| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2024 |
| Session | September |
| Marks | 5 |
| Topic | Product & Quotient Rules |
| Type | Find equation of tangent |
| Difficulty | Moderate -0.3 This is a straightforward application of the quotient rule followed by finding a tangent line equation. While it requires multiple steps (differentiate, evaluate at x=2, find y-coordinate, use point-slope form, rearrange), each step is routine and the question type is a standard textbook exercise with no conceptual challenges or novel insights required. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07m Tangents and normals: gradient and equations1.07q Product and quotient rules: differentiation |
\begin{enumerate}
\item The curve $C$ has equation
\end{enumerate}
$$y = \frac { 5 x ^ { 3 } - 8 } { 2 x ^ { 2 } } \quad x > 0$$
Find an equation for the tangent to $C$ at $x = 2$ writing your answer in the form\\
$a x + b y + c = 0$, where $a , b$ and $c$ are integers.\\
(5)
\section*{(Total for Question 2 is 5 marks)}
\hfill \mbox{\textit{SPS SPS SM Pure 2024 Q2 [5]}}