Exam
Chapter 1
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response.
1) Simplify the expressions (2x)0 and (2x0 ) and explain how you arrived at your answers.
1)
2) For what values, if any, of x (x 0) and n will x-n be a negative number?
2)
3) What steps would you take to factor x2 + 17x + 70 ?
3)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the expression. Write answer with positive exponents. Variables are positive real numbers. 4) z-2/7 z3/7
A) z7/6
Solve the equation. 5) 5(y + 7) = 6(y - 4) A) -11
B) z1/7
C) z6/7
5) B) 11
C) -59
D) 59
Solve the problem. 6) How many liters of a 20% alcohol solution must be mixed with 70 liters of a 50% solution to get a 30% solution? A) 210 liters B) 21 liters C) 140 liters D) 14 liters Use factoring to solve the equation. 7) x2 + 3x - 70 = 0
A) -10, 1
B) 10, 7
C) 10, -7
D) -10, 7
8)
y2 + 2y - 35
A) 4y - 21 2y - 35
6)
7)
Write the expression in lowest terms. y2 + 4y - 21
8)
4)
D) z-1/7
B) 4y - 3
C) y - 3
2y - 5
y- 5
1
2
D) - y + 4y - 21 y2 + 2y - 35
Use inequality symbols to rewrite the statement. Let x represent the unknown. 9) Computer company XYZ can't possibly spend less than $42 million in advertising to regain its market share. A) x > $42 million B) x $42 million
C) x < $42 million
9)
D) x $42 million
Solve the equation for the indicated variable. 10) E = mc2 for c
A) c = Em
10)
B) c = E m
C) c = ± Em
D) c = ±
E m
Solve the problem.
11) The time T in seconds for a pendulum of length L feet to make one swing is given by T = 2
L . 44
11)
How long is a pendulum (to nearest hundredth) if it makes one swing in 1.3 seconds? Use 3.14 for . A) 11.84 ft B) 18.59 ft C) 1.89 ft D) 74.36 ft
Factor completely. 12) 16y2 + 24y + 9
A) Prime
12) B) (16y + 3)(y + 3)
C) (4y + 3)(4y + 3)
Name the property illustrated. 13) 8 + (6 + 9) = (8 + 6) + 9 A) Associative property
D) (4y - 3)(4y - 3)
13) B) Distributive property D) Commutative property
C) Identity property Find approximate solutions of the equation. 14) 6x2 - 5x = 1
A) 2 or -0.34
14)
B) 0.17 or -1
C) 1 or -0.17
D) 0.5 or 0.33
Solve the problem.
15) The polynomial 0.0039x4 + 0.0035x3 + 0.0035x2 + 0.14x + 1.13 gives the predicted sales volume of a
15)
company, in millions of items, where x is the number of years from now. Determine the predicted sales 20 years from now. A) 583.99 million B) 653.2 million C) 657.33 million D) 853.83 million
Name the property illustrated. 16) 8 + 3 = 3 + 8 A) Identity property
16) B) Distributive property D) Commutative property
C) Associative property Determine whether the statement is true or false. 17) Every integer is an irrational number. A) True
17) B) False 2
Provide an appropriate response. 18) A binomial is a polynomial. A) Sometimes Factor completely. 19) x2 + 40x + 400
A) (x + 20)(x - 20)
18) B) Never
C) Always
19) B) (x + 20)2
C) (x - 20)2
D) Prime
Solve the problem. 20) A square plywood platform has a perimeter which is 9 times the length of a side decreased by 20. Find the length of a side. A) 9 B) 4 C) 5 D) 1 Add or subtract as indicated. 21) (8n 5 + 9n 3 - 2n) + (5n5 - 4n3 + 7n)
21)
A) 13n 5 + 5n 3 + 5n
B) 3n5 + 4n3 + 16n
C) 23n 9
D) 13n + 5n 5 + 5n 3
Write the expression in lowest terms. 22) 3k - 15 30 - 6k
A) 1
22) B) - 1
2
C) 1
2
D) -1
Write the rational exponent expression as an equivalent radical expression. 23) (7x)-1/7
A) -7 7
20)
B) 7
7
x
C)
x
1 7
7x
23) D)
1 7
-7x
Solve the problem. 24) The two charts show the weight gain of some people and the weight loss of other people. Use the information given to answer the questions below.
How much more weight did Ed lose than Frank? A) -3,034 grams B) 1,320 grams
C) 3,034 grams
D) -1,320 grams
25) At the end of the day, a storekeeper had $1,605 in the cash register, counting both the sale of goods and the sales tax of 7%. Find the amount of the tax. A) $95 B) $110
3
C) $100
24)
D) $105
25)
Simplify the expression. Write answer with positive exponents. 5 -1
26)
26)
59
A) 1
5 10
Solve the equation. 27) 12(8c - 3) = 7c - 2 A) - 34 89
C) 1
B) 58
58
D) 510
27) B) 34
C) 34
103
89
D) 38 89
Find expressions for the Revenue, Cost, and Profit from selling x thousand items. 28) Item Price Fixed Cost Variable Cost $3.00 $131,282 -3x2 + 3480x - 100
28)
A) R = 3,000x; C = -3x2 + 3480x + 131,282; P = 3x2 - 3,180x - 131,182 B) R = 3,000x; C = 3x2 + 3480x + 131,182; P = -3x2 - 3,180x - 131,182 C) R = 3,000x; C = -3x2 + 3480x + 131,182; P = 3x2 - 3,180x - 131,182 D) R = 3,000x; C = -3x2 + 3480x + 131,182; P = 3x2 - 3,180x - 131,282
Use factoring to solve the equation. 29) 16k2 - 81 = 0
A) 9, 0
29) B) 4 , 0 9
C) 4 , - 4 9 9
D) 9 , - 9 4 4
Factor completely. 30) 15z 2 + 14z - 8
A) Prime
30) B) (3z - 4)(5z + 2)
C) (3z + 4)(5z - 2)
Simplify. Leave answer with exponent. 31) (2y)4 · (2y)8
A) 4y32
D) (15z + 4)(z - 2)
31)
B) (2y)12
C) 2y32
D) 4y12
Solve the problem. 32) A picture is to be mounted on a piece of matte board 10 inches by 16 inches so that there is an even amount of matting all around the picture. How wide will the border be if the area of the mounted picture is 120 square inches? A) 3 in. B) 4 in. C) 4.5 in. D) 2 in. Solve the equation. 33) 3s + 7 = s + 5 A) - 1
32)
33) B) - 1, - 3
C) No solution
4
D) 1, 3
Evaluate the expression using order of operations. 34) 3 · 52
A) 15
34)
B) 375
C) 75
D) 225
Simplify the expression. Write answer with positive exponents. 3 -9
35)
35)
3 -7
A) 3-2
B) -3 2
C) 32
D) 1
36) 7-4 · 7 7 A) 493
B) 4928
C) 73
D) 7-28
32
36)
Find the product. 37) (x + 5y)(x + 10y)
37) B) x2 + 15xy + 15y2 D) x2 + 15xy + 50y2
A) x + 15xy + 50y C) x2 + 12xy + 50y2 Write the expression in lowest terms. 3x + 3 38) 2 15x + 21x + 6
A)
3x 5x + 2
38) B)
C) 3x + 5
3x + 3 2 15x + 21x + 6
5x + 21
D)
1 5x + 2
Solve the equation for the indicated variable. 39) A = r2 for r
A) r = A
39)
B) r = A
C) r = ±
A
D) r = ±
A
Perform the indicated operations. Give the answer in lowest terms. 40) 6x + 7 + 2x + 9 x 3x
A) 20x - 12 3x
B) 16x + 30
40)
C) 20x + 30 3x2
3x
Use a calculator to solve the equation. Round to the nearest hundredth. 41) -0.07(4.5 + 4.3x) = 1.23x + 3.5667 A) -2.54 B) -2.12 C) 4.18
5
D) 20x + 30 3x
41) D) 3.50
Rationalize the denominator. Assume all variables represent positive real numbers. 5 42) 7+9
A)
35 - 9 5 -74
35 - 9 5 16
B)
C)
35 + 9 5 -74
42) D) 3 35 + 75 63
Factor completely. 43) -75x3 + 40x2 + 80x
43)
A) x(5x + 4)(-15x + 20) C) -5x(5x + 4)(3x - 4)
B) x(-25x - 20)(3x - 4) D) -5(5x2 + 4)(3x - 4)
Solve the equation. 44) b - 6 = -4 9
A) -20
44) B) 18
C) 20
Determine whether the statement is true or false. 45) Some real numbers are integers. A) True
D) -18
45) B) False
Evaluate the expression. Write answer without exponents. 46) 1001/2
A) 10
46)
B) 20
C) 40
D) 5
Solve the equation. 47) 8 + 3 = 1 x 4
A) 11
47) B) 11
C) 4
4
Graph the inequality on a number line. 48) [-3, )
D) 32
48)
A)
B)
C)
D)
6
Identify the degree of the polynomial and list its coefficients. 49) 3x - 8 A) degree: 1 coefficients: 3, -8 C) degree: 1 coefficients: 3, 8 Add or subtract as indicated. 50) (4n 6 + 6n 5 + 9) + (4n6 - 8n5 - 4)
A) 8 - 2n6 + 5n5
49) B) degree: 3
coefficients: 3, 8 D) degree: 0 coefficients: 3, -8
50)
B) 8n6 - 2n 5 + 5
C) 13n 6 - 4n5 + 2
Fill in the blank with either =, <, or > to make the statement true. 51) - -11 11 A) > B) <
D) 11n 11
51) C) =
Simplify the expression. Write answer with positive exponents. 43
52)
52)
4 -8
A) 1
B) 1
4 11
C) 411
45
D) 45
Solve the formula for the specified variable. 53) V = 1 Bh for h 3
A) h = 3V B
53)
B) h = B
C) h = V
3V
D) h = 3B
3B
V
Use the discriminant to determine the number of real solutions of the equation. 54) 9x2 + 12x + 4 = 0
A) 2
B) 1
54) C) No real solutions
Fill in the blank with either =, <, or > to make the statement true. 55) 3 - (-1) -3 - 1 A) < B) =
55) C) >
Simplify the expression. Write answer with positive exponents. 2 11
56)
56)
25
A) 1
26
C) 26
B) 2-2
7
D) 216
Solve the equation. 57) -2x + 7 + 9 = - 5x 7 7 4
A) - 8
27
57) B) - 64
C) 64
27
43
D) 8
27
Evaluate the expression. Write answer without exponents. 1 2/3
58)
58)
27
A) 1 4
Solve the problem.
59) The formula A =
B) 1
C) 1
13
9
D) - 1 9
24f gives the approximate annual interest rate for a consumer loan paid off b(p + 1)
59)
with monthly payments, where f is the finance charge on the loan, p is the number of payments, and b is the original amount of the loan. Find the approximate annual interest rate for an automobile loan to be repaid in 18 monthly installments if the finance charge on the loan is $680 and the original loan balance is $3,330. (Round answer to two decimal places.) A) 25.79% B) 22.75% C) 27.22% D) 28.83%
Evaluate the expression. Write answer without exponents.
60)
9 1/2 16
A) 3 4
60) B) 3
C) 2
5
5
D) 2 4
Solve the problem.
61) The polynomial -0.1t2 + 1.8t represents the yearly income (or loss) from a real estate investment, where t is time in years. After what year does income begin to decline? A) year 18 B) year 9 C) year 8
D) year 12.00
62) Use the formula A = P(1 + r)2 to find what the rate of interest is if a principal amount of $5,500 grows to $6,415.20 in 2 years, if interest is compounded annually. A) 6% B) 10% C) 9%
62)
D) 8%
Solve the equation. 63) a - 1 = -6 4 4
A) 23
61)
63) B) 25
Evaluate the expression using order of operations. 64) (6 + (-3))[3 + (2 + 6)] A) 33 B) 35
C) -25
D) -23
C) 10
D) 14
64)
8
Solve the problem. 65) Total profit is defined as total revenue minus total cost. R and C are the revenue and cost from the sale of x televisions. If R = 290x - 0.6x2 and C = 3,000 + 0.5x2 , find the profit from the sale of 90 televisions. A) $28,290
B) $14,190
C) $20,190
65)
D) $22,290
66) Roberto invested some money at 7%, and then invested $3,000 more than twice this amount at
66)
10%. His total annual income from the two investments was $3,810. How much was invested at 10%? A) $9,000 B) $26,000 C) $2,900 D) $29,000
Write the expression in lowest terms. 67) (y + 8)(5 - y) (-y + 5)(8 + y)
A) -1
67) B) 1
C) 0
D) -y
Solve the problem. 68) A rectangular Persian carpet has a perimeter of 192 inches. The length of the carpet is 24 inches more than the width. What are the dimensions of the carpet? A) 72 inches, 96 inches B) 60 inches, 84 inches
C) 84 inches, 108 inches
D) 36 inches, 60 inches
69) A plane flies 480 miles with the wind and 320 miles against the wind in the same length of time. If the speed of the wind is 27 mph, what is the speed of the plane in still air? A) 160 mph B) 125 mph C) 140 mph
Add or subtract as indicated. 71) (8n 7 + 11n5 + 15n) - (3n7 + 7n5 + 4n)
70)
71)
A) 20n 13
B) 5n7 + 14n 5 + 19n
C) 5n7 + 4n5 + 19n
D) 5n7 + 4n5 + 11n
Simplify the complex fraction. 1 k+ 6
72)
3
k2 - 36
A) k - 6
69)
D) 135 mph
Determine whether the statement is true or false. 70) The absolute value of any nonzero number is positive. A) True B) False
72)
68)
B)
3 k- 6
C) k - 6 3
9
D) k + 6 3
Find the product. 73) (8.3x - 1.7)(0.6x - 1.2) A) 8.9x2 - 10.98x - 10.98
73) B) 8.9x2 - 10.98x + 2.04 D) 4.98x2 - 10.98x + 2.04
C) 4.98x2 - 10.98x - 10.98 Solve the equation for the indicated variable. 74) 4 r2 = A for r
A) r = ± 2 A
74)
B) r = 2
A
C) r = ±
A 2
Use a calculator to solve the equation. Round to the nearest hundredth. 75) 1.26x + 4.91(2.4 + 4.5x) = 3.82x + 4.5345 A) 0.84 B) -0.27 C) -0.37
D) r = ± 1 A 2
75) D) 0.60
Find approximate solutions of the equation. 76) 2x2 + 3.1x - 7.3 = 0
A) 2.84 or -1.29 Solve the equation for x. 77) x = (6x - 2)(3k + 1) A) x = 6k + 2 18k + 7
76)
B) 1.29 or -1.29
C) 2.84 or -2.84
D) 1.29 or -2.84
77) B) x = 6k - 2
C) x = 6k + 2
18k + 5
18k - 5
D) x = 6k + 2
18k + 5
Solve the problem. 78) The finance charge on a loan taken out by Ximena is $755. If there were 24 equal monthly installments needed to repay the loan, and the loan is paid in full with 6 months remaining, find the total finance charge paid. (Round answer to the nearest cent.) A) $430.35 B) $52.85 C) $702.15 D) $755.00 Simplify. Leave answer with exponent. 79) 44 · 4 9
A) 413
79)
B) 1636
C) 436
D) 1613
Solve the problem. 80) A sign is in the shape of an isosceles triangle. The third side is 17 inches less than the length of each equal side. Find the length of one equal side if the perimeter is 64 inches. A) 27 in. B) 10 in. C) 30 in. D) 21 in. Solve the equation. 81) -6.4q + 1.1 = -23.9 - 1.4q A) -30
78)
80)
81) B) 5
C) 3.9
10
D) 4.1
Solve the equation for x. 82) 5(x - a) + b = 6x + a
A) x = 6a - b
82) C) x = 6a - b
B) x = 5a + b
D) x = -6a + b
11
Perform the indicated operations. Give the answer in lowest terms. 2 6 83) + y2 - 3y + 2 y2 - 1
83)
A)
8y - 10 (y - 1)(y - 2)
B)
8y - 10 (y - 1)(y + 1)(y - 2)
C)
10y - 8 (y - 1)(y + 1)(y - 2)
D)
24y - 10 (y - 1)(y + 1)(y - 2)
Solve by the square-root property. 84) (x - 5)2 = 9
A) 3, -3
84) B) 8, 2
C) 2, -8
D) 14
Use the discriminant to determine the number of real solutions of the equation. 85) 7 + 2z 2 = -5z
A) 2
B) No real solutions
Determine whether the statement is true or false. 86) The absolute value of any number is positive. A) True
85) C) 1
86) B) False
Simplify the expression. Write answer with positive exponents. Variables are positive real numbers. 87) (b5 )3/5 A) b1/5 B) b3 C) b3/25 D) b8/5 Evaluate the expression. Write answer without exponents. 88) (-2)0
88)
B) 1
A) -1
C) -2
Express each of the following statements in symbols, using <, >, , or . 89) w is positive. A) w 0 B) w 0 C) w > 0
D) 0
89) D) w < 0
Perform the indicated operations. Give the answer in lowest terms. 90) x + 12 7 11
A) 11x + 84 77
87)
B) x + 12
90)
C) x + 12
77
18
11
D) 11x - 84 84
Insert <, =, or > to write a true statement. 91) 7 ___ 0.875 8
91)
A) >
B) =
C) <
Evaluate the expression. Write answer without exponents. 92) (10.48)1/3
A) 1,151.02259
92)
B) 2.18837
C) 0.00087
D) 31.44
Provide an appropriate response. 93) Decide whether the statement is true or false by using the simplification procedures. A) True B) False
48 = 2 12
Evaluate the expression using order of operations. 94) (-2) · (8 - 7) + (-2) · 4 (-2) · (4 - 1)
A) 11 6
94)
B) 5
C) 3
3
D) 50
5
3
Solve the equation. 95) p - 3p = 2 4 8
A) 14
93)
95) C) 16
B) -16
Express each of the following statements in symbols, using <, >, , or . 96) p is at least 92 A) p > 92 B) p 92 C) p < 92 Perform the indicated operations. Give the answer in lowest terms. 6 97) x 2 2 x - 16 x + 5x + 4
D) -14
96) D) p 92
97)
A)
x2 - 5 (x - 4)(x + 4)(x +1)
B) x - 5x + 24
2
C)
x2 - 5x + 24 (x - 4)(x + 4)(x + 1)
D)
(x - 4)(x + 4) x2 + 5x + 24 (x - 4)(x + 4)(x + 1)
Factor completely. 98) 12x2 + 25xt + 12t2
98)
A) (3x - 4t)(4x - 3t) C) (3x + 4t)(4x + 3t)
B) Prime D) (12x + 4t)(x + 3t)
12
Solve the equation. 99) 5x + 1 = 3 x-1
A) 2, -8 Factor completely. 100) 49x2 - 112x + 64
A) Prime
99) B) 4, 2
C) 1 , - 1
B) (7x - 8)2
C) (7x + 8)2
D) - 2, 1
2
4
100)
Name the property illustrated. 101) (7 + 9) + 6 = (9 + 7) + 6 A) Commutative property
D) (7x - 8)(7x + 8)
101) B) Identity property D) Associative property
C) Distributive property Factor completely. 102) x3 - 8
102)
A) (x + 2)(x2 - 2x + 4) C) (x - 2)(x2 + 2x + 4)
B) (x + 8)(x2 - 1) D) (x - 2)(x2 + 4)
Solve the equation for x. 103) a2 x - 2x = 3a 2
A) x = 3 2
103) 2 C) x = 3a
B) x = - 3 2
2 D) x = 3a
a2 + 2
a2 - 2
Rationalize the denominator. Assume all variables represent positive real numbers. 2 104) 2 7- 2
A) 1 ( 7 + 1) 13
B) 1 ( 14 - 1)
C) 1 ( 14 + 1)
13
13
104) D) 1 ( 14 + 1) 15
Use the discriminant to determine the number of real solutions of the equation. 105) 4y2 = 5y - 8
A) 2
B) 1
105) C) No real solutions
Graph the inequality on a number line. 106) (- , -6)
106)
A)
B)
C)
D) 13
Evaluate the expression. 107) - -15 - 17 A) -2
107) B) 32
D) 2
C) -32
Solve the equation. 108) 2 = t t -4t - 6
108) B) 0, 6
A)
Insert <, =, or > to write a true statement. 109) -9 ___ -2 A) <
D) 0, 36
C) -2, -6
4
109) B) =
C) >
Determine whether the statement is true or false. 110) Some rational numbers are integers. A) True
110) B) False
Find approximate solutions of the equation. 111) 3y2 + 7.4y - 2.8 = 0
A) 0.33 or -0.33
111)
B) 2.80 or -2.80
C) 0.33 or -2.80
D) 2.80 or -0.33
Solve the problem. 112) Jay drove 284 kilometers at the average rate of 71 kilometers per hour. How long did the trip take? A) 4 hours B) 3 hours C) 2 hours D) 5 hours Simplify the expression. Write answer with positive exponents. 4 -11
113)
113)
49
A)
1 -20 4
B) 1
C) 1
4 20
112)
4 17
D) 1
42
Solve the problem.
114) The position of an object moving in a straight line is given by s = 9t2 - 3t, where s is in meters and
114)
t is the time in seconds the object has been in motion. How far will an object move in 6 seconds? A) 306 m B) 216 m C) 54 m D) 36 m
Write the expression in lowest terms. 115) (y + 2)(y - 6) (y - 6)(y + 7)
A) y + 6 y+ 1
115) B) 2y - 6
C) y + 2
2y + 1
y+ 7
14
D) y - 2 y- 7
Use factoring to solve the equation. 116) x2 - x = 42
116)
A) -6, -7
B) -6, 7
C) 6, 7
D) 1, 42
117) x2 - 12x + 36 = 16 A) 4, -4
B) 22
C) 2, -10
D) 10, 2
117)
Use a calculator to evaluate the expression. 5 2
118)
118)
2
A) 1.25
B) 6.25
C) 12.5
D) 5
Evaluate the expression. Write answer without exponents. -3 1 119) 5
A) 1
-15
119)
B) 0.01
D) 3
C) 125
5
Solve the problem. 120) In a chemistry class, 3 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed? A) 3.0 liters B) 2.5 liters C) 1.5 liters D) 0.5 liters Write the rational exponent expression as an equivalent radical expression. 121) -5x-1/5
A)
1 5
5x
B) -5 5
C) 5
5
121)
x
D)
x
1 5
-5x
Use the discriminant to determine the number of real solutions of the equation. 122) v2 + 8v + 5 = 0
A) 1
B) No real solutions
122) C) 2
Perform the indicated operation. Give the answer in lowest terms. 2 2 123) z + 12z + 27 ÷ z + 3z z 2 + 16z + 63 z 2 + 14z + 49
A) z + 7 z
B) z + 7
C)
Name the property illustrated. 124) 5 · 6 = 6 · 5 A) Identity property
120)
123) z 2 z + 16z + 63
D) z + 7
z 2 + 7z
124) B) Associative property D) Commutative property
C) Distributive property
15
Factor completely. 125) 5x3 + 5x2y - 100xy2
125)
A) (5x2 + 20xy)(x - 5y)
B) (x - 4y)(5x2 + 25xy)
C) 5x(x - 4y)(x + 5y)
D) 5x(x + 4y)(x - 5y)
Fill in the blank with either =, <, or > to make the statement true. 126) - 17 -17 A) = B) >
126) C) <
Evaluate the expression, given x = -2, y = 3, and a = -4. 127) -7(x + 2) + 3a 2
A) -12 128) (-8 + x)(2 + y)(-9 - a) A) -250
127)
B) 20
C) -48
D) 48 128)
B) 390
C) 650
D) 250
Provide an appropriate response. 129) 16x2 - 9 cannot be factored because there is no x term. Is this statement true?
A) No, it is not true. Simplify. Leave answer with exponent. 130) (-3)9 · (-3)3
A) 912
129)
B) Yes, it is true.
130)
B) -3 12
Use a calculator to evaluate the expression. 131) 34 A) 34 B) 12
C) 927
D) 312
C) 3
D) 81
131)
Solve by the square-root property. 132) (r + 2)2 = 14
132)
A) -2 + 14, -2 - 14 C) 12
B) 14, 14 D) 2 + 14, 2 - 14
Determine whether the statement is true or false. 133) Some rational numbers are irrational. A) True
133) B) False
Factor completely. 134) 27a 3 - 125b3
134)
A) (3a + 5b2 )(9a2 - 15ab + 25b2 ) C) (27a - 5b)(a2 + 15ab + 25b2 )
B) (3a - 5b)(9a 2 + 25b2) D) (3a - 5b)(9a 2 + 15ab + 25b2)
16
135) 5x3 + 10x2 y - 40xy2 A) Prime B) (5x2 + 10xy)(x - 4y) C) 5x(x - 2y)(x + 4y) D) 5x(x + 2y)(x - 4y) E) (x - 2y)(5x2 + 20xy)
135)
Use a calculator to evaluate the expression. 136) (-8.4)4 A) 4,978.7 B) 33.6
136) C) -33.6
D) -4,978.7
Evaluate the expression. Write answer without exponents. 137) (7.16)-4
A) 28.64
137)
B) 2,628.16174
C) 0.00038
Express each of the following statements in symbols, using <, >, , or . 138) p is at most 77 A) p 77 B) p > 77 C) p 77 Solve the equation. 139) -5x + 9 - 4x = -4x + 49
A) 8
D) 1.63579
138) D) p < 77
139) B) - 1 8
C) - 8
Factor completely. 140) 343y3 - 512
D) - 13 40
140)
A) (7y - 8)(49y2 + 56y + 64) C) (7y + 8)(49y2 - 56y + 64)
B) (343y - 8)(y2 + 56y + 64) D) (7y - 8)(49y2 + 64)
Use inequality symbols to rewrite the statement. Let x represent the unknown. 141) The new software product will cost between $235 and $425 per unit. A) x 425 B) $235 < x < $425
C) x > $235, x < $425 Solve the equation. 142) -9.6 = z - 6.3 A) -3.3
143)
141)
D) $235 x $425
142) B) 15.9
C) -15.9
D) 3.3
x 2x - 3 -2x =0 2x + 2 4x + 4 x+1
A) 3
143) B) - 12
C) -3
5
17
D) 3 2
Solve the problem.
144) A manufacturer's cost is given by C = 200
3
n + 200, where C is the cost and n is the number of
parts produced. Find the cost when 343 parts are produced. A) $3,904 B) $900 C) $29
D) $1,600
Factor completely. 145) x2 - x - 45
A) (x + 5)(x - 9) Solve the equation. 146) -6.0y = 58.80 A) -52.80
145) B) (x - 45)(x + 1)
C) (x - 5)(x + 9)
D) Prime
146) B) 9.8
C) 64.80
D) -9.8
Simplify the expression. Write answer with positive exponents. 45
147)
147)
42
A) 1
43
C) 1
B) 43
D) 47
47
Find the product. 148) (0.011x + 0.36)(0.9x - 0.23) A) 0.0099x2 + 0.32147x - 0.0828
148) B) 0.911x2 + 0.32147x + 0.32147 D) 0.911x2 + 0.32147x - 0.0828
C) 0.0099x2 + 0.32147x + 0.32147 Evaluate the expression. Write answer without exponents. 149) (13.4)-2
A) 26.8 Evaluate the expression. 150) - 18 - -21 A) 3
149)
B) 179.56
C) 3.6606
D) 0.00557
150) B) 39
C) -39
D) -3
Perform the indicated operation. Give the answer in lowest terms. 2 2 151) k + 8k + 15 · k + 12k + 36 k2 + 11k + 30 k2 + 9k + 18
A) 1
B) k + 6
C)
k+ 6
151) 1 k+ 6
D) k + 3 k+ 6
Solve the formula for the specified variable. 152) I = nE for n nr + R
A) n = IR(Ir - E)
144)
152)
B) n = -IR
C) n = -R
Ir - E
Ir - E
18
D) n = IR
Ir + E
Name the property illustrated. 153) 2 · 1 = 2 A) Identity property
153) B) Distributive property D) Commutative property
C) Associative property Simplify the complex fraction. 3 9+ s
154)
154)
s 1 + 4 12
A) 1
C) 36
B) 36
D) s
s
36
Solve the problem. 155) The distance d in miles that can be seen on the surface of the ocean is given by d = 1.6 h, where h is the height in feet above the surface. How high (to the nearest foot) would a platform have to be to see a distance of 16.5 miles? A) 435 ft B) 106 ft C) 103 ft D) 272 ft Factor out the greatest common factor. 156) 5(x + 2)4 + 6(x + 2)6
156)
A) (x + 2)4 (6x2 + 24x + 29)
B) (x + 2)4 (6x2 + 29) D) 11(x + 2)4
C) 11(x + 2)
Use the quadratic formula to solve the equation. Give both exact and approximate answers. 157) 3m 2 + 9m + 3 = 0
A) -3 ± 13 ; 0.303, -3.303 2
B) -9 ± 5 ; -3.382, -5.618 2
C) -3 ± 5 ; -0.382, -2.618
D) -3 ± 5 ; -0.127, -0.873
2
157)
6
Simplify the complex fraction. 3 5 + x-3 x+5
158)
155)
158)
5 3 x+5 x-2
A)
8x2 - 16x 2x2 - 31x + 75
B) 8x + 46 + 60
2
C)
8x2 - 16x 8x2 - 23x + 75
D) -(x - 2)
8x2 + 49x + 75
x-3
19
Solve the problem. 159) 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 12 feet by 15 feet and the area of the rug is 108 square feet, how wide will the border be? A) 3.5 ft B) 1.5 ft C) 4 ft D) 2.5 ft Perform the indicated operations. Give the answer in lowest terms. 160) 2 + 3 r r+ 6
A) -12r - 5
r(-6 - r)
B) 5r + 12
160)
C) 5r + 12
r(-6 - r)
r(r + 6)
D) -12r - 5 r(r + 6)
Solve the problem. 161) The finance charge on a loan taken out by Jane is $749. If there were 36 equal monthly installments needed to repay the loan, and the loan is paid in full with 4 months remaining, find the amount of unearned interest. (Round answer to the nearest cent.) A) $7.13 B) $589.69 C) $11.25 D) $593.80 Perform the indicated operation. Give the answer in lowest terms. 2 162) 4x · 35 5 x3
A) x
28
Find the product. 163) (2x + 3)(2x - 3) A) 4x2 + 12x - 9
2
C) 140x
B) 2x2 - 12x - 9
C) 4x2 - 12x - 9
5x3
D) 28x
2
x3
163) D) 4x2 - 9
Solve the equation for the indicated variable. 164) x = ± r2 - y2 for r
A) r = x + y
164)
B) r = ± x2 - y2
C) r = ± x + y
Factor completely. 165) 729p3 - 1
D) r = ± x2 + y2
165)
A) (9p + 1)(81p2 - 9p + 1) C) (9p - 1)(81p2 + 1)
B) (729p - 1)(p2 + 9p + 1) D) (9p - 1)(81p2 + 9p + 1)
Perform the indicated operations. Give the answer in lowest terms. 166) 8x + 6x - 2 - 5x x+7 x+7 x+7
A) 9x - 2 x+7
161)
162)
B) 28 x
159)
B) 9x - 2
166)
C) 19x - 2
3x + 21
x+7
20
D) 19x + 2 x-7
Solve the equation. 167) 14b + 10 = 6b A) - 5 4
167) B) - 4
C) 1
5
D) 5
2
4
Express each of the following statements in symbols, using <, >, , or . 168) 4 is less than 7. A) 7 < 4 B) 4 < 7 C) 4 7
168) D) 4 > 7
Evaluate the expression. Write answer without exponents. 169) 161/4
A) 2
169)
B) 32
C) 8
D) 16
Perform the indicated operation. Give the answer in lowest terms. 2 2 170) z + 11z + 30 ÷ z + 5z z 2 + 15z + 54 z 2 + 6z - 27
A) z - 3
z 2 + 9z
B) z - 3
C)
170) z
z 2 + 15z + 54
D) z - 3 z
Solve the problem. 171) On Monday, an investor bought 100 shares of stock. On Tuesday, the value of the shares went up 9%. How much did the investor pay for the 100 shares if he sold them Wednesday morning for $ 1,526? A) $1,450 B) $1,400 C) $1,476 D) $1,663 Find approximate solutions of the equation. 172) 5.46x2 + 7.2x + 1.5 = 0
A) 1.06 or -1.06
172)
B) 1.06 or 0.26
C) -0.26 or -1.06
D) -0.26 or 0.26
Solve the equation for the indicated variable. 173) S = 1 gt2 for t 2
A) t = ±
g 2S
Simplify the expression. 3 3 174) 8 · 216 A) -12
173)
B) t = ±2 gs
C) t = 2gS
D) t = ±
2S g
174) B) 8
C) -4
D) 12
Use a calculator to evaluate the expression. 175) 23
A) 8
171)
175)
B) 5
C) 6
21
D) 4
Perform the indicated operation. Give the answer in lowest terms. 176) 3p - 3 ÷ 10p - 10 p 9p2 3
A) 27p - 27p
2
176)
B) 10
27p
10p2 - 10p 2
C) 30p + 60p + 30
D) 27p 10
9p3
Factor completely. 177) x2 + 53x + 54
A) (x + 54)(x - 1) Use factoring to solve the equation. 178) (x + 8)(x - 15) = 0 A) -8, 15
177) B) (x + 9)(x - 6)
C) Prime
D) (x - 9)(x + 6)
B) -15, 8
C) 8, -15
D) 15, 8
178)
Use the discriminant to determine the number of real solutions of the equation. 179) w2 + 3w + 6 = 0
A) 2
B) No real solutions
179) C) 1
Factor completely. 180) 8x2 - 28x - 16
180)
A) 4(2x + 1)(x - 4) C) 4(2x - 1)(x + 4)
B) (8x - 4)(x + 4) D) (2x - 1)(4x + 16)
Simplify the expression. Write answer with positive exponents. Variables are positive real numbers. 181) -6k1/7(-9k4/7 + 8k5/7)
181)
Add or subtract as indicated. 182) (5x9 + 8x6 - 2x2 + 10) - (10x9 - 9x5 + 4x2 - 9)
182)
A) 54k5/7 + 48k6/7 C) -15k5/7 - 14k6/7
B) 54k5/7 - 48k6/7 D) 54k-3/7 + 48k-4/7
A) -5x9 + 8x6 - 9x5 - 6x2 + 19
B) 5x9 + 8x6 + 9x5 - 6x2 + 19
C) -5x9 + 8x6 + 9x5 - 6x2 + 19
D) 5x9 + 8x6 - 9x5 - 6x2 + 19
Factor completely. 183) 9x2 - 3xt - 2t2
A) Prime
183) B) (9x + t)(x - 2t)
C) (3x + t)(3x - 2t)
22
D) (3x - t)(3x + 2t)
Factor out the greatest common factor. 184) 80x7y9 - 64x4 y7 - 112x2 y3
184) B) 16(5x7 y9 - 4x4 y7 - 7x2 y3 )
A) No common factor C) 16x2(5x5 y9 - 4x2 y7 - 7y3 )
D) 16x2y3 (5x5 y6 - 4x2 y4 - 7)
Perform the indicated operations. Give the answer in lowest terms. 185) b + 5 - 6 b2 - 25 b + 5 b 2
185)
A) 6b - 25b + 150
B)
-25(b - 6) b(b + 5)(b - 5)
25(b + 6) b(b + 5)(b - 5)
D)
25(b - 6) (b + 5)(b - 5)
b(b + 5)(b - 5)
C)
Evaluate the expression using order of operations. 186) (8 + 3)[8 + (7 + 3)] A) 25 B) 98
C) 29
D) 198
Evaluate the expression, given x = -2, y = 3, and a = -4. 187) (7x + 5y)(-4a) A) -644 B) -16
C) 176
D) 16
Solve the equation. 188) 12x - 4 = 10 A) - 7 6
B) 7 6
C) 1 2
D) 13 12
B) (x - 10)(x + 5)
C) (x - 10)(x + 1)
D) (x + 10)(x - 5)
186)
187)
188)
Factor completely. 189) x2 + 5x - 50
A) Prime
189)
Rationalize the denominator. Assume all variables represent positive real numbers. 190) 10 - 3 10 + 3
A) 1 Use factoring to solve the equation. 191) 12y2 + 25y + 12 = 0
A) 4 , - 3 3 4
190)
B) 103 + 20 3
C) 97 - 20 3
D) 103 - 20 3
B) - 4 , - 3 3 4
C) 4 , 3 3 4
D) - 1 , - 1 3 4
97
103
97
191)
23
Find expressions for the Revenue, Cost, and Profit from selling x thousand items. 192) Item Price Fixed Cost Variable Cost $7.00 $41,723 4,236x A) R = 7,000x; C = 41,723 + 4,236x; P = 2,864x - 41,723
192)
B) R = 7,000x; C = 41,723 + 4,236x; P = 2,764x - 41,723 C) R = 7,000x; C = 83,446 + 4,236x; P = 2,764x - 41,723 D) R = 14,000x; C = 41,723 + 4,236x; P = 2,764x - 41,723 Use factoring to solve the equation. 193) 30n 2 + 8n = 0
A) - 4 15
193) B) 0
C) - 4 , 8 15
D) - 4 , 0 15
B) - 6
C) - 6, - 2 3
D) 6, 2 3
Solve the equation. 194) 2s + 4 = s - 2
A) No solution
194)
Write the expression in lowest terms. 4x + 8 195) 2 3x + 10x + 8
A)
4x + 8 2 3x + 10x + 8
195) B)
4x 3x + 4
C)
4 3x + 4
D) 4x + 3
3x + 10
Identify the degree of the polynomial and list its coefficients. 196) 4x2 - 3x + 7
A) degree: 2
196) B) degree: 4
coefficients: 4, 3, 7 C) degree: 2 coefficients: 4, -3, 7
coefficients: -3, 7
D) degree: 4
coefficients: 4, -3, 7
Solve the equation for the indicated variable. 197) c = ± E for E m
A) E = ±c m
197)
B) E = mc2
C) E = ±
c m
D) E = mc
Evaluate the expression using order of operations. 198) 7(8 + 10) - 5 2
A) 71 2
198)
B) 121
C) 61
2
2
24
D) 2
61
Simplify the expression. 199) 81 - 4 A) 11
199) B) 77
C) 7
D) 79
Solve the problem. 200) If Gloria received a 12 percent raise and is now making $22,400 a year, what was her salary before the raise? A) $21,000 B) $20,000 C) $21,400 D) $20,400 Perform the indicated operation. Give the answer in lowest terms. 2 2 201) k + 7k + 10 · k + 8k k2 + 10k + 16 k2 + 9k + 20 2
A) k + 8k k+ 4
B)
k 2 k + 10k + 16
C)
201) k k+ 4
Determine whether the statement is true or false. 202) Every irrational number is an integer. A) True
B) False
Evaluate the expression, given x = -2, y = 3, and a = -4. 203) (-8a)(8x + 4y) A) 896 B) -128
C) 128
D)
1 k+ 4
202)
203) D) 512
Factor completely. 204) x2 + 6xy - 160y2
204)
A) (x + 16y)(x - 10y) C) (x - 16y)(x + y)
B) Prime D) (x - 16y)(x + 10y)
Express each of the following statements in symbols, using <, >, , or . 205) s is negative. A) s 0 B) s < 0 C) s 0
205) D) s > 0
Identify the degree of the polynomial and list its coefficients. 206) -2x3 - 6x2 + 8x + 5
A) degree: 2
206) B) degree: -2
coefficients: 2, -6, 8, 5 C) degree: 3 coefficients: 2, 6, 8, 5
coefficients: 3, 2, 1, 0 D) degree: 3 coefficients: -2, -6, 8, 5
Write the rational exponent expression as an equivalent radical expression. 207) 7x-1/7
A)
1
7
7x
200)
C) 7 7
B) -7 7 x
25
207) D)
x
1 7
-7x
Simplify the expression. Write answer with positive exponents. Variables are positive real numbers. -2/5 4 -2 208) n (n -1/8 r-1/6 ) -5/4 r
A) n
27/20
r16/3
14/3
16/3
B) r
C) r
n 37/20
D) n
n 27/20
37/20
r14/3
Find the product. 209) (x + 9y)(-5x + 10y) A) x2 - 35xy + 90y2
B) -5x2 - 35xy - 35y2
C) x2 - 35xy - 35y2
D) -5x2 - 35xy + 90y2
209)
Solve the problem. 210) Kafka Inc. imports hard drives and sells them on the internet. The profit is given by the equation P = 143n - 8,250, where n is the number of hard drives sold. Estimate the profit, to the nearest ten dollars, corresponding to the sale of 900 hard drives. A) $120,470 B) $120,440 C) $120,460 D) $120,450 Solve the equation for the indicated variable. 211) r = ± A for A 2
A) A = ± 2 r
B) A = 2 r
C) A = ±2
r
D) A = 2 r2
212) B) -4x2 + 32x - 60 D) -4x2 + 30x - 60
C) -4x2 - 60x + 32
Use the quadratic formula to solve the equation. Give both exact and approximate answers. 213) 6n2 = -8n - 1
A) -4 ± 10 ; -0.14, -1.194
B) -8 ± 10 ; -0.806, -1.86
C) -4 ± 10 ; -0.07, -0.597
D) -4 ± 22 ; 0.115, -1.448
6
213)
6
12
6
Factor completely. 214) x2 - x - 72
214) B) (x + 8)(x - 9)
C) (x + 1)(x - 72)
D) Prime
Solve the equation. 215) 5 - a + 3 = 7 a 4 a
A) 8
210)
211)
Find the product. 212) (x - 5)(-4x + 12) A) -4x2 + 32x + 32
A) (x + 9)(x - 8)
208)
215) B) -4
C)
26
29 20
D) -8
Factor completely. 216) 8x2 + 18x + 9
A) (4x + 3)(2x + 3)
216) B) Prime
C) (4x - 3)(2x - 3)
D) (8x + 3)(x + 3)
Solve the problem. 217) The speed of a stream is 4 mph. If a boat travels 94 miles downstream in the same time that it takes to travel 47 miles upstream, what is the speed of the boat in still water? A) 8 mph B) 14 mph C) 15 mph D) 12 mph Perform the indicated operations. Give the answer in lowest terms. m+8 2m - 3 218) + 2 2 m - 9m + 20 m - 3m - 4
A)
3m 2 - 4m + 23 (m - 4)(m - 5)(m + 1)
C) 3m + 5
218)
B)
3m + 5 2 2m - 12m + 16
D)
3m 2 - 4m + 23 (m + 4)(m + 5)(m - 1)
Use the quadratic formula to solve the equation. Give both exact and approximate answers. 219) 6m 2 + 10m + 1 = 0
A) -5 ± 19 ; -0.107, -1.56
B) -5 ± 31 ; 0.095, -1.761
C) -10 ± 19 ; -0.94, -2.393
D) -5 ± 19 ; -0.053, -0.78
6
219)
6
6
12
Use a calculator to evaluate the expression. 220) -6.14
A) 1,384.58
217)
220)
B) -24.40
C) -1,384.58
D) 24.40
Solve the problem. 221) The length of a rectangle is 4 inches more than the width. The perimeter of the rectangle is 64 inches. Find the width of the rectangle. A) 18 in. B) 14 in. C) 15 in. D) 16 in.
222) The polynomial -0.015x3 + 1.05x gives the alcohol level in an average person's bloodstream x
221)
222)
hours after drinking 8 oz of 100-proof whiskey. If the level exceeds 1.5 units, a person is legally drunk. Would a person be drunk after 7 hours? A) No B) Yes
Factor completely. 223) x2 + 7x + 12
A) Prime
223) B) (x - 4)(x + 3)
C) (x - 4)(x + 1)
27
D) (x + 4)(x + 3)
Provide an appropriate response.
224) Which statement tells how to evaluate 9 3 ? A) Divide 9 by 3. C) Multiply 9 times itself 3 times.
Solve the equation for x. 225) 7x - (6a + 6) = a(x + 1) A) x = 5a - 6 7-a
224) B) Multiply 9 times 3. D) Multiply 3 times itself 9 times.
225) B) x = 7a - 6
C) x = 5a + 6
7-a
7-a
D) x = 7a + 6 7-a
Use factoring to solve the equation. 226) r2 + 8r + 16 = 17
226)
A) 4 + 17, 4 - 17 C) 17, 17
B) 13 D) -4 + 17, -4 - 17
Perform the indicated operation. Give the answer in lowest terms. 2 2 227) k + 10k + 24 · k + 7k k2 + 13k + 42 k2 + 2k - 8
A)
k
k2 + 13k + 42
2
B) k + 7k
C)
k- 2
Add or subtract as indicated. 228) (-3 + 2x7 + 4x9 + 4x8 ) + (5x8 + 7x7 + 7 + 7x9 )
k k- 2
D)
1 k- 2
228)
A) 11x18 + 9x16 + 9x14 + 4 C) 11x9 + 9x8 + 9x7 + 4
B) 2x9 + 2x8 + 11x7 + 11 D) 29x48 + 4
Evaluate the expression using order of operations. 229) 2[-4 + 8(-6 + (-5))] A) -184 B) -92
229) C) -88
Factor out the greatest common factor. 230) 6(2y - 1)4 + 8(2y - 1)5
D) -96
230)
A) 2(2y + 1)4 (8y + 1) C) (2y - 1)(8y - 1)
B) 2(2y - 1)4 (8y - 1) D) (2y + 1)(8y + 1)
Solve the formula for the specified variable. 231) a + b = s + r for r
A) r = s(a + b)
227)
231) C) r = a + b s
B) r = a + b - s
28
D) r = a + b s
Solve the problem. 232) An open box is to be made from a rectangular piece of tin by cutting two inch squares out of the corners and folding up the sides. The volume of the box will be 100 cubic inches. Find the dimensions of the rectangular piece of tin. A) Not enough information B) 5 in. by 9 in.
C) 5 in. by 10 in.
D) 4 in. by 9 in.
Provide an appropriate response. 233) Which of the following is the correct way to evaluate the expression 4 + 6 · 4? A) 4 + 6 · 4 = 4 + 24 = 28 B) 4 + 6 · 4 = 24 + 6 = 22
C) 4 + 6 · 4 = 10 · 4 = 40
233)
D) 4 + 6 · 4 = 16 + 24 = 40
Factor completely. 234) 2x2 - 20x + 50
A) 2(x - 5)(x - 5)
234) B) (x - 5)(2x - 10)
C) 2(x - 25)(x + 1)
D) (2x - 10)(x - 5)
Evaluate the expression using order of operations. 235) (-5) · (2 + 5) + (-5) · 7 (-5) · (7 - 1)
A) 3 7
235)
B) 14
C) 7
3
D) 71
3
30
Graph the inequality on a number line. 236) (-5, -2]
236)
A)
B)
C)
D)
Simplify the complex fraction. 2 4+ x
237)
237)
x 1 + 4 8
A) 16 x
B) 16
C) x
D) 1
C) h = S - 1
2 D) h = S - 2 r 2 r
16
Solve the formula for the specified variable. 238) S = 2 rh + 2 r2 for h
A) h = 2 (S - r)
232)
238)
B) h = S - r
2 r
29
Evaluate the expression. Write answer without exponents. 27 -2/3
239)
239)
8
A) 4
B) 4
9
C) - 4
13
D) 3
9
4
Write the expression in lowest terms. y2 - 2y - 15
240)
240)
y2 + 3y - 40
A) -2y - 15 3y - 40
Solve the equation for x. 241) 8x + 1 = (2x - 1)(m + 4) A) x = m + 5 2m
2
B) -2y - 3
C) - y - 2y - 15
D) y + 3
B) x = m + 5 16 + 2m
C) x = m + 3 2m
D) x = 5 - m 2m
3y - 8
y2 + 3y - 40
y+ 8
241)
Rationalize the denominator. Assume all variables represent positive real numbers. 242) 3 7- 6
A) 3 - 3 7
6
B) 21 - 3 6
C) 21 + 3 6
43
43
242) D) 21 + 3 6 -1
Use the quadratic formula to solve the equation. Give both exact and approximate answers. 243) 4n2 = -12n - 4
A) -3 ± 5 ; -0.095, -0.655 8
B) -3 ± 13 ; 0.303, -3.303 2
C) -3 ± 5 ; -0.382, -2.618
D) -12 ± 5 ; -4.882, -7.118
2
2
Simplify. Leave answer with exponent. 244) 43 · 4 6
A) 49
243)
244)
B) 1618
C) 169
D) 418
Simplify the complex fraction. x x+9
245)
245)
6
x2 - 81
A) x(x + 9) 6
B) x(x - 9)
C) 6(x - 9)
6
x
30
D) 6(x + 9) x
Solve the problem. 246) The length a spring is stretched from its natural length with work, W foot-pounds, is given by 2W L= k
246)
where k is a constant for the given spring. If a certain spring has a constant of 38.0, and the spring is to be stretched 3.5 feet from its natural length, how much work will be necessary? A) 465.5 foot-pounds B) 66.5 foot-pounds
C) 232.8 foot-pounds
D) 35.5 foot-pounds
247) A rectangular garden has dimensions of 22 feet by 10 feet. A gravel path of equal width is to be
247)
built around the garden. How wide can the path be if there is enough gravel for 228 square feet? A) 3 ft B) 5.5 ft C) 4 ft D) 5 ft
Use a calculator to evaluate the expression. 248) -8 3
A) 24
248)
B) 512
C) -24
Express each of the following statements in symbols, using <, >, , or . 249) x is less than or equal to 1. A) 1 x B) x 1 C) x 1
D) -512
249) D) x < 1
Evaluate the expression. Write answer without exponents. 250) 2434/5
A) 2,187
250)
B) 19,683
C) 6,561
Name the property illustrated. 251) 1 + 0 = 1 A) Commutative property
251) B) Associative property D) Identity property
C) Distributive property Solve the equation. 252) 2s - 8 = s + 4
A) - 12, - 4
D) 81
252) B) No solution
C) 12, - 20
D) 12, 4 3
Simplify the expression. Write answer with positive exponents. 2435 · 3 -3
253)
253)
275
A) 1
B) 97
C) 35
Add or subtract as indicated. 254) (9x5 + 5x7 + 6 - 8x6 ) - (5 - 2x6 + 7x7 - 6x5 )
D) 37
254)
A) 12x7 - 10x6 + 3x5 + 11
B) -2x7 - 10x6 + 3x5 + 11
C) 12x7 - 10x6 + 3x5 + 1
D) -2x7 - 6x6 + 15x5 + 1 31
Factor completely. 255) u2 - 3uv - 18v2
255)
A) (u + 3v)(u - 6v) C) (u - 3v)(u + 6v)
B) (u - 3v)(u + v) D) Prime
Perform the indicated operation. Give the answer in lowest terms. 2 256) 3p - 3 · 5p p 8p - 8 3
A) 15p - 15p
2
256)
B) 8
15p
8p2 - 8p
2
D) 24p + 48p + 24
C) 15p 8
5p3
Solve the problem. 257) Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 6 mi, the distance between the cars was 2 mi more than the distance traveled by the car heading east. How far had the eastbound car traveled? A) 10 mi B) 6 mi C) 8 mi D) 12 mi Solve the equation. 258) y + 8 = 10 6
A) 12
258) B) -12
C) -14
Use a calculator to solve the equation. Round to the nearest hundredth. 259) -4.99a + 3.23 + 5.99a = 5.56 - 28.01 A) -25.68 B) -36.80 C) 25.68
D) 14
259) D) 36.80
Find approximate solutions of the equation. 260) (m + 3.20)2 = 23.04
A) 1.60
260)
B) 4.45 or -4.45
C) 1.60 or -8.00
D) 3.01 or -6.59
Solve the equation. 261) 1 - 3 = 7 2x 4
A) 1 2
Factor completely. 262) 9x2 - 25
A) (3x - 5)2
257)
261) B) 2
C) -2
D) - 1 2
262) B) (3x + 5)2
C) Prime
32
D) (3x + 5)(3x - 5)
Solve the equation for the indicated variable. 263) A = 6s2 for s
A) s = A 6
263)
B) s = ± 6A
C) s = ±
Factor completely. 264) 64c3 + 729
A 6
D) s = 36A2
264)
A) (4c + 9)(16c2 + 81)
B) (64c + 9)(c2 - 36c + 81)
C) (4c - 9)(16c2 + 36c + 81)
D) (4c + 9)(16c2 - 36c + 81)
Evaluate the expression. Write answer without exponents. 265) 2-4
A) 1 -16
265) C) 1 16
B) 16
D) -16
Fill in the blank with either =, <, or > to make the statement true. 266) 4 - 2 2-4 A) < B) >
266) C) =
Determine whether the statement is true or false. 267) The absolute value of any nonzero number is an irrational number. A) True B) False
267)
Fill in the blank with either =, <, or > to make the statement true. 268) 19 -19 A) < B) >
268) C) =
Perform the indicated operations. Give the answer in lowest terms. 269) 2 - 6 + 1 3x - 6 5x + 5 2x + 4 2
2
A) -1x + 45x + 13
B) 71x + 45x + 154
10x + 15
C)
269) 10x + 15
-1x2 + 45x + 154 30(x - 2)(x + 1)(x + 2)
D)
71x2 + 45x + 154 30(x - 2)(x + 1)(x + 2)
Insert <, =, or > to write a true statement. 270) 29 ___ 2,456 401
A) >
270) B) =
C) <
33
Solve the problem.
271) The position of an object moving in a straight line is given by s = 2t2 - 3t, where s is in meters and
271)
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 20 meters? A) 3.8 sec B) 21.0 sec C) 74.0 sec D) 4.0 sec
Solve the equation. 272) 28 = 1 + 30 x-2 x+2
A) -30, 12
272) C) 10, -12
B)
D) -10, 12
Solve the problem. 273) Jill is 9 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at 2 kilometers per hour. They meet in 2 hours. How fast is Joe walking? A) 2.5 kilometers per hour B) 3.5 kilometers per hour
C) 4.5 kilometers per hour
273)
D) 2 kilometers per hour
Use the quadratic formula to solve the equation. Give both exact and approximate answers. 274) 2x2 + 10x = -6
A) -5 ± 37 ; 0.541, -5.541
B) -10 ± 13 ; -3.197, -6.803
C) -5 ± 13 ; -0.349, -2.151
D) -5 ± 13 ; -0.697, -4.303
2
274)
2
4
2
Simplify the expression. Write answer with positive exponents. Variables are positive real numbers. 275) (16k4m -8 )1/4 A) 4km 2 B) 4k C) 2km 2 D) 2k 2 m m2 Solve the problem. 276) The radius of a sphere depends on its surface area, S, and is given by the formula S r= . 4
275)
276)
What is the surface area of a sphere with radius of 9 inches? Use 3.14 for . A) 1,017.4 square inches B) 113 square inches
C) 254.3 square inches
D) 28.3 square inches
Factor out the greatest common factor. 277) 17m 2 - 10r3
277)
A) m 2(17 - 10m)
B) 3(5m 2 - 3r3 )
C) No common factor
D) 2(8m 2 + 5r3 )
34
Solve the problem. 278) Mardi received an inheritance of $70,000. She invested part at 11% and deposited the remainder in tax-free bonds at 9%. Her total annual income from the investments was $7,500. Find the amount invested at 11%. A) $62,500 B) $30,000 C) $60,000 D) $59,000 Factor out the greatest common factor. 279) 60x9y9 - 36x2 y6 - 96x7y2
279) B) 12(5x9 y9 - 3x2 y6 - 8x7 y2 )
A) No common factor C) 12x2y2 (5x7 y7 - 3y4 - 8x5 )
D) 12x2(5x7 y9 - 3y6 - 8x5 y2 )
Evaluate the expression using order of operations. 280) -13 + (5 · 4 + 40) ÷ 5 A) 15 B) -1
C) -3
D) 1
Solve the equation. 281) 3(4r - 1) = 6 A) 5 4
C) 3 4
D) 9 4
280)
281) B) 1 4
Perform the indicated operation. Give the answer in lowest terms. 2 3 282) 2x ÷ x 3 9
A) 18x
2
3x3
282)
C) 6x
B) x 6
2
D) 6
x
x3
Insert <, =, or > to write a true statement. 283) 3 ___ 0.27 11
A) >
278)
283) B) =
C) <
Simplify the expression. 284) ( 7 + 3)( 2 + 3) A) 14 + 9
284) B) 7 14 + 9 D) 14 + 3 7 + 3 2 + 9
C) 14 + 6 2 + 9
Perform the indicated operations. Give the answer in lowest terms. 1 14 285) 81x + 2(9x + 1) 2x(9x + 1) x 2
285) 2
A) 81x + 252x + 27
B) 81x + 252x + 27
C) 9(x + 3)
D) 9(x + 3)
18x2 + 2x
2x
18x2 + 2x
2x
35
Solve the formula for the specified variable. 286) F = 9 C + 32 for C 5
A) C = F - 32 9
286)
B) C = 9 (F - 32)
C) C = 5 (F - 32)
5
9
D) C =
5 F - 32
Use a calculator to solve the equation. Round to the nearest hundredth. 287) 3.63x - 4.07 - 2.87x - 3.15 = x 3.12 1.21
A) -0.20
B) 0.31
C) 0.09
287) D) 0.59
Evaluate the expression. Write answer without exponents. 288) -8 0
A) -8
288) C) 0
B) -1
D) 1
Graph the inequality on a number line. 289) [-6, -3]
289)
A)
B)
C)
D)
Solve the problem. 290) Tony bought some stock for $450. If each share had cost $7 less he could have bought 7 more shares for the same $450. How many shares of stock did he buy? A) 15 shares B) 20 shares C) 13 shares D) 18 shares Simplify the expression. 291) ( 6 + 1)( 6 - 1) A) 5 - 2 6
291) C) 5 + 2 6
B) 7
D) 5
Simplify the complex fraction. 4 -3 y- 2
292)
292)
1 +3 y- 2
A) 3y - 2 3y - 5
Solve the equation. 293) -4.5q = -7 - 1.0q A) 1.6
290)
B) -3y + 10
C) -3y - 2
3y - 5
3y - 5
D) 3y - 10 3y - 5
293) C) 2
B) -10 36
D) 1.8
Simplify the expression. Write answer with positive exponents. Variables are positive real numbers. 4 1/4 294) x y-8
B) xy1/2
A) xy
C) xy2
D) x
y2
Write the rational exponent expression as an equivalent radical expression. 295) -5x1/5
A) 5 5
B)
5
5x
C)
5
-5x
295) D) -5
5
x
x
Evaluate the expression using order of operations. 296) (8 + (-3))[4 + ( 36 + 32 )]
A) 17
296)
B) 29
C) 95
D) 21
Find approximate solutions of the equation. 297) x2 - 1.5x - 6.9 = 0
A) 1.98 or -3.48
297)
B) 1.98 or -1.98
C) 3.48 or -3.48
Name the property illustrated. 298) (7 · 8) · 8 = 7 · (8 · 8) A) Associative property
D) 3.48 or -1.98
298) B) Commutative property D) Distributive property
C) Identity property
Write the rational exponent expression as an equivalent radical expression. 299) (-7x)1/7
A)
7
294)
-7x
B)
7
C) 7 7
7x
299) D) -7
7
x
x
Solve the problem. 300) Walt made an extra $9,000 last year from a part-time job. He invested part of the money at 8% and the rest at 7%. He made a total of $690 in interest. How much was invested at 7%? A) $6,000 B) $3,000 C) $4,500 D) $7,000 Solve the equation. 301) 18t + 5 = 6t + 14 A) 24 19
300)
301) B) - 3 4
C) 3 4
37
D) 8 3
Solve the formula for the specified variable. 302) A = 1 h(b1 + b2 ) for b1 2
302)
A) b1 =
(b2 )2A - h h
B) b1 =
C) b1 =
h(b2 ) - 2A h
D) b1 =
A - h(b2 ) 2h 2A - (h)(b2 ) h
Use inequality symbols to rewrite the statement. Let x represent the unknown. 303) When a baseball player is in a slump, he may get fewer than 5 hits in 18 times at bat. Let x represent the number of hits. A) 5 < x < 18 B) x < 18 C) x < 5 D) x > 5 18 Evaluate the expression using order of operations. 304) 8[2 + 5(6 - 4)] A) 26 B) 96
304) C) 108
Factor out the greatest common factor. 305) 8m 8 - 40m 6 + 36m 3
D) 112
305) B) 4m 3 (2m 5 - 10m 3 + 9)
A) No common factor C) m 3(8m 5 - 40m 3 + 36)
D) 4(2m 8 - 10m 6 + 9m 3 )
Solve the problem. 306) Janet drove 292 kilometers and the trip took 4 hours. How fast was Janet traveling? A) 73 kilometers per hour B) 63 kilometers per hour
C) 93 kilometers per hour
306)
D) 83 kilometers per hour
Use factoring to solve the equation. 307) 5x2 - 40x + 75 = 0
A) 5, 3, 5
307) B) 3, 5
C) 0, 3, 5
D) -3, -5
Write the rational exponent expression as an equivalent radical expression. 308) (-3x)-1/3
A)
1 3
-3x
B)
1 3
C) 3
3
3x
x
308) D) -3 3
Perform the indicated operation. Give the answer in lowest terms. 3 309) 2z · 9 3 z2
A) 6z
2
z3
303)
B) 6
C) 6z
z
38
x
309) D) z 6
Solve the equation. 310) r + 6 = r + 8 3 6
A) -4 Simplify the expression. 3 311) 3 6 3 A) 3 6
312) 13 · 12 A) 4 39
310) B) 3
C) -12
D) 4
311) B) 27
C) 3
D) 9 312)
B) 2 39
C) 25
D) 25
Write the rational exponent expression as an equivalent radical expression. 313) 7x-1/7
A)
7
-7x
B) 7 7
C)
7
7x
313) D) -7
7
x
x
Factor completely. 314) 4x2 - 12xy - 16y2
314)
A) (4x - 4y)(x + 4y) C) 4(x + y)(x - 4y)
B) Prime D) 4(x - y)(x + 4y)
Perform the indicated operations. Give the answer in lowest terms. 315) 6x + 9 - 5x + 3 - 9x x+2 x+2 x+2
A) -8x + 6 x+2
B) -20x + 12
315)
C) -8x + 6
x+2
3x + 6
Name the property illustrated. 316) 8(x + 2) = 8x + 8 · 2 A) Commutative property
D) x + 6 x+6
316) B) Identity property D) Distributive property
C) Associative property Solve the equation. 317) 4 = 3 y-6
A) - 7 , 7 2 2
317) B) 22, 14
C) 9, 3
39
D) 22 , 14 3
3
Factor completely. 318) t3 + 27
318)
A) (t - 27)(t2 - 1) C) (t - 3)(t2 + 3t + 9)
Solve the equation. 319) 6x + 3 = 5
A) 8, -2
B) (t + 3)(t2 + 9) D) (t + 3)(t2 - 3t + 9)
319) B) 1 , - 4 3 3
C) 2, -8
D) 4 , - 1 3 3
Simplify the expression. Write answer with positive exponents. Variables are positive real numbers. -5/7 4 -2 320) t (t-1/8 r1/6 ) -4/5 r 43/15
A) r
t73/28
73/28
87/28
B) t
C) t
r43/15
r53/15
Factor out the greatest common factor. 321) 12m 9 - 32m 4 - 24m 2
320)
53/15
D) r
t87/28
321) B) 4(3m 9 - 8m 4 - 6m 2)
A) No common factor C) m 2(12m 7 - 32m 2 - 24)
D) 4m 2 (3m 7 - 8m 2 - 6)
Graph the inequality on a number line. 322) (6, )
322)
A)
B)
C)
D)
Use inequality symbols to rewrite the statement. Let x represent the unknown. 323) A detective makes more money than 70% of the population and is better educated than 65%. Find the average status and status incongruity for this person. A) 2.5 and 67.5 B) 2.5 and 32.5 C) 67.5 and 2.5 D) 32.5 and 2.5
40
323)
Solve the problem. 324) The two charts show the weight gain of some people and the weight loss of other people. Use the information given to answer the questions below.
324)
What is the difference between the weight gain of Abe and the weight loss of Don? A) 93 grams B) -6,009 grams C) 6,009 grams D) -93 grams
Use factoring to solve the equation. 325) 14m 2 - 12m = 0
A) 6 , - 6 7
7
325) B) - 6 , 0
C) 0
7
D) 6 , 0 7
Solve the problem. 326) Bert is 26 kilometers away from Brenda. Both begin to walk toward each other at the same time. Bert walks at 4.5 kilometers per hour. They meet in 4 hours. How fast is Brenda walking? A) 4 kilometers per hour B) 4.5 kilometers per hour
C) 3 kilometers per hour
D) 2 kilometers per hour
Perform the indicated operations. Give the answer in lowest terms. 327) 4a + 6b - 4a - 6b 2 2
A) 36b
326)
B) 4a
327)
C) 6b
D) 0
Solve the problem.
328) If an object is dropped, the distance it falls is given by d = 1 gt2 , where g is about 32 ft/sec2 . Find 2
the distance an object would fall in 10 seconds. A) 1,600 ft B) 160 ft
C) 800 ft
D) 3,200 ft
Perform the indicated operations. Give the answer in lowest terms. 329) 2 + 4 r r- 9
A) 18r - 6
r(r - 9)
329)
B) 6r - 18
C) 18r - 6
D) 6r - 18
B) (x - 7y)(x + y)
C) Prime
D) (x + 7y)(x + 8y)
r(r - 9)
r(9 - r)
r(9 - r)
Factor completely. 330) x2 + 15xy + 56y2
A) (x - 7y)(x + 8y)
328)
330)
41
Solve the problem.
331) The position of an object moving in a straight line is given by s = t2 - 8t, where s is in feet and t is
331)
the time in seconds the object has been in motion. How long (to the nearest tenth) will it take the object to move 17 feet? A) 15.3 sec B) 9.6 sec C) 9.8 sec D) 18.0 sec
Simplify the expression. Write answer with positive exponents. Variables are positive real numbers. y9/8
332)
y5/8
A) y1/2
B) y9/8
C) y
332)
D) 1
y
Find the product.
333) (3y - 4)(9y2 + 12y + 16)
333)
A) 27y3 + 64
B) 27y3 - 64
C) 27y3 + 48y2 - 64
D) 9y3 + 64
Simplify the complex fraction. 1 +1 a
334)
334)
1 -1 a
A)
a
1 - a2
B) 1 + a
C) 1 - a2
1-a
D) 1
Solve the problem.
335) If the average cost per unit C to produce x units of plywood is given by C = 1,200 , what is the x + 40
unit cost for 50 units? A) -$16.00
B) $0.60
C) $13.33
335)
D) $24.00
Simplify the expression. Write answer with positive exponents. Variables are positive real numbers. 336) y2/9 (y5/9 - 4y4/9)
336)
Provide an appropriate response. 337) 244 means?
337)
A) y10/81 - 4y8/81 C) y2/5 - 4y1/2
B) y7/9 - 4y2/3 D) y-1/3 - 4y-2/9
A) 24 · 24 · 24 · 24 C) 24 · 24 · 24 · 24 · 24
B) 24 · 4 D) 24 ÷ 4
42
Fill in the blank with either =, <, or > to make the statement true. 338) 5 - 1 5 - 1 A) < B) = Provide an appropriate response. 339) A trinomial is a polynomial. A) Never
338) C) >
339) B) Always
C) Sometimes
Solve the formula for the specified variable. 340) A = 1 bh for b 2
A) b = 2A h
340)
B) b = h
C) b = A
2A
D) b = Ah
2h
2
Perform the indicated operations. Give the answer in lowest terms. 341) - 1 - 9 14 6x
A) 3x - 63 42x
B)
-12 42 - 6x
341)
C) -3x - 63
D) -3x + 63
C) (3z - 2)(2z + 3)
D) (3z + 2)(2z - 3)
42x
42x
Factor completely. 342) 6z 2 + 5z - 6
A) Prime
342) B) (6z - 2)(z + 3)
Simplify the expression. 3 343) -343
A) 49
343) B) -49
D) 7
C) -7
Solve the problem. 344) Kafka Inc. imports hard drives and sells them on the internet. The profit is given by the equation P = 124n - 7,000, where n is the number of hard drives sold. How many hard drives must be sold for the company to break even? Round your answer to the units place, in other words, to the nearest number of hard drives. A) 76 hard drives B) 54 hard drives C) 60 hard drives D) 56 hard drives Simplify the expression. 345) 6( 150 - 96) A) 6 5 - 24
345) C) 36 - 6 3
B) 6
D) 54
Use the discriminant to determine the number of real solutions of the equation. 346) t2 + 10t + 25 = 0
A) 2
344)
B) No real solutions
43
346) C) 1
Write the rational exponent expression as an equivalent radical expression. 347) (3x)1/3
A)
3
3x
B) -3
3
C) 3 3
x
347) D)
3
-3x
x
Express each of the following statements in symbols, using <, >, , or . 348) -6 is greater than -9. A) -6 < -9 B) -9 > -6 C) -6 -9
D) -6 > -9
Solve the equation. 349) 56s + 35 = 11s A) 7 9
D) 35 67
348)
349) B) - 7 9
C) 9 7
Determine whether the statement is true or false. 350) Every whole number is a real number. A) True
350) B) False
Add or subtract as indicated. 351) (4n 6 + 11n3 + 11) - (-17n 3 + 2n6 - 16)
351)
A) 2n6 + 28n 3 - 5
B) 57n 9
C) 2n6 + 28n 3 + 27
D) 2n6 + 13n 3 - 5
Solve the formula for the specified variable. 352) P = s1 + s2 + s3 for s1
352)
A) s1 = s2 + s3 - P C) s1 = s2 + P - s3
B) s1 = P + s2 + s3 D) s1 = P - s2 - s3
Find the product. 353) (3x + 6)(-5x - 1) A) -15x2 - 33x - 6
B) -2x2 - 33x - 6
353)
C) -2x2 - 33x - 33
D) -15x2 - 33x - 33
Use the quadratic formula to solve the equation. Give both exact and approximate answers. 354) x2 - x = -30
Evaluate the expression. 355) - -2 - -25 - 22 A) -45
354)
B) 5, 6 D) No real number solutions
A) -5, -6 C) 1, 30
355) C) 45
B) -49
44
D) 49
Simplify the expression. Write answer with positive exponents. 6 -7
356)
356)
6 -5
A) 62
C) 1
B) 612
D) 1
6 12
62
Solve the equation for the indicated variable. 357) v2 = 2as for v
A) v = ±
2a s
357)
B) v = 2a
C) v = 2a s
s
D) v = ± 2as
Solve the equation for x. 358) 3a = a - 6b x+1
A) x = 2a + 6b a - 6b
358) B) x = 4a + 6b
C) x = 2a - 6b
a - 6b
D) x = 3a - 1
a - 6b
a - 6b
Solve the problem. 359) Tom Quig traveled 260 miles east of St. Louis. For most of the trip he averaged 60 mph, but for one period of time he was slowed to 10 mph due to a major accident. If the total time of travel was 6 hours, how many miles did he drive at the reduced speed? A) 20 miles B) 40 miles C) 15 miles D) 30 miles Fill in the blank with either =, <, or > to make the statement true. 360) 9 · -4 4(9) A) < B) =
360) C) >
Solve the problem. 361) It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 50 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired strength? A) 25 liters B) 20 liters C) 12.5 liters D) 16.7 liters Find approximate solutions of the equation. 362) 4.24y2 - 9.2y - 1.2 = 0
A) 0.12 or -2.29 Factor completely. 363) 4x2 + 9
A) Prime 364) x2 - 16xy + 64y2 A) (x + 8y)2
359)
361)
362)
B) 0.12 or -0.12
C) 2.29 or -0.12
D) 2.29 or -2.29
363) B) (2x + 3)2
C) (2x - 3)2
B) Prime
C) (x - 8y)2
D) (2x + 3)(2x - 3) 364)
45
D) (x - 8y)(x + 8y)
Solve the equation. 365) -3 = y + 2.6 A) 5.6
365) B) 0.4
Simplify. Leave answer with exponent. 366) (-6)6 · (-6)5
A) -6 11
C) -0.4
D) -5.6
C) 3630
D) 611
366)
B) 3611
Find the product.
367) -3x(7x2 + 3x + 8) A) -21x3 - 9x2 + 8x C) -21x3 - 33x2
367) B) -21x3 + 3x2 - 24x D) -21x3 - 9x2 - 24x
Solve the problem. 368) The length of a rectangular billboard is 6 inches more than the width. The perimeter of the billboard is 28 inches. Find the width of the billboard. A) 6 in. B) 10 in. C) 7 in. D) 4 in. Perform the indicated operations. Give the answer in lowest terms. 369) 6 - 4 z2 z
A) 2(3 + 2z) z2
B) 2(2z - 3)
369)
C) 2(3z + 2)
z
368)
z2
D) 2(3 - 2z) z2
Solve the problem. 370) The distance, s, in feet, traveled by a body falling freely from rest in t seconds is approximated by the equation s = 16t2 . An experimenter on a ladder releases a marble from rest. The marble takes 5
370)
Name the property illustrated. 371) 5(9 + 13) = (9 + 13)5 A) Commutative property
371)
seconds to fall to the ground. How high was the marble when it was released? A) 80 ft B) 25 ft C) 6,400 ft D) 400 ft
B) Identity and associative properties D) Distributive and associative properties
C) Associative and commutative properties Evaluate the expression. Write answer without exponents. 372) -321/5
A) -8
372)
B) 32
C) 16
D) -2
Solve the problem.
373) A manufacturer's cost is given by C = 300
3
n + 200, where C is the cost and n is the number of parts produced. How many parts are produced when the cost is $5,900? A) 6,859 B) 361 C) 5,700 D) 54,872
46
373)
Evaluate the expression, given x = -2, y = 3, and a = -4. 374) -9a - 7y + 8x A) -1 B) -31
374) C) 74
Factor out the greatest common factor. 375) x6 - 13xy3 + 11x3 y8 - 3x6 y3
D) 70
375)
A) xy(x5 - 13y2 + 11x2 y7 - 3x5 y2 )
B) x2 (x5 - 13y2 + 11x2 y7 - 3x5 y2 )
C) xy3 (x5 - 13 + 11x2 y5 - 3x5 )
D) x(x5 - 13y3 + 11x2 y8 - 3x5 y3)
Use a calculator to evaluate the expression. 376) (-3)4
A) 81
376) C) 12
B) -81
D) -12
Find approximate solutions of the equation. 377) x2 + 3.4x + 2.89 = 1,149.21
377)
A) 32.2 or 35.6 C) 1,147.51 or -1,150.91
B) 32.2 or -35.6 D) 32.2
Solve the equation for the indicated variable. 378) A = 1 r2 for r 3
A) r = 3 A
B) r = ±
378) 3A
C) r = ±
A 3
D) r = 3
A
Factor completely. 379) x3 y - 9x2y2 + 20xy3
379)
A) xy(x2 - 9x + 20y2)
B) xy(x - 5y)(x - 4y) D) y(x - 5y)(xy - 4y2 )
C) x(xy - 5y2)(x - 4y) Write the expression in lowest terms. a 2 - 4a
380)
380)
(a + 2)(a - 4)
A)
1 a+2
B)
a a+2
2 D) a
C) a - 4 a+2
a+2
Use the discriminant to determine the number of real solutions of the equation. 381) -1 - 3a 2 = 7a - 4
A) No real solutions
B) 1
381) C) 2
Factor completely. 382) 343x2 - 490xy + 175y2
382)
A) 7(7x - 5y)2 C) (49x - 35y)(7x - 5y)
B) 7(49x2 - 70xy + 25y) D) 7(7x + 5y)(7x - 5y) 47
Determine whether the statement is true or false. 383) Every rational number is an integer. A) True Solve the equation. 384) 2(2z - 2) = 3(z + 4) A) 8
383) B) False
384) B) -8
C) 10
D) 16
C) 0
D) -1
Evaluate the expression. Write answer without exponents. 385) 110
A) 1
385)
B) 11
Simplify the complex fraction. 3 4 + x+5 x-2
386)
386)
5 1 x-1 x+5
2
A) 7x + 7x - 14
B) 3x - 30 9x + 10
4x2 + 18x - 52 2
2
C) 7x + 7x - 14
D) 7x - 33x + 26
6x2 - 37x + 8
-4x2 + 4x - 52
Graph the inequality on a number line. 387) (- , 2]
387)
A)
B)
C)
D)
Factor completely. 388) 343x2 + 294x + 63
388)
A) 7(7x + 3)2
B) 7(49x2 + 42x + 9)
C) (49x + 21)(7x + 3)
D) 7(7x - 3)(7x + 3)
389) 216s3 + 1 A) (6s + 1)(36s2 - 6s + 1) C) (6s - 1)(36s2 + 6s + 1)
389) B) (216s + 1)(s2 - 6s + 1) D) (6s + 1)(36s2 + 1)
48
Solve the problem. 390) From a point on a river, two boats are driving in opposite directions, one at 10 miles per hour and the other at 5 miles per hour. In how many hours will they be 30 miles apart? A) 2 hours B) 4 hours C) 1 hour D) 3 hours Use a calculator to evaluate the expression. 391) (-3.9)10 A) 814,040.608 B) 39
391) C) -39
D) -814,040.608
Simplify the complex fraction. 5 -5 4r - 1
392)
392)
5 +5 4r - 1
A) 2 - r r
B)
4r 2 - 4r
C) 2 - 4r 4r
D) 2 + 4r 4r
Solve the equation. 393) 2y + 3 = 3 y 2
A) 2
393) C) 0
B) -6
D) 6
Solve the problem. 394) 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 76 feet?
A) 2.0 sec
B) 1.4 sec
C) 2.2 sec
B) 2
394)
D) 1.2 sec
Use the discriminant to determine the number of real solutions of the equation. 395) s2 + 2s - 3 = 0
A) 1
390)
395) C) No real solutions
Solve the problem. 396) Candy and Delvis are riding bicycles in the same direction. Candy is traveling at the speed of 3 miles per hour, and Delvis is traveling at the speed of 12 miles per hour. In 4 hours what is the distance between them? A) 45 miles B) 36 miles C) 33 miles D) 37 miles
49
396)
397) The cost of producing x thousand units of a certain product is given by
397)
C = -5.5x2 + 4,595x + 190,000, for x 150. Write a rational expression that gives the average cost per unit when x thousand are produced. Then find the average cost per unit when 50,000 units are produced. 2 2 A) -5.5x + 4,595x + 190,000 ; $8,120.00 B) -5.5x + 4,595x + 190,000 ; $266.61 x 1000x
2
2
C) -5.5x + 4,595x + 190,000 ; $8.12
D) -5.5x + 4,595x + 190,000 ; $8.12
x
1000x
Use a calculator to evaluate the expression.
398) 3
7
398)
4
A) 0.1335
B) 9.3333
Solve the formula for the specified variable. 399) A = P(1 + nr) for r A) r = P - A B) r = A - P Pn Pn
C) 7.4915
D) 5.25
C) r = Pn A-P
D) r = A n
399)
Solve the problem. 400) A triangle has a perimeter of 108 inches. Its shortest side measures 15 inches shorter than its middle side, and its longest side measures 18 inches longer than its middle side. Find the lengths of the triangle's three sides. A) 52 inches, 37 inches, 19 inches B) 40 inches, 25 inches, 43 inches
C) 32 inches, 47 inches, 29 inches
D) 20 inches, 35 inches, 53 inches
Factor completely. 401) 5x2 - 5x - 30
A) Prime
401) B) 5(x + 2)(x - 3)
C) 5(x - 2)(x + 3)
D) (5x + 10)(x - 3)
Use the quadratic formula to solve the equation. Give both exact and approximate answers. 402) 6x2 + 8x = - 1
A) -4 ± 10 ; -0.14, -1.194
B) -4 ± 10 ; -0.07, -0.597
C) -4 ± 22 ; 0.115, -1.448
D) -8 ± 10 ; -0.806, -1.86
6
6
Evaluate the expression. Write answer without exponents. 403) 274/3
403)
B) 2,187
C) 243
D) 729
C) 169
D) 15
Use a calculator to evaluate the expression. 404) 132
A) 338
402)
12
6
A) 81
400)
404)
B) 26 50
Simplify the expression. Write answer with positive exponents. Variables are positive real numbers. 405) x1/6 x5/6
A) x5/36
B) x5/6
C) x
Express each of the following statements in symbols, using <, >, , or . 406) y is greater than or equal to -4. A) y -4 B) y -4 C) -4 y
406) D) y > -4
Solve the problem. 407) Find the length of a rectangular lot with a perimeter of 100 meters if the length is 8 meters more than the width. (P = 2L + 2W) A) 21 m B) 58 m C) 50 m D) 29 m Use a calculator to solve the equation. Round to the nearest hundredth. 408) 2.27x + 3.12 - 1.79x - 4.08 = x 1.11 3.69
A) 0.21
B) -0.12
C) -0.27
D) -6.99
409)
A) -2 + 2 22, -2 - 2 22 C) 2 11, -2 11
B) 2 11 - 2, 2 11 + 2 D) -2 + 2 11, -2 - 2 11
Solve the equation for x. 410) ax - b = 5(x + a) A) x = 5a + b a+5
B) x = 5a - b a-5
C) x = a + b a-5
D) x = 5a + b a-5
Simplify the expression. 411) 81 - 4 A) 77
B) 79
C) 79
D) 77
410)
411)
Solve the equation. 412) -9 - -3 = 0 x-8 x-5 2
407)
408)
Solve by the square-root property. 409) (x + 2)2 = 44
A) 7
405)
D) 1 x
412) C) - 1 , - 1
B) 8, 5
8
5
D) - 23 4
Solve the problem. 413) Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 180 miles in the same time that Dana travels 156 miles. If Chuck's rate of travel is 4 mph more than Dana's, and they travel the same length of time, at what speed does Chuck travel? A) 35 mph B) 26 mph C) 25 mph D) 30 mph
51
413)
Use inequality symbols to rewrite the statement. Let x represent the unknown. 414) The market shakeout could result in as few as 10 companies remaining in business. A) x = 10 B) x - 10 = 0 C) x 10 D) x 10 Factor completely. 415) 250k3 m - 16m 4
415)
A) 2m(5k - 2m)(25k2 + 10km + 4m 2 ) C) (10km - 4m 2)(25k2 + 4m 2 )
B) 2m(125k - 2m)(k2 + 10km + 4m 2 ) D) 2m(5k + 2m 2 )(25k2 - 10km + 4km2)
Solve the problem. 416) Helen Weller invested $14,000 in an account that pays 10% simple interest. How much additional money must be invested in an account that pays 13% simple interest so that the average return on the two investments amounts to 11%? A) $14,000 B) $7,000 C) $10,000 D) $11,000 Perform the indicated operations. Give the answer in lowest terms. 417) 2 - 2y - 3 - 8y 30 48
A) -56y + 31 240
418)
414)
B) -56y + 1
417)
C) 24y + 1
240
416)
D) 24y + 31
240
240
1 9 -49x + 4(7x + 1) 4x(7x + 1) x
418)
2
A) -49x - 252x - 35
B) - 7(x + 5)
2
D) - 7(x + 5)
28x2 + 4x
28x2 + 4x
C) -49x - 252x - 35
4x
4x
Find the product.
419) (5p - 1)(25p2 + 5p + 1) A) 125p3 + 30p2 - 1
B) 125p3 + 1
C) 25p3 - 1
D) 125p3 - 1
419)
Evaluate the expression. Write answer without exponents. 420) -2 -1
A) -2 Simplify the expression. 4 4 421) 12 · 12 4 A) 144
420) C) 1 2
B) 2
D) - 1 2
421) B) 2
4
9
C) 2
52
4
3+2
4
3
D) 4 2
Evaluate the expression, given x = -2, y = 3, and a = -4. 422) -3x + 4y + 7a A) 10 B) -45
422) C) 11
D) -10
Solve the problem.
423) The polynomial 0.0051x3 - 0.0053x2 + 0.185x + 1.4 gives the approximate total earnings of a
423)
company, in millions of dollars, where x = 0 corresponds to 1996, x = 1 corresponds to 1997, and so on. This model is valid for the years from 1996 to 2000. Determine the earnings for 1998. A) $1.58 million B) $2.05 million C) $1.79 million D) $1.83 million
Write the expression in lowest terms. y2 + 7y + 10
424)
424)
y2 + 13y + 40
A) y + 2
B) 7y + 10
2
D) 7y + 1
y+ 8
13y + 40
C) - y + 7y + 10
13y + 4
y2 + 13y + 40
3
425) 6k
425)
3k
A) 2k2
B) 2k
C) 3
D) 3k2
B) -4 ± 3
C) -2 ± 3
D) -1, 7
Solve by the square-root property. 426) (x + 4)2 - 3 = 0
A) 4 ± 3
426)
Simplify the expression. Write answer with positive exponents. 816
427)
427)
96
A) 96
B) 1
C) 9
96
D) 912
Use inequality symbols to rewrite the statement. Let x represent the unknown. 428) A Software company could lose up to 7% of its market share due to slow product delivery. Let x be the market share lost. A) x 0.07 B) x -0.07 C) x -0.07 D) x 0.07 Identify the degree of the polynomial and list its coefficients. 429) 7x5 - 9x3 - 8x2 + 9
429)
A) degree: 5
B) degree: 7
C) degree: 5
D) degree: 11
coefficients: 7, -9, -8, 9
coefficients: -9, -8, 9
coefficients: 7, 9, 8, 9
coefficients: 7, -9, -8, 9
53
428)
Answer Key Testname: CHAPTER 1
1) (2x)0 = 1, because the exponent is applied to the entire quantity in the parentheses. (2x0 ) = 2 because the exponent is applied only to the x.
2) If x is negative and n is odd, the answer will be negative. 3) Answers vary but they should find a number such that their product is 70 and their sum is 17. 4) B 5) D 6) C 7) D 8) C 9) B 10) D 11) C 12) C 13) A 14) C 15) C 16) D 17) B 18) C 19) B 20) B 21) A 22) B 23) C 24) B 25) D 26) A 27) C 28) C 29) D 30) C 31) B 32) D 33) B 34) C 35) D 36) C 37) D 38) D 39) D 40) D 41) A 54
Answer Key Testname: CHAPTER 1
42) A 43) C 44) B 45) A 46) A 47) D 48) B 49) A 50) B 51) B 52) C 53) A 54) B 55) B 56) C 57) B 58) C 59) A 60) A 61) B 62) D 63) D 64) A 65) B 66) D 67) B 68) D 69) D 70) A 71) D 72) C 73) D 74) D 75) C 76) D 77) D 78) C 79) A 80) A 81) B 82) D 83) B 55
Answer Key Testname: CHAPTER 1
84) B 85) B 86) B 87) B 88) B 89) C 90) A 91) B 92) B 93) A 94) B 95) B 96) D 97) C 98) C 99) D 100) B 101) A 102) C 103) D 104) C 105) C 106) B 107) C 108) C 109) A 110) A 111) C 112) A 113) B 114) A 115) C 116) B 117) D 118) B 119) C 120) C 121) B 122) C 123) A 124) D 125) C 56
Answer Key Testname: CHAPTER 1
126) C 127) D 128) D 129) A 130) D 131) D 132) A 133) B 134) D 135) C 136) A 137) C 138) A 139) C 140) A 141) B 142) A 143) A 144) D 145) D 146) D 147) B 148) A 149) D 150) C 151) A 152) B 153) A 154) C 155) B 156) A 157) C 158) A 159) B 160) C 161) C 162) B 163) D 164) D 165) D 166) A 167) A 57
Answer Key Testname: CHAPTER 1
168) B 169) A 170) D 171) B 172) C 173) D 174) D 175) A 176) D 177) C 178) A 179) B 180) A 181) B 182) C 183) C 184) D 185) B 186) D 187) D 188) B 189) D 190) D 191) B 192) B 193) D 194) C 195) C 196) C 197) B 198) B 199) C 200) B 201) C 202) B 203) B 204) A 205) B 206) D 207) C 208) C 209) D 58
Answer Key Testname: CHAPTER 1
210) D 211) D 212) B 213) A 214) B 215) D 216) A 217) D 218) A 219) A 220) C 221) B 222) B 223) D 224) C 225) D 226) D 227) C 228) C 229) A 230) B 231) B 232) A 233) A 234) A 235) C 236) A 237) A 238) D 239) A 240) D 241) A 242) C 243) C 244) A 245) B 246) C 247) A 248) D 249) B 250) D 251) D 59
Answer Key Testname: CHAPTER 1
252) D 253) D 254) D 255) A 256) C 257) C 258) A 259) A 260) C 261) C 262) D 263) C 264) D 265) C 266) C 267) B 268) C 269) C 270) C 271) D 272) C 273) A 274) D 275) D 276) A 277) C 278) C 279) C 280) B 281) C 282) D 283) A 284) D 285) C 286) C 287) D 288) B 289) A 290) D 291) D 292) B 293) C 60
Answer Key Testname: CHAPTER 1
294) C 295) D 296) C 297) D 298) A 299) A 300) B 301) C 302) D 303) C 304) B 305) B 306) A 307) B 308) A 309) C 310) A 311) D 312) B 313) B 314) C 315) A 316) D 317) D 318) D 319) B 320) A 321) D 322) C 323) C 324) C 325) D 326) D 327) C 328) A 329) B 330) D 331) C 332) A 333) B 334) B 335) C 61
Answer Key Testname: CHAPTER 1
336) B 337) A 338) B 339) B 340) A 341) C 342) C 343) C 344) D 345) B 346) C 347) A 348) D 349) B 350) A 351) C 352) D 353) A 354) D 355) B 356) D 357) D 358) A 359) A 360) B 361) C 362) C 363) A 364) C 365) D 366) A 367) D 368) D 369) D 370) D 371) A 372) D 373) A 374) A 375) D 376) A 377) B 62
Answer Key Testname: CHAPTER 1
378) B 379) B 380) B 381) C 382) A 383) B 384) D 385) A 386) A 387) B 388) A 389) A 390) A 391) A 392) C 393) B 394) B 395) B 396) B 397) D 398) A 399) B 400) D 401) B 402) A 403) A 404) C 405) C 406) B 407) D 408) D 409) D 410) D 411) A 412) A 413) D 414) D 415) A 416) B 417) C 418) D 419) D 63
Answer Key Testname: CHAPTER 1
420) D 421) B 422) D 423) C 424) A 425) A 426) B 427) A 428) A 429) A
64
Exam
Chapter 2
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Choose one of the four lines graphed which most closely resembles the graph of the given equation. 1) y = -3x + 4
A)
B)
C)
D)
1
1)
2) y = 5x A)
B)
C)
D)
2)
2
3) y = -4 A)
B)
C)
D)
3)
3
4) y = -3x - 5 A)
B)
C)
D)
4)
4
5) y = 5x - 6 A)
B)
C)
D)
5)
5
6) y = 2x + 6 A)
B)
C)
D)
6)
Determine whether the given ordered pair is a solution of the given equation. 7) 2x + y = 11; (4, 3) A) Yes B) No
8) (x - 5)2 + (y + 4)2 = 13; (2, -2) A) No Convert the temperature. 9) 2°F = °C A) -16.7°C
7)
8) B) Yes
9) B) 28.4°C
C) 35.6°C
Use technology to compute r, the correlation coefficient. 10) Consider the data points with the following coordinates: x 62 53 64 52 52 54 58 y 158 176 151 164 164 174 162 A) .7537 B) -.0810 C) -.7749
6
D) 30.9°C
10) D) 0