COR140 Maths and Statistics Final Exam – Version A

United Business Institutes Bachelor of Arts in Business (Honours) Programme
COR140 Maths and Statistics Final Exam – Version A
This is the final exam for COR140 Mathematics and Statistics with a pass mark of 50%. You have 2
hours to finish the exam and you must answer ALL the questions to get full marks.
You may NOT use a graphical scientific calculator nor one capable of algebraic manipulation. The
use of mobile computers and/or communication devices, of any type, capable of storing information
or retrieving information from any external source, including, but not limited to, the World Wide Web
(WWW), is expressly forbidden by the Institute’s Examination Regulations. Anyone breaking this
rule will have their exam script declared null and void.
When answering the questions show your working out so that you can be credited for incomplete
answers or even answers that are mostly correct.
Student Name
UBI Campus
This exam covers all the Learning Objectives for the course as stated in the Module Narrative.
Question Points Score
1 9
2 5
3 9
4 10
5 13
6 14
Total: 60
COR 140 Mathematics and Statistics I Final Exam
1. (a) Find: (1 mark)
log4(1024)
(b) Find: (2 marks)
ln(e
4t
)
(c) Calculate the point of intersection of the two straight lines, y = 3x + 6 and y = 2x + 9 (3 marks)
(d) Evaluate the definite integral below, giving your answer as a top-heavy fraction with denom- (3 marks)
inator 3.
Z 5
3
(x
2
) dx
COR140 – Mathematics and Statistics I – Final Version A Page 2 of 8
COR 140 Mathematics and Statistics I Final Exam
2. Given the function: x
2 − 3x + 2
(a) Find the roots of the equation by factorisation (show your working out). (3 marks)
(b) Find the coordinates of the minimum of the function. (2 marks)
COR140 – Mathematics and Statistics I – Final Version A Page 3 of 8
COR 140 Mathematics and Statistics I Final Exam
3. (a) What is the value of an investment of e2500 at 3.5% compounded annually for:
i. 2 years? (1 mark)
ii. 6 years? (1 mark)
(b) Your grandfather has placed e5500 into an investment fund paying 6% a year. How long (3 marks)
will it take for the fund to reach e9000? Give your answer in years and months rounded up
to the month above.
(c) Calculate the daily interest rate needed to increase your grandfather’s investment from (4 marks)
e5500 to e9000 over 5 years. Assume that a financial year comprises 360 days. Give your
answer to 4 decimal places.
COR140 – Mathematics and Statistics I – Final Version A Page 4 of 8
COR 140 Mathematics and Statistics I Final Exam
4. You have made an investment based on the terms and conditions given by your financial institution. Your mathematical education at UBI means that you are able to derive a simple exponential
function to model the investment conditions. The function that you derive for an investment of
e3000 is:
g(t) = 2.5e
1.05t + 3000 (1)
Using this model:
(a) What is the value of your investment after 3 years? (2 marks)
(b) Find the first derivative of the function, g(t). (3 marks)
(c) How fast is the investment growing per year at:
i. 4 years? (2 marks)
ii. 5 years? (1 mark)
(d) Are these good investment terms? Explain your answer. (1 mark)
(e) Are these realistic investment terms? Explain your answer. (1 mark)
COR140 – Mathematics and Statistics I – Final Version A Page 5 of 8
COR 140 Mathematics and Statistics I Final Exam
5. The Harrison Watch Company are planning an expensive, limited edition “Longitude” timepiece.
The price demand and average cost functions (in thousands of euros per timepiece) modelled by
the chief economist in the company’s marketing department are:
P + Q = 25
and
AC = 3 +
21
Q
where Q is the number of timepieces sold and P is the price.
(a) Derive an expression for the profit function in this model. (3 marks)
(b) What is the order of the profit function polynomial? (1 mark)
(c) Evaluate the discriminant of the profit function. (2 marks)
(d) Find the roots of the profit function. (2 marks)
(e) What is the lowest number of timepieces that the company needs to sell in order to break (2 marks)
even?
(f) How many timepieces must the company sell to maximize its profits? (2 marks)
COR140 – Mathematics and Statistics I – Final Version A Page 6 of 8
COR 140 Mathematics and Statistics I Final Exam
(g) What is the maximum profit that the company can generate according to the chief econom- (1 mark)
ist’s model?
COR140 – Mathematics and Statistics I – Final Version A Page 7 of 8
COR 140 Mathematics and Statistics I Final Exam
6. Mr Fisher and Mr Spearman play Scrabble1
at least three times a week. In the game, a bonus of
50 points is awarded if one can use all seven letter tiles in one turn. They record the number of
times that either of them uses all 7 tiles during a turn. The weekly figures for each of 18 weeks
are shown in the table below.
Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
7-tile Turns 7 9 7 10 8 12 19 8 7 9 7 6 4 7 6 10 11 9
(a) Compute the minimum, first quartile, median, third quartile, maximum and range of the (3 marks)
weekly scores.
(b) On squared (graph) paper, draw a labelled box plot that includes all of the scores. (4 marks)
(c) Compute the IQR and state whether any of the data points are outliers. Explain how you (2 marks)
identify an outlier.
(d) Draw a second box plot, on the same page as the first, that excludes the outlier. (3 marks)
(e) Calculate the population standard deviation for the scores. (2 marks)
1Scrabble is a game where players try to create words on a 15-by-15 board using from 1 to 7 letters tiles from their letter
rack.
COR140 – Mathematics and Statistics I – Final Version A Page 8 of 8