Name: ________________________
Class: ___________________
Date: __________
Summer work for students entering Algebra 1 / Algebra 1 Honors
Find the greatest common factor of the numbers.
1. 14 and 38
2. 35, 63, and 84
Find the least common multiple of the set of numbers.
3. 6, 9, and 12
Find the value of x that completes the statement.
4.
x
10
=
36
6
Write the fraction in simplest form.
5.
6.
14
24
148
264
1
ID: A
Name: ________________________
ID: A
Write as a decimal.
7.
1
2
Write as a fraction in simplest form.
8. 0.32
9. 0.111111. . .
Add or subtract. Write each answer in simplest form.
10.
6
9
+
10
10
11.
1
2
+
5
12
12. 6
1
5
+5
3
6
13. 8
3
1
–4
4
4
2
Name: ________________________
ID: A
Multiply or divide. Write your answer in simplest form.
14.
3
7
×
6
10
15.
5
2
÷
12
8
16. 1
1
5
×1
3
9
17. 1
1
1
÷2
3
2
Write as a percent.
18.
1
5
19. Write 50% as a decimal.
20. Write 670% as a fraction or mixed number in simplest form.
3
Name: ________________________
ID: A
2
21. Write 5 in standard form.
22. Write 3954 in expanded form using powers of 10.
What is each number written in standard notation?
23. 3.6 × 10 6
24. 6.49 × 10 −4
Find the product or quotient. Write the answer in scientific notation and in standard form. Round
to the appropriate number of significant digits.
25. (8.55 × 10 2 ) (4.36 × 10 −4 )
26. (−8.35 × 10 2 ) (3.14 × 10 −4 )
27. (3.3 × 10 2 ) ÷ (6.43 × 10 3 )
4
Name: ________________________
ID: A
Find the perimeter of the figure.
28.
Find the area of the figure.
29.
30.
5
Name: ________________________
ID: A
Find the volume of the solid. Round to the nearest tenth if necessary. Use 3.14 for π.
31.
32.
33. A cylinder has a volume of 19 cm3 . If the radius is doubled, what is the volume of the new cylinder?
34. A large aquarium is 8 m by 6 m by 5 m. What is the difference in the volume of the aquarium if its dimensions
are doubled?
35. Display the set of data in a line plot.
58, 55, 54, 61, 56, 54, 61, 55, 53, 54
6
Name: ________________________
ID: A
36. The frequency table below shows the ages of the first ten people in line at the movie theater. Make a line plot
that shows the same data as the frequency table.
Ages
Frequency
22
3
23
2
27
2
29
1
30
2
37. List all the factors of 16.
Estimate by rounding.
38. $14.49 + $68.64 + $128.05
39. 436 + 317
Use front-end estimation.
40. $4.79 + $3.51 + $2.26
41. 9.456 + 6.166
7
Name: ________________________
ID: A
Draw a circle graph for the given data.
42.
Expense
Cost per Month ($)
Housing
320
Food
200
Other
280
43.
Cost of Owning a Car
Category
Purchase price
Interest
Insurance
Gas, oil, and maintenance
License and registration
Percent
52%
12%
13%
20%
3%
Make a back-to-back stem-and-leaf plot of the set of data.
44. Set 1:
33 32 41 58 25 23 16 17 19 21 25 32
Set 2:
20 22 32 15 17 19 35 44 50 12 51 52
What is an algebraic expression for the word phrase?
45. the difference of r and 3
8
Name: ________________________
ID: A
46. the quotient of j and 8
47. the quotient of 8 and the difference of x and m
48. 6 times the difference of b and p
What word phrase can you use to represent the algebraic expression?
49. 3m
What is the simplified form of each expression?
2
50. 5 (14 − 2 ) ÷ 2
51. 4(20 + 12) ÷ (4 − 3)
52. 5(4 + 10) ÷ (8 − 1)
3
53. 3 ⋅ 32 + 12 ÷ 4
9
Name: ________________________
ID: A
54. Evaluate u + xy, for u = 18, x = 10, and y = 8.
55. Evaluate
u
2
+ xy , for u = 20, x = 4, y = 7, and z = 10.
z
2
56. Evaluate (ab) for a = 4 and b = 3.
What is the simplified form of each expression?
57.
169
58.
25
100
59.
1
169
60. A square field has an area of 479 ft2 . What is the approximate length of a side of the field? Give your answer
to the nearest foot.
10
Name: ________________________
ID: A
61. To which subsets of the real numbers does the number 22 belong?
62. To which subsets of the real numbers does the number
63. What is an inequality that compares the numbers
64. What is the order of
5 , –0.1, –
65. What is the order of
5 , 0.6,
5
, 0.7,
3
4
, 0.7,
9
42 belong?
70 and 8
1
?
2
2 from least to greatest?
2 from least to greatest?
What property is illustrated by each statement?
66. −2.1 × 1 = −2.1
67. 0 + x = x
68. 8 + 8.3 = 8.3 + 8
11
Name: ________________________
ID: A
69. At the video store, you buy two CDs for $18.90 each and a DVD for $20.50. Use mental math to find the
total cost of your purchases.
70. At the grocery store, you buy a carton of milk for $3.90, a loaf of bread for $1.95, and a bag of cookies for
$3.05. Use mental math to find the total cost of the groceries.
What is each sum?
71. –7 + 5
72. –6 + (–3)
73. –6.1 + 1.7
What is each difference?
74. –1.8 – 3.9
75. 8 – 8
12
Name: ________________________
ID: A
76. A mountain climber ascends a mountain to its peak. The peak is 12,740 ft above sea level. The climber then
descends 200 ft to meet a fellow climber. Find the climber’s elevation above sea level after meeting the other
climber.
77. You made two deposits to your bank account this month. One deposit was $17.92, and the second deposit was
$15.33. Your balance at the end of the month is $72.31, and you made no withdrawals. Write and evaluate an
expression for your balance at the beginning of the month.
What is each product?
78. 8(–1)
79. 4.3(–2.9)
80.
5 10
•
10 3
81. (−6.8 )
2
What is the simplified form of each expression?
82. −
196
13
Name: ________________________
83. ±
ID: A
100
49
What is the simplified form of each expression?
84.
1
(21m + 27)
3
85.
3
(–28m + 20)
4
86. (4 – c)(–1)
87. (2 – 9c)(–8)
What is the simplified form of each expression?
2
2
88. 1.7m + 6.5n − 4n + 2.5m − n
2
2
89. 2.5m + 7.8n − 3.2n + 5.3m − 5.9n
14
Name: ________________________
ID: A
What sum or difference is equivalent to the expression?
90.
3x + 2
8
91.
3x − 2
9
What is the simplified form of each expression?
92. − (8d − 3w)
93. T-shirts cost $12.90 each. What is the total cost of 4 T-shirts? Use mental math.
What is the solution of each equation? Use mental math.
94. x + 3 = 17?
95.
x
= 10?
9
9
C + 32 changes a temperature reading from the Celsius scale C to the Fahrenheit scale F.
5
What is the temperature measured in degrees Fahrenheit when the Celsius temperature is 10°C?
96. The formula F =
15
Name: ________________________
ID: A
97. In the expression 6pq + 8p − 6r, what is the coefficient of the term 6pq?
Is the equation true, false, or open? Explain.
98. 20 − 1 = 1 + 17
Is the statement true or false? If it is false, give a counterexample.
2
2
99. For all real numbers a and b, 2a ⋅ b = a + b .
16