Download 245 practice for 1.1- 2.2 Disclaimer: The actual exam need not mirror

245 practice for 1.1- 2.2
Disclaimer: The actual exam need not mirror this practice set. This is an aid to help you study.__
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
x-5 x+3
1)
=
7
2
A) -
26
5
1)
B) -
11
5
C) -
2) -2x + 4 + 5(x + 1) = -(4x - 4)
5
13
A)
B)
2
2
31
5
D)
31
9
2)
13
C) 7
5
D) 7
Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
3) 40x + 15 = 5(5x - 18)
3)
A) Conditional; {-7}
B) Conditional; {5}
C) Contradiction; ∅
D) Identity; {all real numbers}
4) 4x - 28 = 2(2x - 16)
A) Contradiction; ∅
C) Identity; {all real numbers}
B) Conditional; {2}
D) Conditional; {-2}
4)
5) 12(x - 3) = 2(6x - 2) - 32
A) Identity; {all real numbers}
C) Contradiction; ∅
B) Conditional; {-36}
D) Conditional; {0}
5)
Solve the formula for the indicated variable.
6) I = Prt, for r
I
P-1
A) r =
B) r =
Pt
It
7) F =
6)
C) r = P - It
D) r =
P-I
1+t
9
C + 32, for C
5
A) C =
F - 32
9
7)
B) C =
5
(F - 32)
9
C) C =
9
(F - 32)
5
D) C =
5
F - 32
Solve for y.
8) 10x - 9y = 5
A) y = 10x + 14
9) 4x + 9 = 7y - 10
4x - 19
A) y =
7
8)
B) y = 10x - 14
10x - 5
C) y =
9
B) y = 4x + 19
4x + 19
C) y =
7
10x + 5
D) y =
9
9)
1
D) y = 4x - 19
Solve the problem.
10) A rectangular Persian carpet has a perimeter of 240 inches. The length of the carpet is 24 in. more
than the width. What are the dimensions of the carpet?
A) Width: 108 in.; length: 132 in.
B) Width: 72 in.; length: 96 in.
C) Width: 48 in.; length: 72 in.
D) Width: 96 in.; length: 120 in.
10)
11) In triangle ABC, angle A is three times as large as angle C. The measure of angle B is 30° less than
that of angle C. Find the measure of the angles.
A) 126° , 12° and 84°
B) 84° , 12° and 84°
C) 126° , 12° and 42°
D) 84° , 12° and 42°
11)
12) In the morning, May drove to an appointment at 50 mph. Her average speed on the return trip in
1
the afternoon was 40 mph. The return trip took hour longer. How far did she travel to the
5
12)
appointment?
A) 0.8 mi
B) 12 mi
C) 40 mi
D) 32 mi
13) How many liters of a 10% alcohol solution must be mixed with 80 liters of a 80% solution to get a
50% solution?
A) 140 L
B) 60 L
C) 14 L
D) 6 L
13)
14) Mardi received an inheritance of $70,000. She invested part at 7% and deposited the remainder in
tax-free bonds at 8%. Her total annual income from the investments was $5300. Find the amount
invested at 7%.
A) $29,000
B) $15,000
C) $30,000
D) $64,700
14)
Write the number as the product of a real number and i.
15) - -16
A) 4
B) i 16
15)
C) 4i
D) -4i
Multiply or divide, as indicated. Simplify the answer.
-10
16)
-160
A)
1
4i
B) -
16)
1
4
C)
1
4
D) -
1
i
4
Write the number in standard form a + bi.
6 - -108
17)
2
A) 3 - 3i 6
17)
B) 3 + 6i 3
C) 3 + 6i 6
Find the sum or difference. Write the answer in standard form.
18) 6i + (-3 - i)
A) -3 + 5i
B) 3 - 7i
C) 3 - 5i
19) (4 + 4i) + (-5 + 7i) - 8i
A) -1 - 3i
D) 3 - 3i 3
18)
D) -3 + 7i
19)
B) 9 + 11i
C) -1 + 3i
2
D) -9 + 3i
Find the product. Write the answer in standard form.
20) (9 - 4i)(2 + 9i)
A) -18 - 89i
B) -36i2 + 73i - 18
20)
C) 54 - 73i
D) 54 + 73i
21) (9 + 9i)(9 - 9i)
A) 81 + 81i2
B) 81 - 81i2
C) 0
D) 162
21)
22) ( 6 - 5i)( 6 + 5i)
A) 31
B) 11
C) 6 + 25i
D) 6 - 25i
B) -i
C) -1
D) 1
22)
Simplify the power of i.
23) i45
A) i
24)
23)
1
i-13
24)
A) -1
B) -i
C) 1
D) i
Find the quotient. Write the answer in standard form.
4 + 3i
25)
5 + 3i
A)
26)
11 27
i
34 34
B)
25)
29
3
i
16 16
C)
29
3
i
+
34 34
D)
11
3
i
16 16
8 + 2i
4 - 8i
A) - 1 +
26)
3
i
16
B)
24 28
i
+
5
5
C)
1
9
i
+
5 10
D) -
1
3
i
+
24 16
Solve the equation by the zero-factor property.
27) x2 + 14x + 40 = 0
A) {2 10, -2 10}
27)
B) {-10, -4}
C) {-20, -8}
D) {4, 10}
B) {±13}
C) {±13i}
D) {84.5}
3
B)
5
3
C) - , 0
5
3 9
D)
,
5 5
C) {-2 ± 2 5}
D) {2, -6}
Solve the equation by the square root property.
28) x2 = -169
A) {13}
29) (5x + 6)2 = 9
3
9
A) - , 5
5
28)
29)
Solve the equation by completing the square.
30) x2 + 4x + 20 = 0
A) {-2 ± 4i}
30)
B) {2 ± 4i}
3
31) x2 + 11x = -28
A) {4, 7}
31)
B) {4, -7}
C) {-4, -7}
D) {-4, 7}
Solve the equation using the quadratic formula.
32) 3x2 + 12x + 2 = 0
A)
33) 2 = A)
-12 ± 30
3
B)
32)
-6 ± 30
6
C)
-6 ± 42
3
D)
-6 ± 30
3
10
5
x
x2
-10 ± 15
2
33)
B)
-5 ± 15
4
C)
-5 ± 15
2
D)
-5 ± 35
2
Solve the cubic equation.
34) x3 - 1 = 0
A) {1, 1 ± i 3}
35) x3 - 64 = 0
A) {4, -2 ± 2i 3}
34)
1
3
B) 1, ±
i
2
2
C) {1, -1 ± i 3}
D) {1, ± i}
35)
B) {4, -2 ± 2i}
C) {4, 2 ± 2i 6}
D) {4, 2 ± 2 5}
Solve the problem.
36) Find two consecutive odd integers whose product is 675.
A) -25, -27
B) 25, 27
C) 25, -27
D) 25, 27 or -25, -27
36)
37) The sum of the squares of two consecutive even integers is 1252. Find the integers.
A) 24, 26
B) 24, 26 or -24, -26
C) -24, -26
D) 25, -27
37)
38) The length of a rectangle is 10 inches more than its width. If 5 inches are taken from the length and
added to the width, the figure becomes a square with an area of 196 square inches. What are the
dimensions of the original figure?
A) 14 in. by 14 in.
B) 9 in. by 19 in.
C) 9 in. by 14 in.
D) 4 in. by 14 in.
38)
39) The area of a square is numerically 21 more than the perimeter. Find the length of the side.
A) 25 units
B) 98 units
C) 7 units
D) 28 units
39)
40) A ladder is resting against a wall. The top of the ladder touches the wall at a height of 9 ft. Find the
length of the ladder if the length is 3 ft more than its distance from the wall.
A) 12 ft
B) 18 ft
C) 15 ft
D) 9 ft
40)
Solve the equation.
2
3
41)
+6=
17x
23x
A)
5
2346
41)
B)
1
2
C)
4
5
6
D) ∅
42) 1 -
5
-
x
36
=0
x2
42)
A) {9, 4}
43)
C) {9, -4}
D) {-9, 4}
24
24
+
=5
x-2 x+2
A)
44)
B) {-9, -4}
2
, -10
5
43)
B) {2, 10}
C) -
5
, -10
2
D) -
2
, 10
5
-5x2 - 6 -15x
=
+6
x-4
x-4
A) -
6
,3
5
44)
B) {3}
C)
-5 ±
105
3
D)
6
, -3
5
Solve the problem.
45) Martha can rake the leaves in her yard in 7 hours. Her brother can do the job in 4 hours. How long
will it take them to do the job working together?
28
28
1
1
A)
hr
B)
hr
C)
hr
D)
hr
3
11
11
28
Solve the equation.
46) x = 4x + 12
A) {6, -2}
47)
49)
46)
x+7+5=x
A) {9, 18}
48)
3x + 1 = 3 +
A) {5, 8}
5
45)
B) {4}
C) {6}
D) ∅
B) {9}
C) {2, 9}
D) {2}
47)
x-4
x2 - 14 = 1
A) {- 14, 14}
50) (x2 + 2)1/2 - (2x + 5)1/2 = 0
A) {3}
48)
B) {-1}
C) {-5, -8}
D) ∅
49)
B) {- 15,
15}
C) { 14}
D) { 15}
C) {-3, 1}
D) ∅
50)
B) {3, -1}
51) x1/2 = 3x1/4
A) {0, 9}
B) {0, 81}
C) {0, 3}
D) ∅
52) 25x4 - 61x2 + 36 = 0
6
A) 1,
5
6
6
B) - , -1, 1,
5
5
5
C) -1, 6
5 5
D) -1, - , , 1
6 6
51)
52)
5
53) 3x-2 - 9x-1 + 6 = 0
53)
1
B) 1,
2
A) - 1, -2
1
C) - 1, 2
D) 1, 2
Solve and graph the inequality. Give answer in interval notation.
54) -4x + 3 ≤ -5x + 11
A) (-∞, -4)
-9
-8
B) [8, ∞)
-7
-6
-5
-4
-3
-2
-1
0
1
3
C) (-4, ∞)
-9
-8
54)
4
5
6
7
8
9
10 11 12 13
5
6
7
8
9
10 11 12 13
D) (-∞, 8]
-7
-6
-5
-4
-3
-2
-1
0
1
3
4
55) -6(3x + 8) < -24x - 42
55)
A) (-∞, -24)
B) (-24, ∞)
-29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19
-29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19
C) (1, ∞)
-4
-3
D) (-∞, 1)
-2
-1
0
1
2
3
4
5
6
-4
-3
-2
-1
0
1
2
3
4
5
6
56) -12 < -3x ≤ 0
56)
A) [-4, 0)
B) [0, 4]
-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
C) [0, 4)
D) (-4, 0]
-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
57) 15 < 4x + 3 ≤ 31
57)
A) [3, 7]
B) [3, 7)
-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
C) (3, 7]
D) (3, 7)
-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
Solve the quadratic inequality. Write the solution set in interval notation.
58) x2 + 7x ≤ -12
A) [-4, -3]
B) (3, 4)
C) (-∞, 3] ∪ [4, ∞)
6
58)
D) [3, 4]
59) x2 - 4x - 21 ≤ 0
A) (-∞, -3] ∪ [7, ∞)
B) [-3, 7]
60) (5 - 2x)2 ≤ -16
9
1
A) -∞,
∪ ,∞
2
2
9 1
B) ,
2 2
59)
C) [7, ∞)
D) (-∞, -3]
60)
C) (-∞, ∞)
Solve the inequality. Write the solution set in interval notation.
61) (x + 6)(x - 2)(x - 9) < 0
A) (-∞, -6) ∪ (2, 9)
B) (9, ∞)
C) (-6, 2) ∪ (9, ∞)
62) (x - 5)(x - 10)(x + 1) < 0
A) (-∞, -5) ∪ (1, 10)
C) (-∞, -1) ∪ (5, 10)
D) ∅
61)
D) (-∞, 2)
62)
B) (-5, -1) ∪ (10, ∞)
D) (-10, -5) ∪ (1, ∞)
Solve the rational inequality. Write the solution set in interval notation.
1
63)
>0
x + 10
A) (-10, ∞)
64)
B) (10, -∞)
C) [10, ∞]
63)
D) (-∞, 10)
5x
≥ 15
-3x + 14
A)
21 14
,
5 3
C) -∞, 0 ∪
65) 4 ≥
64)
B) 0,
14
,∞
3
14
3
D) -∞,
21
21
,∞
∪
5
5
1
x
65)
A) -∞, 0 ∪ 4,∞
B) -∞, 0 ∪
1
,∞
4
C) 0,
1
4
D) 0, 4
Solve the problem.
66) The profit made when t units are sold, t > 0, is given by P = t2 - 30t + 200. Determine the number of
units to be sold in order for P = 0 (the break- even point).
A) t = 30
B) t = 20 or t = 10
C) t = -20 or t = -10
D) t > 20
Solve the equation.
67) |2x - 8| = 5
3
13
A)
,2
2
68)
67)
3
13
B) - , 2
2
13
C)
2
13 3
D)
,
2 2
8
=5
x+5
A)
17 33
,
5 5
66)
68)
B) {-5}
C) -
7
17
33
,5
5
D)
33 17
,
5 5
69) |9x - 2| = |8x - 5|
69)
3
B) ,7
17
A) - 7, 1
7
D) - 3,
17
C) 7, 1
Solve the inequality. Write the solution set in interval notation.
70) |5 - 4x| > 8
13
3
3
13
A) ,B) -∞, ,∞
∪
4
4
4
4
C)
71)
3
13
,4
4
D) -∞,
70)
1
15
,∞
∪ 4
4
5 1
2
- x >
2 3
5
A)
71)
63 87
,
10 10
C) -∞,
B) -∞, -
63
87
,∞
∪
10
10
D) (-∞, ∞)
72) 2 - 3x ≤ 11
13
A) -3,
3
C) (-∞, 3] ∪
72)
13
B) ,3
3
13
,∞
3
Solve the equation or inequality.
73) 5x + 3 + 6 = 10
1 7
A) - ,
5 5
D) (-∞, -3] ∪
B)
1
7
,3
3
C)
Solve the equation.
76) 3x3 - 4x2 - 7x = 0
3
A)
,0
7
1
7
,5
5
D) ∅
74)
5
B) -∞, 8
5
1
∪ - ,∞
8
8
75) |8x - 8| - 8 ≥ -1
15
A)
,∞
8
13
,∞
3
73)
74) |8x + 3| + 6 < 8
5
1
A) - , 8
8
C) -∞, -
87
63
,∞
∪
10
10
D) ∅
75)
1
15
B) ∞,
,∞
∪
8
8
1 15
C) ,
8 8
D) ∅
3
B)
, 1, 0
7
7
C)
, -1, 0
3
3
D)
, -1
7
76)
For the points P and Q, find the distance d(P, Q).
77) P(4, -1), Q(6, -7)
A) 2 10
B) 32
77)
C) 8
8
D) 32 2
For the points P and Q, find the coordinates of the midpoint of the segment PQ.
78) P(-3, -2), Q(4, -9)
7 7
A) (1, -11)
B) (-7, 7)
C) - ,
2 2
78)
1
11
D) , 2
2
Graph the equation by determining the missing values needed to plot the ordered pairs.
79) y + x = 4; (1, ), (4, ), (3, )
79)
y
10
5
-10
-5
5
10
x
-5
-10
A)
B)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C)
5
10
x
5
10
x
D)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
Graph the equation by plotting points.
9
80) y =
x+3
80)
y
10
5
-10
-5
5
10
x
-5
-10
A)
B)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C)
5
10
x
5
10
x
D)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
10
81) y = 8 - x
81)
y
10
5
-10
-5
5
10
x
-5
-10
A)
B)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C)
5
10
x
5
10
x
D)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
Find the center-radius form of the equation of the circle.
82) center (4, 0), radius 7
A) (x - 4)2 + y2 = 49
82)
B) x2 + (y + 4)2 = 7
C) x2 + (y - 4)2 = 7
D) (x + 4)2 + y2 = 49
83) center (-8, -6), radius 17
A) (x + 6)2 + (y + 8)2 = 289
83)
B) (x - 8)2 + (y - 6)2 = 17
D) (x + 8)2 + (y + 6)2 = 17
C) (x - 6)2 + (y - 8)2 = 289
11
Find the center and radius of the circle.
84) x2 + y2 + 8x - 10y - 8 = 0
84)
A) center: (-5, 4); radius: 49
C) center: (-4, 5); radius: 7
B) center: (5, -4); radius: 7
D) center: (4, -5); radius: 49
85) 5x2 + 5y2 - 20x - 30y + 60 = 0
A) center: (3, 2), radius: 1
C) center: (2, 3), radius: 1
85)
B) center: (-2, -3), radius: 1
D) center: (-3, -2), radius: 1
12
Answer Key
Testname: 245EXAM1P
1) C
2) D
3) A
4) A
5) A
6) A
7) B
8) C
9) C
10) C
11) C
12) C
13) B
14) C
15) D
16) C
17) D
18) A
19) C
20) D
21) D
22) A
23) A
24) D
25) C
26) C
27) B
28) C
29) A
30) A
31) C
32) D
33) C
34) B
35) A
36) D
37) B
38) B
39) C
40) C
41) A
42) C
43) D
44) A
45) B
46) C
47) B
48) A
49) B
50) B
13
Answer Key
Testname: 245EXAM1P
51) B
52) B
53) B
54) D
55) D
56) C
57) C
58) A
59) B
60) D
61) A
62) C
63) A
64) A
65) B
66) B
67) D
68) C
69) D
70) B
71) C
72) A
73) C
74) A
75) B
76) C
77) A
78) D
79) C
80) D
81) B
82) A
83) D
84) C
85) C
14