MATH 141-501
Final Exam Information
• The Final Exam is cumulative. You should expect at least one question
from each section we have covered.
• The sections will be weighted roughly equally.
• While the questions will not be exactly the same, they will be roughly
the same difficulty as those in the textbook, WebAssign and the previous
exams. These sources would all be good for review.
• This review is intended to help get you started by pointing out questions
that were sources of difficulty the first time they were covered. These
questions are only a starting point, and you should do a thorough look
back through previous class notes, homeworks, assignments, and exams.
Questions from Chapter 1
1. TRUE or FALSE: The point (−1, 23 ) lies on the line x + 3y + 1 = 0.
Answer: TRUE
2. Find the equation of the vertical line that passes through the point (−1, 4).
Answer: x = −1
3. Find the equation of the horizontal line that passes through the point
(−1, 4). Answer: y = 4
4. Find the slope-intercept equation of the line with slope - 12 which passes
through the point (2, 4). Answer: y = − 12 x + 5
5. Researchers have found that the percentage of middle-income adults in
the United States is well-approximated by the equation
y = −2.5t + 61.2,
where t is measured in decades with t = 0 corresponding to 1971 and y is
percentage of middle-income adults.
(a) What does the y-intercept tell you in this problem? Answer: In
1971, middle-income adults formed 61.2% of the US population
(b) According to this model, what percentage of the current (2014) US
population is middle-income adults? Answer: -2.5(4.3) + 61.2 =
50.45 (Remember that t is measured in decades since 1971).
6. A division of BearCo makes pink teddy bears. Each pink teddy bear sells
for $9, and the cost of producing each unit is 40% of the selling price. The
monthly fixed costs are $50,000. What is the break-even point for this
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divison?
Answer: 9259 units, with a revenue of $83,331.
7. The quantity demanded for MP3Co’s MP3 players is 3000/week when the
unit price is $48.50. For each decrease in unit price of $2 below $50, the
quantity demanded increases by 250 units. Suppliers will not market any
MP3 players if the unit price is $30 or lower. At a unit price of $52.50,
suppliers will make available to 2500 units to the market. The demand
and supply equations are known to be linear.
(a) Find the demand equation.
Answer: p = 72.5 − 0.008x
(b) Find the supply equation.
Answer: p = 0.009x + 30
(c) Find the equilibrium quantity and price.
Answer:The equilibrium quantity is approximately 2500, and the
equilibrium quantity is approximately $52.50
8. The questions from Joe Kahlig’s Section 1-Q (located on WebAssign).
Questions from Chapter 2
9. Solve the following system of linear equations:
−x2 + x3 = 2
4x1 − 3x2 + 2x3 = 16
3x1 + 2x3 + x3 = 11
Answer: x = 3, y = 0, z = 2
10. Solve the following system of linear equations:
x − 2y2
7x − 14y = 14
3x − 6y = 6
Answer: x = 2t + 2, y = t, where t is a parameter
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11. Solve the following system of linear equations:
x + y − 2z = −3
2x − y + 3z = 7
x − 2y + 5z = 0
Answer: No solution
12. Given the rref form of a matrix, be able to determine the number of
solutions of the original linear system. Be able to find solutions.
13. TRUE or FALSE: if A, B, andC are matrices, then
(AB)C = A(BC),
provided the matrix products are defined.
Answer: TRUE
14. TRUE or FALSE: If A and B are matrices, then AB = BA, provided
the matrix products are defined.
Answer: FALSE
Questions from Chapter 3
15. Best to do exercises from WebAssign and from the book. Be sure to know
the theorems about when an optimization problem takes a minimum and
maximum value.
Questions from Chapter 6
For the following questions, let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 3, 5, 7, 9},
B = {2, 4, 6, 8, 10}, and C = {1, 2, 4, 5, 8, 9}.
16. List the elements in Ac .
Answer: {2,4,6,8}
17. List the elements in B ∪ C
Answer: {1, 2, 4, 5, 6, 8, 9, 10}
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18. TRUE or FALSE: C ∪ C c = U
Answer: TRUE (in fact, this is true for any set)
19. List the elements in (A ∩ B) ∪ C
Answer: (A ∩ B) ∪ C = {1,2,4,5,8,9}
20. Be able to use Venn diagrams to represent set-theoretic information.
21. Be able to describe sets in words, or translate verbal descriptions of information to
22. Know how to calculate the number of elements in a finite set, given certain
information (as in Section 6-3).
23. Know how to solve counting problems. Joe Kahlig’s 3 handouts are a
great resource for this. I have included additional problems for practice
below.
24. A warranty number for a certain product consists of two letters followed
by five digits. How many warranty numbers are possible if...
...there are no restrictions?
Answer: 262 105
...the first digit can not be 0?
Answer: (262 )9(104 )
...there are no restrictions on the digits, but letters can not be repeated?
Answer: (26)(25)(105 )
...there are no restrictions on the letters, but the digits can not be repeated?
Answer: (26)2 (10)(9)(8)(7)(6) or (26)2 P (10, 5)
... neither letters nor digits can be repeated?
Answer: (26)(25)(10)(9)(8)(7)(6) or P (26, 2)P (10, 2)
25. If a PIN number consists of 4 digits and at least two distinct digits must
be used, how many PIN numbers are possible?
Answer: 104 − 10 = 9990
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26. A computer password must consist of exactly one upper-case letter, exactly two digits, and either six or 7 lower-case letters. How many different
passwords are possible?
Answer: 9(26)C(8, 2)(102 )(266 )+10(26)C(9, 2)(102 )(267 ) = 7720175941171200
27. How many distinguishable arrangements are there of the letters in the
word AGGIEBASEBALLTEAM?
18!
Answer: 4!2!1!2!1!3!2!1!1!
Questions from Chapter 5
28. The WebAssign homeworks.
Questions from Chapter 7
29. The question from Joe Kahlig’s Probability handout, as well as exercises
from the book.
Questions from Chapter 8
30. Exercises from the book, and WebAssign.
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