| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2007 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find second derivative |
| Difficulty | Easy -1.3 This is a straightforward C1 question testing basic differentiation and integration of polynomials and simple surds. All three parts require direct application of standard power rule formulas with no problem-solving or conceptual insight needed—purely mechanical computation that's easier than average A-level content. |
| Spec | 1.07d Second derivatives: d^2y/dx^2 notation1.07i Differentiate x^n: for rational n and sums1.08b Integrate x^n: where n != -1 and sums |
Given that $y = 3 x ^ { 2 } + 4 \sqrt { } x , x > 0$, find
\begin{enumerate}[label=(\alph*)]
\item $\frac { \mathrm { d } y } { \mathrm {~d} x }$,
\item $\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }$,
\item $\int y \mathrm {~d} x$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2007 Q3 [7]}}