Algebra I Gateway Practice

1
Algebra I Gateway Practice

• For a few objectives

2
Click on the correct answer for each problem.
Keep in mind that this review does NOT cover all
of the Gateway objectives!
3

• Simplify c c c d d c d
• A. c4 d3
• B. 12cd
• C. 4c 3d
• D. c4 d3

4

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6

• Simplify 2 a a a b a
• A. 2a b
• B. 2a3 b2
• C. 2a4 b
• D. 8ab3

7

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8

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9

• Simplify 3 f f (2) f
• A. 6f3
• B. 3f 2f
• C. 5f3
• D. f6

10

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11

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12

• Karen wants to fence in her rectangular garden
  plot. How much fence will she need if her garden
  measures 60 feet by 100 feet?
  
• A. 320 feet
• B. 160 feet
• C. 220 feet
• D. 600 feet

13

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14

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15

• 5. How much chain link fence will Bob need to
  enclose the rectangular lot shown in the
  drawing?
  
• 
  25
  
• 30
• A. 750 feet
• B. 55 feet
• C. 110 feet
• D. 7500 feet

16

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17

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18

• Simplify (2x 1)(x 5)
• A. 3x 4
• B. 2x2 10x 5
• C. 2x2 9x 5
• D. 2x2 11x 4

19

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20

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21

• Simplify (3x 2)(4x 1)
• A. 7x 1
• B. 12x2 5x 2
• C. 12x2 11x 2
• D. 12x2 5x 3

22

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23

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24

• (4x 5)(2x 3)
• A. 6x 8
• B. 8x2 15
• C. 6x2 26x 15
• D. 8x2 22x 15

25

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26

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27

• 9. Which of these lines has a 0 slope?
• A. C.
• B. D.

28

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30

• Which of these lines has a
• negative slope?
• A. C.
• B. D.

31

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32

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33

• There are 15 glazed donuts
• and 9 crème-filled donuts in a
• box. Which of these is the
• correct ratio of glazed donuts
• to crème-filled donuts?
• A. 3 to 5
• B. 8 to 3
• C. 5 to 3
• D. 7 to 3

34

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36

• On an English test, 18 students
• received an A while 15 students
• received a B. What is the correct
• ratio of students receiving an A
• to students receiving a B?
• A. 5 to 6
• B. 3 to 2
• C. 4 to 3
• D. 6 to 5

37

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39

• A league has 780 players
• with 400 nine year-olds and
• the rest ten year-olds. What
• is the ratio of nine year-olds
• to ten year-olds?
• A. 39 to 20
• B. 20 to 19
• C. 39 to 19
• D. 9 to 10

40

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42

• 14. A team played 28 games
• and lost 7. If there were no
• tie games, what is the correct ratio of
  wins to total
  
• games?
• A. 3 to 2
• B. 3 to 1
• C. 4 to 3
• D. 3 to 4

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45

• There are 1200 cars in a
• fleet and 640 are new cars.
• What is the ratio of new cars to old
  cars?
  
• A. 75 to 4
• B. 15 to 8
• C. 8 to 7
• D. 7 to 15

46

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48

• What is the circumference of
• a circular Frisbee with a
• radius of 14 inches? Give your answers
  in terms of p.
  
• A. 28 p in.
• B. 7 p in.
• C. 14 p in.
• D. 42 p in.

49

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51

• A CD has a radius of 3 cm.
• What is the area of the CD?
• (Round your answer to
• the nearest whole number.)
• A. 28 cm2
• B. 9 cm2
• C. 7 cm2
• D. 19 cm2

52

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54

• A pool is in a circular shape
• with a diameter of 17 feet.
• What is the circumference of
• the pool? (Round your
• answer to the nearest whole
• number.)
• A. 27 ft. C. 53 ft.
• B. 70 ft. D. 107 ft.

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57
19. Katie is decorating a ceramic
plate with a diameter of 12
inches. What is the area of
the plate she must cover.
Give your answer in terms
of p. A. 24 p in.2 B. 12 p in.2
C. 144 p in.2 D. 36 p in.2
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60

• What is the next number
• in the sequence below?
• 2, 3, 5, 8, 12, _____
• A. 16
• B. 17
• C. 24
• D. 36

61

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63

• What is the next number
• in the sequence below?
• 1, 2, 4, 8, 16, _____
• A. 18
• B. 20
• C. 256
• D. 32

64

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65

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66

• What is the next number
• in the sequence below?
• 4, 9, 16, 25, 36, _____
• A. 49
• B. 64
• C. 41
• D. 58

67

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68

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69

• What is the next number
• in the sequence below?
• 4, 28, 196, 1372, _____
• A. 2,744
• B. 5,488
• C. 9,604
• D. 10,976

70

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71

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72

• What is the next number
• in the sequence below?
• 1, 3, 7, 15, 31, _____
• A. 49
• B. 63
• C. 55
• D. 32

73

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75

• How many different
• sandwiches can Mike
• create from 2 kinds of
• bread 4 kinds of meat,
• and 3 different cheeses?
• A. 4!
• B. 2 4 3
• C. 2 4 3
• D. 2! 4! 3!

76

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77

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78

• Janice is making a scrapbook of her vacation
  pictures. How many different ways can she
  arrange the pages if she
  
• has 14 pictures?
• A. 14!
• B. 1413121110
• C. 14! 13!
• D. 1413121110

79

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80

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81

• 5 people entered a race. In how many
  different orders can they finish?
  
• A. 5 4 3
• B. 54321
• C. 5! 4! 3! 2! 1!
• D. 5!

82

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83

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84

• How many different valentines can Sheri make
  with 4 colors of background paper, 5 styles of
  hearts, and 12 different colored markers?
  
• A. 12! 5! 4!
• B. 4 5 12
• C. 12!
• D. 4 5 12

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87

• A scientist is studying soldier beetles in a
  field for 5 days.
  
• He saw the numbers of soldier beetles listed
  below on each of the 5 days.
  
• 10, 13, 6, 16, 25
• What is the mean number of soldier beetles the
  scientist saw per day?
  
• A. 8 C. 12
• B. 14 D. 17

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90

• Mr. Shaw is running for mayor. He received
  votes from the 6 districts in his city as listed
  below.
  
• 112, 243, 92, 189, 360, 96
• What was the mean number of votes he received
  per district?
  
• A. 151 C. 189
• B. 1,092 D. 182

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93

• Marcus gets a base hit 62.3 of the time. In
  29
  
• at-bats, estimate how many base hits he will
  make.
  
• A. 29
• B. 19
• C. 17
• D. 18

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96

• When Carrie attempts a three-point shot, she
  succeeds 49.2 of the time. If Carrie attempts
  67 3-point shots, estimate how many times she
  will succeed.
• A. 33
• B. 67
• C. 35
• D. 49

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98

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99
33. Which of these functions generalizes the
pattern in the table? x f(x)
2 12 4 22
6 32 A. f(x) 3x 6
B. f(x) 6x 2 C. f(x) 5x 2 D. f
(x) 6x
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102
34. Which of these functions generalizes the
pattern in the table? x f(x)
1 1 2
4 3 7 A. f(x)
x B. f(x) 2x C. f(x) 3x 2 D.
f(x) 2x 1
103

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105

• Evaluate 3x2 4x 9,
• if x 2.
• A. 6
• B. 11
• C. 65
• D. 1

106

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107

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108

• Evaluate x2 4x 5, if x 5.
• A. 0
• B. 30
• C. 10
• D. 40

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111

• Evaluate x3 2x2 5x 3, if x 2.
• A. 29
• B. 13
• C. 25
• D. 12

112

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113

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114

• Evaluate ¾ x2, given
• x 2.
• A. 3
• B. 4
• C. 12.25
• D. 16

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117

• Evaluate ½ x2, given
• x 4.
• A. 4
• B. 8
• C. 4
• D. 8

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119

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120

• Solve 2(x 5) x 1.
• A. 9
• B. 4
• C. 6
• D. 10

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123

• Solve
• 2(2 x) 3x x 10.
• A. 2
• B. 3
• C. 3
• D. 6

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126

• Simplify 64 .
• A. 8
• B. 8
• C. 8 2
• D. 32

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128

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129
43. Simplify 169 . A. 16 9 B.
84
C. 13 D. 13 13
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132

• Which of these lists the correct order of
  operations to simplify the expression below?
  
• 2(3 4) 6 3
• A. add, multiply, divide, subtract
• B. add, multiply, subtract, divide
• C. add, subtract, multiply, divide
• D. multiply, add, sbtract, divide

133

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135

• Which of these lists the correct order of
  operations to simplify the expression below?
  
• 8 3(9 2) 6
• A. add, multiply, subtract, divide
• B. subtract, multiply, divide, add
• C. subtract, multiply, add, divide
• D. subtract, divide, multiply, add

136

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138

• What is the opposite of ¾ ?
• A. 4/3
• B. ¾
• C. 4/3
• D. ¾

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141

• What is the opposite of 3.75?
• A. 4
• B. 4
• C. 3.75
• D. 3.75

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144

• What is the reciprocal of ½?
• A. ½
• B. 2
• C. ½
• D. 2

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147

• What is the reciprocal of 0.8?
• A. 4/5
• B. 8/5
• C. 4/5
• D. 5/4

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150

• What is the absolute value of 35 ?
• A. 35
• B. 1/35
• C. 35
• D. 1/35

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153

• Which of these sets of numbers is ordered from
  least to greatest?
  
• A. 3.2, 4.1, 5.6, 7.3, 8.5
• B. 3.5, 3.1, 1.3, 2.3, 3.2
• C. 5.2, 5, 4.3, 4.5, 4.7
• D. 3.5, 3, 2.3, 2, 3.4

154

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156

• Which of these sets of numbers is in
  descending order?
  
• A. ¼ , ½, ¾ , 0, ¼, ½ , ¾
• B. ¼ , ½ , ¾ , 0, ½, ¼, ¾
• C. ¾ , ½, ¼, 0, ¼ , ½ , ¾
• D. ¾ , ½ , ¼ , 0, ¼, ½, ¾

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159

• Find the median of the following numbers.
• 15, 23, 8, 27, 13, 10, 18
• A. 15.5
• B. 18
• C. 27
• D. 15

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162

• Find the median of the following numbers.
• 26, 31, 42, 53, 44, 28, 37, 40
• A. 37
• B. 38.5
• C. 40
• D. 48.5

163

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165

• Find the mode of the following numbers.
• 23, 38, 26, 23, 39, 23, 26, 35, 23
• A. 39
• B. 23
• C. 23 and 26
• D. no mode

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168
56. Find the mode of the following numbers.
102, 107, 111, 107, 115, 119, 111 A. 1
02
B. 111 C. 107 D. 107 and 111
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171

• Larry is buying carpet for his new game room.
  If the room measures 35 feet by 45 feet, how
  much carpet does Larry need to buy?
  
• A. 160 feet2
• B. 1,575 feet2
• C. 80 feet2
• D. 6,300 feet2

172

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174

• What is the domain of the following set of
  ordered pairs?
  
• (2, 5), (7, 11), (14, 19), (22, 38)
• A. 2, 11, 14, 38
• B. 2, 7, 14, 22
• C. 5, 11, 19, 38
• D. 2, 7, 19, 38

175

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176

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177

• Find the distance between the points
• (5, 11) and (2, 8).
• A. 7.62
• B. 7.65
• C. 11.66
• D. 0

178

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179

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180

• Find the missing side of a right triangle
  with
  
• a 5 and c 11.
• A. 9.8
• B. 3.31
• C. 12.08
• D. 7.99

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183

• Joe walks 2 miles due west and then 3 miles
  due south. How far is Joe from his starting
  point?
  
• A. 5 miles
• B. 1 mile
• C. 3.61 miles
• D. 3 miles

184

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186

• Evaluate 3x2 5y 2z
• if x 6, y 4, and z 8.
• A. 104
• B. 112
• C. 1,270
• D. 104

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189

• Simplify 5x 3y 11y 19x
• A. 6xy
• B. 24x 14y
• C. 14x 8y
• D. 14x2 8y2

190

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191

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192

• Simplify
• 7(2x 3) 8(5x 3).
• A. 105x
• B. 54x 45
• C. 17x 37x
• D. 54x 3

193

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194

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195

• Simplify
• (5x2 8x 3) (11x2 2x 19)
• A. 6x3
• B. 6x2 10x 22
• C. 16x2 6x 16
• D. 6x2 6x 16

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198

• Which is the most expensive per pound?
• A. 5 lb for 7.23
• B. 8 lb for 9.82
• C. 11 lb for 11.45
• D. 15 lb for 14.91

199

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201

• Find the slope of the line through the points
  (5, 9) and (3, 14).
  
• A. 5/8
• B. 19/6
• C. 8/5
• D. 5/8

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204
68. Which of these represents the average rate
of change in the number of students between
1985 and 2000 per year?
Year of Students 1980
1,643 1985 1,725
1990 1,713
1995 1,882
2000 1,971
2004 2,014
Answers choices on next slide.
205
A. 2014 2004 1643
1980 B. 1971 1725 20
00 1985 C. 1725 1985 19
71 2000 D. 1971 2000 1
725 1985
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208

• Janet is making strawberry pie for dessert
  for a family reunion. She plans to slice the
  pies so that there are 6 slices per pie. If
  she plans to make enough for each person to
  have 2 slices of pie, how many pies should she
  make if there will be 25 people at the
  reunion?
• A. 8 C. 9
• B. 25 D. 7

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211

• A boy 6 feet tall casts a 3.5 foot shadow. At
  the same time, a flag pole casts a 22 foot
  shadow. What is the height of the flag pole?
  
• A. 44 feet
• B. 0.95 feet
• C. 12.8 feet
• D. 37.71 feet

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214

• Congratulations!
• You are now finished!
• Remember, this is not all of the Gateway
  Objectives. Keep practicing!