| Exam Board | WJEC |
|---|---|
| Module | Further Unit 4 (Further Unit 4) |
| Year | 2024 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | 3x3 Matrices |
| Type | Geometric interpretation of systems |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question on matrix applications. Part (a) requires recognizing that a non-zero determinant means a unique solution exists (basic matrix theory recall). Part (b) is a standard application of solving 3×3 simultaneous equations using matrices, with the context making the setup obvious. The determinant is given, so no calculation needed. While it's Further Maths content, it's a routine textbook-style application requiring no novel insight. |
| Spec | 4.03k Determinant 3x3: volume scale factor4.03r Solve simultaneous equations: using inverse matrix |
| \multirow{2}{*}{Hotel} | Types of room | \multirow{2}{*}{Total revenue} | ||
| \cline{2-4} | Single | Double | Family | |
| A | 12 | 30 | 8 | £2,668 |
| B | 18 | 25 | 20 | £3,402 |
| C | 19 | 50 | 16 | £4,581 |
The matrix $\mathbf{M}$ is defined by
$$\mathbf{M} = \begin{pmatrix} 12 & 30 & 8 \\ 18 & 25 & 20 \\ 19 & 50 & 16 \end{pmatrix}.$$
\begin{enumerate}[label=(\alph*)]
\item Given that $\det \mathbf{M} = -1040$, give a geometrical interpretation of the solution to the following equation. [2]
$$\begin{pmatrix} 12 & 30 & 8 \\ 18 & 25 & 20 \\ 19 & 50 & 16 \end{pmatrix} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 2668 \\ 3402 \\ 4581 \end{pmatrix}$$
\item Three hotels A, B, C each have different types of room available to book: single, double and family rooms. For each type of room, the price per night is the same in each of the three hotels.
The table below gives, for each hotel, details of the number of each type of room and the total revenue per night when the hotel is full.
\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\hline
\multirow{2}{*}{\textbf{Hotel}} & \multicolumn{3}{c|}{\textbf{Types of room}} & \multirow{2}{*}{\textbf{Total revenue}} \\
\cline{2-4}
& Single & Double & Family & \\
\hline
A & 12 & 30 & 8 & £2,668 \\
\hline
B & 18 & 25 & 20 & £3,402 \\
\hline
C & 19 & 50 & 16 & £4,581 \\
\hline
\end{tabular}
\end{center}
Find the price per night of each type of room. [6]
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 4 2024 Q6 [8]}}