| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2014 |
| 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 | Easy -1.2 This is a straightforward C1 differentiation and integration question requiring only direct application of power rule formulas. Students need to rewrite 6/√x as 6x^(-1/2), then apply standard rules mechanically. No problem-solving, curve sketching, or optimization required—pure routine calculation below average difficulty. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.08b Integrate x^n: where n != -1 and sums |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(x^n \to x^{n-1}\) | M1 | For \(x^n \to x^{n-1}\), i.e. \(x^4\) or \(x^{-\frac{3}{2}}\) or \(\left(\frac{1}{x^{\frac{3}{2}}}\right)\) seen |
| \(2\times5x^4\) or \(6\times-\frac{1}{2}x^{-\frac{3}{2}}\) | A1 | (oe). Ignore \(+c\) for this mark |
| \(\frac{dy}{dx} = 10x^4 - 3x^{-\frac{3}{2}}\) | A1 | For simplified expression \(10x^4-3x^{-\frac{3}{2}}\) or \(10x^4-\frac{3}{x^{\frac{3}{2}}}\) o.e. and no \(+c\). Apply ISW. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(x^n \to x^{n+1}\) | M1 | For \(x^n\to x^{n+1}\), i.e. \(x^6\) or \(x^{\frac{1}{2}}\) or \((\sqrt{x})\) seen. Do not award for integrating answer to part (a) |
| \(= \frac{x^6}{3} + 12x^{\frac{1}{2}} + c\) | A1 | For either \(2\frac{x^6}{6}\) or \(6\times\frac{x^{\frac{1}{2}}}{\frac{1}{2}}\) or simplified/unsimplified equivalents |
| A1 | For fully correct and simplified answer with \(+c\) |
## Question 4:
### Part (a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $x^n \to x^{n-1}$ | M1 | For $x^n \to x^{n-1}$, i.e. $x^4$ or $x^{-\frac{3}{2}}$ or $\left(\frac{1}{x^{\frac{3}{2}}}\right)$ seen |
| $2\times5x^4$ **or** $6\times-\frac{1}{2}x^{-\frac{3}{2}}$ | A1 | (oe). Ignore $+c$ for this mark |
| $\frac{dy}{dx} = 10x^4 - 3x^{-\frac{3}{2}}$ | A1 | For simplified expression $10x^4-3x^{-\frac{3}{2}}$ or $10x^4-\frac{3}{x^{\frac{3}{2}}}$ o.e. and no $+c$. Apply ISW. |
### Part (b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $x^n \to x^{n+1}$ | M1 | For $x^n\to x^{n+1}$, i.e. $x^6$ or $x^{\frac{1}{2}}$ or $(\sqrt{x})$ seen. Do not award for integrating answer to part (a) |
| $= \frac{x^6}{3} + 12x^{\frac{1}{2}} + c$ | A1 | For either $2\frac{x^6}{6}$ **or** $6\times\frac{x^{\frac{1}{2}}}{\frac{1}{2}}$ or simplified/unsimplified equivalents |
| | A1 | For fully correct and simplified answer with $+c$ |4. Given that $y = 2 x ^ { 5 } + \frac { 6 } { \sqrt { } x } , x > 0$, 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 C1 2014 Q4 [6]}}