Download Name Hour ______ Pre-Algebra: Semester 1 Review Circled

Name ___________________________
Hour ______
Pre-Algebra: Semester 1 Review
Circled questions will be on the non-calculator portion of the exam
1. Use the formula V= s3to find the volume of the cube with side length s.
2. Write the expression using exponents.
3. Evaluate the expression
14 • 14 • 14 • 14 • 14 • 14
a. 1 + 4 · 5 – 6 + 4
b.
8.7 + 5.3
7+6
c. 5(2 + 8) + 3
4. Evaluate the expression when x = 5, y = 10, and z = 3.
a.
(x 3 y 2 )
+z
x
b. z2 + x (3 – 1)
5. Order the following from least to greatest
6. Evaluate the expression
c. 4(y – z2)
- 12, - 8, - 7, 12, - 20
8 – (-x) when x = - 9.
7. Evaluate the following expressions when x = 7, y = 8, and z = -5
a. 2x – y + 3z
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b. -5 – x – z
1
8. Find the difference
a.
13 – 26
b.
-26 – (-9)
9. Evaluate the expression xy, when x = -1 and y = 5
10. Use the distributive property to write an equivalent variable expression.
a. 3(4x – 7y)
b. 4(x + 3)
c. -7 (x – 2)
d. -5(x – 10)
11. Simplify the expression.
12. Solve:
a. 2(x – 9) + 4(x – 7)
b.
c. 12(x – 4) – 14(x + 9)
d. 7x + 6(x + 5) + 5(x + 2)
a.
18 + t = 32
7x + 14x
b.
c
= 27
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13. Tom owns 5 times as many videos as Paul. Paul owns 17 videos. How many videos does Tom own?
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2
14. Solve and check your solution:
a. j – 7 = 14
b. x – 8 = 35
15. You receive $52 for babysitting for 6 hours. Write an equation that would show how much you make per hour?
16. Each story of a building is 12.4 feet tall. If the height of the building is 235.6 feet, how many stories does the
building have?
17. Solve
a.
-22 + 5x = 8
b.
-
x
+ 3 = 18
4
c.
t
=9
3
18. A car-rental company charges a flat fee of $150 and $0.25 per mile to rent a popular model of a sports-utility
vehicle. If the total cost to rent the vehicle for a 5-day ski trip was $650, how many miles were driven?
19. A local nursery sells rhododendrons and azaleas to landscapers. One month they sold 184 more rhododendrons
than azaleas. The total number of plants sold was 530. What is an equation could be used to solve for a, the
number of azaleas sold?
a. 2a + 184 = 530
b. a – 184 = 530
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c. 2a – 184 = 530
d. a + 184 = 530
3
20. Solve.
a.
- 3(5n – 8) = - 6
b. 9n + 29 – 5n + 29 = 2
c.
– n + 11 + 4n + 22 = - 6
d.
e. 2(2x – 3) = x + 7
21. Write an inequality:
a. x + 3 < 8
b. x – 3 > 8
22. Write an inequality:
11x – 18 = 5x + 12
f. 19 – x = - 8x - 9
When a number is decreased by 3 the result is greater than 8.
c. x + 3 > 8
d. X – 3 < 8
When a number is decreased by 5, the result is less than -6.
23. Which problem could be solved using the inequality 5n < 55?
a.
b.
c.
d.
Marty earned $55 for 5 hours of work.
Jenny spends more than $55 for 5 iTune downloads.
Five students split a restaurant bill that came to $55.
Five equal-priced shirts came to under $55.
24. Write an inequality to represent the verbal sentence.
When a number is multiplied by 4, the result is less than 8.
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4
25. The biology club at Jersey High School is sponsoring a dance to raise money for their spring project. They will
charge $6 per student admission, but must pay $120 for publicity and chaperones. If n is the number of students
who attend the dance, how many students must attend if the science club needs to earn at least $480 after
paying for publicity and chaperones?
26. Solve the inequality. Then graph its solution.
14 + y < 2
a.
-3 -2 -1
0
1 2
3
4
5
6 7
8
9 10
b.
-2.3x > 11.5
-3 -2 -1
0
1 2
3
4
5
6 7
8
9 10
c.
3 + 4x < 5
-3 -2 -1
0
1 2
3
4
5
6 7
8
9 10
d.
7b – 11 < 2b + 4
-3 -2 -1
0
27. Write in simplest form
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1 2
3
4
5
6 7
8
9 10
a.
54
96
b.
c.
r7
r4
d. 4x3 y6 7x2 y4
e.
r 8 d11
r 10 d 6
f. 34 ∙ 37
11k 3
33k 2
5
28. Find the missing exponent.
29. Find the product.
a.
4? ∙ 43 = 412
Write your answer using only positive exponents.
m-2 ∙ m3 ∙ m-7
b. 7-5 ∙ 711
c. x0 ∙ x-11
30. Find the quotient. Write your answer using only positive exponents.
a.
a
12
b.
a7
x
7
x9
a. -24 x8 y -4
31. Write the expression using only positive exponents.
b. -20 x5 y-2
120
32. Simplify
29 7 11
,
,
32 8 16
33. Order the numbers from least to greatest.
34. Jerome needs to draw a line that is 0.125 inch long using a ruler. What is the length of the line Jerome needs to
draw expressed as a fraction reduced to lowest terms?
a.
1
in.
16
b.
1
in
8
c.
35. Order the decimals from least to greatest.
36. Order the numbers from least to greatest.
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6
in.
48
0.336,
.7, -1,
d.
0.3 6 ,
4
in.
25
0. 36 ,
0. 336
5 4
9
,
, -2.3,
4 3
2
6
19
–
34p
37. Simplify the expression.
a.
38. Find the sum or difference.
a. 11
c.
39. Find the product.
40. Find the quotient.
a.
a.
6
-
7
34p
3
2
+2
7
7
1
1
–3
4
6
2 4
∙
3 5
b. -10
7
4
÷
11
11
b.
9b
15b
–
26
26
b.
-
b.
5
7
– 16
16
d.
8
2
–
9
3
3
5
7
÷ 4
3
+
3
16
c. 4
1
2
c. -5 ÷
5
11
4
of the mineral rights on a piece of property. She wants to divide these rights equally among 4
9
children. What fractional part of the mineral rights will each child get?
41. Jennifer owns
42. Solve the equation and check your solution.
a.
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140 =
5
x
7
b. -
2
x = 36
7
7
43. Maureen O'Brien teaches a drafting and architecture class in the evening. She charges a materials fee of $20.00
plus $9.00 per hour of instruction. How many hours of instruction must Mrs. O'Brien teach in order to collect
$110.00? Model the situation using an equation, then solve the equation.
44. A class is attended by 28 boys and 20 girls. Write the ratio of boys to students in the class as a fraction in lowest
terms.
45. Write the ratio 45 : 20 as a fraction in simplest form and in two other ways.
Simpliest Form: _________________
46. Write the equivalent rate.
_____________ and _____________
$75
? dollars
=
day
year
47. Which is the best buy?
a. $10.12 for 4 cans of salsa
c. $40.64 for 16 cans of salsa
48.
Solve
b. $12.80 for 5 cans of salsa
d. $18.06 for 7 cans of salsa
12
m
=
16
144
49. Two ounces of a breakfast shake provides 6 grams of protein. How many ounces of the product would be
needed to provide 72 grams of protein?
50. A worker in an assembly line takes 4 hours to produce 23 parts. At that rate, how many parts can she produce in
16 hours?
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51. Andrew owns a lawn-mowing business and mows the lawns of 43 customers each week.
Last week the business earned $870.75. How many weeks will it take to earn $6095.25?
52. Name the corresponding sides and the corresponding angles.
N
ΔRUN
H
R
ΔOHP
O
U
P
53. The two rectangles are similar. Find the width of the smaller rectangle. (The figures may not be drawn to scale.)
8m
12.8m
w
9.92m
54. A building casts a shadow 92 meters long. At the same time, a pole 5 meters high casts a shadow 10 meters
long. What is the height of the building?
55. Felix wants to find the height of the tallest building in his city. He stands 388 feet away
from the building. There is a tree 38 feet in front of him, which he knows is 15 feet tall.
How tall is the building? (Round to the nearest foot.)
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56. On a blueprint, the scale indicates that 6 centimeters represent 20 feet. What is the length and the width
of a room that is 13.2 centimeters long and 5 centimeters wide on the blueprint?
57. A jar contains 10 blue marbles, 4 red marbles, and 8 white marbles. What are the odds of drawing a blue
marble from the bag? not drawing a red marble from the bag?
58. You spin the spinner shown. Each section of the spinner has the same area. Find the probability of not
landing on white.
59. A lock has a 4-digit combination. Each of the digits is a number from 0 to 9. Find the probability that the
combination of the lock is "1234".
60. A clothing store offers a sweater in 4 different sizes, 3 different colors, and 2 types of sleeves.
How many types of the sweater does the store sell?
61. Find 25% of 36
62. 18 is 60% of what number?
63. What number is 35% of 400?
64. What percent of 20 is 12?
65. A golf group planned a trip to Hawaii and 26 of the members signed up to go. If this is 20% of the total
membership, how many members are in the golf group?
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66. Write the percent as a decimal 123%
67. Write
17
as a percent.
18
68. Find the new amount
a. Increase 90 by 60%.
b. Decrease 35 by 80%.
69. Tell whether the change is an increase or decrease. Then find the percent of change.
Round your answer to the nearest tenth if necessary.
Original: 92
New:
89.9
Original: 137
New:
459
70. In 1985, the circulation of a local newspaper was 4880. In 1986, its circulation was 1470.
Find the percent of change in the newspaper's circulation. Is this a percent of increase or
decrease?
71. Find the new amount:
Original price: $9
Discount percent: 30%
Original price: $14.57
Markup percent: 105%
72. Find the simple interest earned on the account.
a.
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P = $1250, r = 6%, t = 3 years
b. P = $4525, r = 4.5%, t = 57 months
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