Pure Mathematics Year 2 (A Level) Unit Test 8: Differentiation
1 a Given that , show that
(4 marks)
b Hence prove that
(2 marks)
2 A toy soldier is connected to a parachute. The soldier is thrown into the air from
ground level. The height, in metres, of the soldier above the ground can be modelled
by the equation , where H is height of the soldier above the
ground and t is the time since the soldier was thrown.
a Show that
(4 marks)
b Using the differentiated function, explain whether the soldier was increasing or
decreasing in height after 2 seconds.
(2 marks)
c Find the exact time when the soldier reaches a maximum height.
(2 marks)
3 A curve has the equation
Show that the equation of the tangent at the point with an x-coordinate of 1 is
(6 marks)
4 Given that , find:
a in terms of y
(2 marks)
b Show that
where k is a constant which should be found.
© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 1
1 a Given that , show that
(4 marks)
b Hence prove that
(2 marks)
2 A toy soldier is connected to a parachute. The soldier is thrown into the air from
ground level. The height, in metres, of the soldier above the ground can be modelled
by the equation , where H is height of the soldier above the
ground and t is the time since the soldier was thrown.
a Show that
(4 marks)
b Using the differentiated function, explain whether the soldier was increasing or
decreasing in height after 2 seconds.
(2 marks)
c Find the exact time when the soldier reaches a maximum height.
(2 marks)
3 A curve has the equation
Show that the equation of the tangent at the point with an x-coordinate of 1 is
(6 marks)
4 Given that , find:
a in terms of y
(2 marks)
b Show that
where k is a constant which should be found.
© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 1
