OCR MEI C3 — Question 2 4 marks

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicChain Rule
TypeChain rule with single composition
DifficultyModerate -0.3 This is a straightforward application of the chain rule to differentiate a composite function. While it requires recognizing the chain rule structure and careful algebraic manipulation, it's a standard single-technique question worth 4 marks with no conceptual challenges beyond routine differentiation.
Spec1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates
Differentiate \(\sqrt{1 + 6x^2}\). [4]
AnswerMarks Guidance
\(y = (1 + 6x^2)^{1/3}\)M1 Chain rule used
\(\frac{dy}{dx} = \frac{1}{3}(1 + 6x^2)^{-2/3} \cdot 12x\)B1 \(\frac{1}{3}u^{-2/3}\) or \(\frac{1}{2}(1 + 2x)^{-1/2}\)
\(= 4x(1 + 6x^2)^{-2/3}\)A1 \(\times 12x\)
A1cao (must resolve \(1/3 \times 12\)) Mark final answer
[4] 
$y = (1 + 6x^2)^{1/3}$ | M1 | Chain rule used
$\frac{dy}{dx} = \frac{1}{3}(1 + 6x^2)^{-2/3} \cdot 12x$ | B1 | $\frac{1}{3}u^{-2/3}$ or $\frac{1}{2}(1 + 2x)^{-1/2}$
$= 4x(1 + 6x^2)^{-2/3}$ | A1 | $\times 12x$
 | A1 | cao (must resolve $1/3 \times 12$) Mark final answer
 | [4] |
Differentiate $\sqrt{1 + 6x^2}$. [4]

\hfill \mbox{\textit{OCR MEI C3  Q2 [4]}}
This paper (8 questions)
View full paper
Q1 18 Q2 4 Q3 6 Q4 8 Q5 4 Q6 18 Q7 7 Q8 7