FOUNDATION YEAR CENTRE
Assessed Problem Sheet
Demonstrate all your workings – marks will not be awarded for ‘answer only’ responses.
1. If and
(a) From first principles, find the derivative of .
Use an appropriate, labelled sketch in your answer.
(b) Find the derivative of . (4 marks)
(c) Find the derivative of (4 marks)
(a) Determine the integral (4 marks)
(b) Show that the integral = 0
where A is a constant. (3 marks)
(c) Using a sketch of the function to help you, determine the area enclosed between y = 0 and the line
in the range (5 marks)
Find an expression for in terms of and , and write this in its simplest form.
Find (2 marks)
Show that (2 marks)
5. Determine the integrals
Give your answer in the form of a single natural logarithm.
6. (a) find the particular solution of
, if the curve passes through the point (1,1).
(b) find the general solution of the differential equation
End of questions
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