| Exam Board | WJEC |
|---|---|
| Module | Further Unit 4 (Further Unit 4) |
| Year | 2024 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Second order differential equations |
| Type | Particular solution with initial conditions |
| Difficulty | Challenging +1.3 This is a coupled differential equations problem requiring systematic elimination to derive a second-order ODE, then solving with initial conditions. While it involves multiple steps (differentiation, substitution, solving auxiliary equation, applying initial conditions), the techniques are standard for Further Maths and follow a predictable procedure without requiring novel insight. The algebra is moderately involved but routine for this level. |
| Spec | 4.10h Coupled systems: simultaneous first order DEs |
| Answer | Marks |
|---|---|
| 10 | 12 |
| Total | 120 |
| Answer | Marks | Guidance |
|---|---|---|
| Hotel | Single | Double |
| A | 12 | 30 |
| B | 18 | 25 |
| C | 19 | 50 |
| Answer | Marks |
|---|---|
| number | Additional page, if required. |
| Answer | Marks |
|---|---|
| number | Additional page, if required. |
Question 10:
10 | 12
Total | 120
Types of room
Hotel | Single | Double | Family | Total revenue
A | 12 | 30 | 8 | £2,668
B | 18 | 25 | 20 | £3,402
C | 19 | 50 | 16 | £4,581
Question
number | Additional page, if required.
Write the question number(s) in the left-hand margin.
Question
number | Additional page, if required.
Write the question number(s) in the left-hand margin.The following simultaneous equations are to be solved.
$$\frac{\mathrm{d}x}{\mathrm{d}t} = 4x + 2y + 6e^{3t}$$
$$\frac{\mathrm{d}y}{\mathrm{d}t} = 6x + 8y + 15e^{3t}$$
\begin{enumerate}[label=(\alph*)]
\item Show that $\frac{\mathrm{d}^2 x}{\mathrm{d}t^2} - 12\frac{\mathrm{d}x}{\mathrm{d}t} + 20x = 0$. [5]
\item Given that $\frac{\mathrm{d}x}{\mathrm{d}t} = 9$ and $\frac{\mathrm{d}^2 x}{\mathrm{d}t^2} = 10$ when $t = 0$, find the particular solution for $x$ in terms of $t$. [7]
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 4 2024 Q10 [12]}}