| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2020 |
| Session | June |
| Marks | 9 |
| Topic | Curve Sketching |
| Type | Parameter values from curve properties |
| Difficulty | Standard +0.3 Part (a) is routine curve sketching of a transformed reciprocal function requiring identification of asymptotes and intercepts. Part (b) requires setting up a quadratic from the intersection condition and applying the discriminant, which is a standard technique. The algebra is straightforward and the problem-solving approach is well-practiced, making this slightly easier than average. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.02o Sketch reciprocal curves: y=a/x and y=a/x^2 |
\begin{enumerate}[label=(\alph*)]
\item Sketch the curve with equation
$$y = k - \frac{1}{2x}$$
where $k$ is a positive constant
State, in terms of $k$, the coordinates of any points of intersection with the coordinate axes and the equation of the horizontal asymptote. [3]
\end{enumerate}
The straight line $l$ has equation $y = 2x + 3$
Given that $l$ cuts the curve in two distinct places,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the range of values of $k$, writing your answer in set notation. [6]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2020 Q11 [9]}}