| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Single transformation sketch |
| Difficulty | Moderate -0.8 This question tests basic understanding of function transformations (horizontal translation and identifying vertical stretch/translation). Part (a) requires applying a standard horizontal shift rule to three key points. Part (b) involves recognizing a transformation from a diagram, which is straightforward pattern matching. Both parts are routine applications of A-level core content with no problem-solving or novel insight required. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Concave up curve and y-coordinate of minimum = –4 | B1 | AO1 |
| x-coordinate of minimum = –6 | B1 | AO1 |
| Both points of intersection with x-axis | B1 | AO1 |
| (b) \(y = -\frac{1}{r}f(x)\) | B2 | AO2 |
| If B2 not awarded: \(y = rf(x)\) with \(r\) negative | (B1) | (AO2) |
**(a)** Concave up curve and y-coordinate of minimum = –4 | B1 | AO1
x-coordinate of minimum = –6 | B1 | AO1
Both points of intersection with x-axis | B1 | AO1
**(b)** $y = -\frac{1}{r}f(x)$ | B2 | AO2
If B2 not awarded: $y = rf(x)$ with $r$ negative | (B1) | (AO2)
**Total: [5]**
---Figure 1 shows a sketch of the graph of $y = f(x)$. The graph has a minimum point at $(-3, -4)$ and intersects the $x$-axis at the points $(-8, 0)$ and $(2, 0)$.
\includegraphics{figure_1}
\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of $y = f(x + 3)$, indicating the coordinates of the stationary point and the coordinates of the points of intersection of the graph with the $x$-axis. [3]
\item Figure 2 shows a sketch of the graph having one of the following equations with an appropriate value of either $p$, $q$ or $r$.
$y = f(px)$, where $p$ is a constant
$y = f(x) + q$, where $q$ is a constant
$y = rf(x)$, where $r$ is a constant
\includegraphics{figure_2}
Write down the equation of the graph sketched in Figure 2, together with the value of the corresponding constant. [2]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 Q7 [5]}}