CAIE P2 2017 March — Question 4 6 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2017
SessionMarch
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicImplicit equations and differentiation
TypeFind dy/dx at a point
DifficultyStandard +0.3 This is a straightforward implicit differentiation question requiring product rule and chain rule application, then substitution of given coordinates. While it involves trigonometric functions, it's a standard textbook exercise with clear methodology and no problem-solving insight required, making it slightly easier than average.
Spec1.07s Parametric and implicit differentiation
4 Find the gradient of the curve $$x ^ { 2 } \sin y + \cos 3 y = 4$$ at the point \(\left( 2 , \frac { 1 } { 2 } \pi \right)\).
Question 4:
AnswerMarks Guidance
AnswerMark Guidance
Use product rule for derivative of \(x^2 \sin y\)M1
Obtain \(2x\sin y + x^2\cos y\frac{dy}{dx}\)A1
Obtain \(-3\sin 3y\frac{dy}{dx}\) as derivative of \(\cos 3y\)B1
Obtain \(2x\sin y + x^2\cos y\frac{dy}{dx} - 3\sin 3y\frac{dy}{dx} = 0\)A1
Substitute \(x = 2\), \(y = \frac{1}{2}\pi\) to find value of \(\frac{dy}{dx}\)M1 dep \(\frac{dy}{dx}\) occurring at least once
Obtain \(-\frac{4}{3}\)A1 from correct work only 
## Question 4:

| Answer | Mark | Guidance |
|--------|------|----------|
| Use product rule for derivative of $x^2 \sin y$ | M1 | |
| Obtain $2x\sin y + x^2\cos y\frac{dy}{dx}$ | A1 | |
| Obtain $-3\sin 3y\frac{dy}{dx}$ as derivative of $\cos 3y$ | B1 | |
| Obtain $2x\sin y + x^2\cos y\frac{dy}{dx} - 3\sin 3y\frac{dy}{dx} = 0$ | A1 | |
| Substitute $x = 2$, $y = \frac{1}{2}\pi$ to find value of $\frac{dy}{dx}$ | M1 | dep $\frac{dy}{dx}$ occurring at least once |
| Obtain $-\frac{4}{3}$ | A1 | from correct work only |

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4 Find the gradient of the curve

$$x ^ { 2 } \sin y + \cos 3 y = 4$$

at the point $\left( 2 , \frac { 1 } { 2 } \pi \right)$.\\

\hfill \mbox{\textit{CAIE P2 2017 Q4 [6]}}
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