| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2020 |
| Session | June |
| Marks | 4 |
| Topic | Function Transformations |
| Type | Stationary points after transformation |
| Difficulty | Moderate -0.8 This question tests basic transformations of functions (vertical stretch, horizontal translation) and interpretation of graphical features (turning points, roots, derivative signs). All parts require direct application of standard transformation rules with no problem-solving or multi-step reasoning. The concepts are fundamental A-level content, making this easier than average, though not trivial since it requires understanding of function notation and transformations. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
\includegraphics{figure_1}
Figure 1 shows a sketch of the curve with equation $y = \text{g}(x)$.
The curve has a single turning point, a minimum, at the point $M(4, -1.5)$.
The curve crosses the $x$-axis at two points, $P(2, 0)$ and $Q(7, 0)$.
The curve crosses the $y$-axis at a single point $R(0, 5)$.
\begin{enumerate}[label=(\alph*)]
\item State the coordinates of the turning point on the curve with equation $y = 2\text{g}(x)$. [1]
\item State the largest root of the equation
$$\text{g}(x + 1) = 0$$ [1]
\item State the range of values of $x$ for which $\text{g}'(x) \leqslant 0$ [1]
\end{enumerate}
Given that the equation $\text{g}(x) + k = 0$, where $k$ is a constant, has no real roots,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item state the range of possible values for $k$. [1]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2020 Q4 [4]}}