©Lynch, November 2015
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Math 150, Fall 2015
Exam 3 – Form A
Multiple Choice
Sections 5B-8D
First Name:
Last Name:
Student ID number:
Section Number:
Directions:
1. No calculators, cell phones, or other electronic devices may be used, and they must all be put away
out of sight.
2. There are 10 multiple choice problems on this exam, and each problem is worth 5 points. No partial
credit will be given.
3. There will be 5 bonus points awarded if you do all of the following (no partial credit):
ˆ bring the correct Scantron form,
ˆ correctly fill out your Scantron including your First and Last name on the TAMU class roster, the
Course #, Section #, student ID number, Signature, Date: Nov 2015, Exam 3, and your exam
version, Form A.
ˆ bring your student ID to the exam, and
ˆ turn in your exam and Scantron on time.
4. Together with the other part of the exam there will be a total of 110 points possible.
5. The Scantron will not be returned to you, so please mark your answers on this exam paper.
6. You may not discuss the contents of the exam with anyone until the exam is returned in class.
THE AGGIE CODE OF HONOR
“On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work.”
Signature:
Note: You are authorized to use a pencil, eraser, TAMU Scantron, and your own TAMU
student ID; use of anything else is a violation of the honor code. If you need any extra paper,
please ask your instructor or TA; do not use your own.
Scantron: Make sure the following is filled out correctly on your Scantron:
Last Name, First Name, Course #, Section #, UIN, Signature, Date: Nov 2015, Exam 3, Form A
©Lynch, November 2015
Math 150 – Exam 3A
1. If a−3 = 2 and b3 = 5, then fully simplify and evaluate
a2 b2
b
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3
.
(a) 20
(b) 1000
(c)
(d)
(e)
5
4
25
8
5
8
2. Find the range and the x-intercept(s), respectively, of the function f (x) = −3ex−4 + 3.
(a) (3, ∞), 4
(b) (0, ∞), no x-intercept
(c) (3, ∞), no x-intercept
(d) (−∞, 3), −3e−4 + 3
(e) (−∞, 3), 4
3. What is the area of the sector of a circle of diameter 8 cm subtended by a central angle of
(a) 12π 2 cm2
(b) 6π cm2
(c) 3π cm2
(d) 24π cm2
(e) 72π 2 cm2
4. If ln 2 = a, ln 3 = b, ln 5 = c, and ln 7 = d, evaluate and fully simplify 4 log7
(a)
12a+4b−8c
d
(c)
4(a3 +b−c2 )
d
12a+4b−8c
2c+d
(d)
12a+b−2c
d
(b)
(e) None of these
24
25
.
3π
4 ?
©Lynch, November 2015
Math 150 – Exam 3A
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5. Solve the equation 3e2x − 8ex + 5 = 0. Find the sum of the solutions; if there is only one solution, just
give it.
(a) No real solution
(b) ln 53 + 1
(c)
ln(5)
3
+1
(d) ln 5 − ln 3
(e) 0
6. Suppose that a bacterial colony with an initial population P doubles its population every 7 hours. What
is the exponential growth model where t is the time in hours?
2
(a) P (t) = P 7t
(b) P (t) =
P t2
7
7t
(c) P (t) = P 2
t
(d) P (t) = P 7 2
t
(e) P (t) = P 2 7
7. What is the half-life of a sample that decayed 57% after 5 years?
(a) −5 ln .57
years
2
(b)
(c)
(d)
−5 ln 2
ln .43 years
−5 ln .57
years
ln 2
ln .43
years
5
(e) None of these
©Lynch, November 2015
Math 150 – Exam 3A
8. Find the domain and x-intercepts for f (x) =
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x3 +x2 −6x
x3 −2x2 −9x+18 .
(a) Domain: (−∞, 3) ∪ (3, ∞); x-int: 0
(b) Domain: (−∞, 3) ∪ (3, ∞); x-int: 0,2,−3
(c) Domain: (−∞, −3) ∪ (−3, 2) ∪ (2, 3) ∪ (3, ∞); x-int: 0
(d) Domain: (−∞, −3) ∪ (−3, 2) ∪ (2, 3) ∪ (3, ∞); x-int: 0,2,−3
(e) None of these
9. If f (x) = 7 sin(5x − 10) − 4, what is its amplitude, period, and phase shift, respectively?
(a) 7,
2π
5 ,
right 10
(b) 7, 10π, right 10
(c) 7,
(d) 7,
2π
5 ,
2π
5 ,
right 2
down 4
(e) None of these
10. Evaluate and fully simplify (rationalize the denominator if needed) sin(2θ) if tan θ =
(a)
(b)
(c)
(d)
√
−3 13
13
12
13
−12
13
−5
13
(e) None of these
3
2
and sin θ < 0.
©Lynch, November 2015
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Math 150, Fall 2015
Exam 3 – Form A
Work Out Problems
Sections 5B-8D
First Name:
Last Name:
Student ID number:
Section Number:
Directions:
1. Show all your work neatly and clearly mark your final answer. You will be graded not only on the final
answer, but also on the quality and correctness of the work leading up to it.
2. No calculators, cell phones, or other electronic devices may be used, and they must all be put away
out of sight.
3. There are 10 problems on this exam worth 5 points each, and a bonus question worth 5 points. You
must show your work to receive credit.
4. Together with the other part of the exam there will be a total of 110 points possible.
5. You may not discuss the contents of the exam with anyone until the exam is returned in class.
THE AGGIE CODE OF HONOR
“On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work.”
Signature:
Note: You are authorized to use a pencil, eraser, and your own TAMU student ID; use of
anything else is a violation of the honor code. If you need any extra paper, please ask your
instructor or TA; do not use your own.
Exam Part
Points Earned
Points
Multiple Choice
50
M.C. Bonus
5
Page 2-3:
25
Page 4-5:
20
Page 6:
10
Exam 1 Grade
100
©Lynch, November 2015
Math 150 – Exam 3A
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1. Find the horizontal asymptotes, vertical asymptotes, and holes for the function f (x) =
If there are none, write none.
(x−1)2 (2x2 +3x)
(x3 −x)(2x+3)2 .
Horizontal Asymptotes:
Vertical Asymptotes:
Holes (give your answers as points):
2. Using the generalized technique, determine the end behavior of the function f (x) =
must show your work).
3x4 −8x9 +3x
7x9 −5x5 +3 .
(You
3. Find the domain, range, x-intercepts, and y-intercept for f (x) = 2 log3 (x − 2) − 1. Also, determine if
the function is increasing or decreasing.
Domain:
Range:
x-intercepts:
y-intercepts:
Is the function increasing or decreasing?
©Lynch, November 2015
Math 150 – Exam 3A
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4. Solve the equation 2 ln x = ln 2 + ln(x + 12).
Solutions:
5. How many milliliters of a 60% saline solution and how many milliliters of a 10% saline solution should
be mixed to obtain 200 ml of a 20% solution?
mL of 60% saline solution:
mL of 10% saline solution:
©Lynch, November 2015
Math 150 – Exam 3A
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6. If tan x = −0.2 and cos x > 0, evaluate the following, and if needed, write your answer as a fraction in
lowest terms with a rationalized denominator.
cos x =
sin x =
cot x =
sec x =
csc x =
7. Write a function in the form of f (x) = a cos k(x − b) + c, whose graph is shown below, where a, k, and
b are positive and as small as possible.
f(x)=
©Lynch, November 2015
Math 150 – Exam 3A
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8. Evaluate and fully simplify (rationalize the denominator if needed) cos( 7π
6 + θ) if csc θ = 5/2 and
tan θ < 0.
cos( 7π
6 + θ) =
9. Solve the system of equations and give your answers as points.
6y = (x − 5)2 − 19
(x − 5)2 + y 2 = 10
Points:
©Lynch, November 2015
Math 150 – Exam 3A
10. Prove the identity tan x − sin x cos x =
sin3 x
cos x .
Put the starting side in the blank.
=
11. (Bonus Question) Find the domain of the function g(x) =
Domain in interval notation:
√
−2 7−2x
1−log6 (3x+12) .
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