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Basic Algebra
No calculator unless specified otherwise.
1. What numbers sum to 10?
2. 2
ex. 1
9, 2
8
10
3. 5 36
4. What coin combinations make a dollar?
31
ex. 4 quarters
5. 800/40
6.
14
7.
5
7
8
20
20 . Find
.
6
. Find
.
12
8. What time is it?
7:40
9. Draw the hour and minute hand of a clock at time 23 : 30
10. 4500
2500
7000
11. 12.34
0.27
12.61
12. 789
3945
5
13. How many zeros do the following large number have?
a. Million
6
b. Billion
9
c. Trillion
12
d. Quadrillion
15
e. Googol
100
10googol
14. What is Googolplex?
15. Approximately how many stars are there in our universe?
16. 5
x
3 . Find x.
2
17. Mentally multiply to up to 15 15
18. True or False: 5
19. True or False:
20. True or False: 0
21. 0/1
22. 1
23.
1 sextillion
3
0
156
true
2
2
ex. 12 13
false
true
0
0
0
0
24. Evaluate 32 27
undefined
undefined
864
25. 2.3 0.8
26. Mentally evaluate 1200
30
27. Use long division to evaluate 168
7
28. Use long division to evaluate 200
3
a. Identify the quotient, remainder, and divisor.
b. Express 200
c. True or False: 2
29.
2
( 3)
31. 2
( 3)
32. 2
2
33.
34.
35.
2
3
3
5
36. 2
37. 2
39.
4
3
5
2
3
2
38. 2
2
3
1
5
2
3
1
2/3
2
2
1
42. 2 3
43. 10
01
44. 210
45. 00
46.
4
47.
100
48.
1
49.
196
50.
0
1
5
40. ( 3 / 4)
41.
( 2)(5)
3
2
3
( 1)
1
1
2
2
means 2
2
( 2) ( 3)( 2)
7
1
5
30. 5
34
2
5
1/ 5
b
2 in the form a
(( 1 / 3) ( 5 / 2))
c
1
2
but 2
1
2
means 2
1
2
1
51.
52.
4
9
16
169
53. List the first 5 perfect squares.
54. List the first 5 perfect cubes.
55. Is 64 a perfect cube?
56. Is 80 a perfect cube?
57. Estimate the square root of 30.
58. List the first 5 prime numbers (hint: 1 is not considered to be a prime number).
59. What is the prime factorization of 180?
60. What are the prime factors of 180?
61. What is the greatest common factor of 4 and 6?
62. What is the least common multiple of 4 and 6?
63. What is the greatest common factor of 4, 10, and 12?
64. What is the least common multiple of 4, 10, and 12?
65. Convert to a decimal number:
a. 1/10
b. 1/3
c. 2/3
d. 5/3
e. 3/1000
66. Rewrite 1/2 as:
a. A decimal number
b. As a percent
c. As a ratio
67. Express 0.2% as a:
a. Decimal
b. Fraction in lowest terms
68. Express 3:12 as a fraction in lowest terms.
69. Draw a jar of jelly beans where three is a ratio of 2:3 white to black jelly beans.
70. A string is cut into three pieces whose lengths form a ratio of 2:3:5. If the string was 200 cm long, how
long are the pieces?
71. Which of the following is the best buy? Deal A: 500 mL of juice for $2.49. Deal B: 250 mL of juice for
$1.89. Deal C: 4L of juice for $11.
72. You decide to build your own computer desktop. Click here to see how fast a new video card is.
Which video card would you choose if you want a strong video card at the best value? Justify your
answer by calculating the unit cost per PassMark performance unit P.
73. Suppose you earn a salary of $50,000 and are taxed at a rate of 20%.
a. How much take home case do you make each day? (assume 365 days in a year).
b. Suppose you have the following monthly bills: rent ($1,000), car bills ($500), student loans
($500). How much take home cash do you have left over each day? You still haven’t paid for
other things including: food, clothes, utilities, travel, investments, etc.
74. There is a “buy one and get one free – equal to or less than in value” sale happening at your favorite
clothing store. You buy three items at the following prices: shirt ($20), pants ($30), and a belt ($10).
You qualify to get one of these items for free. With a tax rate of 12%, how much do you end up paying
in total?
75. Suppose you have two Starbucks drinks a day at $6 for each drink. If you were to invest this money at
a rate of 8% interest, how much money would you have by the time you retire? Try this compound
interest calculator.
76. Simplify
a. 1x
3x
b.
x
c.
2
12 . Solve x.
77. 3x
78. Distance Speed Time formula: d
s
t
a. You travel at the rate of 10 m/s for 50 seconds. How far do you travel? Specify units.
b. You travel 40 km in 8 hours. What is your average speed?
79. Solve the following basic equations
a.
3a
a
10
b. 3x
2
7
c.
z
5z
3z
2
80. Expand:
a. 2(x
b.
3)
x)
2(3
c.
5(1
d.
(t
4w )
3)
81. Do you have to use cross multiplying to solve the following?
a.
x
3
2
5
b.
c.
d.
e.
f.
g.
h.
i.
p
5
2
t
3
4
5
3
5
x
7
1
3
2
x
1
5
w
2x
7
3
2
3
7
3x
5
x
2
2x
3
2
1
3
82. Draw a right triangle with square boxes on each side to show that c 2
a2
b 2 is a plausible equation.
83. Challenge: Prove the Pythagorean Theorem.
84. Solve x in the triangle below:
85. Solve x in the triangle below:
86. Use the Pythagorean Theorem twice to find the diagonal distance across a 3 4 12 m box.
87. 1
2
88. 1
2x
(4 / 5)2
3
2 / 3(x
6)
89. Simplify
a. (x 2
2x
4)
(2x 2
b. (5x
7)
(2x
3)
c.
2n (n
d. (15k 2
90. Represent (2x
3x
4)
7)
10k )
(5k )
1) (x
2) using algebra tiles.