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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.
B.
C.
D.
c4 d3
12cd
4c + 3d
c4 + d3
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2. Simplify: 2 ∙ a ∙ a ∙ a ∙ b ∙ a
A.
B.
C.
D.
2a + b
2a3 + b2
2a4 b
8ab3
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3. Simplify: 3 ∙ f ∙ f ∙ (–2) ∙ f
A.
B.
C.
D.
–6f3
3f – 2f
–5f3
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.
B.
C.
D.
320 feet
160 feet
220 feet
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.
B.
C.
D.
750 feet
55 feet
110 feet
7500 feet
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6. Simplify: (2x + 1)(x – 5)
A.
B.
C.
D.
3x – 4
2x2 – 10x – 5
2x2 – 9x – 5
2x2 + 11x + 4
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7. Simplify: (3x + 2)(4x – 1)
A.
B.
C.
D.
7x + 1
12x2 + 5x – 2
12x2 + 11x – 2
12x2 – 5x – 3
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8. (4x + 5)(2x + 3)
A.
B.
C.
D.
6x + 8
8x2 + 15
6x2 + 26x + 15
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.
B.
C.
D.
3 to 5
8 to 3
5 to 3
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.
B.
C.
D.
5 to 6
3 to 2
4 to 3
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.
B.
C.
D.
39 to 20
20 to 19
39 to 19
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.
B.
C.
D.
3 to 2
3 to 1
4 to 3
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.
B.
C.
D.
75 to 4
15 to 8
8 to 7
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.
B.
C.
D.
28 π in.
7 π in.
14 π in.
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.
B.
C.
D.
28 cm2
9 cm2
7 cm2
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.
B. 70 ft.
C. 53 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.
B.
C.
D.
24 π in.2
12 π in.2
144 π in.2
36 π in.2
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20. What is the next number
in the sequence below?
2, 3, 5, 8, 12, _____
A.
B.
C.
D.
16
17
24
36
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21. What is the next number
in the sequence below?
1, 2, 4, 8, 16, _____
A.
B.
C.
D.
18
20
256
32
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22. What is the next number
in the sequence below?
4, 9, 16, 25, 36, _____
A.
B.
C.
D.
49
64
41
58
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23. What is the next number
in the sequence below?
4, 28, 196, 1372, _____
A.
B.
C.
D.
2,744
5,488
9,604
10,976
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24. What is the next number
in the sequence below?
1, 3, 7, 15, 31, _____
A.
B.
C.
D.
49
63
55
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.
B.
C.
D.
14!
14+13+12+11+10
14! 13!
14∙13∙12∙11∙10
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27. 5 people entered a race.
In how many different
orders can they finish?
A.
B.
C.
D.
5∙4∙3
5+4+3+2+1
5! 4! 3! 2! 1!
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.
B.
C.
D.
12! 5! 4!
4 ∙ 5 ∙ 12
12!
4 + 5 + 12
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29. 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
B. 14
C. 12
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
B. 1,092
C. 189
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.
B.
C.
D.
29
19
17
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-point
shots, estimate how many
times she will succeed.
A.
B.
C.
D.
33
67
35
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.
B.
C.
D.
f(x) = 3x + 6
f(x) = 6x – 2
f(x) = 5x + 2
f(x) = 6x
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34. Which of these functions
generalizes the pattern in
the table?
x
1
2
3
A.
B.
C.
D.
f(x) = x
f(x) = 2x
f(x) = 3x – 2
f(x) = 2x + 1
f(x)
1
4
7
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35. Evaluate
if x = 2.
A.
B.
C.
D.
6
11
65
–1
2
3x
+ 4x – 9,
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36. Evaluate
if x = –5.
A. 0
B. –30
C. –10
D. 40
2
x
– 4x – 5,
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37. Evaluate x3 – 2x2 + 5x – 3,
if x = –2.
A.
B.
C.
D.
–29
–13
25
–12
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38. Evaluate ¾ x2, given
x = 2.
A.
B.
C.
D.
3
4
12.25
16
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39. Evaluate ½
x = –4.
A.
B.
C.
D.
–4
–8
4
8
2
x,
given
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40. Solve 2(x – 5) = x – 1.
A.
B.
C.
D.
9
4
6
10
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41. Solve
2(2 + x) – 3x = x + 10.
A.
B.
C.
D.
–2
–3
3
6
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42. Simplify
A. 8
B. 8
C. 8 2
D. 32
64 .
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43. Simplify
A.
B.
C.
D.
16 9
84
13
13 13
169 .
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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.
B.
C.
D.
add, multiply, divide, subtract
add, multiply, subtract, divide
add, subtract, multiply, divide
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.
B.
C.
D.
add, multiply, subtract, divide
subtract, multiply, divide, add
subtract, multiply, add, divide
subtract, divide, multiply, add
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46. What is the opposite
of ¾ ?
A.
B.
C.
D.
4/3
–¾
–4/3
¾
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47. What is the opposite
of –3.75?
A.
B.
C.
D.
4
–4
3.75
–3.75
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48. What is the reciprocal
of ½?
A.
B.
C.
D.
–½
2
½
–2
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49. What is the reciprocal
of 0.8?
A.
B.
C.
D.
4/5
8/5
–4/5
5/4
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50. What is the absolute
value of │–35 │?
A.
B.
C.
D.
35
–1/35
–35
1/35
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51. Which of these sets of
numbers is ordered from
least to greatest?
A.
B.
C.
D.
–3.2, –4.1, –5.6, –7.3, –8.5
–3.5, –3.1, –1.3, 2.3, 3.2
–5.2, –5, –4.3, –4.5, –4.7
–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.
B.
C.
D.
15.5
18
27
15
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54. Find the median of the
following numbers.
26, 31, 42, 53, 44, 28, 37, 40
A.
B.
C.
D.
37
38.5
40
48.5
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55. Find the mode of the
following numbers.
23, 38, 26, 23, 39, 23, 26, 35, 23
A.
B.
C.
D.
39
23
23 and 26
no mode
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56. Find the mode of the
following numbers.
102, 107, 111, 107, 115, 119, 111
A.
B.
C.
D.
102
111
107
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.
B.
C.
D.
160 feet2
1,575 feet2
80 feet2
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.
B.
C.
D.
7.62
7.65
11.66
0
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60. Find the missing side
of a right triangle with
a = 5 and c = 11.
A.
B.
C.
D.
9.8
3.31
12.08
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.
B.
C.
D.
5 miles
1 mile
3.61 miles
3 miles
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62. Evaluate 3x2 – 5y + 2z
if x = –6, y = 4, and z = 8.
A.
B.
C.
D.
–104
–112
1,270
104
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63. Simplify: 5x – 3y + 11y – 19x
A.
B.
C.
D.
–6xy
24x + 14y
–14x + 8y
–14x2 + 8y2
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64. Simplify:
7(2x + 3) + 8(5x – 3).
A.
B.
C.
D.
105x
54x 45
17x + 37x
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.
B.
C.
D.
5/8
–19/6
8/5
–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
1980
1985
1990
1995
2000
2004
# of Students
1,643
1,725
1,713
1,882
1,971
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
B. 25
C. 9
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.
B.
C.
D.
44 feet
0.95 feet
12.8 feet
37.71 feet
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Congratulations!
You are now finished!
*** Remember, this is not all of the Gateway
Objectives. Keep practicing!