| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2022 |
| Session | February |
| Marks | 8 |
| Topic | Stationary points and optimisation |
| Type | Prove curve has no turning points |
| Difficulty | Moderate -0.3 Part (i) is a straightforward quadratic-in-disguise (substituting u=x²) requiring basic algebraic manipulation. Part (ii) is routine differentiation using the power rule. Part (iii) connects these by setting dy/dx=0, which gives the equation from part (i), making it a guided multi-part question. While it requires recognizing the connection between parts, each individual step is standard A-level technique with no novel problem-solving required. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.07i Differentiate x^n: for rational n and sums1.07n Stationary points: find maxima, minima using derivatives |
\begin{enumerate}[label=(\roman*)]
\item Solve the equation $x^4 - 10x^2 + 25 = 0$. [4]
\item Given that $y = \frac{2}{5}x^5 - \frac{20}{3}x^3 + 50x + 3$, find $\frac{dy}{dx}$. [2]
\item Hence find the number of stationary points on the curve $y = \frac{2}{5}x^5 - \frac{20}{3}x^3 + 50x + 3$. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2022 Q2 [8]}}