algebra i gateway practice for a few objectives…
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Algebra I Gateway Practice
For a few objectives…
Click on the correct answer for each problem.
Keep in mind that this review does NOT cover all of the Gateway objectives!
1. Simplify: c ∙ c ∙ c ∙ d ∙ d ∙ c ∙ d
A. c4 d3
B. 12cd
C. 4c + 3d
D. c4 + d3
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2. Simplify: 2 ∙ a ∙ a ∙ a ∙ b ∙ a
A. 2a + b
B. 2a3 + b2
C. 2a4 b
D. 8ab3
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3. Simplify: 3 ∙ f ∙ f ∙ (–2) ∙ f
A. –6f3
B. 3f – 2f
C. –5f3
D. f6
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4. 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
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5. How much chain link fence will Bob need to enclose the rectangular lot shown in the drawing?
25’
30’
A. 750 feetB. 55 feetC. 110 feetD. 7500 feet
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6. Simplify: (2x + 1)(x – 5)
A. 3x – 4
B. 2x2 – 10x – 5
C. 2x2 – 9x – 5
D. 2x2 + 11x + 4
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7. Simplify: (3x + 2)(4x – 1)
A. 7x + 1
B. 12x2 + 5x – 2
C. 12x2 + 11x – 2
D. 12x2 – 5x – 3
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8. (4x + 5)(2x + 3)
A. 6x + 8
B. 8x2 + 15
C. 6x2 + 26x + 15
D. 8x2 + 22x + 15
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9. Which of these lines has a 0 slope?
A. C.
B. D.
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10. Which of these lines has a
negative slope?
A. C.
B. D.
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11. 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
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12. 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
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13. 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
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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 2B. 3 to 1
C. 4 to 3 D. 3 to 4
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15. 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
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16. What is the circumference of
a circular Frisbee with a
radius of 14 inches? Give your answers in terms of π.
A. 28 π in.
B. 7 π in.
C. 14 π in.
D. 42 π in.
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17. 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
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18. 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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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 π.
A. 24 π in.2
B. 12 π in.2
C. 144 π in.2
D. 36 π in.2
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20. What is the next number
in the sequence below?
2, 3, 5, 8, 12, _____
A. 16B. 17C. 24D. 36
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21. What is the next number in the sequence below?
1, 2, 4, 8, 16, _____
A. 18B. 20C. 256D. 32
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22. What is the next number in the sequence below?
4, 9, 16, 25, 36, _____
A. 49B. 64C. 41D. 58
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23. What is the next number in the sequence below?
4, 28, 196, 1372, _____
A. 2,744B. 5,488C. 9,604D. 10,976
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24. What is the next number in the sequence below?
1, 3, 7, 15, 31, _____
A. 49B. 63C. 55D. 32
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25. 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!
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26. 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. 14+13+12+11+10C. 14! 13!D. 14∙13∙12∙11∙10
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27. 5 people entered a race. In how many different
orders can they finish?
A. 5 ∙ 4 ∙ 3 B. 5+4+3+2+1 C. 5! 4! 3! 2! 1! D. 5!
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28. 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 ∙ 12C. 12!D. 4 + 5 + 12
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29. A scientist is studying soldierbeetles 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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30. 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. 189B. 1,092 D. 182
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31. Marcus gets a base hit 62.3% of the time. In 29
at-bats, estimate how many base hits he will make.
A. 29B. 19C. 17D. 18
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32. When Carrie attempts a three-point shot, she succeeds 49.2% of the time. If Carrie attempts 67 3-pointshots, estimate how many times she will succeed.
A. 33B. 67C. 35D. 49
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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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34. Which of these functions generalizes the pattern in
the table?
x f(x) 1 1 2 4 3 7
A. f(x) = xB. f(x) = 2x C. f(x) = 3x – 2D. f(x) = 2x + 1
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35. Evaluate 3x2 + 4x – 9, if x = 2.
A. 6 B. 11 C. 65 D. –1
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36. Evaluate x2 – 4x – 5, if x = –5.
A. 0 B. –30 C. –10 D. 40
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37. Evaluate x3 – 2x2 + 5x – 3, if x = –2.
A. –29B. –13C. 25D. –12
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38. Evaluate ¾ x2, given x = 2.
A. 3 B. 4 C. 12.25 D. 16
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39. Evaluate ½ x2, given x = –4.
A. –4B. –8C. 4D. 8
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40. Solve 2(x – 5) = x – 1.
A. 9 B. 4 C. 6 D. 10
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41. Solve
2(2 + x) – 3x = x + 10.
A. –2 B. –3 C. 3 D. 6
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42. Simplify 64 .
A. 8 B. 8 C. 8 2 D. 32
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43. Simplify 169 .
A. 16 9 B. 84 C. 13 D. 13 13
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44. Which of these lists the correct order of operations
to simplify the expression below?
2(3 + 4) – 6 ÷ 3
A. add, multiply, divide, subtractB. add, multiply, subtract, divideC. add, subtract, multiply, divideD. multiply, add, sbtract, divide
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45. Which of these lists the correct order of operations
to simplify the expression below?
8 + 3(9 – 2) ÷ 6
A. add, multiply, subtract, divideB. subtract, multiply, divide, addC. subtract, multiply, add, divideD. subtract, divide, multiply, add
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46. What is the opposite of ¾ ?
A. 4/3 B. –¾ C. –4/3 D. ¾
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47. What is the opposite of –3.75?
A. 4 B. –4 C. 3.75 D. –3.75
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48. What is the reciprocal of ½?
A. –½ B. 2 C. ½ D. –2
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49. What is the reciprocal of 0.8?
A. 4/5 B. 8/5 C. –4/5 D. 5/4
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50. What is the absolute value of │–35 │?
A. 35 B. –1/35 C. –35 D. 1/35
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51. 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
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52. 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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53. Find the median of the following numbers.
15, 23, 8, 27, 13, 10, 18
A. 15.5B. 18C. 27D. 15
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54. Find the median of the following numbers.
26, 31, 42, 53, 44, 28, 37, 40
A. 37B. 38.5C. 40D. 48.5
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55. Find the mode of the following numbers.
23, 38, 26, 23, 39, 23, 26, 35, 23
A. 39B. 23C. 23 and 26D. no mode
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56. Find the mode of the following numbers.
102, 107, 111, 107, 115, 119, 111
A. 102B. 111C. 107D. 107 and 111
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57. 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
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58. 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}
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59. Find the distance between the points (5, 11) and (–2, 8).
A. 7.62 B. 7.65 C. 11.66 D. 0
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60. 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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61. Joe walks 2 miles due west and then 3 miles due
south. How far is Joe from his starting point?
A. 5 milesB. 1 mileC. 3.61 milesD. 3 miles
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62. 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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63. Simplify: 5x – 3y + 11y – 19x
A. –6xy
B. 24x + 14y
C. –14x + 8y
D. –14x2 + 8y2
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64. Simplify: 7(2x + 3) + 8(5x – 3).
A. 105xB. 54x 45C. 17x + 37xD. 54x – 3
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65. 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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66. 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
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67. Find the slope of the line through the points (–5, 9) and (3, 14).
A. 5/8B. –19/6C. 8/5D. –5/8
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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.
A. 2014 – 2004 1643 – 1980
B. 1971 – 1725 2000 – 1985
C. 1725 – 1985 1971 – 2000
D. 1971 – 2000 1725 – 1985
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69. 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. 9B. 25 D. 7
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70. 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 feetB. 0.95 feetC. 12.8 feetD. 37.71 feet
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Congratulations!
You are now finished!
*** Remember, this is not all of the Gateway Objectives. Keep practicing!