| Date | May 2016 | Marks available | 2 | Reference code | 16M.2.sl.TZ1.4 |
| Level | SL only | Paper | 2 | Time zone | TZ1 |
| Command term | Hence | Question number | 4 | Adapted from | N/A |
Question
Find the term in \({x^6}\) in the expansion of \({(x + 2)^9}\).
Hence, find the term in \({x^7}\) in the expansion of \(5x{(x + 2)^9}\).
Markscheme
valid approach to find the required term (M1)
eg\(\,\,\,\,\,\)\(\left( {\begin{array}{*{20}{c}} 9 \\ r \end{array}} \right){(x)^{9 - r}}{(2)^r},{\text{ }}{x^9} + 9{x^8}(2) + \left( {\begin{array}{*{20}{c}} 9 \\ 2 \end{array}} \right){x^7}{(2)^2} + \ldots \), Pascal’s triangle to the 9th row
identifying correct term (may be indicated in expansion) (A1)
eg\(\,\,\,\,\,\)4th term, \(r = 6,{\text{ }}\left( {\begin{array}{*{20}{c}} 9 \\ 3 \end{array}} \right),{\text{ }}{(x)^6}{(2)^3}\)
correct calculation (may be seen in expansion) (A1)
eg\(\,\,\,\,\,\)\(\left( {\begin{array}{*{20}{c}} 9 \\ 3 \end{array}} \right){(x)^6}{(2)^3},{\text{ }}84 \times {2^3}\)
672\({x^6}\) A1 N3
[4 marks]
valid approach (M1)
eg\(\,\,\,\,\,\)recognizing \({x^7}\) is found when multiplying \(5x \times 672{x^6}\)
\(3360{x^7}\) A1 N2
[2 marks]
Examiners report
Many candidates approached this question using an appropriate and efficient method to identify the required term. While many of those who were successful in (a) were also successful in (b), a significant number of candidates did not realize that multiplying their answer in (a) by \(5x\) would give them the term in \({x^7}\). This led to an attempt to find a binomial expansion, which was generally unsuccessful. Some candidates continue to be unable to distinguish between the “coefficient” and the “term” and lost a point as a result.
Many candidates approached this question using an appropriate and efficient method to identify the required term. While many of those who were successful in (a) were also successful in (b), a significant number of candidates did not realize that multiplying their answer in (a) by \(5x\) would give them the term in \({x^7}\). This led to an attempt to find a binomial expansion, which was generally unsuccessful. Some candidates continue to be unable to distinguish between the “coefficient” and the “term” and lost a point as a result.
