| Exam Board | AQA |
|---|---|
| Module | Paper 1 (Paper 1) |
| Year | 2024 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Horizontal stretch y = f(ax) |
| Difficulty | Standard +0.3 This question tests basic curve sketching of a cubic with given roots and understanding of horizontal transformations. Part (a) requires identifying roots at 0, a, and 6, determining the cubic shape (positive leading coefficient), which is routine. Part (b) applies the transformation x → -2x, requiring students to find new roots and recognize the reflection/compression, which is a standard A-level technique but slightly beyond pure recall. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| 11(a) | Draws cubic graph with exactly | |
| two turning points | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| points. | 1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| on the y-axis. | 1.1b | R1 |
| Subtotal | 3 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 11(b) | Draws cubic graph of correct |
| Answer | Marks | Guidance |
|---|---|---|
| the x-direction. | 3.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | 2.2a | R1 |
| Subtotal | 2 | |
| Question 11 Total | 5 | |
| Q | Marking instructions | AO |
Question 11:
--- 11(a) ---
11(a) | Draws cubic graph with exactly
two turning points | 1.1a | M1
Draws cubic graph of correct
orientation passing through the
origin and positive x-axis at two
points. | 1.1b | A1
Draws fully correct sketch with
x-axis intercepts correctly
labelled a and 6. Ignore labelling
on the y-axis. | 1.1b | R1
Subtotal | 3
Q | Marking instructions | AO | Marks | Typical solution
--- 11(b) ---
11(b) | Draws cubic graph of correct
orientation passing through the
origin and negative x-axis at two
points.
Or
Substitutes –2x into f(x)
Or
Describes the reflection in
the y-axis and a stretch of scale
1
factor in the x-direction
2
1
or a stretch scale factor − in
2
the x-direction. | 3.1a | M1
Draws fully correct sketch with
x-axis intercepts correctly
a
labelled − and -3.
2 | 2.2a | R1
Subtotal | 2
Question 11 Total | 5
Q | Marking instructions | AO | Marks | Typical solutionIt is given that
$$f(x) = x(x - a)(x - 6)$$
where $0 < a < 6$
\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of $y = f(x)$ on the axes below.
[3 marks]
\includegraphics{figure_11a}
\item Sketch the graph of $y = f(-2x)$ on the axes below.
[2 marks]
\includegraphics{figure_11b}
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 1 2024 Q11 [5]}}