| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2022 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Stationary points and optimisation |
| Type | Classify nature of stationary points |
| Difficulty | Standard +0.3 This is a slightly above-average A-level question combining standard calculus (finding and classifying stationary points via first/second derivative) with graphical reasoning about roots. Part (a) is routine differentiation and solving a quadratic. Part (b) requires recognizing that the equations relate to horizontal translations of the original curve and using the stationary points to count intersections with the x-axis—a nice application but still within standard A-level problem-solving expectations. |
| Spec | 1.07n Stationary points: find maxima, minima using derivatives1.07o Increasing/decreasing: functions using sign of dy/dx |
A curve $C$ has equation $f(x) = 3x^3 - 5x^2 + x - 6$.
\begin{enumerate}[label=(\alph*)]
\item Find the coordinates of the stationary points of $C$ and determine their nature. [8]
\item Without solving the equations, determine the number of distinct real roots for each of the following:
\begin{enumerate}[label=(\roman*)]
\item $3x^3 - 5x^2 + x + 1 = 0$,
\item $6x^3 - 10x^2 + 2x + 1 = 0$. [4]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 2022 Q14 [12]}}