| Exam Board | Edexcel |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2022 |
| Session | October |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Solutions from graphical analysis |
| Difficulty | Moderate -0.8 This is a straightforward graphical interpretation question requiring students to read information directly from a given curve. Part (a) involves identifying where the curve is below a horizontal line, (b) requires understanding horizontal scaling, and (c) involves reflection in the y-axis. All parts are routine applications of basic transformation concepts with no algebraic manipulation or problem-solving insight required—easier than average A-level questions. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(-1 < x < 2\) | M1A1 | M1 for one correct end of inside region; A1 for \(-1 < x < 2\) or equivalent e.g. \((-1,2)\); do not allow two separate inequalities without AND |
| \(x < -4\), \(x > 3\) | B1 | Ignore use of OR/AND between the regions |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(x = 1.5\) | B1 | Or \(\frac{3}{2}\); condone \((1.5, 6)\) or \(x=1.5\), \(y=6\) only if y-coordinate is correct |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Sketch reflected in y-axis; higher maximum in quadrant 1, lower maximum in quadrant 2 | B1 | Do not be concerned which side of y-axis the minimum turning point is |
| Either two correct coordinate pairs or all x-coordinates correct or all y-coordinates correct; labelled \((-3,6)\), \((-2,6)\), \((1,6)\), \((4,6)\) | B1 | See guidance on coordinate precedence |
| All four coordinates correct | B1 | Sketch with labelled coordinates in main working takes precedence over figure |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(-3\), \(x\), \(-2\) | B1 | — |
## Question 7(a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $-1 < x < 2$ | M1A1 | M1 for one correct end of inside region; A1 for $-1 < x < 2$ or equivalent e.g. $(-1,2)$; do not allow two separate inequalities without AND |
| $x < -4$, $x > 3$ | B1 | Ignore use of OR/AND between the regions |
## Question 7(b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $x = 1.5$ | B1 | Or $\frac{3}{2}$; condone $(1.5, 6)$ or $x=1.5$, $y=6$ only if y-coordinate is correct |
## Question 7(c)(i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Sketch reflected in y-axis; higher maximum in quadrant 1, lower maximum in quadrant 2 | B1 | Do not be concerned which side of y-axis the minimum turning point is |
| Either two correct coordinate pairs **or** all x-coordinates correct **or** all y-coordinates correct; labelled $(-3,6)$, $(-2,6)$, $(1,6)$, $(4,6)$ | B1 | See guidance on coordinate precedence |
| All four coordinates correct | B1 | Sketch with labelled coordinates in main working takes precedence over figure |
## Question 7(c)(ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $-3$, $x$, $-2$ | B1 | — |7.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{db979349-3415-420f-a39f-8cc8c24a69d0-16_732_1071_248_497}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows the curve with equation $y = \mathrm { f } ( x )$.\\
The points $P ( - 4,6 ) , Q ( - 1,6 ) , R ( 2,6 )$ and $S ( 3,6 )$ lie on the curve.
\begin{enumerate}[label=(\alph*)]
\item Using Figure 1, find the range of values of $x$ for which
$$\mathrm { f } ( x ) < 6$$
\item State the largest solution of the equation
$$f ( 2 x ) = 6$$
\item \begin{enumerate}[label=(\roman*)]
\item Sketch the curve with equation $y = \mathrm { f } ( - x )$.
On your sketch, state the coordinates of the points to which $P , Q , R$ and $S$ are transformed.
\item Hence find the set of values of $x$ for which
$$f ( - x ) \geqslant 6 \text { and } x < 0$$
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{Edexcel P1 2022 Q7 [8]}}