| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2019 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chain Rule |
| Type | Integration using chain rule reversal |
| Difficulty | Moderate -0.8 Part (a) is a straightforward application of the chain rule for differentiation. Part (b) is a direct reversal where students recognize the integrand as a multiple of the derivative just found, requiring only adjustment of the constant. This is a standard textbook exercise testing basic understanding of the chain rule and its reversal in integration, with minimal problem-solving required. |
| Spec | 1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates1.08a Fundamental theorem of calculus: integration as reverse of differentiation |
| Answer | Marks |
|---|---|
| \(k(x^2+5)^{11}\) seen | M1 (AO 1.1a) |
| \(24x(x^2+5)^{11}\) | A1 (AO 1.1) |
| Answer | Marks | Guidance |
|---|---|---|
| \(a(x^2+5)^{12}\) | M1 (AO 1.1) | |
| \(2(x^2+5)^{12}(+c)\) | A1 (AO 1.1) | condone omission of \(+c\) |
## Question 2:
### Part (a)
$k(x^2+5)^{11}$ seen | M1 (AO 1.1a) |
$24x(x^2+5)^{11}$ | A1 (AO 1.1) |
**[2 marks]**
### Part (b)
$a(x^2+5)^{12}$ | M1 (AO 1.1) |
$2(x^2+5)^{12}(+c)$ | A1 (AO 1.1) | condone omission of $+c$ | A1 FT their $kx(x^2+5)^{11}$ from part (a)
**[2 marks]**
---2 Given that $y = \left( x ^ { 2 } + 5 \right) ^ { 12 }$,
\begin{enumerate}[label=(\alph*)]
\item Find $\frac { \mathrm { d } y } { \mathrm {~d} x }$.
\item Hence find $\int 48 x \left( x ^ { 2 } + 5 \right) ^ { 11 } \mathrm {~d} x$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 2019 Q2 [4]}}