| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Solving quadratics and applications |
| Type | Quadratic in higher integer powers |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question testing standard techniques: (a) is a disguised quadratic via substitution u=x³, (b) requires routine differentiation and solving a cubic (which factors nicely), and (c) applies the second derivative test mechanically. All parts follow textbook procedures with no conceptual challenges, making it slightly easier than average but not trivial due to the algebraic manipulation required. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.07n Stationary points: find maxima, minima using derivatives1.07p Points of inflection: using second derivative |
\begin{enumerate}[label=(\alph*)]
\item Determine the two real roots of the equation $8x^6 + 7x^3 - 1 = 0$. [3]
\item Determine the coordinates of the stationary points on the curve $y = 8x^7 + \frac{49}{4}x^4 - 7x$. [4]
\item For each of the stationary points, use the value of $\frac{d^2y}{dx^2}$ to determine whether it is a maximum or a minimum. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q6 [11]}}