©Fry Texas A&M University
Math 150 Precalculus
Spring 2014
4. (5 points) If a circle has a radius of 10 centimeters, find the exact area of the sector
7π
subtended by a central angle of
radians.
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a) 14π cm 2
c)
b) 14 cm 2
14π
cm 2
5
d)
7π
cm 2
5
e) None of these
5. (8 points) Here is a quadratic equation in general form f (x) = −4x 2 − 12x − 11 . Use your
algebraic skills to put this into standard form.
!
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!
!
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!
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4
©Fry Texas A&M University
Math 150 Precalculus
Spring 2014
6. (12 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 − 4x ! !
b) g(x) = 9x 2 − 1 !
!
c) h(x) = 5x 2 − 2x − 3 !
!
!
!
!
!
____________ _____________
!
!
!
!
!
____________ _____________
!
!
!
!
!
____________ _____________
⎛ 1⎞
7. (6 points) If p(x) = − ⎜ ⎟ (x − 2)(x + 4) , then the maximum value of this function is ________
⎝ 2⎠
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©Fry Texas A&M University
8. (4 points) Factor:
Math 150 Precalculus
Spring 2014
8x 3 + 1 = _________________________________________
9. (3 points) If ax 2 + bx + c = 0 then x = ____________________________________
10. (7 points) Perform polynomial long division:
( 2x
4
+ x 3 − 54x − 27 ) ÷ ( x 2 + 3x + 9 ) = ______________________________________
6
©Fry Texas A&M University
Math 150 Precalculus
11. (11 points) Let f (x) = − x + 2 − 3
Determine the following:
a) Domain _____________
b) Range _____________
c) Vertex _____________
d) y − intercept _____________
e) f (x) is increasing on _____________
f) f (x) is decreasing on _____________
g) Graph f (x) on Cartesian plane provided.
12. (11 points) Let g(x) = 2 + 4 − x
Determine the following:
a) Domain _____________
b) Range_____________
c) Anchor point_____________
d) y − intercept _____________
e) g(x) is increasing on _____________
f) g(x) is decreasing on _____________
g) Graph g(x) on Cartesian plane provided.
7
Spring 2014
©Fry Texas A&M University
Math 150 Precalculus
Spring 2014
13. (14 points) Circle one:
a) All odd functions pass the vertical line test. ! !
!
TRUE !
!
FALSE
b) Every real number has a multiplicative inverse.!
!
TRUE !
!
FALSE
!
TRUE !
!
FALSE
3 + 24 + 97 = 3 + 97 + 24
illustrates the associative property of addition. ! !
TRUE !
!
FALSE
!
TRUE !
!
FALSE
1
!
3
TRUE !
!
FALSE
!
TRUE !
!
FALSE
d) y = x !
e) none of these
c)
d)
!
π
is a rational number.!
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e) 0 is the additive identity.!
!
!
!
!
!
!
f) The slope of the line perpendicular to y = 3x + 2 is
g)
f ( x) =
1
is an odd function.! !
x
!
!
14. (2 points) All odd functions are symmetric about
a) x -axis !
b) y − axis ! !
!
15. (2 points)
c) origin!
!
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 )
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d) f (x1 ) > f (x2 ) e) None of these