| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find derivative of simple polynomial (integer powers) |
| Difficulty | Easy -1.2 This is a straightforward application of basic differentiation and integration rules for polynomials and powers of x. Part (a) requires applying the power rule to each term (rewriting 1/x³ as x⁻³), and part (b) requires reversing the process. Both are routine procedures from early Core modules with no problem-solving or conceptual challenges beyond direct rule application. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.08b Integrate x^n: where n != -1 and sums |
4. Given that $y = 2 x ^ { 5 } + 7 + \frac { 1 } { x ^ { 3 } } , x \neq 0$, find, in their simplest form,
\begin{enumerate}[label=(\alph*)]
\item $\frac { \mathrm { d } y } { \mathrm {~d} x }$,
\item $\int y \mathrm {~d} x$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 Q4 [7]}}