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MAT 105 Intersession 2001 Exam: Election Methods, Graphing, and Apportionment - Prof. Robe, Exams of Mathematics

Eastern Kentucky University (EKU)Mathematics
Prof. Robert Buskirk

The solutions manual for exam 2a of mat 105 intersession 2001. It includes problems on finding the winner of an election using different methods (plurality, plurality-with-elimination, borda count), graphing equations, and apportionment using jefferson's and hamilton's methods. Students are expected to show their work and justify their answers.

Typology: Exams

2009/2010

Uploaded on 02/24/2010

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MAT 105 Intersession 2001 Exam 2A
Write your name on the back of this exam only.
Before you begin, make sure you have a complete exam. There are 10 problems. Skip around and
completely work as many problems as possible. You must show all work on all problems. Each problem is
worth a possible 10 points Partial credit will be given only for work that is part of a correct solution.
Neatness counts.
1. An election is held among 4 candidates (A, B, C, D). The results of the election are summarized in
the following table. Find the winner under the plurality method. Show some work to justify your
answer.
Number of voters 40 25 20 15
1st Choice A C B B
2nd Choice D B D A
3rd Choice B D A D
4th Choice C A C C
2. An election is held among 4 candidates (A, B, C, D) The results of the election are summarized in the
following table. Find the winner under the Plurality-with-Elimination Method. Show some work to
justify your answer.
Number of voters 40 25 20 15
1st Choice A C B B
2nd Choice D B D A
3rd Choice B D A D
4th Choice C A C C
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MAT 105 Intersession 2001 Exam 2A

Write your name on the back of this exam only.

Before you begin, make sure you have a complete exam. There are 10 problems. Skip around and completely work as many problems as possible. You must show all work on all problems. Each problem is worth a possible 10 points Partial credit will be given only for work that is part of a correct solution. Neatness counts.

  1. An election is held among 4 candidates (A, B, C, D). The results of the election are summarized in the following table. Find the winner under the plurality method. Show some work to justify your answer. Number of voters 40 25 20 15 1 st^ Choice A C B B 2 nd^ Choice D B D A 3 rd^ Choice B D A D 4 th^ Choice C A C C
  2. An election is held among 4 candidates (A, B, C, D) The results of the election are summarized in the following table. Find the winner under the Plurality-with-Elimination Method. Show some work to justify your answer. Number of voters 40 25 20 15 1 st^ Choice A C B B 2 nd^ Choice D B D A 3 rd^ Choice B D A D 4 th^ Choice C A C C
  1. Graph y = − 2 x + 6. Neatness counts.
  2. Graph the system of inequalities:

0

y

x

y x

y x

. Neatness counts.

  1. Briefly describe the three important facts about the Great Compromise of 1787. One fact should be its relationship to what we have studied in class. List them from most to least important.
  2. Tutoring-by-Telephone has 225 tutors working in four shifts: Shift A, Shift B, Shift C and Shift D. The number of tutors is based on the average number of calls for tutoring per shift and is given in the following table. Use Hamilton’s method to apportion the tutors. Label the columns to show the work necessary to perform this apportionment.

Shift Calls for Tutoring A 871

B 1029

C 610

D 190

Total

  1. Use Jefferson’s method to apportion 150 representatives from the states A, B, C, D, and E. Neatly organize your work in the table(s) below (or on separate paper, put you name on the back). Indicate clearly the divisor. (Note: the modified divisor is within 200 of the standard divisor.)

State Population A 112,

B 224,

C 848,

D 45,

E 586,

Total

State

A

B

C

D

E

Total

State

A

B

C

D

E

Total