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1.6 C: Coordinate geometry in the (x, y) plane

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Question 52

At time ttt hours after a high tide, the height, hhh metres, of the tide and the velocity, vvv knots, of the tidal flow are modelled using the parametric equations

v=9−(3t4−3)2 v = 9 - \left(\frac{3t}{4}-3\right)^2 v=9−(43t​−3)2 h=4−3t−43 h = 4 - 3\sqrt[3]{t-4} h=4−33t−4​

High tides and low tides occur alternately when the velocity of the tidal flow is zero.

A high tide occurs at 4 am.

ai.

Use the model to find the height of this high tide.

[2]
aii.

Find the time of the first low tide after 4 am.

[3]
aiii.

Find the height of this low tide.

[2]
b.

Use the model to find the height of the tide when it is flowing with maximum velocity.

[2]
c.

Comment on the validity of the model.

[1]
Markscheme

1.6 C: Coordinate geometry in the (x, y) plane Questions

  1. A Level
  2. /Maths
  3. /1.6 C: Coordinate geometry in the (x, y) plane

143 exam-style questions on AQA A Level Maths 1.6 C: Coordinate geometry in the (x, y) plane, covering 1.6.1 Equation of a straight line, 1.6.2 Coordinate geometry of the circle, 1.6.3 Parametric equations of curves (A-level only), and 1.6.4 Parametric equations in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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