| Exam Board | OCR |
|---|---|
| Module | FP1 AS (Further Pure 1 AS) |
| Year | 2021 |
| Session | June |
| Marks | 6 |
| Topic | Matrices |
| Type | Solving linear systems using matrices |
| Difficulty | Standard +0.3 This is a straightforward matrix inversion problem requiring students to write the system in matrix form, find the determinant and inverse of a 2×2 matrix, then multiply to find x and y. Part (b) requires recognizing that the determinant a²b² + 2 is always positive (hence non-zero) for real a and b, ensuring the inverse exists. While it involves parameters rather than numbers, the techniques are standard FP1 content with no novel insight required. |
| Spec | 4.03o Inverse 3x3 matrix4.03r Solve simultaneous equations: using inverse matrix |
2 You are given the system of equations
$$\begin{array} { r }
a ^ { 2 } x - 2 y = 1 \\
x + b ^ { 2 } y = 3
\end{array}$$
where $a$ and $b$ are real numbers.
\begin{enumerate}[label=(\alph*)]
\item Use a matrix method to find $x$ and $y$ in terms of $a$ and $b$.
\item Explain why the method used in part (a) works for all values of $a$ and $b$.
\end{enumerate}
\hfill \mbox{\textit{OCR FP1 AS 2021 Q2 [6]}}