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1.10 G: Differentiation

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Question 3

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The depth of water in a storage tank, H H\,H metres, at time t t\,t hours after midnight is modelled by the equation

H=6+4cos⁡t2+sin⁡t,0≤t≤2π H = \frac{6 + 4 \cos t}{2 + \sin t}, \quad 0 \le t \le 2\pi H=2+sint6+4cost​,0≤t≤2π

The point M M\,M on the curve represents the time at which the water depth reaches its local minimum.

a.

Show that the ttt-coordinate of M M\,M is a solution of the equation

4sin⁡t+3cos⁡t=−2 4 \sin t + 3 \cos t = -2 4sint+3cost=−2
[4]
b.

Hence find, to 3 significant figures, the ttt-coordinate of MMM.

[4]

1.10 G: Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.10 G: Differentiation

Practise AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

Question bank