| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 1 (Further Pure Core 1) |
| Year | 2020 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | 3x3 Matrices |
| Type | Transformation mapping problems |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths question testing basic 3D matrix operations: matrix powers (which reveals a pattern after A²), identifying a rotation from a matrix, writing down a simple reflection matrix, and applying it to a point. While 3D transformations are beyond standard A-level, these are routine exercises for Further Maths students with no novel problem-solving required. |
| Spec | 4.03a Matrix language: terminology and notation4.03b Matrix operations: addition, multiplication, scalar4.03f Linear transformations 3D: reflections and rotations about axes |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (a) | A4 = I |
| Answer | Marks |
|---|---|
| (b) | Rotation |
| Clockwise 900 about x-axis | B1 |
| B1 | 2.2a |
| 2.2a | Or 2700 anticlockwise |
| Answer | Marks |
|---|---|
| (c) | −1 0 0 |
| Answer | Marks | Guidance |
|---|---|---|
| 0 0 1 | B1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| (d) | (−2, 3, 4) | B1 |
Question 3:
3 | (a) | A4 = I | B1 | 1.1 | Accept 3×3 matrix
[1]
(b) | Rotation
Clockwise 900 about x-axis | B1
B1 | 2.2a
2.2a | Or 2700 anticlockwise
Accept radians
[2]
(c) | −1 0 0
0 1 0
0 0 1 | B1 | 1.1 | All correct
[1]
(d) | (−2, 3, 4) | B1 | 1.1 | −1 0 02 −2
0 1 0 3 = 3
0 0 14 4
Allow vector as answer
[1]3 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 $\mathbf { A }$ represents.
The matrix $\mathbf { B }$ represents a reflection in the plane $x = 0$.
\item Write down the matrix $\mathbf { B }$.
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 2020 Q3 [5]}}