Metropolitan State University
Math 115, College Algebra
Midterm Exam, Summer 2016
Name__________________________________
Submit the completed test to the D2L Midterm Exam folder in the Dropbox no later than
11 PM Saturday, June 25, 2016.
You can use your book, e-book, notes, and calculator. You must not get help from
anyone else, real or virtual. All the work on the test should be your own. Be sure to show
how you solved the problems—there is a penalty for giving answers without justification.
Good luck!
I attest that I completed this exam on my own.
Signature: ________________________________________
Problem 1. (5 points) Evaluate the following arithmetical expression. Show every
single step necessary to find the solution.
6 − 4 ∗ (2 + 32 + 7 ∗ 5 − 16 ÷ 4) − 27 ÷ 3
2
Problem 2. (6 points) Classify each of the following numbers as natural, integer,
rational, irrational, real, or complex. Place each number in as many categories as
possible.
(a.) 4.123456789101112131415
(b.) √−4
(c.) 0
(d.) −
2
5
(e.) −4
(f.) √2
3
Problem 3. (10 points) Calculate the following operations with complex numbers.
Give your final answer in the form 𝑎 + 𝑏𝑖.
(a.) (2 − 3𝑖)(4 + 5𝑖)
(b.)
6−𝑖
2𝑖
(c.) (5𝑖 − 3)(4 + 6𝑖)
(d.) (𝑖 − 1)2
(e.) (𝑥 − 𝑖𝑦)(𝑥 + 𝑖𝑦), where 𝑥 and 𝑦 are real numbers
4
Problem 4. (4 points)
(a.) Expand the algebraic expression (3𝑥 + 2𝑦)2 in the variables 𝑥 and 𝑦. Show
every step in the expansion and give your answer in simplest form.
(b.) Find the value of the constant c so that the point (5, 𝑐) lies on the graph of
the linear function 𝑓(𝑤) = 6𝑤 − 3. Justify your answer.
Problem 5. (5 points) Find an equation for the line that passes through the points
(0,4) and (3,12).
5
Problem 6. (10 points) Solve the following equations for 𝑥. Show each step
necessary to find the solution.
(a.)
3 − [4𝑥 − 7(𝑥 − 2) + 6] = 2𝑥 + 3(𝑥 − 3)
(b.)
𝑎𝑥 − 𝑏 = 𝑏𝑥 − 𝑎
6
Problem 7. (4 points) The following table comes from a function 𝑓
𝑥 𝑓(𝑥)
2 11
4 19
6 25
8 32
Prove that 𝑓 cannot be a linear function. Justify your conclusion.
Problem 8. (6 points) Find an algebraic equation whose graph is the following
line. Justify your answer. Assume the horizontal axis is represented by the
variable 𝑥 and the vertical axis by the variable 𝑦.
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
-2 -1 0 1 2 3
7
Problem 9. (10 points) Consider the graph of a function 𝑓 below. Use this graph to
complete the work that follows. (Assume the graph does not continue outside of box.)
Estimate…
(a.) The domain of 𝑓
(b.) The range of 𝑓
(c.) The intervals where 𝑓 is increasing
(d.) The relativ
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Metropolitan State University Math 115, College Algebra .docx
1. Metropolitan State University
Math 115, College Algebra
Midterm Exam, Summer 2016
Name__________________________________
Submit the completed test to the D2L Midterm Exam folder in
the Dropbox no later than
11 PM Saturday, June 25, 2016.
You can use your book, e-book, notes, and calculator. You must
not get help from
anyone else, real or virtual. All the work on the test should be
your own. Be sure to show
how you solved the problems—there is a penalty for giving
answers without justification.
Good luck!
I attest that I completed this exam on my own.
3. 2
Problem 2. (6 points) Classify each of the following numbers as
natural, integer,
rational, irrational, real, or complex. Place each number in as
many categories as
possible.
(a.) 4.123456789101112131415
(b.) √−4
(c.) 0
(d.) −
4. 2
5
(e.) −4
(f.) √2
3
Problem 3. (10 points) Calculate the following operations with
complex numbers.
Give your final answer in the form � + ��.
6. (d.) (� − 1)2
(e.) (� − ��)(� + ��), where � and � are real numbers
4
Problem 4. (4 points)
(a.) Expand the algebraic expression (3� + 2�)2 in the
variables � and �. Show
every step in the expansion and give your answer in simplest
form.
7. (b.) Find the value of the constant c so that the point (5, �) lies
on the graph of
the linear function �(�) = 6� − 3. Justify your answer.
Problem 5. (5 points) Find an equation for the line that passes
through the points
(0,4) and (3,12).
8. 5
Problem 6. (10 points) Solve the following equations for �.
Show each step
necessary to find the solution.
(a.)
3 − [4� − 7(� − 2) + 6] = 2� + 3(� − 3)
9. (b.)
�� − � = �� − �
6
Problem 7. (4 points) The following table comes from a
function �
� �(�)
10. 2 11
4 19
6 25
8 32
Prove that � cannot be a linear function. Justify your
conclusion.
Problem 8. (6 points) Find an algebraic equation whose graph is
the following
line. Justify your answer. Assume the horizontal axis is
represented by the
variable � and the vertical axis by the variable �.
11. -5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
-2 -1 0 1 2 3
7
Problem 9. (10 points) Consider the graph of a function �
below. Use this graph to
complete the work that follows. (Assume the graph does not
continue outside of box.)
Estimate…
12. (a.) The domain of �
(b.) The range of �
(c.) The intervals where � is increasing
(d.) The relative maxima of �
(e.) �(3)
(f.) (� ∘ �)(−1)
(g.) We call an input value � a fixed point of � if �(�) = �.
Show that � has at
least three fixed points.
-5
-4
-3
13. -2
-1
0
1
2
3
4
5
6
7
8
9
10
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
8
Problem 10. (10 points) The data in the table below gives the
tuition at a state university
14. for the years 1997-2002.
Year Tuition
1997 9800
1998
1999
10,350
10,800
2000 11,600
2001 12,100
2002 12,700
Show your work and justify your answers in each of the
following:
(a.) Find the linear regression function that models the data.
Define each
variable used.
(b.) Use the function you found to estimate the tuition at the
