| Exam Board | AQA |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2024 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find derivative of simple polynomial (integer powers) |
| Difficulty | Moderate -0.8 Part (a) is straightforward differentiation of a quadratic (expand then differentiate or use product rule). Part (b) requires sketching the gradient function (a linear function) and finding axis intercepts, which is routine for AS-level but tests understanding of the relationship between a function and its derivative. This is a standard textbook-style question with no problem-solving insight required. |
| Spec | 1.07c Sketch gradient function: for given curve1.07i Differentiate x^n: for rational n and sums |
| Answer | Marks |
|---|---|
| 9(a) | Expands bracket and |
| Answer | Marks | Guidance |
|---|---|---|
| term correct | 3.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| Obtains 6 – 2x | 1.1b | A1 |
| Subtotal | 2 | |
| Q | Marking instructions | AO |
| Answer | Marks | Guidance |
|---|---|---|
| 9(b) | Obtains y intercept at 6 | 1.1b |
| Answer | Marks | Guidance |
|---|---|---|
| 6 on the x-axis | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| at approximately (3, 0) | 1.1b | A1 |
| Subtotal | 3 | |
| Question 9 Total | 5 | |
| Q | Marking instructions | AO |
Question 9:
--- 9(a) ---
9(a) | Expands bracket and
differentiates with at least one
term correct | 3.1a | M1 | f(x) = 6x – x2
f ′(x) = 6 – 2x
Obtains 6 – 2x | 1.1b | A1
Subtotal | 2
Q | Marking instructions | AO | Marks | Typical solution
--- 9(b) ---
9(b) | Obtains y intercept at 6 | 1.1b | B1 | Cuts x-axis at (3, 0)
Cuts y-axis at (0, 6)
Draws a straight line graph from
a point between 0 and 10 on the
y-axis to a point between 0 and
6 on the x-axis | 1.1a | M1
Obtains x intercept at 3 with
straight line graph cutting x-axis
at approximately (3, 0) | 1.1b | A1
Subtotal | 3
Question 9 Total | 5
Q | Marking instructions | AO | Marks | Typical solutionA curve has equation $y = f(x)$ where
$$f(x) = x(6 - x)$$
\begin{enumerate}[label=(\alph*)]
\item Find $f'(x)$
[2 marks]
\item The diagram below shows the graph of $y = f(x)$
On the same diagram sketch the gradient function for this curve, stating the coordinates of any points where the gradient function cuts the axes.
[3 marks]
\includegraphics{figure_9}
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 1 2024 Q9 [5]}}