| Exam Board | AQA |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Transformation of specific function type |
| Difficulty | Standard +0.3 This question tests basic knowledge of the inverse sine function's domain and range, followed by applying standard transformations (horizontal shift and reflection). Part (a) requires recall of arcsin endpoints: P=(-1,-π/2), Q=(1,π/2). Part (b) applies routine transformation rules. While it involves the less common arcsin function, the transformations themselves are mechanical and follow standard patterns taught in C3, making it slightly easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(y = -f(3x)\): horizontal stretch SF \(\frac{1}{3}\), reflection in x-axis. Key points: y-intercept \((0, -4)\), x-intercept \((2, 0)\) | B1 shape, B1 coordinates | Curve passes through \((0,-4)\) and \((2,0)\) |
| (b) \(y = f( | x | )\): reflect the part of \(f(x)\) for \(x \geq 0\) in the y-axis. Key points: \((\pm 6, 0)\), \((0, 4)\) |
| (c) \(f\!\left(-\frac{1}{2}x\right)\): Transformation 1: Stretch parallel to x-axis, scale factor 2. Transformation 2: Reflection in the y-axis | B2 each transformation fully described (direction + scale factor) | Order matters; must specify "parallel to x-axis, SF 2" and "reflection in y-axis" |
## Question 7:
**(a)** $y = -f(3x)$: horizontal stretch SF $\frac{1}{3}$, reflection in x-axis. Key points: y-intercept $(0, -4)$, x-intercept $(2, 0)$ | **B1** shape, **B1** coordinates | Curve passes through $(0,-4)$ and $(2,0)$
**(b)** $y = f(|x|)$: reflect the part of $f(x)$ for $x \geq 0$ in the y-axis. Key points: $(\pm 6, 0)$, $(0, 4)$ | **B1** right half correct, **B1** reflected left half, **B1** coordinates $(\pm 6, 0)$ and $(0,4)$
**(c)** $f\!\left(-\frac{1}{2}x\right)$: **Transformation 1:** Stretch parallel to x-axis, scale factor 2. **Transformation 2:** Reflection in the y-axis | **B2** each transformation fully described (direction + scale factor) | Order matters; must specify "parallel to x-axis, SF 2" and "reflection in y-axis"
---7
\begin{enumerate}[label=(\alph*)]
\item The sketch shows the graph of $y = \sin ^ { - 1 } x$.\\
\includegraphics[max width=\textwidth, alt={}, center]{9aac4ee4-2435-4315-a87d-fe9fa8e15665-006_819_824_456_591}
Write down the coordinates of the points $P$ and $Q$, the end-points of the graph.
\item Sketch the graph of $y = - \sin ^ { - 1 } ( x - 1 )$.
\end{enumerate}
\hfill \mbox{\textit{AQA C3 Q7}}