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3.6.6 Differentiation (A-level only)

3.6.6 Differentiation (A-level only)

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Question 30

The movement of a precision robotic arm across a flat surface is defined by the parametric relationship

\cos 2y \quad 0 \le x \le 6, \quad 0 \le y \le \frac{\pi}{4}

where $x$ is the horizontal position in millimetres and $y$ is the control angle in radians.

a.

Find $dxdy\frac{dx}{dy}$ in terms of $y$ .

[2]

b.

Hence show that

\frac{dy}{dx} = \frac{k}{\sqrt{36-x^2}}

where $k$ is a constant to be found.

[3]

c.

A specific calibration point $P (a, b)$ lies on the path of the arm. Given that

the gradient of the path at $P$ is $−16-\frac{1}{6}$
both $a$ and $b$ are positive constants

find the exact values of $a$ and $b$ .

[4]

Markscheme

3.6.6 Differentiation (A-level only) Questions

A Level
Maths
3.6.6 Differentiation (A-level only)

82 exam-style questions on WJEC A Level Maths 3.6.6 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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