| Exam Board | AQA |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2022 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Identify transformation from equations |
| Difficulty | Moderate -0.8 This question tests understanding of function transformations, specifically identifying that y = 9/x² is a vertical stretch of y = 1/x² by scale factor 3. While students must recognize both transformations work (y-stretch by 3 OR x-stretch by 1/3), this is a standard A-level concept requiring recall and basic algebraic verification rather than problem-solving. The 3-mark allocation reflects explanation requirements, but the mathematics itself is routine. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Sketches a branch of the curve with correct shape in 1st or 2nd quadrant with correct asymptotes and not touching the axes | M1 (AO 1.2) | |
| Sketches a fully correct curve with correct asymptotes and not touching the axes | A1 (AO 1.1b) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Describes a stretch of scale factor 3 or 9 in either direction | M1 (AO 2.4) | |
| The curve can be stretched in the \(y\)-direction by a scale factor of 9, i.e. \(9f(x)\); OR the curve can be stretched in the \(x\)-direction by a scale factor of 3, i.e. \(f\!\left(\frac{x}{3}\right)\) | A1 (AO 2.4) | Explains that the curve can be stretched in the \(y\)-direction by scale factor of 9, or stretched in the \(x\)-direction by scale factor of 3 |
| Both correct with conclusion that Beth and Paul are both correct | R1 (AO 2.2a) | Must explain both transformations AND conclude both are correct |
| Subtotal: 3 marks | Question 8 Total: 5 marks |
## Question 8(a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Sketches a branch of the curve with correct shape in 1st or 2nd quadrant with correct asymptotes and not touching the axes | M1 (AO 1.2) | |
| Sketches a fully correct curve with correct asymptotes and not touching the axes | A1 (AO 1.1b) | |
**Subtotal: 2 marks**
---
## Question 8(b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Describes a stretch of scale factor 3 or 9 in either direction | M1 (AO 2.4) | |
| The curve can be stretched in the $y$-direction by a scale factor of 9, i.e. $9f(x)$; OR the curve can be stretched in the $x$-direction by a scale factor of 3, i.e. $f\!\left(\frac{x}{3}\right)$ | A1 (AO 2.4) | Explains that the curve can be stretched in the $y$-direction by scale factor of 9, or stretched in the $x$-direction by scale factor of 3 |
| Both correct with conclusion that Beth and Paul are both correct | R1 (AO 2.2a) | Must explain both transformations AND conclude both are correct |
**Subtotal: 3 marks | Question 8 Total: 5 marks**
---8
\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of $y = \frac { 1 } { x ^ { 2 } }$\\
\includegraphics[max width=\textwidth, alt={}, center]{ad6590e8-6673-45ca-bef3-a14716978827-12_1273_1083_404_482}
8
\item The graph of $y = \frac { 1 } { x ^ { 2 } }$ can be transformed onto the graph of $y = \frac { 9 } { x ^ { 2 } }$ using a stretch in one direction.
Beth thinks the stretch should be in the $y$-direction.\\
Paul thinks the stretch should be in the $x$-direction.\\
State, giving reasons for your answer, whether Beth is correct, Paul is correct, both are correct or neither is correct.\\[0pt]
[3 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 2 2022 Q8 [5]}}