| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Year | 2018 |
| Session | October |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chain Rule |
| Type | Basic power rule differentiation |
| Difficulty | Easy -1.2 This is a straightforward C1/C2 question requiring routine application of power rule for differentiation and integration. Students must rewrite the fraction as a negative power, then apply standard rules mechanically. No problem-solving or conceptual insight needed—pure procedural recall. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.08b Integrate x^n: where n != -1 and sums |
| VIIN SIHI NI IIIIM ION OC | VIIN SIHI NI JYHM IONOO | VI4V SIHI NI JIIIM ION OC |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| Differentiation attempted | M1 | \(x^n \to x^{n-1}\) seen at least once. Allow \(7 \to 0\) as evidence |
| \(3\times 2x^2\) or \(-2 \times \frac{-5}{3}x^{-3}\) | A1 | One correct term unsimplified or simplified |
| \(6x^2 + \frac{10}{3x^3}\) | A1 | Fully correct answer on one line: \(6x^2 + \frac{10}{3}x^{-3}\). Allow \(3\frac{1}{3}\) or \(3.\dot{3}\). If \(+c\) present score A0. Do not allow double-decker fractions |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| Integration attempted | M1 | \(x^n \to x^{n+1}\) seen at least once. Allow \(7 \to 7x\) as evidence. Attempt to integrate part (a) answer is M0 |
| \(2\frac{x^4}{4}\) or \(\frac{-5}{3}\times\frac{x^{-1}}{-1}\) | A1 | One of first two terms correct unsimplified or simplified |
| Both \(2\frac{x^4}{4}\) and \(\frac{-5}{3}\times\frac{x^{-1}}{-1}\) | A1 | Both of first two terms correct unsimplified or simplified |
| \(\frac{x^4}{2} + \frac{5}{3x} + 7x + c\) | A1 | Fully correct answer on one line including \(+c\). For \(\frac{5}{3x}\) allow \(\frac{5}{3}x^{-1}\) or \(1\frac{2}{3}x^{-1}\) or \(1.\dot{6}x^{-1}\). Do not allow \(x^1\) for \(x\). Do not allow double-decker fractions |
## Question 3(a):
| Working | Mark | Guidance |
|---------|------|----------|
| Differentiation attempted | M1 | $x^n \to x^{n-1}$ seen at least once. Allow $7 \to 0$ as evidence |
| $3\times 2x^2$ **or** $-2 \times \frac{-5}{3}x^{-3}$ | A1 | One correct term unsimplified or simplified |
| $6x^2 + \frac{10}{3x^3}$ | A1 | Fully correct answer on one line: $6x^2 + \frac{10}{3}x^{-3}$. Allow $3\frac{1}{3}$ or $3.\dot{3}$. If $+c$ present score A0. Do not allow double-decker fractions |
## Question 3(b):
| Working | Mark | Guidance |
|---------|------|----------|
| Integration attempted | M1 | $x^n \to x^{n+1}$ seen at least once. Allow $7 \to 7x$ as evidence. **Attempt to integrate part (a) answer is M0** |
| $2\frac{x^4}{4}$ **or** $\frac{-5}{3}\times\frac{x^{-1}}{-1}$ | A1 | One of first two terms correct unsimplified or simplified |
| Both $2\frac{x^4}{4}$ **and** $\frac{-5}{3}\times\frac{x^{-1}}{-1}$ | A1 | Both of first two terms correct unsimplified or simplified |
| $\frac{x^4}{2} + \frac{5}{3x} + 7x + c$ | A1 | Fully correct answer on one line including $+c$. For $\frac{5}{3x}$ allow $\frac{5}{3}x^{-1}$ or $1\frac{2}{3}x^{-1}$ or $1.\dot{6}x^{-1}$. Do not allow $x^1$ for $x$. Do not allow double-decker fractions |3. Given that $y = 2 x ^ { 3 } - \frac { 5 } { 3 x ^ { 2 } } + 7 , x \neq 0$, find in its simplest form
\begin{enumerate}[label=(\alph*)]
\item $\frac { \mathrm { d } y } { \mathrm {~d} x }$,
\item $\int y \mathrm {~d} x$.
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
VIIN SIHI NI IIIIM ION OC & VIIN SIHI NI JYHM IONOO & VI4V SIHI NI JIIIM ION OC \\
\hline
\end{tabular}
\end{center}
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 2018 Q3 [7]}}