OCR MEI C3 2008 June — Question 7 5 marks

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Year2008
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicImplicit equations and differentiation
TypeShow dy/dx equals given expression
DifficultyModerate -0.3 This is a straightforward implicit differentiation question requiring application of the product rule and chain rule to find dy/dx. It's slightly easier than average because it's a direct application of a standard technique with no additional complications, though it does require careful algebraic manipulation of the resulting expression.
Spec1.07s Parametric and implicit differentiation
7 Given that \(x ^ { 2 } + x y + y ^ { 2 } = 12\), find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\).
Question 7:
AnswerMarks Guidance
AnswerMark Guidance
\(x^2 + xy + y^2 = 12\)M1 Implicit differentiation
\(2x + x\frac{dy}{dx} + y + 2y\frac{dy}{dx} = 0\)B1 \(x\frac{dy}{dx} + y\)
\((x + 2y)\frac{dy}{dx} = -2x - y\)A1 correct equation
\(\frac{dy}{dx} = -\frac{2x+y}{x+2y}\)M1 collecting terms in \(dy/dx\) and factorising
A1oe cao
[5] 
# Question 7:
| Answer | Mark | Guidance |
|--------|------|----------|
| $x^2 + xy + y^2 = 12$ | M1 | Implicit differentiation |
| $2x + x\frac{dy}{dx} + y + 2y\frac{dy}{dx} = 0$ | B1 | $x\frac{dy}{dx} + y$ |
| $(x + 2y)\frac{dy}{dx} = -2x - y$ | A1 | correct equation |
| $\frac{dy}{dx} = -\frac{2x+y}{x+2y}$ | M1 | collecting terms in $dy/dx$ and factorising |
| | A1 | oe cao |
| | [5] | |

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7 Given that $x ^ { 2 } + x y + y ^ { 2 } = 12$, find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ in terms of $x$ and $y$.

\hfill \mbox{\textit{OCR MEI C3 2008 Q7 [5]}}
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