| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2024 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Stationary points and optimisation |
| Type | Classify nature of stationary points |
| Difficulty | Moderate -0.3 This is a straightforward calculus question requiring differentiation to find stationary points (solving a quadratic), second derivative test for nature, and identifying decreasing intervals. All techniques are standard AS-level procedures with no novel problem-solving required, making it slightly easier than average but not trivial due to the multi-step nature and 10 total marks. |
| Spec | 1.02h Express solutions: using 'and', 'or', set and interval notation1.07n Stationary points: find maxima, minima using derivatives1.07o Increasing/decreasing: functions using sign of dy/dx |
A curve C has equation $y = -x^3 + 12x - 20$.
\begin{enumerate}[label=(\alph*)]
\item Find the coordinates of the stationary points of C and determine their nature. [7]
\item Determine the range of values of $x$ for which the curve is decreasing. Give your answer in set notation. [3]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 2024 Q12 [10]}}