| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2015 |
| Session | June |
| Marks | 6 |
| 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 C1 question testing basic differentiation and integration of power functions. Students need only rewrite the fraction as a negative power and apply standard rules—no problem-solving or conceptual insight required, making it easier than average. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.08b Integrate x^n: where n != -1 and sums |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(12x^2+\frac{10}{x^3}\) | M1 | \(x^n \to x^{n-1}\). e.g. sight of \(x^2\) or \(x^{-3}\) or \(\frac{1}{x^3}\) |
| A1 | \(3\times4x^2\) or \(-5\times-2x^{-3}\) (oe). Ignore \(+c\) for this mark | |
| \(12x^2+\frac{10}{x^3}\) or \(12x^2+10x^{-3}\) all on one line, no \(+c\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(x^4+\frac{5}{x}+c\) or \(x^4+5x^{-1}+c\) | M1 | \(x^n \to x^{n+1}\). e.g. sight of \(x^4\) or \(x^{-1}\) or \(\frac{1}{x}\). Do not award for integrating answer to part (a) |
| A1 | \(4\frac{x^4}{4}\) or \(-5\times\frac{x^{-1}}{-1}\) | |
| \(x^4+5x^{-1}+c\) fully correct and simplified with \(+c\), all on one line. Allow \(x^4+5\times\frac{1}{x}+c\). Allow \(1x^4\) for \(x^4\) | A1 |
# Question 3:
## Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| $12x^2+\frac{10}{x^3}$ | M1 | $x^n \to x^{n-1}$. e.g. sight of $x^2$ or $x^{-3}$ or $\frac{1}{x^3}$ |
| | A1 | $3\times4x^2$ or $-5\times-2x^{-3}$ (oe). Ignore $+c$ for this mark |
| $12x^2+\frac{10}{x^3}$ or $12x^2+10x^{-3}$ all on one line, no $+c$ | A1 | |
## Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| $x^4+\frac{5}{x}+c$ **or** $x^4+5x^{-1}+c$ | M1 | $x^n \to x^{n+1}$. e.g. sight of $x^4$ or $x^{-1}$ or $\frac{1}{x}$. **Do not award for integrating answer to part (a)** |
| | A1 | $4\frac{x^4}{4}$ or $-5\times\frac{x^{-1}}{-1}$ |
| $x^4+5x^{-1}+c$ fully correct and simplified with $+c$, all on one line. Allow $x^4+5\times\frac{1}{x}+c$. Allow $1x^4$ for $x^4$ | A1 | |
---Given that $y = 4 x ^ { 3 } - \frac { 5 } { x ^ { 2 } } , x \neq 0$, 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 C1 2015 Q3 [6]}}