Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve. Give exact solutions.
1)
y2=21
A)
21
B)
±21
C)
10.5
D)
441
2)
x2=16
A)
8
B)
±5
C)
4
D)
±4
3)
x2+ 5 =230
A)
15
B)
±15
C)
±14
D)
115
4)
3z2+432 = 0
A)
±12i
B)
±12
C)
12
D)
12i
5)
-5k2– 13 =-58
A)
±3
B)
-29
C)
±6
D)
3
6)
4x2=52
A)
±13
B)
14
C)
26
D)
±13
7)
(x – 4)2=4
A)
2, -2
B)
2, -6
C)
6, 2
D)
8
8)
(r + 5)2=14
A)
9
B)
–5+14, -5 –14
C)
14, 14
D)
5+14, 5–14
9)
(x + 6)2=20
A)
2 5 – 6, 2 5+ 6
B)
–6+ 2 10, -6 – 2 10
C)
2 5, –2 5
D)
–6+ 2 5, -6 – 2 5
10)
(x + 9)2– 3 = 0
A)
-6, 12
B)
9±3
C)
–9±3
D)
–3±3
1
11)
(p – 2)2=17
A)
17 – 2, –17 – 2
B)
17 + 2
C)
17 + 2, –17 + 2
D)
17 –-2
12)
(x + 4)2– 6 = 0
A)
-4 +6, -4 –6
B)
-2 +6, -2 –6
C)
-4 + i 6, -4 – i 6
D)
2, 10
13)
x2– 14x +49 =9
A)
3, -3
B)
16
C)
4, -10
D)
10, 4
14)
x2+ 12x +36 =17
A)
11
B)
17, 17
C)
–6+17, -6 –17
D)
6+17, 6–17
15)
x2+ 10x +25 =28
A)
–5+ 2 14, -5 – 2 14
B)
2 7, –2 7
C)
2 7 – 5, 2 7+ 5
D)
–5+ 2 7, -5 – 2 7
16)
x2– 1
2x + 1
16 =
7
24
A)
1
2+42
6, 1
2–42
6
B)
1
2+42
12 , 1
2–42
12
C)
1
2+42
12 , – 1
2+42
12
D)
1
4+42
12 , 1
4–42
12
17)
4x2+36 = 0
A)
±3i
B)
3± i
C)
±3
D)
±3+ i
18)
(x – 1)2= – 16
A)
1 ±4
B)
4i + 1
C)
4i
D)
1 ±4i
Find the x–intercepts.
19)
f(x) = x2– 10
A)
x–intercepts (0, 10) and (0, –10)
B)
x–intercepts (0, 10) and (0, –10)
C)
No x–intercepts
D)
x–intercepts ( 10, 0) and (–10, 0)
20)
f(x) = x2+ 7x
A)
x–intercepts (0, 0) and (7, 0)
B)
x–intercepts (0, -7) and (-7, 0)
C)
No x–intercept
D)
x–intercepts (0, 0) and (-7, 0)
21)
f(x) = – x2+ 19x – 90
A)
x–intercepts (9, 0) and (-10, 0)
B)
x–intercepts (-9, 0) and (-10, 0)
C)
No x–intercepts
D)
x–intercepts (9, 0) and (10, 0)
22)
f(x) = 2x2– 12x – 54
A)
x–intercepts (9, 0) and (3, 0)
B)
x–intercepts (9, 0) and (– 3, 0)
C)
No x–intercepts
D)
x–intercepts (-6, 0) and ( 9
2, 0)
23)
f(x) = 2x2– 20x + 18
A)
x–intercepts (1, 0) and (9, 0)
B)
x–intercepts (-1, 0) and (9, 0)
C)
x–intercepts (-1, 0) and (-9, 0)
D)
x–intercepts (1, 0) and (-9, 0)
24)
4x2+9= 0
A)
x–intercepts (–
3
2, 0), ( 3
2, 0)
B)
x–intercepts (– i 3
2, 0), (i 3
2, 0)
C)
x–intercepts (0, – i 3
2), (0, i 3
2)
D)
No x–intercepts
Solve the equation by completing the square.
25)
a2+ 4a + 3 = 0
A)
6, -3
B)
1, 3
C)
3, –3
D)
-1, -3
26)
z2+ 10z + 11 = 0
A)
5±11
B)
–10 +11
C)
–5±14
D)
5+14
27)
p2+ 3p – 9 = 0
A)
–
3
2±3 5
2
B)
–3±3 5
C)
3
2±3 5
2
D)
–
3
2+3 5
2
3
28)
7x2+ 2x – 5 = 0
A)
7
5, 1
B)
7
5, –1
C)
7
5, 0
D)
5
7, –1
29)
4d2+ 16d + 15 = 0
A)
–5
2, –3
2
B)
–2
5, –3
2
C)
5
2, 3
2
D)
2
5, 2
3
30)
11m2+ 3m = 0
A)
3
11 , 0
B)
0
C)
–3
11 , 0
D)
±3
11
31)
x2–12x +45 = 0
A)
–6±3i
B)
9, 3
C)
12 ±6i
D)
6±3i
32)
x2+ x + 9 = 0
A)
– 1
2±
35
2
B)
1
2±
35
2
C)
– 1
2±
35
2i
D)
1
2±
35
2i
Solve by completing the square.
33)
y2+ 5y – 5 = 0
A)
-5 – 3 5
2
B)
5+ 3 5
2
C)
-5 ±3 5
2
D)
–5±3 5
34)
x2+ 4x =3
A)
–2±2 7
B)
–1±7
C)
–2±7
D)
2+7
35)
x2=3– 8x
A)
–4±219
B)
–1±19
C)
–4±19
D)
4+19
36)
y2=– 5y + 5
A)
-5 – 3 5
2
B)
-5 ±3 5
2
C)
5+ 3 5
2
D)
–5±3 5
37)
q2+ 4q – 9 = 0
A)
2+13
B)
–2±13
C)
–1±13
D)
–2±213
4
38)
y2+ 8y – 5 = 0
A)
4+21
B)
–1±21
C)
–4±21
D)
–4±221
39)
x2+ 3x – 9 = 0
A)
-3 – 3 5
2
B)
-3 ±3 5
2
C)
3+ 3 5
2
D)
–3±3 5
40)
z2+ 4z – 9 = 0
A)
–2±13
B)
–1±13
C)
–2±213
D)
2+13
Solve the problem. Give the answer to the nearest tenth.
41)
The hang–time function V(T) = 48T2, relates vertical leap to hang time. A player has a vertical leap of 39 in.
What is his hang time?
A)
0.8 sec
B)
43.3 sec
C)
1.1 sec
D)
0.9 sec
42)
The position of an object moving in a straight line is given by s = 2t2– 3t, where s is in meters and t is the time
in seconds the object has been in motion. How long (to the nearest tenth) will it take the object to move 19
meters?
A)
3.9 sec
B)
3.7 sec
C)
20.0 sec
D)
66.5 sec
43)
The position of an object moving in a straight line is given by s = t2– 8t, where s is in feet and t is the time in
seconds the object has been in motion. How long (to the nearest tenth) will it take the object to move 19 feet?
A)
20.0 sec
B)
9.9 sec
C)
9.7 sec
D)
20.9 sec
44)
A ball is thrown downward from a window in a tall building. Its position at time t in seconds is s = 16t2+ 32t,
where s is in feet. How long (to the nearest tenth) will it take the ball to fall 54 feet?
A)
1.2 sec
B)
1.1 sec
C)
0.9 sec
D)
1.8 sec
Solve.
45)
4x2+ 6x =– 1
A)
-3 ±5
4
B)
-3 ±13
4
C)
-3 ±5
8
D)
-6 ±5
4
46)
6n2=-12n – 1
A)
-6 ±42
6
B)
-6 ±30
12
C)
-12 ±30
6
D)
-6 ±30
6
47)
3m2+ 12m + 5 = 0
A)
-6 ±51
3
B)
-6 ±21
3
C)
-12 ±21
3
D)
-6 ±21
6
48)
4r2+ 24r =– 19
A)
-24 ±17
2
B)
-6 ±55
2
C)
-6 ±17
2
D)
-6 ±17
8
49)
7x2=-12x – 2
A)
-6 ±2
7
B)
-6 ±22
7
C)
-6 ±22
14
D)
-12 ±22
7
50)
4x2=-14x – 9
A)
-7 ±85
4
B)
-14 ±13
4
C)
-7 ±13
8
D)
-7 ±13
4
51)
41m2+ 100m + 53 = 0
A)
-50 ±4673
41
B)
-50 ±327
82
C)
-100 ±327
41
D)
-50 ±327
41
52)
3= – 9
x–3
x2
A)
-3 ±5
2
B)
-9 ±5
2
C)
-3 ±5
6
D)
-3 ±13
2
53)
4
x+4
x +6= 1
A)
6
B)
4
C)
-4, 6
D)
4, -6
54)
x2+ x + 7 = 0
A)
– 1
2±
3 3
2
B)
1
2±
3 3
2
C)
– 1
2±
3 3
2i
D)
1
2±
3 3
2i
55)
5x2– 3x =-7
A)
3
10 ±131
10 i
B)
– 3
10 ±131
10
C)
3
10 ±131
10
D)
– 3
10 ±131
10 i
56)
7x2=-9x – 3
A)
– 9
14 ±3
14
B)
9
14 ±3
14
C)
– 9
14 ±3
14 i
D)
9
14 ±3
14 i
57)
7x2– 3x + 1 = 0
A)
– 3
14 ±19
14 i
B)
– 3
14 ±19
14
C)
3
14 ±19
14
D)
3
14 ±19
14 i
58)
1
x+6
x2= – 1
A)
1
2±
23
2
B)
– 1
2±
23
2i
C)
– 1
2±
23
2
D)
1
2±
23
2i
Find the x–intercepts.
59)
f(x) =3x2+ 3x – 5
A)
-3 +69
6, 0 and -3 –69
6, 0
B)
3+69
6, 0 and 3–69
6, 0
C)
3+51
6, 0 and 3–51
6, 0
D)
-3 +51
6, 0 and -3 –51
6, 0
60)
f(x) =2x + x(x – 7)
A)
(0, 0) and (-5, 0)
B)
(0, 0) and (5, 0)
C)
(5, 0)
D)
(-5, 0)
61)
f(x) =11x2– 3x – 6
A)
No x–intercepts
B)
(9, 0) and (6, 0)
C)
(3+273
22 , 0) and ( 3–273
22 , 0)
D)
(3+261
22 , 0) and ( 3–261
22 , 0)
62)
f(x) =25x2– 10x + 1
A)
1
5, 0 and –1
5, 0
B)
–1
5, 0
C)
1
5, 0
D)
No x–intercepts
Solve. Round results to the nearest thousandth.
63)
x2+ 6x =2
A)
-0.354, -5.646
B)
6.317, -0.317
C)
0.317, -6.317
D)
-2.683, -2.683
7
C
64)
4z2– 6z=1
A)
1.309, 0.191
B)
0.151, -1.651
C)
1.651, -0.151
D)
3.302, -0.302
65)
3y2– 4y=1
A)
1.000, 0.333
B)
0.215, -1.549
C)
1.549, -0.215
D)
3.098, -0.430
66)
x2+ 10x – 19 = 0
A)
1.633, -11.633
B)
11.633, -1.633
C)
13.958, -3.958
D)
3.958, -13.958
67)
10x2– 3x – 15 = 0
A)
1.384, -1.084
B)
1.084, -1.384
C)
0.779, -1.079
D)
1.079, -0.779
68)
9x2=2+ 17x
A)
2.000, -0.111
B)
1.763, 0.126
C)
-0.126, -1.763
D)
0.111, -2.000
Solve.
69)
Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 15
mi, the distance between the cars was 5 mi more than the distance traveled by the car heading east. How far had
the eastbound car traveled?
A)
25 mi
B)
20 mi
C)
30 mi
D)
15 mi
70)
A ladder is resting against a wall. The top of the ladder touches the wall at a height of 6 ft. Find the length of the
ladder if the length is 2 ft more than its distance from the wall.
A)
8 ft
B)
6 ft
C)
10 ft
D)
12 ft
71)
A lot is in the shape of a right triangle. The shorter leg measures 120 m. The hypotenuse is 40 m longer than the
length of the longer leg. How long is the longer leg?
A)
160 m
B)
120 m
C)
240 m
D)
200 m
72)
The area of a square is 81 square centimeters. If the same amount is added to one dimension and removed from
the other, the resulting rectangle has an area 9 square centimeters less than the area of the square. How much is
added and subtracted?
A)
12 cm
B)
4 cm
C)
3 cm
D)
9 cm
73)
A square has an area of 49 square inches. If the same amount is added to the length and removed from the
width, the resulting rectangle has an area of 45 square inches. Find the dimensions of the rectangle.
A)
3 in. by 4 in.
B)
4 in. by 9 in.
C)
5 in. by 10 in.
D)
5 in. by 9 in.
74)
A rectangular garden has dimensions of 23 feet by 16 feet. A gravel path of equal width is to be built around the
garden. How wide can the path be if there is enough gravel for 612 square feet?
A)
8.5 ft
B)
6 ft
C)
8 ft
D)
7 ft
75)
A picture 9 inches by 18 inches is to be mounted on a piece of matboard so that there is an even amount of mat
all around the picture. How wide will the border be if the area of the border is 124 square inches?
A)
4.5 in
B)
4 in
C)
3 in
D)
2 in
76)
A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 18 feet by 20 feet
and the area of the rug is 120 square feet, how wide will the border be?
A)
6 ft
B)
5 ft
C)
6.5 ft
D)
4 ft
77)
Bill can row 3 mph in still water. It takes him 3 hours 36 minutes to go 3 miles upstream and return. Find the
speed of the current.
A)
3 mph
B)
2 mph
C)
2.5 mph
D)
1.5 mph
78)
A jet plane traveling at a constant speed goes 1200 miles with the wind, then turns around and travels for 1000
miles against the wind. If the speed of the wind is 50 mph and the total flight took 4 hours, find the speed of the
plane in still air.
A)
435 mph
B)
550 mph
C)
605 mph
D)
525 mph
79)
A man rode a bicycle for 12 miles and then hiked an additional 8 miles. The total time for the trip was 5 hours. If
his rate when he was riding a bicycle was 10 miles per hour faster than his rate walking, what was each rate?
A)
Bike: 12 mph
Hike: 2 mph
B)
Bike: 14.5 mph
Hike: 4.5 mph
C)
Bike: 11.5 mph
Hike: 1.5 mph
D)
Bike: 13 mph
Hike: 3 mph
80)
Sue rowed her boat across Lake Bend and back in 3 hours. If her rate returning was 2 mph less than the rate
going, and if the distance each way was 7 miles, find her rate going.
A)
5.5 mph
B)
5.9 mph
C)
1.5 mph
D)
3.7 mph
Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers.
81)
v2= 2as for v
A)
v =2a
s
B)
v =2as
C)
v = 2a s
D)
v =2a
s
82)
A =1
3r2 for r
A)
r =3A
B)
r =3
A
C)
r = 3 A
D)
r =A
3
83)
S =1
2gt2 for t
A)
t =g
2S
B)
t =2S
g
C)
t =2gs
D)
t = 2gS
84)
x =r2– y2 for r
A)
r =x2– y2
B)
r =x + y
C)
r = x + y
D)
r =x2+ y2
85)
q =p
p2+ 1
, for p
A)
p =q
q2+ 1
B)
p =q
1 – q2
C)
p =q
q2– 1
D)
p =q
1 – q2
86)
c2+ d2+ f2= g2, for c
A)
c = g2– d2– f2
B)
c = – g + d + f
C)
c = g – d – f
D)
c =g2– d2– f2
87)
aS2+ bS = c, for S
A)
S =–b + b2– 4ac
2a
B)
S =–b + b2+ 4ac
2a
C)
S =–b +b2+ 4ac
2a
D)
S =–b +b2– 4ac
2a
88)
H =F
F2+ G2, for F
A)
F = H F2+ G2
B)
F =GH
1 – H
C)
F =GH
1 – H2
D)
F =G2+ H2
G
Determine the nature of the solutions of the equation.
89)
s2– 6s – 7 = 0
A)
Two nonreal
B)
Two real
C)
One real
90)
t2– 4t + 4 = 0
A)
Two nonreal
B)
Two real
C)
One real
91)
v2– 4v – 2 = 0
A)
Two nonreal
B)
One real
C)
Two real
92)
w2+ 2w + 3 = 0
A)
Two real
B)
One real
C)
Two nonreal
93)
36x2– 12x + 1 = 0
A)
One real
B)
Two nonreal
C)
Two real
94)
7y2=-8y – 3
A)
Two real
B)
Two nonreal
C)
One real
95)
2+ 5z2=4z
A)
One real
B)
Two nonreal
C)
Two real
96)
-1 – 5a2=-7a – 4
A)
One real
B)
Two real
C)
Two nonreal
97)
9x2–6 7 +7= 0
A)
Two real
B)
Two nonreal
C)
One real
98)
4x2–5 2 –7= 0
A)
One real
B)
Two nonreal
C)
Two real
Write a quadratic equation having the given numbers as solutions.
99)
-4, -7
A)
x2+ 28x + 11 = 0
B)
x2+ 11x + 28 = 0
C)
x2+ 28x – 11 = 0
D)
x2– 11x + 28 = 0
100)
– 7
3, – 3
2
A)
6x2– 23x + 21 = 0
B)
6x2+ 23x + 21 = 0
C)
2x2+ 7x – 9 = 0
D)
2x2 – 9x + 7 = 0
101)
– 1
5, – 1
2
A)
10x2+ 7x – 1 = 0
B)
100x2+ 1x + 70 = 0
C)
100x2+ 70x + 1 = 0
D)
10x2+ 7x + 1 = 0
102)
19, -3 19
A)
x2– 57 19x – 2 = 0
B)
x2– 2 19x – 57 = 0
C)
x2+ 2 19x – 57 = 0
D)
x2– 57 19x + 2 = 0
103)
–3, 33
A)
x2– 2 3x – 9 = 0
B)
x2+ 9 3x + 2 = 0
C)
x2+ 2 3x – 9 = 0
D)
x2+ 9 3x – 2 = 0
104)
n
7, only solution
A)
49x2+14nx +n2= 0
B)
49x2–14nx +n2= 0
C)
49x2–n2= 0
D)
49x2–14n+n2= 0
105)
7i, –7i
A)
x2–14x +49
B)
x2+14x +49
C)
x2+49
D)
x2–49
Solve.
106)
(3m – 7)2+ 5(3m – 7) – 6 = 0
A)
–13
7, 6
3
B)
13
3, –6
3
C)
–1
3, –8
3
D)
1
3, 8
3
107)
6k–2– 22k–1+ 12 = 0
A)
3
2, 1
3
B)
– 2
3, -3
C)
– 3
2, – 1
3
D)
2
3, 3
108)
6y–2– 35y–1+ 25 = 0
A)
6
5, 1
5
B)
– 5
6, -5
C)
– 6
5, – 1
5
D)
5
6, 5
109)
(p – 1)2/3 + 9(p – 1)1/3 + 20 = 0
A)
-63, -124
B)
-4, -5
C)
3-4, 3-5
D)
63, –124
110)
6x2/5 + 13x1/5 + 6 = 0
A)
–
243
32 , –32
243
B)
2, 3
C)
–
3
2, –2
3
D)
243
32 , 32
243
111)
x=2– x
A)
–4, -1
B)
±3
C)
±2
D)
1
112)
x4–14x2+45 = 0
A)
±3, ±25
B)
±3, ±5
C)
3, 5
D)
±3, ±5
12
113)
x4–9x2+8= 0
A)
±1, ±2
B)
±2, ±2
C)
±1, ±22
D)
±1, ±23
114)
x –14 x+24 = 0
A)
2, 12
B)
4
C)
4, 144
D)
No solution
115)
(x2+ 11x)2+ 4(x2+ 11x) – 60 = 0
A)
-1, -10, -11 ±145
2
B)
-1, -10, 11 ±145
2
C)
-11 ±145
2
D)
-1, -10
116)
(x2–2)2–4(x2–2) +3= 0
A)
±5
B)
±5 , ±6
C)
5 , 3
D)
±5 , ±3
117)
(x2–4)2–9(x2–4) +18 = 0
A)
10 , 7
B)
±10
C)
±10 , ±7
D)
±6 , ±13
118)
(x2–8)2–13(x2–8) +42 = 0
A)
±15 , ±14
B)
15 , 14
C)
±7 , ±6
D)
±15
119)
(x2–8)2+5(x2–8) +6= 0
A)
6 , 5
B)
±6
C)
±3 , ±5
D)
±6 , ±5
120)
8+x2– 16 8+x+17 = 0
A)
–47
B)
47
C)
47
D)
No solution
121)
9x –4
x –3
2+6x –4
x –3+ 1 = 0
A)
27
8
B)
9
4
C)
15
4
D)
9
8
122)
x – 2
x + 2
2–x – 2
x + 2 – 12 = 0
A)
– 1, – 10
3
B)
3, -4
C)
1, – 5
2
D)
-3, 4
Find the x–intercepts of the function.
123)
f(x) =5x +14 x– 24
A)
(1.2, 0), (-4, 0)
B)
(1.2, 0)
C)
(1.44, 0), (-16, 0)
D)
(1.44, 0)
124)
f(x) = (x2– 4x)2+3 (x2– 4x) – 1120
A)
(-8, 0), (4, 0), (7, 0), (5, 0)
B)
(32, 0), (-35, 0)
C)
(8, 0), (-4, 0)
D)
(-32, 0), (35, 0)
125)
f(x) = x1/2 + 3x1/4 – 10
A)
(5, 0)
B)
(16, 0), (625, 0)
C)
(16, 0)
D)
(2, 0), (-5, 0)
Graph.
126)
f(x) =3x2
A)
B)
14
D
C)
D)
127)
f(x) =1
3x2
A)
B)
15
C)
D)
128)
f(x) = (x – 2)2
A)
B)
16
C)
D)
129)
f(x) = – (x – 4)2
A)
B)
17
C)
D)
130)
f(x) =
2
17 (x – 3)2
A)
B)
18
C)
D)
131)
f(x) =-4(x + 4)2+ 4
A)
B)
19
C)
D)
132)
f(x) =-4(x – 1)2+ 1
A)
B)
20