| Exam Board | AQA |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2013 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Integration by Substitution |
| Type | Finding curve equation from derivative |
| Difficulty | Standard +0.3 Part (a) is a standard integration by substitution with u = x² + 3, requiring recognition of the derivative pattern. Part (b) is a separable differential equation requiring routine separation of variables, integration of both sides using part (a), and application of initial conditions. This is a typical C4 question testing standard techniques with no novel insight required, making it slightly easier than average. |
| Spec | 1.08h Integration by substitution1.08k Separable differential equations: dy/dx = f(x)g(y) |
5
\begin{enumerate}[label=(\alph*)]
\item Find $\int x \sqrt { x ^ { 2 } + 3 } \mathrm {~d} x$.\\
(2 marks)
\item Solve the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { x \sqrt { x ^ { 2 } + 3 } } { \mathrm { e } ^ { 2 y } }$$
given that $y = 0$ when $x = 1$. Give your answer in the form $y = \mathrm { f } ( x )$.
\end{enumerate}
\hfill \mbox{\textit{AQA C4 2013 Q5 [9]}}