| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 6 |
| 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 integration question requiring only the reverse power rule and using a point to find the constant of integration. It's easier than average as it involves basic C1 integration with a simple fractional power and no problem-solving complexity beyond applying standard techniques. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.08a Fundamental theorem of calculus: integration as reverse of differentiation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Notes |
| \(\text{f}(x) = 3x^{\frac{4}{3}} - 5x + c\) | M1 A2 | |
| \((8,7)\): \(7 = 3(\sqrt[3]{8})^4 - 40 + c\), i.e. \(7 = 48 - 40 + c\) | M1 | |
| \(c = -1\) | M1 | |
| \(\text{f}(x) = 3x^{\frac{4}{3}} - 5x - 1\) | A1 | (6) |
## Question 3:
| Answer/Working | Marks | Notes |
|---|---|---|
| $\text{f}(x) = 3x^{\frac{4}{3}} - 5x + c$ | M1 A2 | |
| $(8,7)$: $7 = 3(\sqrt[3]{8})^4 - 40 + c$, i.e. $7 = 48 - 40 + c$ | M1 | |
| $c = -1$ | M1 | |
| $\text{f}(x) = 3x^{\frac{4}{3}} - 5x - 1$ | A1 | **(6)** |
---\begin{enumerate}
\item The curve with equation $y = \mathrm { f } ( x )$ passes through the point (8, 7).
\end{enumerate}
Given that
$$\mathrm { f } ^ { \prime } ( x ) = 4 x ^ { \frac { 1 } { 3 } } - 5$$
find $\mathrm { f } ( x )$.\\
\hfill \mbox{\textit{Edexcel C1 Q3 [6]}}