©Fry Texas A&M University
1. (5 points) If tan θ = −
a) −
3 13
3
!
Math 150 Precalculus
Spring 2016! 3
3
and sin θ > 0 determine cosθ
2
b) −
2 13
3
c)
2 13
3
d)
3 13
3
e) None of these
2. (5 points) Determine the length of the hypotenuse of the following right triangle.
π
The horizontal leg measures 7 cm. The angle measures radians .
3
π
3
7 cm
a) 14 cm
b) 7 3 cm
c) 7 2 cm
d)
7 3
cm
2
e)
7 3
cm
3
©Fry Texas A&M University
1. (5 points) If tan θ = −
a) −
3 13
3
!
Math 150 Precalculus
Spring 2016! 3
3
and cosθ < 0 determine sin θ
2
b) −
2 13
3
c)
2 13
3
d)
3 13
3
e) None of these
2. (5 points) Determine the length of the hypotenuse of the following right triangle.
π
The horizontal leg measures 5 cm. The angle measures radians .
3
π
3
5 cm
a)
5 3
cm
3
b)
5 3
cm
2
c) 5 2 cm
d) 5 3 cm
e) 10 cm
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2016! 4
!
!
!
!
!
For 3 - 8, circle the function corresponding to the graph. (2 points each)
3
a) f (x) = ( x + 1) ( x − 1)
2
3
b) g(x) = − ( x + 1) ( x − 1)
2
c) h(x) = ( x + 1) ( x − 1)
3
3
2
d) p(x) = − ( x + 1) ( x − 1)
3
2
e) r(x) = x ( x + 1) ( x − 1)
4
a) f (x) = ( x + 1) ( x − 1)
3
b) g(x) = − ( x + 1) ( x − 1)
c) h(x) = ( x + 1) ( x − 1)
2
3
3
d) p(x) = − ( x + 1) ( x − 1)
2
e) r(x) = ( x + 1) ( x − 1)
2
5
a) f (x) = x ( x − 1)
b) g(x) = x ( x + 1)
2
2
2
c) h(x) = −x ( x − 1)
2
d) p(x) = x ( x + 1) ( x − 1)
e) r(x) = −x ( x + 1) ( x − 1)
3
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2016! 4
For 3 - 8, circle the function corresponding to the graph. (2 points each)
3
a) f (x) = x ( x − 1)
b) g(x) = x ( x + 1)
2
2
c) h(x) = −x ( x − 1)
2
d) p(x) = x ( x + 1) ( x − 1)
e) r(x) = −x ( x + 1) ( x − 1)
4
a) f (x) = ( x + 1) ( x − 1)
3
b) g(x) = − ( x + 1) ( x − 1)
c) h(x) = ( x + 1) ( x − 1)
2
3
3
d) p(x) = − ( x + 1) ( x − 1)
2
e) r(x) = ( x + 1) ( x − 1)
2
5
2
a) f (x) = ( x + 1) ( x − 1)
2
3
b) g(x) = − ( x + 1) ( x − 1)
2
c) h(x) = ( x + 1) ( x − 1)
3
3
3
2
d) p(x) = − ( x + 1) ( x − 1)
3
e) r(x) = x ( x + 1) ( x − 1)
2
©Fry Texas A&M University
6
!
Math 150 Precalculus
Spring 2016! 5
a) f (x) = x ( x + 1) ( x − 1)
b) g(x) = −x ( x + 1) ( x − 1)
c) h(x) = x 2 ( x + 1) ( x − 1)
2
d) p(x) = −x 2 ( x + 1) ( x − 1)
2
e) r(x) = −x 2 ( x + 1) ( x − 1)
7
2
a) f (x) = x ( x + 1) ( x − 1)
2
b) g(x) = −x ( x + 1) ( x − 1)
2
c) h(x) = x ( x + 1) ( x − 1)
2
d) p(x) = −x ( x + 1) ( x − 1)
e) r(x) = − ( x + 1) ( x − 1)
2
8
a) f (x) = x ( x − 1)
2
b) g(x) = −x ( x − 1)
c) h(x) = x ( x + 1)
2
2
2
d) p(x) = −x ( x + 1)
2
e) r(x) = −x ( x + 1) (x − 1)
2
©Fry Texas A&M University
6
!
Math 150 Precalculus
Spring 2016! 5
a) f (x) = x ( x − 1)
2
b) g(x) = −x ( x − 1)
c) h(x) = x ( x + 1)
2
2
d) p(x) = −x ( x + 1)
2
e) r(x) = −x ( x + 1) (x − 1)
7
a) f (x) = x ( x + 1) ( x − 1)
b) g(x) = −x ( x + 1) ( x − 1)
c) h(x) = x 2 ( x + 1) ( x − 1)
2
d) p(x) = −x 2 ( x + 1) ( x − 1)
2
e) r(x) = −x 2 ( x + 1) ( x − 1)
8
2
a) f (x) = x ( x + 1) ( x − 1)
2
b) g(x) = −x ( x + 1) ( x − 1)
2
c) h(x) = x ( x + 1) ( x − 1)
2
d) p(x) = −x ( x + 1) ( x − 1)
e) r(x) = − ( x + 1) ( x − 1)
2
2
2
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2016! 6
x 2 + 4x + 3
9. (12 points) If f (x) =
, then give the following. If there are none, write NONE in
3x 2 − 27
the blank provided.
a) State the domain of f (x) in interval notation. ______________________________
b) List the coordinates of all of the x -intercepts.
c) List the coordinates of all of the y -intercepts.
___________________________
___________________________
d) List the equations of all of the vertical asymptotes.___________________________
e) List the coordinates of all the holes. __________________________
f) List the equations of all of the horizontal asymptotes ______________________________
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2016! 6
x 2 + 5x + 6
9. (12 points) If f (x) =
, then give the following. If there are none, write NONE in the
2x 2 − 8
blank provided.
a) State the domain of f (x) in interval notation. ______________________________
b) List the coordinates of all of the x -intercepts.
c) List the coordinates of all of the y -intercepts.
___________________________
___________________________
d) List the equations of all of the vertical asymptotes.___________________________
e) List the coordinates of all the holes. __________________________
f) List the equations of all of the horizontal asymptotes ______________________________
©Fry Texas A&M University
10. (5 points)
Solve
!
Math 150 Precalculus
Spring 2016! 7
x
−5 >3
2
a) (16, ∞)
b) (4, 16)
c) (−∞, 4) ∪ (16, ∞)
d) (−∞, − 16) ∪ (4, ∞)
e) (−∞, ∞)
11. (4 points) Fully simplify the expression
(
)
4x + 9 − 1
Circle the best answer (correct and completely simplified):
a) 4x + 10
b) 4x + 8
c) 4x + 10 − 2 4x + 9
d) 4x + 8 − 2 4x + 9
e) 4x + 10 − 2 2x + 3
2
©Fry Texas A&M University
!
Math 150 Precalculus
10. (4 points) Fully simplify the expression
(
Spring 2016! 7
)
9x + 4 − 1
Circle the best answer (correct and completely simplified):
a) 9x + 3
b) 9x + 5
c) 9x + 5 − 2 3x + 2
d) 9x + 5 − 2 9x + 4
e) 9x + 4 − 2 9x + 4
11. (5 points)
Solve
a) (4, 16)
b) (16, ∞)
c) (−∞, − 16) ∪ (4, ∞)
d) (−∞, 4) ∪ (16, ∞)
e) (−∞, ∞)
x
−5 >3
2
2
©Fry Texas A&M University
12. (8 points) Solve
(
!
Math 150 Precalculus
Spring 2016! 8
)
5− x − x = 7
13. (6 points) Solve x 2 + 11 = 6x !!
!
!
________________________________
©Fry Texas A&M University
12. (8 points) Solve
(
!
)
6− x − x = 6!
13. (6 points) Solve x 2 + 7 = 4x !!
Math 150 Precalculus
Spring 2016! 8
!
!
________________________________
!
________________________________
©Fry Texas A&M University
14. (5 points) Solve
!
Math 150 Precalculus
Spring 2016! 9
3
<2!
x +1
State your answer in interval notation: __________________________________________
15. (6 points) Determine the x-intercepts of the graph of f (x) = x 6 + 7x 3 − 8
!
!
!
!
!
!
!
__________________________________
©Fry Texas A&M University
14. (5 points) Solve
!
Math 150 Precalculus
Spring 2016! 9
2
<3
x −1
State your answer in interval notation: __________________________________________
15. (6 points) Determine the x-intercepts of the graph of f (x) = x 6 − 7x 3 − 8
!
!
!
!
!
!
!
__________________________________
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2016! 10
16. (6 points) Solve x 2 − 4x > 5
State your answer in interval notation: __________________________________________
17.
(10 points)
z1 = 2 − 3i ,
z2 = −1+ 4i
a) Put the following in standard form:
i) z1 + z2 = _____________________________________________________________
ii) z1z2 = _____________________________________________________________
iii) z1 = _____________________________________________________________
b) Determine
c)
z1 = __________________________________________________
z1 represents ______________________________________________________
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2016! 10
16. (6 points) Solve x 2 + 2x > 3 .
State your answer in interval notation: __________________________________________
17.
(10 points)
z1 = −3 + 2i ,
z2 = 4 − i
a) Put the following in standard form:
i) z1 + z2 = _____________________________________________________________
ii) z1z2 = ______________________________________________________________
iii) z1 = _____________________________________________________________
b) Determine
c)
z1 = __________________________________________________
z1 represents ______________________________________________________
©Fry Texas A&M University
18. (4 points) Fully simplify
!
Math 150 Precalculus
1
1
− 2
!
x+3 x −9
19. (4 points) Determine the domain of
a) (−∞, -1) ∪ (−1, ∞)
b) (−∞, 1) ∪ (1, ∞)
c) (−∞, -1) ∪ (−1, 1) ∪ (1, ∞)
d) (−∞, -1) ∪ (−1, 0) ∪ (0, 1) ∪ (1, ∞)
e) (−∞, ∞)
!
f (x) =
Spring 2016! 11
________________________________
(x − 1)2
x2 + 1
©Fry Texas A&M University
!
Math 150 Precalculus
18. (4 points) Determine the domain of
Spring 2016! 11
(x − 1)2
f (x) = 2
x +1
a) (−∞, -1) ∪ (−1, ∞)
b) (−∞, 1) ∪ (1, ∞)
c) (−∞, -1) ∪ (−1, 1) ∪ (1, ∞)
d) (−∞, -1) ∪ (−1, 0) ∪ (0, 1) ∪ (1, ∞)
e) (−∞, ∞)
19. (4 points) Fully simplify
1
1
− 2
!
x+2 x −4
!
________________________________
©Fry Texas A&M University
!
20. (5 points) Fully simplify
a)
1
x5
b)
a) −∞
a) −∞
23. (2 points) !
a) −∞
−x 2
(1− x 3 )
(1− x 3 )
p(x) =
−x 2
b) ∞
!
b) ∞
1
x
c)
b) ∞
22. (2 points) !
Spring 2016! 12
x −3 + x −2
1
x2
h(x) =
21. (2 points) !
Math 150 Precalculus
d)
As x → −∞ ,
x +1
x3
h(x) →
c)
−1
!
As x → −∞ , p(x) →
c)
−1
−x 2
r(x) =
(1− x 2 )
c)
e) None of these
d) 0
d) 0
e) 1
e) 1
As x → −∞ , r(x) →
−1
d) 0
e) 1
©Fry Texas A&M University
22. (2 points) !
a) −∞
p(x) =
1
x5
(1− x 3 )
−x 2
r(x) =
!
1
x2
h(x) →
−1
!
As x → −∞ , p(x) →
c)
−1
−x 2
(1− x 2 )
b) ∞
b)
Spring 2016! 12
c)
b) ∞
23. (5 points) Fully simplify
a)
As x → −∞ ,
b) ∞
21. (2 points) !
a) −∞
Math 150 Precalculus
−x 2
h(x) =
(1− x 3 )
20. (2 points) !
a) −∞
!
d) 0
d) 0
e) 1
e) 1
As x → −∞ , r(x) →
c)
−1
c)
1
x
d) 0
e) 1
x −3 + x −2
d)
x +1
x3
e) None of these