| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Year | 2018 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Two stretches from same function |
| Difficulty | Moderate -0.5 This is a standard transformations question requiring knowledge of reflections and horizontal stretches. While it involves multiple steps (finding intercepts and stationary points for two transformations), these are routine applications of well-practiced transformation rules with no problem-solving insight required. Slightly easier than average due to being purely procedural. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Sketch: positive cubic with max and min in second quadrant, reaching both axes | B1 | Reflection in the \(y\)-axis. Needs to be a positive cubic with one maximum and one minimum in the second quadrant. Must be a curve not straight lines |
| Passes through \((-6, 0)\) and \((0, 5)\) | B1 | Allow \(-6\) and \(5\) marked in correct places; allow \((0,-6)\) and \((5,0)\) as long as in correct places. If ambiguity, sketch takes precedence but if correct coordinates seen in script, allow sign errors when transferring to sketch |
| Maximum at \((-4, 7)\) and minimum at \((-1, 3)\) in second quadrant | B1 | Must be seen as correct coordinate pairs or as numbers marked on axes. If ambiguity, sketch takes precedence but if correct coordinates seen in script, allow sign errors when transferring to sketch |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Stretch in \(x\)-direction: \((x, y) \rightarrow (kx, y)\) where \(k \neq 1\) for all points shown. No change in any \(y\)-coordinates. Must reach both axes. Curve not straight lines | B1 | A stretch in the \(x\)-direction |
| Passes through \((3, 0)\) and \((0, 5)\) | B1 | Allow \(3\) and \(5\) marked in correct places; allow \((0,3)\) and \((5,0)\) as long as in correct places. If ambiguity, sketch takes precedence |
| Minimum at \(\left(\frac{1}{2}, 3\right)\) and maximum at \((2, 7)\) in first quadrant | B1 | Must be seen as correct coordinate pairs or numbers on axes. If ambiguity, sketch takes precedence |
# Question 8:
## Part (a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Sketch: positive cubic with max and min in second quadrant, reaching both axes | B1 | Reflection in the $y$-axis. Needs to be a positive cubic with one maximum and one minimum in the second quadrant. Must be a curve not straight lines |
| Passes through $(-6, 0)$ and $(0, 5)$ | B1 | Allow $-6$ and $5$ marked in correct places; allow $(0,-6)$ and $(5,0)$ as long as in correct places. If ambiguity, sketch takes precedence but if correct coordinates seen in script, allow sign errors when transferring to sketch |
| Maximum at $(-4, 7)$ and minimum at $(-1, 3)$ in second quadrant | B1 | Must be seen as correct coordinate pairs or as numbers marked on axes. If ambiguity, sketch takes precedence but if correct coordinates seen in script, allow sign errors when transferring to sketch |
**(3 marks)**
## Part (b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Stretch in $x$-direction: $(x, y) \rightarrow (kx, y)$ where $k \neq 1$ for all points shown. No change in any $y$-coordinates. Must reach both axes. Curve not straight lines | B1 | A stretch in the $x$-direction |
| Passes through $(3, 0)$ and $(0, 5)$ | B1 | Allow $3$ and $5$ marked in correct places; allow $(0,3)$ and $(5,0)$ as long as in correct places. If ambiguity, sketch takes precedence |
| Minimum at $\left(\frac{1}{2}, 3\right)$ and maximum at $(2, 7)$ in first quadrant | B1 | Must be seen as correct coordinate pairs or numbers on axes. If ambiguity, sketch takes precedence |
**(3 marks) — Total 6**
---\begin{enumerate}[label=(\alph*)]
\item $y = \mathrm { f } ( - x )$
\item $y = \mathrm { f } ( 2 x )$
On each diagram, show clearly the coordinates of any points of intersection of the curve with the two coordinate axes and the coordinates of the stationary points.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 2018 Q8 [6]}}