| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find derivative after algebraic simplification (fractional/mixed powers) |
| Difficulty | Moderate -0.8 This is a straightforward C2 calculus question testing basic differentiation and integration rules. Part (i) requires simplifying algebraic expressions and applying power rule (including fractional and negative powers). Part (ii) is a definite integral with simple terms. Both parts are routine applications of standard techniques with no problem-solving or conceptual challenges beyond direct recall and computation. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.08b Integrate x^n: where n != -1 and sums1.08d Evaluate definite integrals: between limits |
| Answer | Marks |
|---|---|
| Divide: \(1 + 2x^{-1}\) | M1 A1 |
| Differentiate: \(6x^2 + \frac{1}{2}x^{-1} - 2x^{-2}\) | M1 A2 (1.0) |
| (5 marks) |
| Answer | Marks |
|---|---|
| \(\frac{x^2}{4} + x^{-1}\) | M1 A1 A1 |
| \(\left[1\right]^4 - \left[-1\right] = \left(4 - \frac{1}{4}\right) - \left(\frac{1}{4} - 1\right) = 4\frac{1}{2}\) | M1 A1 |
| (5 marks) | |
| (10 marks total) |
## (i)
Divide: $1 + 2x^{-1}$ | M1 A1 |
Differentiate: $6x^2 + \frac{1}{2}x^{-1} - 2x^{-2}$ | M1 A2 (1.0) |
| (5 marks) |
## (ii)
$\frac{x^2}{4} + x^{-1}$ | M1 A1 A1 |
$\left[1\right]^4 - \left[-1\right] = \left(4 - \frac{1}{4}\right) - \left(\frac{1}{4} - 1\right) = 4\frac{1}{2}$ | M1 A1 |
| (5 marks) |
| **(10 marks total)** |
---\begin{enumerate}[label=(\roman*)]
\item Differentiate $2x^2 + \sqrt{x} + \frac{x^2 + 2x}{x^2}$ with respect to $x$ [5]
\item Evaluate $\int_1^4 \left(\frac{x}{2} + \frac{1}{x^2}\right) dx$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q5 [10]}}