Math 112 Chapter 2 Practice Test
Name___________________________________
Simplify. Write your answer in the form a + bi, where a and
b are real numbers.
Use the given graph to find the x-intercepts.
18)
1) (-7 - 6i) + (14 + 4i)
25
y
20
15
2) (-5 - 6i) - (7 - i)
10
5
3) (-9 + 15i) - (5 - 2i)
1 2 3 4 5 6x
-6 -5 -4 -3 -2 -1
-5
Simplify. Write your answers in the form of a+bi, where a
and b are real numbers.
-10
-15
-20
4) (3 - 3i)(5 + 7i)
-25
5) (3 + 4i)(3 - 5i)
19)
y
6) (8 + -9) (6 + -64)
25
20
15
7) (6 - 4i)2
10
5
7 + 2i
8)
8 - 5i
-5
-5
5
x
-10
9)
10)
-15
5 - i
-3 + 6i
-20
-25
i
7 + i
Use the quadratic formula to find the exact solution.
20) x2 - 12x + 61 = 0
11)
1 - 5i
(1 + 5i)2
21) x2 = 15 + 3x
Solve.
22) 5x2 - 19x - 4 = 0
12) 25x2 - 50x - 24 = 0
23) 3t2 - 7t = 1
13) 3x2 = 15x
Consider only the discriminant, b2 - 4ac, to determine
whether one real-number solution, two different
real-number solutions, or two different imaginary -number
solutions exist.
14) 5x2 = 35
15) x2 - 14x + 49 = 25
24) x2 + 8x + 16 = 0
16) 25b3 + 3b = -20b2
25) x2 - 4x + 6 = 0
17) 4x3 + x2 - 4x - 1 = 0
26) 3x2 = -3x - 4
1
27) -6 - 5x2 = -4x - 11
43) y = -(x + 6)2 + 4
A)
Find the zeros of the function algebraically. Give exact
answers.
10
8
28) f(x) = x2 - 5x - 6
y
6
4
2
29) f(x) = 2x2 + 9x + 3
2 4 6 8 10 x
-10 -8 -6 -4 -2-2
-4
30) f(x) = x2 - 5x - 8
-6
-8
-10
Solve.
31) (4m - 5)2 - 5(4m - 5) - 6 = 0
B)
10
Solve the problem.
y
8
6
4
32) How long would it take an object to fall freely
from a bridge 965 ft above the water? (Use the
formula s = 16t2 .)
2
2 4 6 8 10 x
-10 -8 -6 -4 -2
-2
-4
33) The length of a rectangle is three inches more
than the width. The area of the rectangle is 270
inches. Find the width of the rectangle.
-6
-8
-10
C)
Find the vertex of the parabola.
34) f(x) = 2x2 - 16x + 4
10
8
y
6
35) f(x) = -3x2 - 30x - 73
4
2
36) f(x) = -x2 + 9x - 5
2 4 6 8 10 x
-10 -8 -6 -4 -2-2
-4
-6
-8
Find the line of symmetry of the given function.
37) y = 4x2 - 8x - 0
-10
D)
38) f(x) = -x2 + 15x - 2
10
y
8
6
39) f(x) = -3x2 + 4x
4
2
Determine whether there is a maximum or minimum value
for the given function, and find that value.
-10 -8 -6 -4 -2
-2
-4
40) f(x) = x2 + 20x + 92
-6
-8
41) f(x) = x2 - 7x + 12
-10
1
42) f(x) = - x2 + 3x - 5
3
Match the equation to the correct graph.
2
2 4 6 8 10 x
1
44) y = - (x + 2)2 - 2
2
45) y = -(x + 7)2 + 2
A)
A)
10
10
8
y
8
6
y
6
4
2
4
2
2 4 6 8 10 x
-10 -8 -6 -4 -2-2
2 4 6 8 10 x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-8
-6
-8
-10
-10
B)
B)
10
8
10
y
y
8
6
4
6
4
2
2
2 4 6 8 10 x
-10 -8 -6 -4 -2
-2
-4
2 4 6 8 10 x
-10 -8 -6 -4 -2-2
-4
-6
-6
-8
-10
-8
-10
C)
C)
10
10
8
y
8
6
6
4
2
4
2
2 4 6 8 10 x
-10 -8 -6 -4 -2-2
2 4 6 8 10 x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-8
-6
-8
-10
-10
D)
D)
10
y
10
y
y
8
6
8
6
4
4
2
2
-10 -8 -6 -4 -2
-2
-4
-10 -8 -6 -4 -2
-2
-4
2 4 6 8 10 x
2 4 6 8 10 x
-6
-8
-6
-8
-10
-10
Find the range of the given function.
46) f(x) = 3x2 - 30x + 73
3
60) 1 - 6x + 12 ≥ -7x + 4
47) f(x) = x2 - 3x + 6
1 2
48) f(x) = - x + 5x - 2
3
Find the intervals on which the function is increasing and
the intervals on which the function is decreasing.
61) -2(2x - 9) < -6x + 8
49) f(x) = x2 - 12x - 28
50) f(x) = x2 - 5x + 10
5
7
47
62) - x - < - 8
8
5
1
51) f(x) = - x2 + 3x - 7
3
Solve.
52) The number of mosquitoes M(x), in millions, in
a certain area depends on the June rainfall x, in
inches, according to the equation
M(x) = 12x - x2 . What rainfall produces the
Solve. Write interval notation.
63) -25 < 5z + 5 ≤ -5
maximum number of mosquitoes?
64) 5 < 53) Bob owns a watch repair shop. He has found
that the cost of operating his shop is given by
c(x) = 3x2 - 168x + 81, where c is cost and x is the
2
3
x - < 11
13
13
65) -14 < 3b + 4 ≤ -2
number of watches repaired. How many
watches must he repair to have the lowest cost?
66) 4x < 20 or x + 2 ≥ 9
54) ∣x∣ = 5.7
67) 5x - 10 < -3 or 5x - 10 > 3
55) ∣12x∣ = 8
Solve the inequality and graph the solution set.
68) |2x + 1| ≤ 11
56) ∣4m + 5∣ = 9
57) 5x = 0
69) |2x - 4| > 2
58) x + 7 - 4 = 11
Solve the inequality. Write the solution set using interval
notation and graph it.
70) x ≥ 3
59) 10x + 10 > 9x + 11
-10
-8
-6
-4
-2
0
2
4
6
8
10
-8
-6
-4
-2
0
2
4
6
8
10
71) x > 8
-10
4
Solve.
72) ∣x∣ ≤ 6
73) ∣7x + 8∣ < 20
74) |x - 4| > 0.8
75) |19x - 7| < -5
5
Answer Key
Testname: MATH 112 CHAPTER 2 PRACTICE TEST
1) 7 - 2i
2) -12 - 5i
3) -14 + 17i
4) 36 + 6i
5) 29 - 3i
6) 24 + 82i
7) 20 - 48i
-10 + 8 7 16 + 5 7
+ i
8)
89
89
9) - 10)
7
1
+ i
50 50
11) - 12)
3
7
- i
15 5
55
37
+ i
338 338
2
12
, - 5
5
13) 0, 5
14) ± 7
15) 12, 2
3
1
16) 0, - , - 5
5
17) 1 , -1 , - 1
4
18) -4, 2
19) -3, 1
20) 6 ± 5i
3 ± 69
21)
2
1
22) - , 4
5
23)
7 ± 61
6
24) One real solution
25) Two different imaginary-number solutions
26) Two different imaginary-number solutions
27) Two different real-number solutions
28) -1, 6
-9 ± 57
29)
4
30)
5 ± 57
2
31) 1, 11
4
32) About 7.8 sec
33) 15 inches
34) (4, -28)
35) (-5, 2)
6
Answer Key
Testname: MATH 112 CHAPTER 2 PRACTICE TEST
36)
9 61
, 2 4
37) x = 1
15
38) x = 2
39) x = 2
3
40) Minimum: -8
1
41) Minimum: - 4
42) Maximum: 7
4
43) C
44) C
45) D
46) [-2, ∞)
15
, ∞
47)
4
48) -∞, 67
4
49) Increasing on (6, ∞); decreasing on (-∞, 6)
5
5
50) Increasing on , ∞ ; decreasing on -∞, 2
2
51) Increasing on -∞, 9
9
; decreasing on , ∞
2
2
52) 6 in.
53) 28 watches
54) -5.7, 5.7
55) -0.67, 1.5
7
56) - , 1
2
57) 0
58) -22, 8
59) (1, ∞)
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
-16 -15 -14 -13 -12 -11 -10 -9
-8
-7
-6
-5
-4
-3
-2
-4
-3
-2
-1
0
1
2
60) [-9, ∞)
61) (-∞, -5)
-12 -11 -10 -9
-8
-7
-6
-5
7
Answer Key
Testname: MATH 112 CHAPTER 2 PRACTICE TEST
62)
341
, ∞
25
341
25
63) (-6, -2]
67 145
, 64)
3
3
65) (-6, -2]
66) (-∞, 5) ∪ [7, ∞)
67) (-∞, 1.4) ∪ (2.6, ∞)
68)
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
-10
-8
-6
-4
-2
0
2
4
6
8
10
-10
-8
-6
-4
-2
0
2
4
6
8
10
69)
70)
71)
72) [-6, 6]
12
73) - 4, 7
74) (-∞, 3.2) ∪ (4.8, ∞)
75) ∅
8