| Date | May 2013 | Marks available | 2 | Reference code | 13M.2.sl.TZ1.3 |
| Level | SL only | Paper | 2 | Time zone | TZ1 |
| Command term | Find | Question number | 3 | Adapted from | N/A |
Question
In the expansion of \({(3x - 2)^{12}}\) , the term in \({x^5}\) can be expressed as \(\left( {\begin{array}{*{20}{c}}
{12}\\
r
\end{array}} \right) \times {(3x)^p} \times {( - 2)^q}\) .
(a) Write down the value of \(p\) , of \(q\) and of \(r\) .
(b) Find the coefficient of the term in \({x^5}\) .
Write down the value of \(p\) , of \(q\) and of \(r\) .
Find the coefficient of the term in \({x^5}\) .
Markscheme
(a) \(p = 5\) , \(q = 7\) , \(r = 7\) (accept \(r = 5\)) A1A1A1 N3
[3 marks]
(b) correct working (A1)
eg \(\left( {\begin{array}{*{20}{c}}
{12}\\
7
\end{array}} \right) \times {(3x)^5} \times {( - 2)^7}\) , \(792\) , \(243\) , \( - {2^7}\) , \(24634368\)
coefficient of term in \({x^5}\) is \( - 24634368\) A1 N2
Note: Do not award the final A1 for an answer that contains \(x\).
[2 marks]
Total [5 marks]
\(p = 5\) , \(q = 7\) , \(r = 7\) (accept \(r = 5\)) A1A1A1 N3
[3 marks]
correct working (A1)
eg \(\left( {\begin{array}{*{20}{c}}
{12}\\
7
\end{array}} \right) \times {(3x)^5} \times {( - 2)^7}\) , \(792\) , \(243\) , \( - {2^7}\) , \(24634368\)
coefficient of term in \({x^5}\) is \( - 24634368\) A1 N2
Note: Do not award the final A1 for an answer that contains \(x\).
[2 marks]
Total [5 marks]
Examiners report
Candidates frequently made reasonable attempts at both parts of the question. Those who correctly stated the values in (a) were generally successful in part (b). Many candidates offered the whole term rather than the coefficient in part (b) and lost the final mark. Some candidates appeared to have misread the order of the variables, stating that \(p = 7\) (instead of \(r = 7\) ), \(q = 5\) (instead of \(p = 5\)) and \(r = 5\) or \(7\) (instead of \(q = 5\) or \(7\)). A large number of candidates did not make the connection between parts (a) and (b).
Candidates frequently made reasonable attempts at both parts of the question. Those who correctly stated the values in (a) were generally successful in part (b). Many candidates offered the whole term rather than the coefficient in part (b) and lost the final mark. Some candidates appeared to have misread the order of the variables, stating that \(p = 7\) (instead of \(r = 7\) ), \(q = 5\) (instead of \(p = 5\)) and \(r = 5\) or \(7\) (instead of \(q = 5\) or \(7\)). A large number of candidates did not make the connection between parts (a) and (b).
Candidates frequently made reasonable attempts at both parts of the question. Those who correctly stated the values in (a) were generally successful in part (b). Many candidates offered the whole term rather than the coefficient in part (b) and lost the final mark. Some candidates appeared to have misread the order of the variables, stating that \(p = 7\) (instead of \(r = 7\) ), \(q = 5\) (instead of \(p = 5\)) and \(r = 5\) or \(7\) (instead of \(q = 5\) or \(7\)). A large number of candidates did not make the connection between parts (a) and (b).
