©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2015
Neatly print first and last names: ________________________________________________
Lecture Time:
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12:40 PM! !
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1:50 PM !
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(Circle one.)
Exam 3
"On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work."
__________________________________________________________
Signature of student
My signature in this blank allows my instructor to place my exam in a stack near the front of the
room where I will pick it up on the day they are returned.
________________________________________________________________
Signature of student
1. Write all solutions in the space provided as full credit might not be given
without complete, correct accompanying work, even if the final answer is
correct.
2. Intervals should be stated in interval notation.
3. Intercepts are points so, when requested, state both coordinates.
4. Unnecessary absolute value signs should be removed.
5. You may not discuss the contents of the exam with anyone until the exam is
returned in class.
6. No calculators are allowed.
7. All cell phones must be turned off and placed in your backpack.
8. Continuing to write on the exam after time is called is considered cheating.
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2015
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2
(1 point) NEATLY PRINT FIRST AND LAST NAMES: ________________________________
(1 point) LECTURE TIME:
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12:40 PM! !
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1:50 PM !
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PAGE 2 ______________________________________
PAGE 3 ______________________________________
PAGE 4 ______________________________________
PAGE 5 ______________________________________
PAGE 6 ______________________________________
PAGE 7 ______________________________________
PAGE 8 ______________________________________
PAGE 9 ______________________________________
PAGE 10 ______________________________________
PAGE 11 ______________________________________
TOTAL ______________________________________
(Circle one.)
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2015
1. (7 points) Label each of the graphs:
A. sin x
B. cos x
C. tan x
D. cot x
E. csc x
F. sec x
G. sin −1 x
H. cos −1 x
I. tan −1 x
a) _____________
b) ______________________
c) ______________________
d) ______________________
e) ______________________
f) _________________
g) ______________
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3
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2015
!
2. (11 points) For f (x) = 2 − x − 5 provide the following information. If there are none, write
NONE in the blank provided.
a) range (in interval notation):_______________
b) coordinates of the y-intercept _______________
c) coordinates of the x-intercept(s) __________________
d) Solve 2 − x − 5 = −1
e) Sketch f (x) = 2 − x − 5
x = ________________
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©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2015
!
3.. (14 points) For h ( x ) = log 2 ( x + 4 ) − 3 provide the following information. If there are none,
write NONE in the blank provided.
a) domain (in interval notation): _______________
b) range (in interval notation):_______________
c) coordinates of the anchor point: _________
d) coordinates of the y-intercept ____________
e) coordinates of the x-intercept(s) _____________
f) Solve log 2 ( x + 4 ) − 3 = −5
g) Sketch h ( x ) = log 2 ( x + 4 ) − 3
x = ________________
5
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2015
!
4. (4 points) Fully simplify ( log e) ( ln100 )
a) 2
b) 100e
c) e + 100
d) e100
e_ None of these
5. (12 points) Fully simplify, if possible. If the expression is undefined. Write, “Undefined.”
a) log 6 (1) =
c)
log 6 4 + log 6 9 =
e) log 6
( 6) =
⎛ 1⎞
b) log 6 ⎜ ⎟ =
⎝ 6⎠
d)
f)
6 log6 1296 =
log 6 6
( 6)
=
6
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2015
!
6. (6 points) Walking through Blocker, a classmate stops you. He is working on a problem
from the section on Law of Sines and Law of Cosines. In the problem two side lengths and
an angle measure of a triangle are given. Specifically,
a = 30 units,
b = 49 units, and A = 15! .
Your classmate did some work with his calculator and determined (correctly) that
B ≈ arcsin(.423) ≈ 25.0! (decimal approximations)
Now he is unsure of what to do. Hopefully you can help.
Circle and complete the best answer:
I. This is a case in which no triangle with the given measurements exists.
II. This is a case in which there is exactly one triangle
B ≈ ___________ and C ≈ _______________
III This is a case in which there are exactly 2 triangles
B ≈ _________ and C ≈ ____________
or
IV This is the case with infinitely many triangles.
V. None of the above.
B ≈ ___________ and C ≈ ____________
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©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2015
!
7. (5 points) The sides of a triangle measure 3, 5, and 7. Determine the cosine of the largest
angle?
______________________
8. (8 points) Given f (x) = −4 cos(3x) + 2
a) What is the amplitude of this function? ________________________
b) What is the period of this function? ___________________________
c) State the range of this function in interval notation. _________________
⎛π⎞
d) f ⎜ ⎟ = _____________________
⎝ 9⎠
8
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2015
!
9. (8 points) A 13 mcg sample of rhodium-101 decays to 3 mcg in 7 years. Determine the
half-life of rhodium-101.
half life = _____________________________
10. (4 points) A population of bacteria at time can be modeled with the following equation
P(t) = 700e0.3t
where t is given in days. How long does it take for the population of bacteria to reach 2500?
t=___________________
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©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2015
!
10
11. (14 points) Let f (x) = e x − 1
a) Sketch (and label) the graph of f (x) = e x − 1
b) The domain of f (x) = e x − 1 is ____________
c) The range of f (x) = e x − 1 is ______________
d) Is f (x) = e x − 1 a one-to-one function? _________
e) Determine f −1 (x) __________________
f) The domain of f −1 (x) is _______________
The range of f −1 (x) is __________________
g) Sketch (and label) the graph of f −1 (x) ___________________
12. (2 points) Circle the best answer. A function is one-to-one if
a) x1 = x2 implies that f (x1 ) = f (x2 )
b) f (x1 ) = f (x2 ) implies that x1 = x2
c) f (−x) = f (x)
d) f (−x) = − f (x)
e) it passes the vertical line test
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2015
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⎛
⎛ 3⎞ ⎞
13. (4 points) Simplify cos ⎜ tan −1 ⎜ ⎟ ⎟
⎝ 4⎠⎠
⎝
a)
−
4
5
b)
−
3
5
c)
3
5
d)
4
5
e) None of these
14. (4 points) ( sin x + cos x ) =
2
a) 1+ cos 2x
b) 1+ sin 2x
c) tan 2 x
d) 1
None of these
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