Moderate -0.3 This is a straightforward quotient rule application with polynomial functions. While it requires careful algebraic manipulation and simplification over 6 marks, it's a standard textbook exercise with no conceptual difficulty—students simply apply the quotient rule formula and simplify to match the given form. Slightly easier than average due to its routine nature.
5. Given that
$$y = \frac { 5 x ^ { 2 } - 10 x + 9 } { ( x - 1 ) ^ { 2 } } \quad x \neq 1$$
show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { k } { ( x - 1 ) ^ { 3 } }\), where \(k\) is a constant to be found.
(6)
5. Given that
$$y = \frac { 5 x ^ { 2 } - 10 x + 9 } { ( x - 1 ) ^ { 2 } } \quad x \neq 1$$
show that $\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { k } { ( x - 1 ) ^ { 3 } }$, where $k$ is a constant to be found.\\
(6)\\
\hfill \mbox{\textit{Edexcel P3 2018 Q5 [6]}}