FC311 Intermediate Mathematics

End of Module Exam

Question Book

Time: 120 Minutes

Instructions to students:

Your FC311 Intermediate Mathematics module assessment is an online timed open book exam.

You will have to complete the exam paper and upload your answers in order to complete this assessment and get a grade for the module.

This examination is ‘open-book’, meaning you can access specific module learning resources. Allowed resources:

• Formula sheet

• Calculator

You are expected to work on this assessment on your own. Please note that you may be required to attend an online meeting to confirm that it is your own work.

You should type your answers into a document. For answers that require equations, formulae, graphs or diagrams you should write your answers clearly on paper and take a photograph of each page. You must upload your answers to the VLE.

In order to complete this assessment, you must:

• read all instructions very carefully

• read the question paper carefully before you begin to answer

• type or write your answers clearly

• upload your answers to the VLE

Question 1

Find  for the following

a) 

(1 mark)

b) 

(1 mark)

c) 

(2 marks)

Question 2

Find

a) 

(1 mark)

b) 

(1 mark)

c) 

(2 marks)

Question 3

Find the derivative of the following function:

(3 marks)

Question 4

Determine the equation of the tangent where x = 0 to the curve

(6 marks)

Question 5

Calculate the following to 3 decimal places

(4 marks)

Question 6

Use integration by parts to integrate the following.

(6 marks)

Question 7

a) Find the value of A, B and C given

(4 marks)

b) Hence find

Give your solution to 4 decimal places.

(6 marks)

Question 8

Evaluate the following integral using the substitution .

Give your answer to 3 decimal places.

(6 marks)

Question 9

The horizontal and vertical coordinates of a firework are described by the following parametric equations.

a) Find .

(7 marks)

b) Hence find the angle from horizontal at which the firework is travelling when t = 0.

(3 marks)

Question 10

A curve is given by the equation

a) Use implicit differentiation to find 

(5 marks)

b) Given that the curve passes through the point (0, -1) find the equation for the normal line to the curve at that point.

(4 marks)

Question 11

For the following differential equation:

a) Solve the differential equation to find y.

(7 marks)

b) Find the particular solution of the differential equation when f (x) passes though the point (, ).

(4 marks)

******************** This is the end of the examination ********************