Skip to content

Course home

Sign up

3.7 Integration (A-level only)

EasyMediumHard
1234567891011121314151617181920212223242526272829303132333435363738394041424344
Question 23

The height of a passenger on a Ferris wheel above the ground, H H\,H metres, is modelled by the differential equation

dHdt=Hsin⁡(0.2t)5\displaystyle \frac{dH}{dt} = \frac{H\sin(0.2t)}{5}dtdH​=5Hsin(0.2t)​

where t t\,t is the time in minutes from the start of the ride and 0.2t 0.2t\,0.2t is measured in radians.

The passenger is 48e\dfrac{48}{e}e48​ metres above the ground at the start of the ride.

a.

Show that H=48e−cos⁡(0.2t)H = 48e^{-\cos(0.2t)}H=48e−cos(0.2t).

[5]
b.

Find the time, to the nearest minute, that it takes for the ride to reach its maximum height.

[2]
Markscheme

3.7 Integration (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.7 Integration (A-level only)

221 exam-style questions on WJEC A Level Maths 3.7 Integration (A-level only), covering 3.7.1 Integration (A-level only), 3.7.2 Integration (A-level only), 3.7.3 Integration (A-level only), 3.7.4 Integration (A-level only), 3.7.5 Integration (A-level only), and 3.7.6 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank