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Date May 2011 Marks available 1 Reference code 11M.2.sl.TZ2.3
Level SL only Paper 2 Time zone TZ2
Command term Write down Question number 3 Adapted from N/A

Question

Consider the expansion of \({(x + 2)^{11}}\) .

Write down the number of terms in this expansion.

[1]
a.

Find the term containing \({x^2}\) .

[4]
b.

Markscheme

12 terms     A1     N1

[1 mark]

a.

evidence of binomial expansion     (M1)

e.g. \(\left( \begin{array}{l}
n\\
r
\end{array} \right){a^{n - r}}{b^r}\)
, an attempt to expand, Pascal’s triangle

evidence of choosing correct term     (A1)

e.g. 10th term , \(r = 9\) , \(\left( {\begin{array}{*{20}{c}}
{11}\\
9
\end{array}} \right)\) , \({(x)^2}{(2)^9}\)

correct working     A1

e.g. \(\left( {\begin{array}{*{20}{c}}
{11}\\
9
\end{array}} \right){(x)^2}{(2)^9}\) , \(55 \times {2^9}\)

\(28160{x^2}\)     A1     N2

[4 marks]

b.

Examiners report

Most candidates attempted this question, and many made good progress. A number of candidates spent time writing out Pascal’s triangle in full. Common errors included 11 for part (a) and not writing out the simplified form of the term for part (b). Another common error was adding instead of multiplying the parts of the term in part (b).

a.

Most candidates attempted this question, and many made good progress. A number of candidates spent time writing out Pascal’s triangle in full. Common errors included 11 for part (a) and not writing out the simplified form of the term for part (b). Another common error was adding instead of multiplying the parts of the term in part (b).

b.

Syllabus sections

Topic 2 - Functions and equations » 2.2 » Use of technology to graph a variety of functions, including ones not specifically mentioned.
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