| Exam Board | OCR MEI |
|---|---|
| Module | Paper 1 (Paper 1) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Product & Quotient Rules |
| Type | Find derivative of quotient |
| Difficulty | Moderate -0.8 This is a straightforward two-part differentiation question testing basic application of chain rule and quotient rule. Part (a) requires rewriting as a power and applying chain rule; part (b) is a standard quotient rule application. Both are routine textbook exercises with no problem-solving element, making this easier than average but not trivial since it requires correct technique application. |
| Spec | 1.07q Product and quotient rules: differentiation1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{dy}{dx} = \frac{1}{2}(1-3x^2)^{-\frac{1}{2}} \cdot (-6x)\) | B1 (1.1) | \(\frac{1}{2}u^{-\frac{1}{2}}\) soi |
| M1 (1.1) | Chain rule | |
| \(= \frac{-3x}{\sqrt{1-3x^2}}\) | A1 (1.1) | oe, but must simplify \(\frac{1}{2} \times 6\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{dy}{dx} = \frac{(3x+2) \cdot 2x - x^2 \cdot 3}{(3x+2)^2}\) | M1 (1.1) | Quotient rule or product rule |
| A1 (1.1) | ||
| \(= \frac{3x^2 + 4x}{(3x+2)^2}\) | A1 (1.1) | oe, but must simplify numerator |
## Question 4(a):
$\frac{dy}{dx} = \frac{1}{2}(1-3x^2)^{-\frac{1}{2}} \cdot (-6x)$ | B1 (1.1) | $\frac{1}{2}u^{-\frac{1}{2}}$ soi
| M1 (1.1) | Chain rule
$= \frac{-3x}{\sqrt{1-3x^2}}$ | A1 (1.1) | oe, but must simplify $\frac{1}{2} \times 6$
**Total: [3]**
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## Question 4(b):
$\frac{dy}{dx} = \frac{(3x+2) \cdot 2x - x^2 \cdot 3}{(3x+2)^2}$ | M1 (1.1) | Quotient rule or product rule
| A1 (1.1) |
$= \frac{3x^2 + 4x}{(3x+2)^2}$ | A1 (1.1) | oe, but must simplify numerator
**Total: [3]**
---4 Differentiate the following.
\begin{enumerate}[label=(\alph*)]
\item $\sqrt { 1 - 3 x ^ { 2 } }$
\item $\frac { x ^ { 2 } } { 3 x + 2 }$
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 1 Q4 [6]}}