©Fry Texas A&M University
1. (5 points)
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Given the linear system
Math 150 Precalculus
2x + 4y = 8
9x + 3y = 21
Spring 2016! 3
, the x -coordinate of the solution is
Circle one:
a) -2
b) -1
c) 0
d) 1
e) 2
f)
None of these because this system does not have a solution.
g) None of these because this system has an infinite number of solutions.
h) This system has a solution, but the x -coordinate of the solution is not listed above.
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2. (5 points) If a circle has a radius of 7 centimeters, find the exact area of the sector
π
subtended by a central angle of radians.
7
a) 49π cm 2
b)
49π
cm 2
2
c) 7π cm 2
d)
7π
cm 2
2
e) π cm 2
©Fry Texas A&M University
1. (5 points)
Math 150 Precalculus
Given the linear system
Spring 2016
4x + 2y = 8
, the x -coordinate of the solution is
3x + 9y = 21
Circle one:
a) -2
b) -1
c) 0
d) 1
e) 2
f)
None of these because this system does not have a solution.
g) None of these because this system has an infinite number of solutions.
h) This system has a solution, but the x -coordinate of the solution is not listed above.
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2. (5 points) If a circle has a radius of 11 centimeters, find the exact area of the sector
π
subtended by a central angle of
radians.
11
a) π cm 2
b)
11π
cm 2
2
c) 11π cm 2
d)
121π
cm 2
2
e) 121π cm 2
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3
©Fry Texas A&M University
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Math 150 Precalculus
Spring 2016! 4
3. (5 points) Here is a quadratic equation in general form f (x) = −4x 2 + 24x − 31 . Use your
algebraic skills to put this into standard form.
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4. (4 points)
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If p(x) = x(x − 6) , then the minimum value of this function is _______
©Fry Texas A&M University
Math 150 Precalculus
Spring 2016
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3. (5 points) Here is a quadratic equation in general form f (x) = −5x 2 + 30x − 41 . Use your
algebraic skills to put this into standard form.
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4. (4 points) If p(x) = x(x − 8) , then the minimum value of this function is ________
4
©Fry Texas A&M University
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Math 150 Precalculus
Spring 2016! 5
5. (8 points) Determine the x − intercepts of the graphs of the following functions. If the graph
of the function does not have any x − intercepts then write NONE.
a) f (x) = x 2 + 5x !
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b) g(x) = 16x 2 − 1 !
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c) h(x) = 6x 2 + 13x − 5 !
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d) p(x) = x 2 − 14x + 49 !
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6. 6 points) Factor:
a)
8x 3 − 1 = ______________________________________
b) 8x 3 − 6x 2 + 20x − 15 = ______________________________________
©Fry Texas A&M University
Math 150 Precalculus
Spring 2016
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5
5. (8 points) Determine the x − intercepts of the graphs of the following functions. If the graph
of the function does not have any x − intercepts then write NONE.
a)
f (x) = x 2 + 7x !
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b) g(x) = 25x 2 − 1 ! !
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c) h(x) = 6x 2 − 7x − 5 !
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d) p(x) = x 2 − 16x + 64 !
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6. (6 points) Factor:
a)
27x 3 − 1 = ______________________________________
b) 8x 3 − 10x 2 + 12x − 15 = ______________________________________
©Fry Texas A&M University
Math 150 Precalculus
Spring 2016
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7. (5 points) Use polynomial long division to simplify:
6x 4 − 8x 3 − x 2 + 20x − 35
= ______________________________________
2x 2 − 5
8. (5 points) A lab assistant needs 120 milliliters of a 50% methyl alcohol solution. She has
access to a 70% solution and a 40% solution. How much of the 70% solutions should she
use?
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____________________________mls
6
©Fry Texas A&M University
7. (5 points)
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Math 150 Precalculus
Spring 2016! 6
Use polynomial long division to simplify:
6x 4 − 12x 3 + x 2 + 18x − 15
2x 2 − 3
= ______________________________________
8. (5 points) A lab assistant needs 120 milliliters of a 50% methyl alcohol solution. She has
access to a 70% solution and a 40% solution. How much of the 40% solutions should she
use?
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____________________________mls
©Fry Texas A&M University
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9. (12 points) Let g(x) = x + 1 − 2
Math 150 Precalculus
Determine
the following:
a) Domain __________________
b) Anchor point _____________
c) y − intercept(s) _____________
d) x − intercept(s) _____________
e) Range_____________
f) Graph g(x) on Cartesian plane provided.
10. (14 points) Let f (x) = − x + 2 + 5
Determine the following:
a) Vertex _____________
b) y − intercept(s) _____________
c) x − intercept(s) _____________
d) Range _____________
e) f (x) is decreasing on _____________
g) Graph f (x) on Cartesian plane provided.
Spring 2016! 7
©Fry Texas A&M University
Math 150 Precalculus
9. (14 points) Let f (x) = − x + 4 + 3
Determine the following:
a) Vertex _____________
b) y − intercept(s) _____________
c) x − intercept(s) _____________
d) Range _____________
e) f (x) is decreasing on _____________
g) Graph f (x) on Cartesian plane
provided.
10. (12 points) Let g(x) = x + 1 − 2
Determine the following:
a) Domain __________________
b) Anchor point _____________
c) y − intercept(s) _____________
d) x − intercept(s) _____________
e) Range_____________
f) Graph g(x) on Cartesian plane provided.
Spring 2016
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7
©Fry Texas A&M University
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Math 150 Precalculus
Spring 2016! 8
11. (5 points) There are many quadratic functions with a vertex at (-3, -5) Write the equation
of the one that intersects the y − axis at (0, 13). State your answer in standard form.
( y = a ( x − h) + k )
2
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12. (3 points) f (x) = 3x + 4 , g ( x ) = 5x + 6
Simplify
( f ! g )( x )
= ______________________
©Fry Texas A&M University
Math 150 Precalculus
Spring 2016
!
8
11. (5 points) There are many quadratic functions with a vertex at (-2, -5) Write the
equation of the one that intersects the y − axis at (0, 7). State your answer in standard form.
( y = a ( x − h) + k )
2
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12. (3 points)
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f ( x ) = 5x + 6 ,
g(x) = 3x + 4
Simplify
( f ! g )( x )
= _____________________
©Fry Texas A&M University
a)
c)
e)
!
48 = ___________________
1
= ___________________
7
Math 150 Precalculus
b)
3
5
⎛ x ⎞
g) ⎜ −2 ⎟ = ______________
⎝x ⎠
f)
48 = ___________________
x 6 = ___________________
d)
3
1
= ___________________
5 −1
Spring 2016! 9
4
16 5 = ___________________
©Fry Texas A&M University
Math 150 Precalculus
Spring 2016
14. (14 points) Simplify completely
a)
3
c)
48 = ___________________
b)
x 6 = ___________________
d)
5
⎛ x ⎞
e) ⎜ −2 ⎟ = ___________________
⎝x ⎠
g)
4
16 5 = ______________
f)
48 = ___________________
1
= ___________________
5
3
1
= ___________________
7 −1
!
9
©Fry Texas A&M University
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Math 150 Precalculus
Spring 2016! 10
13. (6 points) Circle one:
a) 1 is the multiplicative identity.! !
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TRUE !
!
FALSE
illustrates the associative property of multiplication. ! TRUE !
!
FALSE
TRUE !
!
FALSE
TRUE !
!
FALSE
TRUE !
!
FALSE
TRUE !
!
FALSE
d) y = x !
e) none of these
b) (17 × 4 ) × 25 = 17 × ( 4 × 25 )
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c) f ( x ) = −
1
is an odd function.!
x2
!
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d) All even functions pass the vertical line test.!!
e)
2
is a rational number.!
2
!
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f) Every real number has a multiplicative inverse.!
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14. (2 points) All odd functions are symmetric about
a) x -axis !
b) y − axis ! !
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15. (2 points)
c) origin!
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A function is even if and only if
a) f (−x) = − f (x)
b) f (−x) = f (x)
c) f (x1 ) < f (x2 )
d) f (x1 ) > f (x2 ) ! e) None of these
16. (2 points) A function is decreasing on an interval I if for x1 , x2 ∈I and x1 < x2 , then
a) f (−x1 ) = − f (x2 )
b) f (−x1 ) = f (x2 )
c) f (x1 ) < f (x2 )
d) f (x1 ) > f (x2 ) e) None of these
©Fry Texas A&M University
Math 150 Precalculus
Spring 2016
!
10
13. (6 points) Circle one:
a) All even functions pass the vertical line test. !
!
TRUE !
!
FALSE
b) Every real number has a multiplicative inverse.!
!
TRUE !
!
FALSE
!
TRUE !
!
FALSE
illustrates the associative property of multiplication. ! TRUE !
!
FALSE
c)
2
is a rational number.!
2
d)
(17 × 4 ) × 25 = 17 × ( 4 × 25 )
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e) 1 is the multiplicative identity.! !
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!
TRUE !
!
FALSE
1
is an odd function.!!
x2
!
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!
TRUE !
!
FALSE
f) f ( x ) = −
14. (2 points) A function is decreasing on an interval I if for x1 , x2 ∈I and x1 < x2 , then
a) f (−x1 ) = − f (x2 )
b) f (−x1 ) = f (x2 )
c) f (x1 ) < f (x2 )
d) f (x1 ) > f (x2 ) e) None of these
15. (2 points) A function is even if and only if
a) f (−x) = − f (x)
b) f (−x) = f (x)
c) f (x1 ) < f (x2 )
d) f (x1 ) > f (x2 ) ! e) None of these
16. (2 points) All odd functions are symmetric about
a) x -axis !
!
b) y − axis ! !
c) origin!
!
d) y = x !
e) none of these