University of Dublin
Trinity College
Faculty of Engineering and Systems Sciences
Department of Computer Science
Diploma in Information Systems
Junior Freshman
Business Methods
Dr. Brendan Browne
Test Paper Part 1
Please answer all Questions
2015
Question 1
(a) Transpose the following
1
 7x2  4  5
1  7x
 ,(iii) q 
(i) y 
, (ii) t  
2 
1  11x
 3  2x 
[7 p
3
 2]  4

[ 3 marks]
(b) Simplify the following expressions.
 3 K 0 .5 
39
28
 3 
(i) 6
(ii)
(iii)
2  2 3
3 7  37
 L 
6
[ 3 marks]
(c) Evaluate
5x
x y
1 4
 4   13 
 . (ii)       . (iii)
(i)
.
10 x
11 7
 3  5 
( x  y)
[ 3 marks]
(d) Solve
(i) 11x  13  15x  8 (ii)
2 9
  7 (iii) x 2  10 x  7  3(2 x  5)
x x
[ 6 marks]
(e) Find the solution of the two simultaneous equations
7 x  11y  29
3x  5 y  7
Confirm your answer by plotting the two equations and finding their
point of intersection.Use graph paper. Confirm your answer
algebraically.
[ 9 marks]
(f) The demand and supply functions for a good are given by
Pd  180  0.5Qd -----demand function
Ps  60  0.7Qs -----supply function
Calculate the equilibrium price and quantity graphically. Confirm your answer
algebraically.
[ 9 marks]
Question 2
a) The distribution of the highest level of education for people aged 25 to 34
years is given in the table below.
Education
Count(millions)
Less than high school
4.7
High school graduate
11.8
Some college
10.9
Bachelors Degree
8.5
Advanced Degree
2.5
Display this information in (i) a bar chart and in a (ii) pie chart.
[ 4 marks]
(b)Evaluate, giving detailed calculations including the deviations (i) the mean,
(ii) the variance and (iii) standard deviation of the following set of data
61 67 91 74 87.
[ 4 marks]
(c) Forty companies took part in a survey to investigate their annual
expenditure on marketing their products. The data (in € 000’s) are
given below
61
68
70
64
32
44
51
41
46
55
54
50
53
56
57
45
41
56
50
53
53
57
55
49
49
58
31
55
54
56
74
42
45
57
51
37
59
62
65
62.
Find (i) the range, (ii) the median, (iii) the interquartile range(IQR) and (iv)the
five number summary of this data.
[ 10 marks]
(d) Construct a frequency distribution table and hence draw a frequency
histogram and polygon for this data. Take 5 equal class sizes.
[ 12 marks]
(e) Comment on your results paying particular attention to the shape of the
histogram.
[ 3 marks]
Question 3
(a) Indicate which of the following sentences are simple propositions or
statements giving your reasons.
(i) Dublin is in Ireland.
(ii) What time is it?
(iii) Give me my computer program.
[ 3 marks]
(b)What is the value of x after each of these statements is encountered in a
computer program if x  25 before the statement is reached?
Give your reasons.
(i) if (17  12  18) then x : x  1 .
(ii) if (( 2  2  4)OR (2  3  3) ) then x : x  1 .
(iii) if (( 2  4  7) AND(4  5  9)) then x : x  1 .
Note 1 OR is  AND is 
Note2 := is an assignment sign.
[ 6 marks]
(c) Define logical equivalence. Prove that the two logical expressions


A   A  B  and  A  B  are logically equivalent.
[ 11 marks]
(d) Using a truth table investigate if the following
A  ( B  C )  ( A  B)  ( A  C )
is a tautology, contradiction or contingency.
[ 14 marks]