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.
(5 marks)
(b) Find the derivative of . (4 marks)
(c) Find the derivative of (4 marks)
2.
(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)
3. If
Find an expression for in terms of and , and write this in its simplest form.
(5 marks)
4. (a)
Find (2 marks)
(b)
Show that (2 marks)
5. Determine the integrals
(a)
Give your answer in the form of a single natural logarithm.
(4 marks)
(b)
(5 marks)
6. (a) find the particular solution of
, if the curve passes through the point (1,1).
(3 marks)
(b) find the general solution of the differential equation
(4 marks)
End of questions
Write your answers on file paper.
Use an app such as fast scanner or adobe scan to scan your answers into a single document and upload them to the where directed.
