| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 1 (Further Pure Core 1) |
| Year | 2021 |
| Session | June |
| Marks | 5 |
| Topic | Linear transformations |
| Type | 3D transformation matrices |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths question testing basic 3D transformation concepts. Part (a) requires matrix multiplication (recognizing A² then squaring again), (b) needs identification of a rotation about the x-axis, (c) is immediate recall of a reflection matrix, and (d) is simple matrix-vector multiplication. While it's Further Maths content, all parts are routine applications with no problem-solving or insight required, making it slightly easier than an average A-level question overall. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear4.03f Linear transformations 3D: reflections and rotations about axes |
2\\
You are given the matrix $\mathbf { A } = \left( \begin{array} { c c c } 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & - 1 & 0 \end{array} \right)$.
\begin{enumerate}[label=(\alph*)]
\item Find $\mathbf { A } ^ { 4 }$.
\item Describe the transformation that A represents.
The matrix $\mathbf { B }$ represents a reflection in the plane $x = 0$.
\item Write down the matrix $B$.
The point $P$ has coordinates $( 2,3,4 )$. The point $P ^ { \prime }$ is the image of $P$ under the transformation represented by $\mathbf { B }$.
\item Find the coordinates of $P ^ { \prime }$.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Pure Core 1 2021 Q2 [5]}}