School of Management MN1507 MATHS AND STATISTICS 1

Individual Coursework Assignments 1) Individual Coursework Assignment 1

This assignment is worth 35% of the overall module mark.

Coursework Brief

For this coursework you are required to solve a series of mathematical problems. Your solution should be word-processed and submitted electronically.

Roots of equations;

1. Find the roots of the following equations.

. (a) 3×2+5x+2 = 0 [5 marks]

. (b) x2+6x+3 = 0 [5 marks]

2. What is the gradient and the vertical intercept of the following expressions?

. (a) g(z) = 6z + 4 [6 marks]

. (b) ps = 8.4qs + 2.4 [6 marks]

3. The supply curve for a product is given by Qs =50–5P
and its demand curve by
P = (Qd – 5)/10
where Qs the quantity supplied and Qd the quantity demanded at a price P. Calculate the equilibrium price. [12 marks]

4. What is the value of t in each of the following expressions?

. (a) 5e-0.6t = 60

. (b) 500 = 800 (1 – e0.7t)

5. Find the sum of the; (a) first 10 terms of

[7 marks] [7 marks]

1⁄4, 3⁄4, 5/4, 7/4,….. [7 marks]

4

(b) first 8 terms of 1/3, 1/9, 1/27, 1/81,…. [7 marks]

6. (a) What is the Annual equivalent percentage rate of interest if the annual interest rate is 8% and interest is compounded monthly? (assume that all months consist of 365/12 days). [8 marks]

(b) Calculate the market price of a bond of redemption value £100 and coupon 8% if the prevailing interest rate is 6.5%. [8 marks]

7. (a) The price of a desktop computer in 2012, 2013, 2014 and 2015 is £800, £750, £600 and £450 respectively. Construct a price index with a base value of 1000 and with a reference year of 2013. [6 marks]

(b) The data in the table below shows the number and price per journey of different types of transport used by a person in 2014 and 2015.

Journey Type

Journeys for 2014

Journeys for 2015

Price per Journey in £

Number of Journeys

Price per Journey in £

Number of Journeys

Train

18.00

5

25.00

18

Bus

3.60

22

4.00

17

Taxi

10.00

18

10.5

20

Underground

4.40

15

4.80

50

Boat

5.00

10

5.25

35

Calculate the Laspayre’s index and the Passche index for the data, and suggest reasons for the difference between the two numbers calculated. [8 marks for each index produced, so 16 marks for the two]

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