| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2010 |
| Session | June |
| 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 C1 differentiation question requiring routine application of power rule after rewriting terms in index form. While it has multiple terms including a fraction that needs simplifying, it involves only standard techniques with no problem-solving or conceptual challenges—easier than the average A-level question. |
| Spec | 1.07i Differentiate x^n: for rational n and sums |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\frac{3x^2+2}{x} = 3x + 2x^{-1}\) | M1 A1 | M1: attempting to divide (one term correct). A1: both terms correct; accept \(3x^1\) for \(3x\) or \(\frac{2}{x}\) for \(2x^{-1}\) |
| \(y' = 24x^2, -2x^{-\frac{1}{2}}, +3, -2x^{-2}\) | M1 A1 A1 A1 | 2nd M1: attempt to differentiate \(x^n \to x^{n-1}\) for at least one term. 2nd A1: \(24x^2\) only. 3rd A1: \(-2x^{-\frac{1}{2}}\); allow \(\frac{-2}{\sqrt{x}}\); must be simplified. 4th A1: \(3 - 2x^{-2}\); both terms needed; if "\(+c\)" included they lose this mark |
| \(\left[24x^2 - 2x^{-\frac{1}{2}} + 3 - 2x^{-2}\right]\) | "Differentiating" \(\frac{3x^2+2}{x}\) and getting \(\frac{6x}{1}\) is M0 |
## Question 7:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{3x^2+2}{x} = 3x + 2x^{-1}$ | M1 A1 | M1: attempting to divide (one term correct). A1: both terms correct; accept $3x^1$ for $3x$ or $\frac{2}{x}$ for $2x^{-1}$ |
| $y' = 24x^2, -2x^{-\frac{1}{2}}, +3, -2x^{-2}$ | M1 A1 A1 A1 | 2nd M1: attempt to differentiate $x^n \to x^{n-1}$ for at least one term. 2nd A1: $24x^2$ only. 3rd A1: $-2x^{-\frac{1}{2}}$; allow $\frac{-2}{\sqrt{x}}$; must be simplified. 4th A1: $3 - 2x^{-2}$; both terms needed; if "$+c$" included they lose this mark |
| $\left[24x^2 - 2x^{-\frac{1}{2}} + 3 - 2x^{-2}\right]$ | | "Differentiating" $\frac{3x^2+2}{x}$ and getting $\frac{6x}{1}$ is M0 |\begin{enumerate}
\item Given that
\end{enumerate}
$$y = 8 x ^ { 3 } - 4 \sqrt { } x + \frac { 3 x ^ { 2 } + 2 } { x } , \quad x > 0$$
find $\frac { \mathrm { d } y } { \mathrm {~d} x }$.\\
(6)\\
\hfill \mbox{\textit{Edexcel C1 2010 Q7 [6]}}