| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Session | Specimen |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Sketch single transformation from given curve |
| Difficulty | Moderate -0.8 This is a straightforward transformations question requiring only recall of standard rules (vertical stretch, horizontal translation, derivative sign analysis, and vertical translation). All parts involve direct application of transformation formulas with no problem-solving or novel insight needed. Easier than average A-level content. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \((4, -3)\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(x = 6\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(x,\ 4\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(k > 1.5\) | B1 |
## Question 4:
**Part (a):**
| Answer/Working | Mark | Guidance |
|---|---|---|
| $(4, -3)$ | B1 | |
**Part (b):**
| Answer/Working | Mark | Guidance |
|---|---|---|
| $x = 6$ | B1 | |
**Part (c):**
| Answer/Working | Mark | Guidance |
|---|---|---|
| $x,\ 4$ | B1 | |
**Part (d):**
| Answer/Working | Mark | Guidance |
|---|---|---|
| $k > 1.5$ | B1 | |
---4.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{fa7abe9f-f5c0-4578-afd1-73176c717536-08_755_775_248_662}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a sketch of the curve with equation $y = g ( x )$.\\
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 $y = 2 \mathrm {~g} ( x )$.
\item State the largest root of the equation
$$g ( x + 1 ) = 0$$
\item State the range of values of $x$ for which $\mathrm { g } ^ { \prime } ( x ) \leqslant 0$
Given that the equation $\mathrm { g } ( x ) + k = 0$, where $k$ is a constant, has no real roots,
\item state the range of possible values for $k$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel AS Paper 1 Q4 [4]}}