| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2020 |
| Session | June |
| Marks | 8 |
| Topic | Tangents, normals and gradients |
| Type | Find tangent at given point (polynomial/algebraic) |
| Difficulty | Moderate -0.3 Part (a) requires solving 3x - 2√x = 8x - 16 by substituting u = √x to get a quadratic, which is a standard technique but involves multiple algebraic steps. Part (b) is straightforward identification of inequalities from a diagram. Overall slightly easier than average due to routine algebraic manipulation with no novel problem-solving required. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.02i Represent inequalities: graphically on coordinate plane1.02q Use intersection points: of graphs to solve equations |
\includegraphics{figure_3}
Figure 3 shows a sketch of the curve $C$ with equation $y = 3x - 2\sqrt{x}$, $x \geqslant 0$ and the line $l$ with equation $y = 8x - 16$
The line cuts the curve at point $A$ as shown in Figure 3.
\begin{enumerate}[label=(\alph*)]
\item Using algebra, find the $x$ coordinate of point $A$. [5]
\item \includegraphics{figure_4}
The region $R$ is shown unshaded in Figure 4. Identify the inequalities that define $R$. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2020 Q10 [8]}}