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9.7 Parametric Differentiation

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Question 10

A micro-robotic probe moves along a path $C\,$ within a high-precision magnetic field. The relationship between its horizontal displacement $x\,$ and its vertical displacement $y\,$ is defined by the equation

3\sec^2 4y, \quad x > 3, \quad 0 < y < \frac{\pi}{8}

Find an expression for $dxdy\dfrac{dx}{dy}$ in terms of $y$ .

[2]

Hence show that

\dfrac{dy}{dx} = \frac{p}{qx\sqrt{x-3}}

where $p\,$ is irrational and $q\,$ is an integer, stating the values of $p\,$ and $q$ .

[4]

Find the equation of the normal to the probe's path $C\,$ at the point where $y=π12\displaystyle y = \frac{\pi}{12}$ , giving your answer in the form $y = m x + c$ where $m\,$ and $c\,$ are exact constants.

[5]

Markscheme

9.7 Parametric Differentiation Questions

A Level
Maths
9.7 Parametric Differentiation

35 exam-style questions on Edexcel A Level Maths 9.7 Parametric Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.

9.7 Parametric Differentiation

Question bank

9.7 Parametric Differentiation

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Question 10

3\sec^2 4y, \quad x > 3, \quad 0 < y < \frac{\pi}{8}

Find an expression for $dxdy\dfrac{dx}{dy}$ in terms of $y$ .

[2]

Hence show that

\dfrac{dy}{dx} = \frac{p}{qx\sqrt{x-3}}

where $p\,$ is irrational and $q\,$ is an integer, stating the values of $p\,$ and $q$ .

[4]

[5]

Markscheme

9.7 Parametric Differentiation Questions

A Level
Maths
9.7 Parametric Differentiation

35 exam-style questions on Edexcel A Level Maths 9.7 Parametric Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.