| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2010 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Show dy/dx equals given expression |
| Difficulty | Challenging +1.2 This is an implicit differentiation question requiring standard technique (part a), algebraic manipulation with the gradient condition (part b), and curve sketching (part c). While it involves multiple parts and some algebraic complexity, the techniques are all standard A-level methods with no novel insight required. The AEA context and multi-step nature elevate it above average, but it remains a straightforward application of learned techniques. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.07s Parametric and implicit differentiation |
3.The curve $C$ has equation
$$x ^ { 2 } + y ^ { 2 } + f x y = g ^ { 2 }$$
where $f$ and $g$ are constants and $g \neq 0$ .
\begin{enumerate}[label=(\alph*)]
\item Find an expression in terms of $\alpha , \beta$ and $f$ for the gradient of $C$ at the point $( \alpha , \beta )$ .
Given that $f < 2$ and $f \neq - 2$ and that the gradient of $C$ at the point $( \alpha , \beta )$ is 1 ,
\item show that $\alpha = - \beta = \frac { \pm g } { \sqrt { } ( 2 - f ) }$ .
Given that $f = - 2$ ,
\item sketch $C$ .
\end{enumerate}
\hfill \mbox{\textit{Edexcel AEA 2010 Q3 [11]}}