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3.6 Differentiation (A-level only)

3.6 Differentiation (A-level only)

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Question 145

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

x=6cos⁡2y0≤x≤6,0≤y≤π4 x = 6 \cos 2y \quad 0 \le x \le 6, \quad 0 \le y \le \frac{\pi}{4} x=6cos2y0≤x≤6,0≤y≤4π​

where xxx is the horizontal position in millimetres and yyy is the control angle in radians.

a.

Find dxdy\frac{dx}{dy}dydx​ in terms of yyy.

[2]
b.

Hence show that

dydx=k36−x2 \frac{dy}{dx} = \frac{k}{\sqrt{36-x^2}} dxdy​=36−x2​k​

where kkk is a constant to be found.

[3]
c.

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

  • the gradient of the path at PPP is −16-\frac{1}{6}−61​
  • both aaa and bbb are positive constants

find the exact values of aaa and bbb.

[4]
Markscheme

3.6 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Differentiation (A-level only)

333 exam-style questions on WJEC A Level Maths 3.6 Differentiation (A-level only), covering 3.6.1 Differentiation (A-level only), 3.6.2 Differentiation (A-level only), 3.6.3 Differentiation (A-level only), 3.6.4 Differentiation (A-level only), 3.6.5 Differentiation (A-level only), 3.6.6 Differentiation (A-level only), 3.6.7 Differentiation (A-level only), and 3.6 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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