©Fry Texas A&M University
1. (3 points)
i)
ln (12 )
e
!
Math 150 Precalculus
Spring 2016! 3
log (12 ) =
ii) 1+ log ( 2 )
iii)
log ( 24 )
log ( 2 )
iv) log ( 24 ) − log ( 2 )
v) None of these
2. (3 points) Determine the domain of h(x) = log(1− x) + log(1+ x)
i) (−1, 1)
ii) (−∞, ∞)
iv) (−1, ∞)
iii) (−∞, − 1) ∪ (−1, 1) ∪ (1, ∞)
v) (−∞, 1)
3. (3 points) ln (1000 ) =
i)
e3
ii)
3− e
iii) 3 − log e
iv)
3
e
v)
3
log e
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2016! 3
1. (3 points) ln (100 ) =
i)
2
log e
2. (3 points)
i)
log ( 24 )
log ( 2 )
ii)
2
e
iii) 2 − log e
iv) 2 − e
v)
e2
log (12 ) =
ii) log ( 24 ) − log ( 2 )
iii) 1+ log ( 2 )
iv)
ln (12 )
e
v) None of these
3. (3 points) Determine the domain of h(x) = log(2 − x) + log(2 + x)
i) (−∞, ∞)
ii) (−2, 2)
iii) (−∞, − 2) ∪ (−2, 2) ∪ (2, ∞)
iv) (−2, ∞)
v) (−∞, 2)
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!
4. (9 points) If
f (x) =
3 − 2x
5x − 4
5x − 4
3 − 2x
ii)
4x + 3
5x + 2
i)
Math 150 Precalculus
, then
iii)
Spring 2016! 4
f −1 (x) = !
2x − 3
4 − 5x
iv)
5x + 2
4x + 3
v) None of these
In interval notation state
b) the domain of f (x) ___________________________________________
c) the range of f (x) ___________________________________________
©Fry Texas A&M University
4. (9 points) If f (x) =
i)
4x − 5
2 − 3x
ii)
!
2 − 3x
4x − 5
4x + 3
5x + 2
Math 150 Precalculus
, then
a)
iii)
Spring 2016! 4
f −1 (x) = !
3x − 2
4 − 4x
iv)
5x + 2
4x + 3
v) None of these
In interval notation state
b) the domain of f (x) ___________________________________________
c) the range of f (x) ___________________________________________
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2016! 5
⎛x π⎞
5. (10 points) f (x) = 2sin ⎜ + ⎟ + 1 . Determine
⎝ 3 3⎠
a) the amplitude of f (x) _____________________
b) the range of f (x) _____________________
c) the period of f (x) _____________________
d) the phase shift is
e) plot 1 period of f (x)
____________________ to the left / right .
(Circle one)
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2016! 5
⎛x π⎞
5. (10 points) f (x) = 3sin ⎜ − ⎟ − 1 . Determine
⎝ 2 2⎠
a) the amplitude of f (x) _____________________
b) the range of f (x) _____________________
c) the period of f (x) _____________________
d) the phase shift is
e) plot 1 period of f (x)
____________________ to the left / right .
(Circle one)
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2016! 6
6. (10 points) For f (x) = −2 x + 3 , determine the following.
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 __________________
d) the coordinates of the point where the graph of
f (x) = −2 x + 3 intersects the line y = −5
e) Sketch f (x) = −2 x + 3
! !
!
_______________________
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2016! 6
6. (10 points) For f (x) = −2 x + 5 , determine the following.
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 __________________
d) the coordinates of the point where the graph of
f (x) = −2 x + 5
intersects the line y = −3
e) Sketch f (x) = −2 x + 5
!!
!
_______________________
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2016! 7
7. (14 points) Evaluate, if possible. Otherwise write, “Undefined” if undefined or “Impossible
without a calculator, “ if the expression cannot be simplified further without a calculator.
a) log 4 64 = ______________
⎛ 1⎞
= ______________
⎝ 16 ⎟⎠
c) log 4 ⎜
e)
ln 0 = ____________
g) log 4
2 = ____________
b)
d)
f)
h)
ln1 = _________________
eln 3 =
______________
2 log 5 + log 4 =
______________
log 6 + log 5 − log 3 =
________
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2016! 7
7. (14 points) Evaluate, if possible. Otherwise write, “Undefined” if undefined or “Impossible
without a calculator, “ if the expression cannot be simplified further without a calculator.
a)
ln1 = ______________
b)
c)
eln 3 =
d) log 4 ⎜
______________
e) log 4 64 = ____________
g)
log 6 + log 5 − log 3 =
ln 0 = __________
⎛ 1⎞
= ______________
⎝ 16 ⎟⎠
f) log 4
____________
h)
2 = ______________
2 log 5 + log 4 =
____________
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2016! 8
8. (5 points) Given an initial amount A(0) of Carbon-14, the amount remaining after t years is
!
!
!
A(t) = A(0)ekt
! !
where
k = −1.2 × 10 −4
Determine the half-life of Carbon-14.
9. (5 points) During its exponential growth phase, a colony of bacteria triples every five days.
If the colony starts with 1000 bacteria, which of the following models predicts the population
t days later?
i)
P(t) = 1000e 3t
ii)
P(t) = 1000e5t
iii)
P(t) = (1000 ) ( 35t )
iv)
P(t) = (1000 ) ( 5 3t )
v)
vi)
⎛t⎞
⎜⎝ ⎟⎠
5
P(t) = (1000 ) i 3
P(t) = (1000 ) i 5
⎛t⎞
⎜⎝ ⎟⎠
3
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2016! 8
8. (5 points) During its exponential growth phase, a colony of bacteria triples every five days.
If the colony starts with 1000 bacteria, which of the following models predicts the population
t days later?
i)
P(t) = 1000e5t
ii)
P(t) = 1000e 3t
iii)
P(t) = (1000 ) ( 5 3t )
iv)
P(t) = (1000 ) ( 35t )
v)
vi)
P(t) = (1000 ) i 5
⎛t⎞
⎜⎝ ⎟⎠
3
⎛t⎞
⎜⎝ ⎟⎠
5
P(t) = (1000 ) i 3
9. (5 points) Given an initial amount A(0) of Plutonium-240, the amount remaining after t
years is
!
!
!
A(t) = A(0)ekt
! !
Determine the half-life of Plutonium-240.
where
k = −1.1× 10 −4
©Fry Texas A&M University
!
Math 150 Precalculus
10. (5 points) Solve log 2 ( 3x + 1) = −1 ! !
!
!
Spring 2016! 9
!
____________________
11. (5 points) Given a triangle with side lengths, 3 cm, 4 cm, and 5cm, what is the cosine of
the smallest angle?
!
!
!
!
!
!
!
!
!
_________________________
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2016! 9
10. (5 points) Given a triangle with side lengths, 3 cm, 4 cm, and 5cm, what is the cosine of
the smallest angle?
!
!
!
!
!
!
11. (5 points) Solve log 2 ( 5x + 1) = −1 !
!
!
!
_________________________
!
!
!
!
____________________
©Fry Texas A&M University
!
Math 150 Precalculus
12. (5 points) Let △ABC be such that
c is
i)
28sin 50!
sin 20!
ii)
28sin 50!
sin110!
iii)
Spring 2016! 10
A = 110! , B = 50! , and b = 28 . Then the length of side
28sin 20!
sin110!
iv)
28sin 20!
sin 50!
v)
28sin110!
sin 50!
vi)
28sin110!
sin 20!
13. (6 points) Evaluate
a) sin −1 ( −1) = ______________
⎛ ⎛ 5π ⎞ ⎞
b) sin −1 ⎜ sin ⎜ ⎟ ⎟ = ______________
⎝ ⎝ 3 ⎠⎠
⎛
⎛ 7 ⎞⎞
c) sin ⎜ sin −1 ⎜
⎟ = ______________
⎝ 3 ⎟⎠ ⎠
⎝
⎛
⎛ 3⎞ ⎞
14. (4 points) Evaluate sin ⎜ tan −1 ⎜ ⎟ ⎟
⎝ 4⎠⎠
⎝
i) −
3
4
ii)
3
4
iii) −
3
5
iv)
3
5
v) −
4
5
vi)
4
5
vii) Undefined
©Fry Texas A&M University
12.
!
Math 150 Precalculus
Spring 2016! 10
⎛
⎛ 3⎞ ⎞
(4 points) Evaluate cos ⎜ tan −1 ⎜ ⎟ ⎟
⎝ 4⎠⎠
⎝
i) −
3
4
ii)
3
4
iii) −
3
5
iv)
3
5
v) −
4
5
vi)
4
5
vii) Undefined
13. (6 points) Evaluate
⎛
⎛ 7 ⎞⎞
a) sin ⎜ sin −1 ⎜
⎟
⎝ 3 ⎟⎠ ⎠
⎝
= ______________
b) sin −1 ( −1) = ______________
c)
⎛ ⎛ 5π ⎞ ⎞
sin −1 ⎜ sin ⎜ ⎟ ⎟ = ______________
⎝ ⎝ 3 ⎠⎠
14. (5 points) Let △ABC be such that
c is
i)
28sin 50!
sin 20!
ii)
28sin 50!
sin110!
iii)
A = 110! , B = 50! , and b = 28 . Then the length of side
28sin110!
sin 50!
iv)
28sin110!
sin 20!
v)
28sin 20!
sin110!
vi)
28sin 20!
sin 50!
©Fry Texas A&M University
15. (8 points)
!
!
Math 150 Precalculus
TRUE OR FALSE
T = True, !
!
F= False, !
!
CN = Calculator necessary to determine
sin 32! = sin148!
T
F
CN
sin 32! = 2sin16!
T
F
CN
T
F
CN
T
F
CN
sin 32 =
!
cos 2! +
( 3 ) sin 2
!
2
sin 2 ( 32! ) + cos 2 ( 32! ) = 1
16. (4 points)
i) sin 2 ( x )
Spring 2016! 11
tan 2 x
=
tan 2 x + 1
ii) cos 2 ( x )
iii) sec 2 ( x )
iv) 1
v) None of these
©Fry Texas A&M University
15. (4 points)
Math 150 Precalculus
ii) sec 2 ( x )
16. (8 points)
Spring 2016! 11
tan 2 x
=
tan 2 x + 1
i) 1
!
!
iii) sin 2 ( x )
iv) cos 2 ( x )
v) None of these
TRUE OR FALSE
T = True, !
!
F= False, !
!
CN = Calculator necessary to determine
sin 2 ( 32! ) + cos 2 ( 32! ) = 1
T
F
CN
sin 32! = 2sin16!
T
F
CN
sin 32! = sin148!
T
F
CN
T
F
CN
sin 32 =
!
cos 2! +
( 3 ) sin 2
2
!
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2016! 12
17. (4 points) Matching
A
B
C
D
E
F
a) sec x
________
b) csc x
________
c) tan x
________
d) cot x
________
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2016! 12
17. (4 points) Matching
A
B
C
D
E
F
a) sec x
________
b) csc x
________
c) tan x
________
d) cot x
________