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3.5 Differentiation (A-level only)

3.5 Differentiation (A-level only)

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Question 141

A robotic arm is programmed to sweep across a linear welding track. Its horizontal position xxx (in cm) relative to a central sensor is modeled by the equation

x=5tan⁡(y−π4)x∈R,−π4<y<3π4 x = 5\tan\left(y - \frac{\pi}{4}\right) \quad x \in \mathbb{R}, \quad -\frac{\pi}{4} < y < \frac{3\pi}{4} x=5tan(y−4π​)x∈R,−4π​<y<43π​

where y y\,y is the angle of rotation of the arm in radians.

a.

Show that

dydx=ax2+b \frac{dy}{dx} = \frac{a}{x^2 + b} dxdy​=x2+ba​

where a a\,a and b b\,b are integers to be found.

[4]
b.

The point P P\,P on the curve C C\,C has yyy-coordinate π2\displaystyle \frac{\pi}{2}2π​. The tangent to C C\,C at P P\,P crosses the xxx-axis at the point QQQ. Find the exact xxx-coordinate of QQQ.

[4]
Markscheme

3.5 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.5 Differentiation (A-level only)

263 exam-style questions on CCEA A Level Maths 3.5 Differentiation (A-level only), covering 3.5.1 Differentiation (A-level only), 3.5.2 Differentiation (A-level only), 3.5.3 Differentiation (A-level only), 3.5.4 Differentiation (A-level only), 3.5.5 Differentiation (A-level only), and 3.5 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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