| Exam Board | OCR MEI |
|---|---|
| Module | Further Pure Core AS (Further Pure Core AS) |
| Year | 2020 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Describe 3D transformation from matrix |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths question requiring recognition of a 3D rotation matrix. Part (a) involves routine determinant calculation (det=1) and stating standard consequences (preserves volume, invertible). Part (b) requires identifying the transformation as a 90° rotation about the z-axis, which is recognizable from the block structure. While it's Further Maths content, the execution is mostly procedural with minimal problem-solving, making it slightly easier than average overall. |
| Spec | 4.03f Linear transformations 3D: reflections and rotations about axes4.03j Determinant 3x3: calculation4.03k Determinant 3x3: volume scale factor |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (a) | (i) |
| [1] | 1.1 | BC |
| 4 | (a) | (ii) |
| and orientation | B1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (b) | Rotation of 90° [anticlockwise] about Oz. |
| [1] | 1.1 |
Question 4:
4 | (a) | (i) | det M = 1 | B1
[1] | 1.1 | BC
4 | (a) | (ii) | It preserves volume
and orientation | B1
B1
[2] | 1.1
1.1
4 | (b) | Rotation of 90° [anticlockwise] about Oz. | B1
[1] | 1.1
M1
A1
no working M1A0A0
condone no check of coefft
of x4 The matrix $\mathbf { M }$ is $\left( \begin{array} { r r r } 0 & - 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{array} \right)$.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Calculate $\operatorname { det } \mathbf { M }$.
\item State two geometrical consequences of this value for the transformation associated with $\mathbf { M }$.
\end{enumerate}\item Describe fully the transformation associated with $\mathbf { M }$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Pure Core AS 2020 Q4 [4]}}