©Fry Texas A&M University
Math 150 Precalculus
Spring 2014
1. (4 points) Determine the slope of the line through the points (-4, 3) and (2, -1).
a) −
3
2
b) −
2
3
c)
2
3
d)
3
2
e)None of these
2. (4 points) Determine the equation of the line with slope -2 through the point (5, -1) .
!
!
!
!
3. (8 points)
!
!
!
Solve
!
!
!
!
!
!
!
_______________________
!
_________________________________
8x + 5y = 11
−3x − 2y = −5
!
!
3
©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
11π
subtended by a central angle of
radians.
25
a)
11π
cm 2
5
b)
22π
cm 2
5
c) 22 cm 2
d) 22π cm 2
e) None of these
5. (8 points) Here is a quadratic equation in general form f (x) = −9x 2 − 12x − 5 . Use your
algebraic skills to put this into standard form.
!
!
!
!
!
!
!
_________________________________
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 − 9x !
!
!
!
!
!
!
____________ _____________
b) g(x) = 4x 2 − 1 !
!
!
!
!
!
!
____________ ____________
c) h(x) = 3x 2 − 4x − 7 !
!
!
!
!
!
____________ _____________
7. (6 points)
⎛ 1⎞
If p(x) = − ⎜ ⎟ (x + 2)(x − 4) , then the maximum value of this function is _______
⎝ 2⎠
5
©Fry Texas A&M University
8. (7 points)
( 6x
4
Math 150 Precalculus
Spring 2014
Perform polynomial long division:
− x 3 − 48x + 8 ) ÷ ( x 2 + 2x + 4 ) = ______________________________________
9. (3 points) Factor:
27x 3 − 1 = ______________________________________
10. (4 points) If ax 2 + bx + c = 0 then x = ____________________________________
6
©Fry Texas A&M University
Math 150 Precalculus
11. (11 points) Let g(x) = 3 + 1− 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.
12. (11 points) Let f (x) = − x + 3 − 1
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.
7
Spring 2014
©Fry Texas A&M University
Math 150 Precalculus
Spring 2014
13. (14 points) Circle one:
a) 0 is the additive identity.!
!
TRUE !
!
FALSE
b) 3 + 24 + 97 = 3 + 97 + 24
!
illustrates the associative property of addition. ! !
TRUE !
!
FALSE
TRUE !
!
FALSE
TRUE !
!
FALSE
TRUE !
!
FALSE
TRUE !
!
FALSE
TRUE !
!
FALSE
d) y = x !
e) none of these
c) f ( x ) =
!
1
is an odd function.! !
x
!
!
!
!
!
d) All odd functions pass the vertical line test. ! !
e) The slope of the line perpendicular to y = 3x + 2 is
f)
π
is a rational number.!!
6
!
!
1
!
3
!
g) Every real number has a multiplicative inverse.!
!
14. (2 points) All even functions are symmetric about
a) x -axis !
b) y − axis ! !
!
15. (2 points)
c) origin!
!
A function is odd 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 increasing 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 )
8
d) f (x1 ) > f (x2 ) e) None of these