1.E: Review Exercises and Sample Exam
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Review Exercises
Choose an appropriate scale and graph the following sets of real numbers on a number line.
- {−4,0,4}
- {−30,10,40}
- {−12,−3,9}
- {−10,8,10}
- Answer
-
1.
Figure 1.E.1
3.
Figure 1.E.2
Fill in the blank with <,=, or >.
- 0_−9
- −75_−5
- −12_−(−3)
- −(−23)_23
- |−20|_−|−30|
- −|6|_−|−(−8)|
- Answer
-
1. >
3. <
5. >
Determine the unknown.
- |?|=2
- |?|=1
- |?|=−7
- |?|=0
- Answer
-
1. ±2
3. Ø, No solution
Translate the following into a mathematical statement.
- Negative eight is less than or equal to zero.
- Seventy-eight is not equal to twelve.
- Negative nine is greater than negative ten.
- Zero is equal to zero.
- Answer
-
1. −8≤0
3. −9>−10
Simplify.
- 12+(−7)
- 20+(−32)
- −23−(−7)
- −8−(−8)
- −3−(−13)+(−1)
- 9+(−15)−(−8)
- (7−10)−3
- (−19+6)−2
- Answer
-
1. 5
3. −16
5. 9
7. −6
Find the distance between the given numbers on a number line.
- −8 and 14
- −35 and −6
- What is 2 less than 17?
- What is 3 less than −20?
- Subtract 30 from the sum of 8 and 12.
- Subtract 7 from the difference of −5 and 7.
- An airplane flying at 22,000 feet descended 8,500 feet and then ascended 5,000 feet. What is the new altitude of the airplane?
- The width of a rectangle is 5 inches less than its length. If the length measures 22 inches, then determine the width.
- Answer
-
1. 22 units
3. 15
5. −10
7. 18,500 feet
Simplify.
- 10÷5⋅2
- 36÷6⋅2
- −6(4)÷2(−3)
- 120÷(−5)(−3)(−2)
- −8(−5)÷0
- −24(0)÷8
- Find the product of −6 and 9.
- Find the quotient of −54 and −3.
- James was able to drive 234 miles on 9 gallons of gasoline. How many miles per gallon did he get?
- If a bus travels at an average speed of 54 miles per hour for 3 hours, then how far does the bus travel?
- Answer
-
1. 4
3. 36
5. Undefined
7. −54
9. 26 miles per gallon
Reduce each fraction to lowest terms.
- 180300
- 252324
- Convert to a mixed number: 238.
- Convert to an improper fraction: 359.
- Answer
-
1. 35
3. 278
Simplify.
- 35(−27)
- −58(−13)
- −34÷67
- 415÷283
- 445÷6
- 5÷813
- 54÷152⋅6
- 524÷32÷512
- 112−14
- 56−314
- 34+23−112
- 310+512−16
- Subtract 23 from the sum of −12 and 29.
- Subtract 56 from the difference of 13 and 72.
- If a bus travels at an average speed of 54 miles per hour for 213 hours, then how far does the bus travel?
- Determine the length of fencing needed to enclose a rectangular pen with dimensions 1212 feet by 834 feet.
- Answer
-
1. −635
3. −78
5. 45
7. 1
9. −16
11. 43
13. −1718
15. 126 miles
- Write as a mixed number: 5.32.
- Write as a decimal: 7325
- Answer
-
1. 5825
Perform the operations.
- 6.032+2.19
- 12.106−9.21
- 4.23×5.13
- 9.246÷4.02
- Answer
-
1. 8.222
3. 21.6999
Convert to a decimal.
- 7.2%
- 538%
- 147%
- 2712%
- Answer
-
1. 0.072
3. 1.47
Convert to a percent.
- 0.055
- 1.75
- 910
- 56
- Mary purchased 3 boxes of t-shirts for a total of $126. If each box contains 24 t-shirts, then what is the cost of each t-shirt?
- A retail outlet is offering 12% off the original $39.99 price of tennis shoes. What is the price after the discount?
- If an item costs $129.99, then what is the total after adding 714% sales tax?
- It is estimated that 8.3% of the total student population carpools to campus each day. If there are 13,000 students, then estimate the number of students that carpool to campus.
- Answer
-
1. 5.5%
3. 90%
5. $1.75
7. $139.41
Simplify.
- 82
- (−5)2
- −42
- −(−3)2
- (29)2
- (123)2
- 33
- (−4)3
- (25)3
- (−16)3
- −(−2)4
- −(−1)5
- √49
- √225
- 2√25
- −√121
- 3√50
- −4√12
- 4√9
- 8√25
- Calculate the area of a square with sides measuring 3 centimeters. (A=s2)
- Calculate the volume of a cube with sides measuring 3 centimeters. (V=s3)
- Determine the length of the diagonal of a square with sides measuring 3 centimeters.
- Determine the length of the diagonal of a rectangle with dimensions 2 inches by 4 inches.
- Answer
-
1. 64
3. −16
5. 481
7. 27
9. 8125
11. −16
13. 7
15. 10
17. 15√2
19. 23
21. 9 square centimeters
23. 3√2 centimeters
Simplify.
- −5(2)−72
- 1−42+2(−3)2
- 2+3(6−2⋅4)3
- 5−3(8−3⋅4)2
- −23+6(32−4)+(−3)2
- 52−40÷5(−2)2−(−4)
- 34[29(−3)2−4]2
- (12)2−34÷916−13
- 2−3(6−32)24⋅5−52
- (2⋅8−62)2−10273−(2(−5)3−7)
- 8−5|3⋅4−(−2)4|
- |14|−|−3−52|
- Answer
-
1. −59
3. −22
5. 31
7. 3
9. 5
11. −12
Find the distance between the given numbers on a number line.
- −14 and 22
- −42 and −2
- 78 and −15
- −512 and −114
- Answer
-
1. 36 units
3. 4340 units
Sample Exam
- List three integers greater than −10.
- Determine the unknown(s): |?|=13.
- Fill in the blank with <,=, or : −|−100|_92.
- Convert to a fraction: 3313%
- Convert to a percent: 234.
- Reduce: 75225.
- Answer
-
1. {−5,0,5} (answers may vary)
3. <
5. 275%
Calculate the following.
- a. (−7)2; b. −(−7)2; c. −72
- a. (−3)3; b. −(−3)3; c. −33
- a. |10|; b. −|−10|; c. −|10|
- Answer
-
1. a. 49; b. −49; c. −49
3. a. 10; b. −10; c. −10
Simplify.
- −(−(−1))
- 23+15−310
- 10−(−12)+(−8)−20
- −8(4)(−3)÷2
- 12⋅(−45)÷1415
- 35⋅12−23
- 4⋅5−20÷5⋅2
- 10−7(3−8)−52
- 3+2|−22−(−1)|+(−2)2
- 13[52−(7−|−2|)+15⋅2÷3]
- √116
- 3√72
- Answer
-
2. 1730
4. 48
6. −1130
8. 20
10. 10
12. 18√2
- Subtract 2 from the sum of 8 and −10.
- Subtract 10 from the product of 8 and −10.
- A student earns 9,8,10,7, and 8 points on the first 5 chemistry quizzes. What is her quiz average?
- An 834 foot plank is cut into 5 pieces of equal length. What is the length of each piece?
- Answer
-
2. −90
4. 134 feet