Many candidates were familiar with the binomial expansion, although some expanded entirely which at times led to careless errors. Others attempted to use Pascal's triangle. Common errors included misidentifying the binomial coefficient corresponding to this term and not squaring the 3 in $(3{x^2})$ .