| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2002 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Second order differential equations |
| Type | Modeling context with interpretation |
| Difficulty | Standard +0.3 This is a first-order (not second-order) linear differential equation requiring an integrating factor or substitution method, followed by straightforward application of initial conditions. While it's Further Maths content, the technique is standard and the modeling context adds minimal complexity—just substituting values. Slightly above average due to the FP2 context and the need to manipulate logarithms correctly, but still a routine textbook exercise. |
| Spec | 4.10c Integrating factor: first order equations |
\begin{enumerate}[label=(\alph*)]
\item Find the general solution of the differential equation $t \frac { \mathrm {~d} v } { \mathrm {~d} t } - v = t , t > 0$ and hence show that the solution can be written in the form $v = t ( \ln t + c )$, where $c$ is an arbitrary cnst.
\item This differential equation is used to model the motion of a particle which has speed $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at time $t \mathrm {~s}$. When $t = 2$ the speed of the particle is $3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. Find, to 3 sf , the speed of the particle when $t = 4$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 2002 Q2 [10]}}