maths homework

Mathematics and Statistics MN-1507 Assignment 1 Submission by turnitin is due by 3.00 on 13th March 2017 You are reminded that this work is individual and personal work and you should not collaborate with other students in any way in its preparation and that such collusion can be evident in solutions presented. It may be necessary (for example when you are asked to draw a graph) for you to be able to scan, or take a good quality photograph of your graph to be incorporated into the document you submit through turnitin. A numerical answer alone is not sufficient for you to obtain full marks for a question; you will need to show your workings and where necessary explain your thinking. Answer all parts of all the questions. 1. (a) Explain in no more than 50 words for each section what is meant by ;

(i) a linear function [4 marks]

(ii) the vertical intercept of a straight line graph [4 marks]

(b) What is the gradient and vertical intercept of the following functions? Explain how you arrived at your answers.

(i) f(x) = 3.7x + 37 [3 marks] (ii) q(z) = pz + b [3 marks] 2. (a) Explain in no more than 50 words for each section what is meant by; (i) a quadratic function [4 marks] (ii) the root or roots of a quadratic function [4 marks]

(b) (i) Plot the following quadratic function on graph paper and, using

the graph estimate its roots to one decimal place. At what value does the graph intersect the y axis? (You will then need to scan or photograph your answer in order to be able to submit it on turnitin; please be sure that your scan or photo is of good quality)

𝑓(𝑥) = 1

16 𝑥2 +

1

8 𝑥 − 3 [6 marks]

(ii) Use an analytical (ie non graphical) approach to find the roots of the following function to 3 decimal places.

g(x) = 8×2 + 4x – 3 [6 marks]

3.

(a) If you deposit £1 000 000 into an account paying 2% annual interest compounded yearly, how much money would be in the account after 25 years if there were no withdrawals in that period? [9 marks]

(b) If the same amount was paid into an account also paying 2% annual

interest but compounded daily, how much money would be in the account after 25 years? [8 marks]

(c) Comment, in no more than 50 words, on your answers for sections (a)

and (b). [4 marks] 4. What is the value of t in each of the following expressions? Calculate your solutions to three decimal places and show your workings.

(a) 7e-0.5t = 60 [7 marks]

(b) 650 = 900 (1 – e0.75t) [7 marks] 5.

(a) Find the 8th terms of the following series;

6.500 , 9.750 , 14.625 ….

Calculate rounding to the third decimal place, and show your workings [7 marks]

(b) The sum of the first 10 terms of; 65.000 , 113.750 , 199.063 ….

Calculate rounding to the third decimal place, and show your workings [7 marks]

6. (i) What, to the nearest penny, is the total interest for the first year on a mortgage for £200,000 at 5% annual interest rate, for 30 years? Assume that the interest is compounded annually. [3 marks]

(ii) What, to the nearest penny, is the total interest for the first year on a

mortgage for £200,000 at 5% annual interest rate, for 30 years when the interest is compounded monthly? Assume that there is no capital repayment each month and that this is calculated at the end of the year only. [8 marks]

(iii) Explain in no more than 30 words the reason for any differences between the solutions of the previous two sections of this question.

(iv) What, to the nearest penny, is the total interest for the sixth year on a mortgage for £200,000 at 5% annual interest rate, for 30 years assuming that the interest is compounded annually and that capital repayments are calculated at the end of each year only? [9 marks]

7. A company is considering investing in a project with the following cash flows

over a 5 year lifecycle. Advise the company on whether it should invest in the company using Net Present Value as the decisive factor and applying a discount factor of 4%.

Year Expenditure (£) Income (£)

0 1000000 0

1 150000 450000

2 0 600500

3 500000 348000

4 0 250000

5 248500 600000

[7 marks]

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