| Exam Board | OCR |
|---|---|
| Module | Further Additional Pure AS (Further Additional Pure AS) |
| Year | 2023 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vector Product and Surfaces |
| Type | Sketching surface sections |
| Difficulty | Challenging +1.8 This question requires synthesizing multiple geometric constraints to visualize and sketch a 3D surface section. Students must interpret contour information (including degenerate cases), understand the relationship between contours and cross-sections, and produce a coherent sketch. While the individual concepts are A-level appropriate, the multi-step spatial reasoning and synthesis of constraints elevates this beyond routine exercises. |
| Spec | 8.05c Sections and contours: sketch and relate to surface |
8 A surface, $C$, is given by the equation $z = \mathrm { f } ( x , y )$ for all real values of $x$ and $y$. You are given that $C$ has the following properties.
\begin{itemize}
\item The surface is continuous for all $x$ and $y$.
\item The contour $z = - 1$ is a single point on the $z$-axis.
\item For $- 1 < a < 1$, the contour $z = a$ is a pair of circles with different radiuses but each having the same centre $( 0,0 , a )$.
\item The contour $z = 1$ consists of the circle, centre $( 0,0,1 )$ and radius 1 .
\end{itemize}
Sketch a possible section of $C$ corresponding to $y = 0$.
\hfill \mbox{\textit{OCR Further Additional Pure AS 2023 Q8 [6]}}