OCR MEI C2 2006 June — Question 8 5 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Year2006
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicChain Rule
TypeBasic power rule differentiation
DifficultyEasy -1.2 This is a straightforward differentiation question requiring only the application of the power rule to polynomial and fractional power terms. It involves two routine differentiations with no problem-solving, making it easier than average for A-level maths.
Spec1.07i Differentiate x^n: for rational n and sums
Given that \(y = 6x^3 + \sqrt{x} + 3\), find \(\frac{dy}{dx}\) and \(\frac{d^2y}{dx^2}\). [5]
AnswerMarks Guidance
\(\sqrt{x} = x^{1/2}\) SOIB1
\(18x^2, \frac{1}{2}x^{-1/2}\)B1B1 –1 if \(d/dx(3)\) not = 0
\(36x\)B1
\(Ax^{-3/2}\) (from \(Bx^{-1/2}\))B1 any \(A, B\) 
$\sqrt{x} = x^{1/2}$ SOI | B1 | |
$18x^2, \frac{1}{2}x^{-1/2}$ | B1B1 | –1 if $d/dx(3)$ not = 0 |
$36x$ | B1 | |
$Ax^{-3/2}$ (from $Bx^{-1/2}$) | B1 | any $A, B$ | $5$ |
Given that $y = 6x^3 + \sqrt{x} + 3$, find $\frac{dy}{dx}$ and $\frac{d^2y}{dx^2}$. [5]

\hfill \mbox{\textit{OCR MEI C2 2006 Q8 [5]}}
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