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1.3 Coordinate Geometry in the x-y Plane

1.3 Coordinate Geometry in the x-y Plane

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Question 61

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

1.3 Coordinate Geometry in the x-y Plane Questions

  1. A Level
  2. /Maths
  3. /1.3 Coordinate Geometry in the x-y Plane

143 exam-style questions on OCR A Level Maths 1.3 Coordinate Geometry in the x-y Plane, covering 1.3.1 Straight lines, 1.3.2 Parallel and perpendicular lines, 1.3.3 Straight line models, 1.3.4 Coordinate geometry of a circle, 1.3.5 Centre and radius by completing the square, 1.3.6 Circle properties, 1.3.7 Parametric equations of curves (A-level only), 1.3.8 Parametric equations in context (A-level only), and 1.3 Coordinate Geometry in the x-y Plane. Each one has a worked solution and a mark scheme showing where the marks go.

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