Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine whether the equation is a conditional equation, an identity, or a contradiction.
1
1) 3(z + 2) - 5z = 4 - z +1 + 2
2
A) Conditional
B) Identity
C) Contradiction
Solve the rational equation.
3
3x - 18
3
2) +
=
x x-7
x-7
A) {7,
3)
1}
2)
B)
5 1
- ,
2 3
C) {1}
}
1}
3)
B) {5}
C) {5,
Solve for the indicated variable.
4) T = cMN2 for N2
cM
cT
A) N2 =
B) N2 =
T
M
5)
D) {
1
5
1
=
x - 4 x + 1 x2 - 3x - 4
A) {-5,
1}
D)
{}
4)
C) N2
=
T
cM
D) N2
= cMT
c
q = (h + r) for r
4
A) r
=
4q - h
c
5)
B) r
=
4c
-h
q
C) r
=
4q
-h
c
D) r
=
q
-h
4c
Solve the equation.
1
1
1
1
6) - x = - (x + 1) - x
4
6
6
12
6)
A) {0}
C) All
1)
real numbers
B) {
}
D)
1
3
-
Solve the problem.
7) If $13,000 is borrowed at 5.8% simple interest for 10 years, how much interest will be
paid for the loan?
A) $20,540.00
B) $9,845.47
C) $22,845.47
D) $7,540.00
1
7)
8)
Two cars are 261 miles apart and travel toward each other on the same road. They meet
in 3 hours. One car travels 3 mph faster than the other. What is the average speed of each
car?
A) 41 mph; 44 mph
B) 39 mph; 42 mph
C) 40 mph; 43 mph
D) 42 mph; 45 mph
8)
9)
A consultant traveled 255 miles to attend a meeting, traveling 45 mph hours for the first
part of the trip, then increasing to a speed of 60 mph for the second part. If the entire trip
took 5 hours, how far did the consultant travel at the faster speed?
A) 120 mi
B) 135 mi
C) 127.5 mi
D) 180 mi
9)
10) It takes
10)
11) One
11)
Terrell 69 minutes to weed his garden if he does it every 2 weeks, while his wife
can get it done in 49 minutes. How long would it take them working together? Round
to the nearest tenth of a minute.
A) 24.5 minutes
B) 34.5 minutes
C) 28.7 minutes
D) 29.5 minutes
number is 33 more than another number. The quotient of the larger number and
smaller number is 5 and the remainder is 1. Find the numbers.
A) 8 and 41
B) 10 and 43
C) 5 and 38
D) 11 and 44
Simplify the expression.
12) -81
-3
A) 9 -3
12)
B) -9
C) -27
3
D) 9
3
Simplify and write the result in standard form, a + bi.
4 + -18
13)
6
A)
14)
2
2
+
i
3
2
B)
2
2
i
3 2
13)
C)
18
3
+
i
5
6
D)
18
2
i
3
6
-8 - 10i
-2
A) 4
14)
B) 4
+ 10i
Solve the equation.
15) 5w (5w + 12) = -32
8 4
A) - ,
5 5
16) (m + 3)(m - 4)
A) {3, -4}
C) 4
- 5i
- 10i
D) 4
+ 5i
15)
B)
8 4
,
5 5
C)
0, -
12
5
D)
8 4
- ,5 5
16)
= -6
B) {-3,
C) {-2,
4}
2
3}
D) {2,
-3}
Solve the quadratic equation by completing the square and applying the square root property.
17) 2v2 + 4v + 12 = 0
17)
A) {-1 - i 5, -1 + i 5}
B) {-1 - 5, -1 + 5}
C) {-2 - i 2, -2 + i 2}
D) {-2 - 2, -2 + 2}
18) 3x2
+ 5x - 6 = 0
47
5
A) ±
3
3
18)
97
5
±
6
6
B) -
C) -
47
5
±
6
6
97
5
±
3
3
D) -
Solve the equation by using the quadratic formula.
4 1
19) = x - 5x2
3 6
A)
20)
959
1
±
i
16
16
y2 = 4y - 9
A) {-4 ± 2i 5}
B)
-8,
19)
9
30
C)
161
1
±
10
10
D)
1 8
- ,
2 15
20)
B) {-
C) {2
2 ± i 5}
± i 5}
D) {4
± 2i 5}
Use the discriminant to determine the type and number of solutions.
21) -2x2 + 5x + 5 = 0
A) Two irrational solutions
B) Two imaginary solutions
C) One rational solution
D) Two rational solutions
22) 6q2 = 1
A) Two
C) Two
22)
B) Two imaginary solutions
D) One rational solutions
irrational solutions
rational solutions
Solve for the indicated variable.
23) c = 9 r for r
c
c
A) r =
B) r =
9
81
24) w
1
= kr2
3
A) r
=
21)
23)
c2
C) r =
9
c2
D) r =
81
24)
for r > 0
3wk
k
B) r
=
3w
k
C) r
Solve the equation.
25) 5(x + 2) + x2 = x(x + 5) + 10
A) No solution
C) 2 5
= 3w
D) r
=
3 w
k
25)
B) All
D) {0}
3
real numbers
Solve the problem.
26) The length of a rectangle is 4 yd more than twice the width x. The area is 390 yd2 . Find
the dimensions of the given shape.
A) 6.5 yd. by 60 yd.
B) 13 yd. by 30 yd.
C) 26 yd. by 15 yd.
D) 13 yd. by 26 yd.
27) The sum of the
A) 11 and 12
squares of two consecutive whole numbers is 25. Find the numbers.
B) 2 and 3
C) 12 and 13
D) 3 and 4
28) The sum of an integer
A) 25 and 36
and its square is 30. Find the integers.
B) 5 and -6
C) 5 and 25
26)
27)
28)
D) -6
and 36
29) A
29)
30) The
30)
rectangular garden covers 46 yd2 . The length is 3 yd longer than the width. Find the
length and width. Round to the nearest tenth of a yard.
A) length = 6.8; width = 9.8 yd
B) length = 5.4; width = 8.4 yd
C) length = 9.8; width = 6.8 yd
D) length = 8.4; width = 5.4 yd
height of a triangular truss is 5 ft less than the base. The amount of drywall needed
to cover the triangular area is 84 ft2 . Find the base and height of the triangle to the
nearest tenth of a foot.
A) base = 21 ft; height = 16 ft
B) base = 15.7 ft; height = 10.7 ft
C) base = 12 ft; height = 7 ft
D) base = 15.9 ft; height = 10.9 ft
Solve the equation.
31) -5(w2 - 7)(w2 + 4)
A) {± 7, ±2i}
32) 180x3
A)
33)
31)
B) {0,
C) {±
± 7, ±2i}
7}
D) {0,
± 7}
32)
+ 36x2 - 5x - 1 = 0
- 5, ±6
B)
-
1
5
C)
1 1
- ,±
5 6
D)
1 1
,± i
5 6
20
10
+5=
c-2
c2 - 2c
A) {0,
2}
33)
B) {2}
C) {
Solve the absolute value equation.
34) 6z - 3 = 7
5 2
2
A) B)
,3 3
3
35) 3
- 3w + 9 = 6
A) {-1, -5}
}
D) {±2}
34)
C)
{7, -6}
D)
5
3
35)
B) {-1}
C) {
4
}
D) {2,
-2}
Solve the equation.
36) -3 + 5x + 5 = 5
69
A)
5
37)
38)
5
10z + 2 =
A) {3}
5
B)
-
1
5
C)
59
5
D)
64
5
37)
7z + 11
11 - p - 2 + p = -1
A) {±2}
39) n4/5
36)
B) {-3}
C) {0}
D) {6}
38)
B) {7,
C) {2}
2}
D) {7}
39)
=3
A) {±35/4 }
B)
±
15
4
C) {35/4 }
D)
15
4
Solve the problem.
40) The amount of time it takes an object dropped from an initial height of h0 feet to reach a
height of h feet is given by the formula
h -h
t= 0
.
16
40)
An object dropped from the top of the Sears Tower in Chicago takes 9.7 seconds to
reach the ground. Use the above equation to approximate the height of the Sears Tower
to the nearest foot.
A) 1,505 feet
B) 1,219 feet
C) 1,584 feet
D) 1,032 feet
Make an appropriate substitution and solve the equation.
5
6
41) + +1=0
a2 a
A) {-3
C)
B)
+ 14, -3 - 14}
-3 + 14 -3 - 14
,
5
5
41)
3 + 14 3 - 14
,
5
5
D) {3
+ 14, 3 - 14}
42) 9t
- 16 t = 0
3
A) 0,
4
42)
B)
0,
4
3
C)
5
0,
81
256
D)
0,
256
81
Solve the problem.
43) The distance d (in miles) that an observer can see on a clear day is approximated by
49
d=
h, where h is the height of the observer in feet. It Rita can see 24.5 mi, how far
40
above ground is her eye level?
A) 6 ft
B) 40 ft
C) 400
D) 20
ft
Solve the inequality. Write the solution set in interval notation.
44) -2(7y - 7) + y > 2y - (-5 + y)
9
9
9
A)
B)
C)
,
,
,
14
14
14
ft
44)
D)
2
,
7
45) -1
45)
- 2(2x + 1) < x - (-1 - x)
2
A) - ,
B) (- , -1)
3
46)
4
1
y5
6
A)
y+
,-
48)
-
,-
2
3
B)
17
,
6
C)
,
1
2
D)
,-
1
2
47)
B) (-
10
,
9
,-
2
- ,
3
+ 0.07
C) (-
, 0.6]
, 6]
B)
21
15
D) [0.6,
)
1
x+1
5
48)
2
,
3
C)
,
2
3
D)
Solve the absolute value inequality. Write the solution in interval notation.
49) 24 2 + -15t + 1
21 23
A) { }
B) ,
15 15
C)
D)
46)
3
1
(x - 2) - (x - 2)
2
4
A)
C)
2
5
17
6
47) 0.31 0.04a
A) [6, )
43)
23
,
15
D) {-22,
,-
10
9
49)
22}
50) |2b
50)
- 23| > -15
A) [4, 19]
C) { }
B) (-
, )
D) (- , 4] [19, )
6
51) 3|x
51)
- 9| + 9 < 15
A) (- , 7) (11, )
C) (1, 17)
B) (-
, 1)
D) (7, 11)
(17, )
52) 3|x
52)
- 5| + 12 15
A) [4, 6]
C) (- , -4] [14, )
B) [-4,
14]
D) (- , 4] [6, )
Solve the problem.
53) Sparky has scores of 71, 60, and 69 on his first three Sociology tests. If he needs to keep
an average of 70 to stay eligible for lacrosse, what scores on the fourth exam will
accomplish this?
A) He must score 84 or higher.
B) He must score more than 80
C) He must score more than 84
D) He must score 80 or higher.
54) The
width of a rectangle is fixed at 30 cm, and the perimeter can be no greater than
170 cm. Find the maximum length of the rectangle.
A) 110 cm
B) 70 cm
C) 140 cm
D) 55 cm
Find the values of x for which the expression equals zero.
-8x(7x + 1) - (-4x2 )(7)
55)
(7x + 1)2
A)
0, -
2
7
B)
0, -
1
7
53)
54)
55)
C) {0}
D)
0,
2
7
Find the midpoint of the line segment whose endpoints are the given points.
56) (5.3, 4.7) and (7.2, -9.7)
A) (6.25, -2.5)
B) (5, -1.25)
C) (6.25, 7.2)
D) (-0.95, 7.2)
56)
Find the exact distance between the points.
57) ( 5, - 3) and (4 5, -7 3)
A) 3 17
B) 2 42
57)
C) 6
7
D) 2
58
Determine if the given points form the vertices of a right triangle.
58) (-3, 5), (-1, 3), and (-4, 0)
A) Yes
B) No
Determine which of the given points are solutions to the given equation.
59) 2x2 + y = 4
I. (3, -14) II. (-3, 14)
III. (-3, -14)
A) II
B) III
C) I and II
D) I and III
7
58)
59)
E) I
Graph the equation by plotting points.
60) x = |y| - 5
60)
A)
B)
C)
D)
8
61) y2 - x
A)
61)
+4=0
B)
C)
D)
9
62) y
62)
= |x - 3|
A)
B)
C)
D)
10
Estimate the x- and y-intercepts from the graph.
63)
63)
A) x-intercepts: (-2, 0) and (2, 0); y-intercept: (0,
B) x-intercept: (4, 0); y-intercepts: (0, -2) and (0,
C) x-intercept: (0, 4); y-intercepts: (-2, 0) and (2,
D) x-intercepts: (0, -2) and (0, 2); y-intercept: (4,
4)
2)
0)
0)
Determine the x- and y-intercepts of the graph whose points are defined in the table.
x -5 0 5 10 15 20
64)
y 9 7 2 0 -2 -9
A) x-intercept: (7, 0); y-intercept: (0, 10)
B) x-intercept: (0, 7); y-intercept: (10, 0)
C) x-intercept: (0, 10); y-intercept: (7, 0)
D) x-intercept: (10, 0); y-intercept: (0, 7)
11
64)
An isosceles triangle is shown. Find the area of the triangle. Assume that the units shown in the grid are
in meters.
65)
65)
A) Area:
B) Area:
2 17 m 2
C) Area: 17 m 2
34 m 2
D) Area: 17 m 2
Solve the problem.
66) Is the point (-3, -1) on the circle defined by (x + 3)2 + (y + 1)2 = 9
A) No
66)
B) Yes
Identify the center and radius of the circle.
67) Identify the center and radius of the circle.
42
x+ y2 = 12
7
67)
A) Center
=
4
, 0 ; r = 12
7
B) Center
= 0,
C) Center
4
= - ,0; r =2 3
7
D) Center
=
4
; r = 12
7
4
,0; r =2 3
7
Use the given information about a circle to find its equation.
68) Center (-1, -5) and radius 3
A) (x - 1)2 + (y - 5)2 = 3
B) (x + 1)2 + (y + 5)2 = 3
C) (x + 1)2 + (y + 5)2 = 3
D) (x - 1)2 + (y - 5)2 = 3
12
68)
Use the given information about a circle to write an equation of the circle in standard form.
69) The endpoints of a diameter are (3, 11) and (-9, -5).
A) (x - 3)2 + (y + 3)2 = 20
B) (x - 3)2 + (y - 11)2 = 100
C) (x + 3)2 + (y - 3)2 = 100
D) (x + 3)2 + (y + 11)2 = 20
Write the equation in standard form to find the center and radius of the circle.
70) x2 + y2 + 6x + 14y + 37 = 0
A) (x + 3)2 + (y + 7)2 = 21; center (3, 7), radius 21
B) (x - 3)2 + (y - 7)2 = 21; center (3, 7), radius 21
C) (x + 3)2 + (y + 7)2 = 21; center (-3, -7), radius 21
D) (x + 3)2 + (y + 7)2 = 21; center (-3, -7), radius 21
69)
70)
Identify the domain and range of the relation, and determine whether the relation is a function.
71) {(-7, -12), (-3, -5), (1, 16), (8, 18)}
71)
A) Domain: {-12, -5, 16, 18}; Range: {-7, -3, 1, 8}; Not a function
B) Domain: {-12, -5, 16, 18}; Range: {-7, -3, 1, 8}; Function
C) Domain: {-7, -3, 1, 8}; Range: {-12, -5, 16, 18}; Not a function
D) Domain: {-7, -3, 1, 8}; Range: {-12, -5, 16, 18}; Function
Determine whether the relation defines y as a function of x.
72)
72)
A) Function
B) Not
a function
73)
73)
A) Function
B) Not
13
a function
74) x
74)
= |y + 1|
A) Not a function
B) Function
Evaluate the function for the indicated value, then simplify.
75) f (x) = 2x2 - 4x; find f (8)
A) -16
B) 124
C) 96
Evaluate as indicated.
76) Find f (a + 2) for the given function.
f(x) = x - 5
A) x + a - 3
B) x + a - 10
77) If
75)
D) 224
76)
C)
D)
a-3
a - 10
77)
f (x) = 3x2 + 8x - 3, find and simplify f (2 + x).
A) 3x2
C) 3x2
B) 25 + x
D) 3x2 + 2x
+ 8x - 5
+ 20x + 25
Find and simplify f (x + h).
78) f (x) = x3 - 5x + 8
A) x3 + h3 - 5x - 5h + 8
C) x3 - 5x - 5h + 8
+ 25
78)
B)
x3 - 5x + h + 8
D) x3 + 3x2 h + 3xh2 + h3 - 5x - 5h + 8
Solve the problem.
79) Consider the function f = {(-6, -3), (-2, 3), (2, -1), (4, 2)} Determine f (-2)
A) 2
B) 3
C) 1
D) 4
Write the domain in interval notation.
x+7
80) f(x) =
x+3
A) (-
, 3)
C) (- , 7)
81) m(x)
=
80)
B) (-
(3, )
(7, )
, -7)
D) (- , -3)
(-7, )
(-3, )
5
|x| + 1
81)
A)
, )
C) (- , -1)
79)
B) (-
, -5)
D) (- , -1)
(-1, )
3
= 5-t
A) (- , 5]
C) (- , )
(-5, )
(-1, 1) (1, )
82) g(t)
82)
B) (-
, 5)
D) [5, )
14
(5, )
Use the graph of y = f (x) to answer the questions.
83)
a. Determine the domain
b. Determine the x-intercept
83)
A) Domain:
B) Domain:
C) Domain:
(- , 4); x-intercept (-1, 0)
[-5, 0]; x-intercept (0, -1)
(- , ); x-intercept (0, -1)
D) Domain: [-5, 0] {2}; x-intercept (-1, 0)
Determine the slope of the line passing through the given points.
84) (1, -1) and (-8, -3)
9
9
2
A) m =
B) m = C) m = 2
2
9
85) (-7, -10)
A) 0
86)
84)
D) m
=
2
9
85)
and (5, -10)
B) Undefined
C) 12
D) 1
3 2
1 8
, and - , 5 3
9 7
A) m
=
285
112
86)
B) m
=-
21
325
C) m
15
=-
285
77
D) m
=-
75
77
Determine the slope of the line.
87)
87)
A) m
B) m
= -3
=-
1
3
C) m
=3
D) m
=
1
3
Solve the problem.
88) If
the slope of a line is
change of 63 ft?
A) 441 ft
7
, how much vertical change will be present for a horizontal
10
B) 90
C) 6.3
ft
Determine the slope and the y-intercept of the line.
89) 6x - 5y = 4
6
A) Slope: Slope: ; y-intercept: 0, 4
5
C) Slope:
ft
D) 44.1
88)
ft
89)
5
5
Slope: ; y-intercept: 0, 6
4
16
B) Slope:
6
4
Slope: ; y-intercept: 0, 5
5
D) Slope:
6
4
- ; y-intercept: 0, 5
5
Write the equation in slope-intercept form. Then, graph the line using the slope and y-intercept.
90) -3x + 5y = -15
90)
A) y
5
= x-3
3
B) y
3
= x+3
5
C) y
3
=- x-3
5
D) y
3
= x-3
5
Use the slope-intercept form to write an equation of the line that passes through the given point and has
the given slope. Use function notation where y = f(x).
91) (-2.5, 4.3); m = -5.2
91)
A) f(x) = -5.2x - 8.7
B) f(x) = -8.7x - 5.2
C) f(x) = -5.2x + 8.7
D) f(x) = -5.2x + 4.3
Determine the average rate of change of the function on the given interval.
92) f (x) = 3x2 + 3 on [3, 5]
3
5
A)
B) 24
C)
D) -24
2
2
17
92)
Write an equation of the line satisfying the given conditions. Write the answer in standard form.
6
93) The line has a slope of 93)
and contains the point (-5, -8).
7
A)
6
83
x+y=
7
7
B) 6x
C)
+ 7y = -86
6
86
y=- x7
7
D) 6x
+ 7y = 86
The slope of a line is given.
a. Determine the slope of a line parallel to the given line, if possible.
b. Determine the slope of a line perpendicular to the given line, if possible.
94) m is undefined
A) a. m = 0; b. m is undefined
B) a. m is undefined; b. m = 0
C) a. m = 0; b. m = 1
D) a. m = 0; b. m = -1
Determine if the lines defined by the given equations are parallel, perpendicular, or neither.
95) -4x - 9y = -4
2
3
x + y = -9
3
2
A) neither
B) parallel
95)
C) perpendicular
96) -5x
96)
- 4y = 6
1
2
x+ y=8
2
3
A) neither
94)
B) parallel
C) perpendicular
18
Use translations to graph the given function.
97) b(x) = |x - 2| + 3
97)
A)
B)
C)
D)
19
Use transformations to graph the given function.
1
98) f(x) =
|x + 2| + 3
2
98)
A)
B)
C)
D)
Write a function based on the given parent function and the transformations in the given order.
99) Parent function y = |x|
99)
1. Shift 4.5 units to the right.
1
2. Shrink horizontally by a factor of .
5
3. Reflect across the y-axis.
A)
y = |-5x + 4.5|
B)
1
y = |- x + 4.5|
5
C)
y = |-5x - 4.5|
D)
1
y = |- x - 4.5|
5
20
Solve the problem.
100) Use interval notation to write the intervals over which f is constant
A) (2,
2)
B) (-1,
C) (-4,
2)
-1)
100)
D) (2,
5)
Use interval notation to write the intervals over which f is (a) increasing, (b) decreasing, and (c) constant.
101)
101)
A) a.
B) a.
(- , 2) (2, )
b. never decreasing
c. (-2, 2)
(-4, )
b. (- , -4)
c. never constant
D) a. never increasing
b. (- , -2) (2, )
c. (-2, 2)
C) a.
(- , -2) (2, )
b. never decreasing
c. (-2, 2)
21
Solve the problem.
102) The graph shows the height h (in meters) of a roller coaster t seconds after the ride
starts.
102)
a. Over what interval(s) does the height increase?
b. Over what interval(s) does the height decrease?
A) a. (50, 70)
B) a. (10, 20) and (30, 40)
b. (10, 50)
b. (50, 70)
C) a. (0, 10) and (30, 50)
D) a. (10, 50)
b. (10, 20) and (50, 70)
b. (50, 70)
Find
f ( x + h) - f ( x )
for the given function.
h
103)
f (x) =
A)
1
x-4
103)
1
(x - 4)(x + h - 4)
C) -
B)
1
(x - 4)(x + h - 4)
1
2x + h - 8
D) -
1
2x + h - 8
Refer to the values of k(x) and p(x) in the table, and evaluate the function for the given value of x.
104)
104)
x
-3
-2
1
6
(p k)(-2)
A) 2
k(x)
-6
6
2
-2
p(x)
-7
1
4
5
B) 4
C) 5
22
D) -3
Solve the problem.
105) If a is b plus nine, and c is the square of a, write c as a function of b.
A) c(b) = (b + 9)2
B) c(b) = b + 81
C) c(b) = 2b + 18
D) c(b) = b2 + 81
106) If
q is r minus six, and s is the square root of q, write s as a function of r.
A) s(r) = r - 6
B) s(r) = r - 6
C) s(r) = 6 - r
D) s(r) = 6 - r
Determine the x- and y-intercepts for the given function.
107) f (x) = -(x - 2)2 - 4
A) x-intercept: (2, 0)
B)
y-intercept: (0, 4)
C) x-intercepts: (0, 0) and (4, 0)
D)
y-intercept: (0, -8)
23
105)
106)
107)
x-intercept: (2, 0)
y-intercept: (0, -4)
x-intercept: none
y-intercept: (0, -8)
Graph the parabola and the axis of symmetry. Label the coordinates of the vertex, and write the
equation of the axis of symmetry.
108) y = - (x - 5)2 + 2
108)
A)
B)
Vertex (-5, 2)
axis of symmetry: x = -5
Vertex (-5, -2)
axis of symmetry: x = -5
C)
D)
Vertex (5, -2)
axis of symmetry: x = 5
Vertex (5, 2)
axis of symmetry: x = 5
Find the vertex.
109) f (x) = -2(x - 19)2 + 13
A) (-19, 13)
B) (13, -19)
109)
C) (13,
19)
D) (19,
13)
Find the vertex of the parabola by applying the vertex formula.
1
110) f (x) = - x2 - 6x - 7
5
A) (-15,
38)
B) (15,
C)
-52)
24
3 76
- ,5 25
110)
D)
3 256
,5
25
111) h
a = 6a 2 + 16
1
385
A)
,12
24
111)
B)
1 385
,
12 24
C)
D)
0, 16
0, - 16
Solve the problem.
112) A model rocket is launched from a raised platform at a speed of 112 feet per second. Its
height in feet is given by h(t) = -16t 2 + 112t + 20 (t = seconds after launch). After how
many seconds does the object reach its maximum height?
A) 1.75 seconds
B) 5.5 seconds
C) 20 seconds
D) 3.5 seconds
Determine the number of x-intercepts of the graph of f (x) = ax2 + bx + c (a
112)
0) based on the
discriminant of the related equation f (x) = 0. (Hint: Recall that the discriminant is b2 - 4ac.)
113) f
(x) = -9x2 + 4x + 6
A) None
113)
B) Two
C) One
Find the value of b that gives the function the given maximum value.
114) f (x) = -x2 + bx + 2; maximum value 6
A) b = -4 or b = 4
B) b = 2
C) b = -2 or b = 2
Find the zeros of the function and state the multiplicities.
115) f (x) = 2x5 + 9x4 + 7x3
7
A) 1 (multiplicity 2.5), (multiplicity 2.5)
2
B) 0
(multiplicity 3), -1 (multiplicity 1), -
C) -1
D) 0
116)
(multiplicity 2.5), -
114)
D) b
=4
115)
7
(multiplicity 1)
2
7
(multiplicity 2.5)
2
(multiplicity 3), 1 (multiplicity 1),
7
(multiplicity 1)
2
f (x) = -2x6 (x + 7)2 (x - 5)6
A) -7 (multiplicity 2), 5 (multiplicity 6)
B) 0 (multiplicity 6), 7 (multiplicity 2), -5 (multiplicity 6)
C) 0 (multiplicity 6), -7 (multiplicity 2), 5 (multiplicity 6)
D) 7 (multiplicity 2), -5 (multiplicity 6)
25
116)
Solve the problem.
117) Given f (x) = 2x3 + 7x2 + 14x - 9. Use the intermediate value theorem to determine
whether f (x) has a zero on the interval [0, 1], find the zero if it exists.
A) -1
C)
B) 1
1
2
D) There
Use synthetic division to divide the polynomials.
118) (s2 + 2s - 8) ÷ (s + 4)
4
A) s - 2
B) s + 2 s+4
is no zero on the interval.
118)
C) s
+2+
4
s+4
D) s
+2
119) (s4
119)
+ 5s3 + 2s2 - 17s + 7) ÷ (s - 1)
2
A) s3 + 6s2 + 8s - 9 s-1
C) s3
117)
+ 6s2 + 8s - 9
-9s + 2
s-1
B) s3
+ 6s2 + 8s +
D) s3
+ 4s2 - 2s - 15 +
22
s+1
Use the remainder theorem to evaluate the polynomial for the given value of x.
120) f (x) = 3x4 - 7x3 - 7x2 + 42x - 19;
f (3)
A) 161
B) -224
C) 224
D) 98
120)
Use the factor theorem to determine if the given binomial is a factor of f (x).
121) f (x) = x4 + 8x3 + 11x2 - 11x + 3; x + 3
A) Yes
B) No
121)
Solve the problem.
122) Factor f (x) = 3x3 - 2x2 - 53x - 60 given that -3 is a zero.
A) (x - 3)(3x - 4)(x - 5)
B) (x + 3)(3x2 + 7x - 32)
C) (x - 3)(3x2 + 7x - 32)
D) (x + 3)(3x + 4)(x - 5)
Write a polynomial f (x) that meets the given conditions. Answers may vary.
123) Degree 3 polynomial with zeros 1, 7, and 6
A) f (x) = x3 - 14x2 + 43x - 42
B) f (x) = x3 + 14x2 + 55x + 42
C) f (x) = x3 + 14x2 + 43x + 42
D) f (x) = x3 - 14x2 + 55x - 42
26
122)
123)
124) Degree
4 polynomial with zeros 4 and -
6
(each with multiplicity 1) and 0 (with
5
multiplicity 2).
A) f (x) = 6x4 - 19x3 - 20x2
C) f (x) = 6x4 - 29x3 - 20x2
124)
B)
f (x) = 5x4 - 14x3 - 24x2
D) f (x) = 5x4 - 26x3 + 24x2
Find all the zeros.
125) f (x) = x3 + 10x2 + 25x + 18
A) 2, -4 ± 7i
B) 2, -4 ± 7
125)
C) -2,
D) -2,
-4 ± 7i
-4 ± 7
Write the domain in interval notation.
7x - 1
126) f (x) =
4x2 - 27x - 81
A)
,-9
C)
,-
9
4
-9, -
9
4
9 1
- ,
4 7
126)
9
,
4
1
,9
7
(9, )
9
4
B)
,-
D)
,-9
9
- ,9
4
-9, -
1
7
Refer to the graph of the function and complete the statements.
127)
The domain is ________.
The range is ________.
A) (-
(-5,
C) (-
(-5, );
(-7, )
, -5)
(- , )
, -5)
(- , -7)
B) (-
);
, );
(- , -5) (-5, )
D) (- , -7) (-7, );
(- , -5) (-5, )
27
(9, )
1 9
- ,
7 4
9
,
4
127)
128) As
-
________.
+
________.
x
-5 , f (x)
As x
-5 , f (x)
A) 6;
6
B)
128)
C) -5,
;
28
-5
D)
;
1
Graph the function by using a transformation of the graph of y = .
x
129)
f (x) =
1
x+2
129)
A)
B)
C)
D)
29
Graph the function.
4x
130) f (x) =
x2 - 4x - 5
130)
A)
B)
C)
D)
30
131) f
-4x2
(x) =
x2 + 4
131)
A)
B)
C)
D)
31
The graph of y = f (x) is given. Solve the inequality.
132) f (x) < 0
132)
A)
B) (-
{0} (3, )
C) (- , 0) (0, 3)
, 3)
D) (3, )
Solve the inequality. Write the solution set in interval notation.
133) 7y2 + 5y -9(7y + 5)
5
A) (-9, )
B) -9, 7
C) (-
D) (-
, -9]
, -9]
133)
5
- ,
7
134) - x2
134)
- 6x + 16 < 0
A) (- , -8) (2, )
C) (- , -2) (8, )
135) 4x2
- 19x - 30
5
A) - , 6
4
C) (-
, -6]
136) (x + 7)(x +
A) {-9}
11)
B) (-
, )
D) (-8, 2) (2, )
135)
0
B)
5
,
4
-6,
D)
5
4
,-
5
4
[6, )
136)
-4
B) [-11,
C) {
-7]
32
}
D) (-
,
)
The graph of y = f (x) is given. Solve the inequality.
137) f (x) > 0
A) (3,
B) (-
4)
137)
C) [3,
, 3)
D) (3,
4]
Solve the inequality. Write the solution set in interval notation.
x+6
138)
>0
x-1
A) (-
, -6]
C) (- , -6)
139)
140)
B) (-
[1, )
(1, )
, 1]
D) (- , 1)
138)
[6, )
(6, )
5
<9
y-4
139)
41
9
A)
4,
C)
41
,
9
)
B) (-
, 4)
D)
,-
31
9
41
,
9
(4, )
9h
> -7
h -1
140)
A)
7
,
16
B)
,
C)
7
,1
16
D)
,-
33
7
16
(1, )
7
2
(1, )
141)
r+7
>0
r2 + 2
141)
A) {
B) (-
}
C) (-7, )
142)
7
1-x
, )
D) (- , -7)
(-2, )
2
3-x
142)
A) (1,
3)
19
,
5
C) (-
, 1)
(3, )
19
5
B)
,
D) (1,
3)
Find the constant of variation k.
143) p is inversely proportional to q. When q is 8, p is 3.
8
3
A) k =
B) k = 72
C) k =
3
8
143)
D) k
= 24
Solve the problem.
144) The number of hours it takes to paint a house is inversely proportional to the number of
people painting. If it takes 3 workers 17.7 hours to paint a certain house, how long
would it take 5 workers? Round to one tenth of an hour.
A) 10.6 hours
B) 19.7 hours
C) 15.7 hours
D) 53.0 hours
145) The
body mass index (BMI) of an individual varies directly as the weight of the
individual and inversely as the square of the height of the individual. The body mass
index for a 154-lb person who is 71 in. tall is 21.48. Determine the BMI for an
individual who is 77 in. tall and 164 lb. Round to 2 decimal places.
A) 19.06
B) 19.45
C) 20.42
D) 18.67
34
144)
145)
Answer Key
Testname: MIDTERM1314
1) B
2) C
3) B
4) C
5) C
6) C
7) D
8) D
9) A
10) C
11) A
12) B
13) A
14) D
15) D
16) C
17) A
18) B
19) D
20) C
21) A
22) A
23) D
24) A
25) B
26) B
27) D
28) B
29) D
30) B
31) A
32) C
33) C
34) B
35) C
36) C
37) A
38) D
39) C
40) A
41) A
42) D
43) C
44) B
45) D
46) A
47) C
48) D
35
Answer Key
Testname: MIDTERM1314
49) C
50) B
51) D
52) D
53) D
54) D
55) A
56) A
57) A
58) B
59) D
60) D
61) C
62) A
63) B
64) D
65) D
66) A
67) D
68) B
69) C
70) D
71) D
72) A
73) B
74) A
75) C
76) C
77) C
78) D
79) B
80) D
81) A
82) C
83) A
84) D
85) A
86) A
87) C
88) D
89) B
90) D
91) A
92) B
93) B
94) B
95) B
96) A
36
Answer Key
Testname: MIDTERM1314
97) D
98) B
99) C
100) B
101) C
102) C
103) C
104) C
105) A
106) A
107) D
108) D
109) D
110) A
111) C
112) D
113) B
114) A
115) B
116) C
117) C
118) A
119) A
120) D
121) A
122) D
123) D
124) B
125) D
126) B
127) C
128) B
129) D
130) D
131) C
132) D
133) B
134) A
135) D
136) A
137) A
138) C
139) B
140) B
141) C
142) A
143) D
144) A
37
Answer Key
Testname: MIDTERM1314
145) B
38