| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2022 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find stationary points |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question requiring standard calculus techniques: finding f'(x) and showing it's always positive (no stationary points), finding f''(x) and solving f''(x)=0 for the inflection point, and sketching. The integration by parts question at the end is also routine A-level fare. All parts are textbook exercises with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.07f Convexity/concavity: points of inflection1.07n Stationary points: find maxima, minima using derivatives1.07p Points of inflection: using second derivative |
| 1 | 4 |
A function is defined by $f ( x ) = 2 x ^ { 3 } + 3 x - 5$.
a) Prove that the graph of $f ( x )$ does not have a stationary point.\\
b) Show that the graph of $f ( x )$ does have a point of inflection and find the coordinates of the point of inflection.\\
c) Sketch the graph of $f ( x )$.
\begin{center}
\begin{tabular}{ | l | l | }
\hline
1 & 4 \\
\hline
\end{tabular}
\end{center} Evaluate the integral $\int _ { 0 } ^ { \pi } x ^ { 2 } \sin x \mathrm {~d} x$.
\hfill \mbox{\textit{WJEC Unit 3 2022 Q13}}