| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2016 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Describe rotation from matrix |
| Difficulty | Standard +0.3 This is a straightforward Further Maths F1 question on matrix transformations. Part (a) requires recognizing a rotation matrix (standard form with ±1/√2 entries), part (b) uses the rotation angle to find when A^n = I (simple calculation), and part (c) involves basic matrix multiplication BA = C, solved by B = CA^(-1). All techniques are routine for F1 students with no novel problem-solving required. Slightly above average difficulty (0.0) only because it's Further Maths content, but well within standard F1 exercises. |
| Spec | 4.03c Matrix multiplication: properties (associative, not commutative)4.03d Linear transformations 2D: reflection, rotation, enlargement, shear4.03o Inverse 3x3 matrix |
4.
$$\mathbf { A } = \left( \begin{array} { c c }
- \frac { 1 } { \sqrt { 2 } } & \frac { 1 } { \sqrt { 2 } } \\
- \frac { 1 } { \sqrt { 2 } } & - \frac { 1 } { \sqrt { 2 } }
\end{array} \right)$$
\begin{enumerate}[label=(\alph*)]
\item Describe fully the single geometrical transformation represented by the matrix $\mathbf { A }$.
\item Hence find the smallest positive integer value of $n$ for which
$$\mathbf { A } ^ { n } = \mathbf { I }$$
where $\mathbf { I }$ is the $2 \times 2$ identity matrix.
The transformation represented by the matrix $\mathbf { A }$ followed by the transformation represented by the matrix $\mathbf { B }$ is equivalent to the transformation represented by the matrix $\mathbf { C }$.
Given that $\mathbf { C } = \left( \begin{array} { r r } 2 & 4 \\ - 3 & - 5 \end{array} \right)$,
\item find the matrix $\mathbf { B }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2016 Q4 [8]}}