| Exam Board | OCR |
|---|---|
| Module | Further Additional Pure (Further Additional Pure) |
| Year | 2023 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vector Product and Surfaces |
| Type | Sketching surface sections |
| Difficulty | Standard +0.8 This is a Further Maths question requiring visualization of 3D surfaces and their plane sections. Students must substitute plane equations into the surface equation and sketch the resulting parabolas. While the algebra is straightforward (substituting x=1 or y=1), interpreting these as curves in 3D space and sketching them correctly requires solid spatial reasoning beyond standard A-level, placing it moderately above average difficulty. |
| Spec | 8.05c Sections and contours: sketch and relate to surface |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (a) | A straight line with positive gradient |
| z = 2y + 1 clearly shown in the y-z plane | M1 |
| Answer | Marks |
|---|---|
| [2] | 2.2a |
| 1.1 | i.e. with correct axes (labelled or otherwise shown or |
| Answer | Marks |
|---|---|
| (b) | A -shaped parabola |
| 𝑧 = 𝑥2 +2𝑥 clearly shown in the x-z plane | M1 |
| Answer | Marks |
|---|---|
| [2] | 2.2a |
| 1.1 | i.e. with correct axes (labelled or otherwise shown or |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | 9 | 17 |
| 1 | 9 | 17 |
Question 1:
1 | (a) | A straight line with positive gradient
z = 2y + 1 clearly shown in the y-z plane | M1
A1
[2] | 2.2a
1.1 | i.e. with correct axes (labelled or otherwise shown or
implied by an equation in y-z)
By intercepts ( − 12 , 0) and ( 0, 1) or any other means
(b) | A -shaped parabola
𝑧 = 𝑥2 +2𝑥 clearly shown in the x-z plane | M1
A1
[2] | 2.2a
1.1 | i.e. with correct axes (labelled or otherwise shown or
implied by an equation in x-z)
By intercepts (-2,0) and (0,0) or any other means
1 | 9 | 17 | 25
1 | 9 | 17 | 251 The surface $S$ is defined for all real $x$ and $y$ by the equation $z = x ^ { 2 } + 2 x y$. The intersection of $S$ with the plane $\Pi$ gives a section of the surface. On the axes provided in the Printed Answer Booklet, sketch this section when the equation of $\Pi$ is each of the following.
\begin{enumerate}[label=(\alph*)]
\item $x = 1$
\item $y = 1$
\end{enumerate}
\hfill \mbox{\textit{OCR Further Additional Pure 2023 Q1 [4]}}