| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matrices |
| Type | Matrix powers and patterns |
| Difficulty | Standard +0.3 This is a straightforward FP1 matrix question requiring matrix multiplication and algebraic manipulation. Part (i) is routine computation, and part (ii) uses a standard technique (multiplying the given relation by A^{-1}) that students are explicitly taught. While it's Further Maths content, it requires no novel insight and follows a predictable pattern, making it slightly easier than average overall. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar4.03o Inverse 3x3 matrix |
The matrices $\mathbf{A}$ and $\mathbf{I}$ are given by $\mathbf{A} = \begin{pmatrix} 1 & 2 \\ 1 & 3 \end{pmatrix}$ and $\mathbf{I} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$ respectively.
\begin{enumerate}[label=(\roman*)]
\item Find $\mathbf{A}^2$ and verify that $\mathbf{A}^2 = 4\mathbf{A} - \mathbf{I}$. [4]
\item Hence, or otherwise, show that $\mathbf{A}^{-1} = 4\mathbf{I} - \mathbf{A}$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR FP1 Q2 [6]}}