Math 1314
Study Guide for Test #1
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve.
1) x2 = -27
1)
A) ± 3 3
B) ± 9i 3
C) ± 9 3
D) ± 3i 3
C) {-8, -6}
D) {7, - 7}
Solve the equation by the zero-factor property.
2) x2 - 14x + 48 = 0
A) {8, 6}
2)
B) {42, 6}
3) 4x2 - 4x - 8 = 0
3)
A) 2, -1
B)
1
,1
2
C)
1
, -1
2
D)
1
,0
2
Use the square root property to solve the equation.
4) (x - 4)2 = 13
4)
A) 4 ±
13
B)
13 - 4, -
C) 4 +
13
D)
13 -
C)
-2 ± 3
2
13 - 4
-4
Solve the equation using the quadratic formula.
5) 4x2 = -8x - 1
A)
-8 ± 3
2
5)
-2 ± 5
B)
2
D)
-2 ± 3
8
6) x2 + x + 1 = 0
6)
A)
1
3
±
2
2
1
3
i
B) - ±
2
2
C)
1
3
±
i
2
2
D)
-
1
3
±
2
2
Solve the cubic equation.
7) x3 + 8 = 0
A) {-2, -1 ±
7)
5}
C) {-2, 1 ± i 3}
B) {-2, ±2i}
D) {-2, 1 ± i 6}
8) x3 - 64 = 0
A) {4, 2 ± 2 5}
8)
C) {4, -2 ± 2i 3}
B) {4, -2 ± 2i}
D) {4, 2 ± 2i 6}
Use the discriminant to determine the number of distinct solutions and whether they are rational, irrational, or nonreal
complex.
9) v2 + 4v + 2 = 0
9)
A) One rational solution (a double solution)
C) Two distinct irrational solutions
B) Two distinct rational solutions
D) Two distinct nonreal complex solutions
1
Solve the problem.
10) The length of a rectangular frame is 5 cm more than the width. The area inside the frame is 66 square
cm. Find the width of the frame.
A) 8 cm
B) 16 cm
C) 11 cm
D) 6 cm
11) A lot is in the shape of a right triangle. The shorter leg measures 180 m. The hypotenuse is 60 m
longer than the length of the longer leg. How long is the longer leg?
A) 180 m
B) 240 m
C) 300 m
D) 360 m
Decide what values of the variable cannot possibly be solutions for the equation.
1
1
+
= 10
12)
x-5 x+9
A) -
1 1
,
9 5
B) -
1 1
,
5 9
C) -9, 5
D) -5, 9
14)
15)
3x + 10 = 5 - 2x
3
,5
A)
4
2x + 5 A) {2}
13)
C) -
46
7
B) {5}
C)
3
4
B) {2, 38}
C) {-2}
D) {3, 8}
B) {2, 3}
32
C) 32,
243
32
D) - 32, 243
B) -
44
5
D)
14)
D)
5
,9
4
x-2=3
16) 6x2/5 + 16x1/5 + 8 = 0
2
A) - 2, 3
11)
12)
Solve the equation.
2
5
3
+
=
13)
x+9 x+2
2
x + 11x + 18
A) - 1
10)
15)
16)
Solve and graph the inequality. Give answer in interval notation.
17) -13x + 6 -12x - 6
17)
A) (- , -13]
B) (-13,
)
C) (- , 12]
D) [-12,
)
2
18) 19 < -5x + 4
18)
39
A) [3, 7)
B) [-7, -3)
C) (3, 7]
D) (-7, -3]
Solve the quadratic inequality. Write the solution set in interval notation.
19) x2 - 4x - 21 0
A) [7, )
C) (- , -3]
20) x2 - 9x + 18 > 0
A) (6, )
B) (- , -3]
D) [-3, 7]
19)
[7,
20)
B) (3, 6)
C) (- , 3)
D) (- , 3)
Solve the rational inequality. Write the solution set in interval notation.
4x
10
21)
-5x + 18
A)
10 18
,
3 5
C) 0,
)
B) - ,
18
5
10
3
D) - , 0
3
(6,
)
21)
10
,
3
18
,
5