20N.2.SL.TZ0.S_5

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

valid approach for expansion (must have correct substitution for parameters, but accept an incorrect value for $r$).       (M1)

eg     $\left(\begin{array}{c}9\\ r\end{array}\right){\left(3x^2\right)}^{9-r}{\left(-\frac{k}{x}\right)}^r , {\left(3x^2\right)}^9+\left(\begin{array}{c}9\\ 1\end{array}\right){\left(3x^2\right)}^8{\left(-\frac{k}{x}\right)}^1+\left(\begin{array}{c}9\\ 2\end{array}\right){\left(3x^2\right)}^7{\left(-\frac{k}{x}\right)}^2+\dots$

valid attempt to identify correct term       (M1)

eg     $2\left(9-r\right)-r=6 , {\left(x^2\right)}^r{\left(x^{-1}\right)}^{9-r}=x^6$

identifying correct term (may be indicated in expansion)       (A1)

eg     $r=4, r=5$

correct term or coefficient in binominal expansion       (A1)

eg     $\left(\begin{array}{c}9\\ 4\end{array}\right){\left(3x^2\right)}^5{\left(-\frac{k}{x}\right)}^4 , 126\left(243x^{10}\right)\left(\frac{k^4}{x^4}\right), 30618k^4$

correct equation in $k$       (A1)

eg     $\left(\begin{array}{c}9\\ 4\end{array}\right)\left(243\right)\left(k^4\right)x^6=6048x^6 , 30618k^4=6048$

$k=\frac{2}{3}$ (exact)  $0.667$       A1  N3 

 

Note: Do not award A1 if additional answers given.

[6 marks]

[N/A]