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9.7 Parametric Differentiation

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Question 9

The path of a light ray reflected off a curved mirror is modeled by the equation

5\sec^2 2y, \quad x > 5, \quad 0 < y < \frac{\pi}{4}

Find $dxdy\displaystyle \frac{\text{d}x}{\text{d}y}$ in terms of $y$ .

[2]

Hence show that

\frac{\text{d}y}{\text{d}x} = \frac{p}{qx\sqrt{x-5}}

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 path 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.

[4]

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

Medium Hard

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Question 9

The path of a light ray reflected off a curved mirror is modeled by the equation

5\sec^2 2y, \quad x > 5, \quad 0 < y < \frac{\pi}{4}

Find $dxdy\displaystyle \frac{\text{d}x}{\text{d}y}$ in terms of $y$ .

[2]

Hence show that

\frac{\text{d}y}{\text{d}x} = \frac{p}{qx\sqrt{x-5}}

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 path 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.

[4]

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.