11.1 Integrating Standard Functions
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A deep-sea research probe is descending through a thermal layer. Its altitude h h\,h in metres, relative to the layer's boundary, is modeled by the function h(t)h(t)h(t) for t>0t > 0t>0, where t t\,t is the time in seconds since the descent began. It is known that:

  • at time t=4t = 4t=4, the probe is at point P(4,−10)P(4, -10)P(4,−10)
  • the rate of change of altitude is given by h′(t)=5t2+at+b3th'(t) = \dfrac{5t^2 + at + b}{3\sqrt{t}}h′(t)=3t​5t2+at+b​, where a a\,a and b b\,b are constants
  • at the instant t=4t = 4t=4, the rate of change of altitude is 12 m s-1
a.

Show that 4a+b=−84a + b = -84a+b=−8.

[3]
b.

Given also that a+2b=−23a + 2b = -23a+2b=−23

Find, in simplest form, the expression for h(t)h(t)h(t).

[6]
c.

The probe's mission data is later adjusted by a time-shift, such that the altitude is modeled by H(t)=h(t−3)H(t) = h(t - 3)H(t)=h(t−3). Given that point P P\,P on the original model is transformed to point Q Q\,Q on the new model,

State the coordinates of QQQ.

[1]

11.1 Integrating Standard Functions Questions

Practise Edexcel A Level Maths 11.1 Integrating Standard Functions with exam-style questions for A Level Maths. 81 questions, matched to the Edexcel A Level Maths (9MA0) 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.

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11.1 Integrating Standard Functions Questions

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