| Exam Board | AQA |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2023 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Stationary points and optimisation |
| Type | Classify nature of stationary points |
| Difficulty | Moderate -0.8 This question tests understanding of stationary points and the distinction between f'(x)=0 being sufficient for a turning point versus necessary. While conceptually important, it requires only sketching curves through given points with specified derivative properties—no calculation, algebraic manipulation, or extended reasoning. The main challenge is recognizing that f'(4)=0 doesn't guarantee a turning point (e.g., point of inflection), which is a standard AS-level concept but presented in an accessible visual format. |
| Spec | 1.07n Stationary points: find maxima, minima using derivatives1.07o Increasing/decreasing: functions using sign of dy/dx |
| Answer | Marks |
|---|---|
| 9(a) | Draws a graph through the |
| Answer | Marks | Guidance |
|---|---|---|
| (4, 5) | 1.1b | B1 |
| Subtotal | 1 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 9(b) | Draws a graph through the |
| Answer | Marks | Guidance |
|---|---|---|
| (4, 5) | 2.2b | B1 |
| Subtotal | 1 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 9(c) | Draws a graph through the |
| Answer | Marks | Guidance |
|---|---|---|
| maximum nor a minimum. | 2.2b | B1 |
| Subtotal | 1 | |
| Question 9 Total | 3 | |
| Q | Marking instructions | AO |
Question 9:
--- 9(a) ---
9(a) | Draws a graph through the
given points with a maximum at
(4, 5) | 1.1b | B1
Subtotal | 1
Q | Marking instructions | AO | Marks | Typical solution
--- 9(b) ---
9(b) | Draws a graph through the
given points with a minimum at
(4, 5) | 2.2b | B1
Subtotal | 1
Q | Marking instructions | AO | Marks | Typical solution
--- 9(c) ---
9(c) | Draws a graph through the
given points with a stationary
point at (4, 5) that is neither a
maximum nor a minimum. | 2.2b | B1
Subtotal | 1
Question 9 Total | 3
Q | Marking instructions | AO | Marks | Typical solutionA continuous curve has equation $y = f(x)$
The curve passes through the points $A(2, 1)$, $B(4, 5)$ and $C(6, 1)$
It is given that $f'(4) = 0$
Jasmin made two statements about the nature of the curve $y = f(x)$ at the point $B$:
Statement 1: There is a turning point at $B$
Statement 2: There is a maximum point at $B$
\begin{enumerate}[label=(\alph*)]
\item Draw a sketch of the curve $y = f(x)$ such that Statement 1 is correct and Statement 2 is correct.
[1 mark]
\item Draw a sketch of the curve $y = f(x)$ such that Statement 1 is correct and Statement 2 is not correct.
[1 mark]
\item Draw a sketch of the curve $y = f(x)$ such that Statement 1 is not correct and Statement 2 is not correct.
[1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 1 2023 Q9 [3]}}