| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2023 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differential equations |
| Type | Exponential growth/decay - direct proportionality (dN/dt = kN) |
| Difficulty | Moderate -0.3 This is a standard separable differential equation problem requiring translation of a word statement into dy/dx = ky, then solving by separation of variables and applying initial conditions. While it involves multiple steps (7 marks total), the techniques are routine and commonly practiced. It's slightly easier than average because the setup is straightforward and the solution method is algorithmic with no conceptual surprises. |
| Spec | 1.07t Construct differential equations: in context1.08k Separable differential equations: dy/dx = f(x)g(y) |
The rate of change of a variable $y$ with respect to $x$ is directly proportional to $y$.
\begin{enumerate}[label=(\alph*)]
\item Write down a differential equation satisfied by $y$. [1]
\item When $x = 1$ and $y = 0.5$, the rate of change of $y$ with respect to $x$ is 2.
Find $y$ when $x = 3$. [6]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 3 2023 Q12 [7]}}