| Exam Board | OCR |
|---|---|
| Module | FP1 AS (Further Pure 1 AS) |
| Year | 2017 |
| Session | Specimen |
| Marks | 6 |
| Topic | Matrices |
| Type | Applied matrix modeling problems |
| Difficulty | Moderate -0.3 This is a straightforward system of linear equations problem requiring matrix setup and solution. Part (i) involves translating word problems into matrix form (standard FP1 skill), part (ii) is routine matrix solving (likely by row reduction or inverse), and part (iii) requires basic interpretation of rounding effects. While it involves multiple steps, each component is a standard textbook exercise with no novel insight required, making it slightly easier than average. |
| Spec | 4.03r Solve simultaneous equations: using inverse matrix |
At the beginning of the year John had a total of £2000 in three different accounts. He has twice as much money in the current account as in the savings account.
• The current account has an interest rate of 2.5% per annum.
• The savings account has an interest rate of 3.7% per annum.
• The supersaver account has an interest rate of 4.9% per annum.
John has predicted that he will earn a total interest of £92 by the end of the year.
\begin{enumerate}[label=(\roman*)]
\item Model this situation as a matrix equation. [2]
\item Find the amount that John had in each account at the beginning of the year. [2]
\item In fact, the interest John will receive is £92 **to the nearest pound**. Explain how this affects the calculations. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR FP1 AS 2017 Q6 [6]}}