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Tec101: Basic Engineering Mathematics I Question Paper
Tec101: Basic Engineering Mathematics I
Course:Bachelor Of Electrical And Electronics Engineering
Institution: Moi University question papers
Exam Year:2011
TEC 101: Basic Engineering Mathematics I
QUESTION ONE
a. Given the following sets: A = {0, 1} B = {1, 2} C = {0, 1, 2} Find;
a. The cartesian product A x B x C
b. The difference of A and B
c. The difference of B and A
d. The symmetric difference of A and B
e. The complement of A in C
f. The power set of
i. A
ii. B
iii. C
g. Show that (A-B) - C = (A-C) - (B-C)
b. In a class of 100 students, the results of a survey on mid popularity of three premier league footbal teams (Chelsea, Arsenal, and Manchester United) showed that all but 15 of the students were fans of at least one team. 20 students were found to be fans of the three teams. All but 15 of the 47 fans of Arsenal were also fans of Chelsea. All the Chelsea fans were not fans of Manchester United. 60% of all the football fans were not fans of Manchester United. The number of students who were either not football fans or were fans of Manchester United only were 25.
Determine
a. The number of students who were fans of Chelsea
b. The numbers of students who were not fans of Manchester United
c. The number of students who were fans of both Chelsea and Manchester United but not Arsenal
QUESTION TWO
Given the following sets:
A = {2,5,10,17,26},
B = {3,9,19,33,51},
C = {9, 19,33},
D = {2,7},
U ={2,3,5,7,9,10,17,19,26,33,51,100}.
Illustrate the set using Venn diagrams hence evaluate:
a. The set of number that are either in A or B and not in C
b. The set of number that are either both in B and D or in the set C
QUESTION THREE
A 60 member constitution review committee on the devolution of power decided to vote in three key proposals, namely:
- Executive President
- Executive Vice President (VP)
- Executive Prime Minister (PM)
Of the total votes cast, 15 were in favour of all the three proposals. All but 10 of the 29 votes cast in favour of an executive VP were also in favour of an executive President. All those who voted for an executive VP were totally opposed to an executive PM. 10 members opted to abstain from voting. 40% of all the votes went against an executive PM. The numbers of those who either abstained or voted for an executive PM only was 20. Determine the following;
a. The number of votes that were cast in favour of an executive president
b. The votes that were cast against an executive PM
c. The number of votes that were cast in favour of both an executive president and executive PM but not an executive VP.
QUESTION FOUR
a. Find the inverse function of (3x+2)/(x-3)
b. Determine whether the inverse function obtained in (a) above is even or odd.
c. Write Cos 60 in terms of Cos 0 and Sin 60 in terms of Sin 0
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