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Mathematics LibreTexts

1.E: Review Exercises and Sample Exam

  • Anonymous
  • LibreTexts

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Review Exercises

Exercise 1.E.1 Real Numbers and the Number Line

Choose an appropriate scale and graph the following sets of real numbers on a number line.

  1. {4,0,4}
  2. {30,10,40}
  3. {12,3,9}
  4. {10,8,10}
Answer

1.

Screenshot (977).png

Figure 1.E.1

3.

Screenshot (979).png

Figure 1.E.2

Exercise 1.E.2 Real Numbers and the Number Line

Fill in the blank with <,=, or >.

  1. 0_9
  2. 75_5
  3. 12_(3)
  4. (23)_23
  5. |20|_|30|
  6. |6|_|(8)|
Answer

1. >

3. <

5. >

Exercise 1.E.3 Real Numbers and the Number Line

Determine the unknown.

  1. |?|=2
  2. |?|=1
  3. |?|=7
  4. |?|=0
Answer

1. ±2

3. Ø, No solution

Exercise 1.E.4 Real Numbers and the Number Line

Translate the following into a mathematical statement.

  1. Negative eight is less than or equal to zero.
  2. Seventy-eight is not equal to twelve.
  3. Negative nine is greater than negative ten.
  4. Zero is equal to zero.
Answer

1. 80

3. 9>10

Exercise 1.E.5 Adding and Subtracting Integers

Simplify.

  1. 12+(7)
  2. 20+(32)
  3. 23(7)
  4. 8(8)
  5. 3(13)+(1)
  6. 9+(15)(8)
  7. (710)3
  8. (19+6)2
Answer

1. 5

3. 16

5. 9

7. 6

Exercise 1.E.6 Adding and Subtracting Integers

Find the distance between the given numbers on a number line.

  1. 8 and 14
  2. 35 and 6
  3. What is 2 less than 17?
  4. What is 3 less than 20?
  5. Subtract 30 from the sum of 8 and 12.
  6. Subtract 7 from the difference of 5 and 7.
  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?
  8. 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

Exercise 1.E.7 Multiplying and Dividing Integers

Simplify.

  1. 10÷52
  2. 36÷62
  3. 6(4)÷2(3)
  4. 120÷(5)(3)(2)
  5. 8(5)÷0
  6. 24(0)÷8
  7. Find the product of 6 and 9.
  8. Find the quotient of 54 and 3.
  9. James was able to drive 234 miles on 9 gallons of gasoline. How many miles per gallon did he get?
  10. 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

Exercise 1.E.8 Fractions

Reduce each fraction to lowest terms.

  1. 180300
  2. 252324
  3. Convert to a mixed number: 238.
  4. Convert to an improper fraction: 359.
Answer

1. 35

3. 278

Exercise 1.E.9 Fractions

Simplify.

  1. 35(27)
  2. 58(13)
  3. 34÷67
  4. 415÷283
  5. 445÷6
  6. 5÷813
  7. 54÷1526
  8. 524÷32÷512
  9. 11214
  10. 56314
  11. 34+23112
  12. 310+51216
  13. Subtract 23 from the sum of 12 and 29.
  14. Subtract 56 from the difference of 13 and 72.
  15. If a bus travels at an average speed of 54 miles per hour for 213 hours, then how far does the bus travel?
  16. 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

Exercise 1.E.10 Decimals and Percents
  1. Write as a mixed number: 5.32.
  2. Write as a decimal: 7325
Answer

1. 5825

Exercise 1.E.11 Decimals and Percents

Perform the operations.

  1. 6.032+2.19
  2. 12.1069.21
  3. 4.23×5.13
  4. 9.246÷4.02
Answer

1. 8.222

3. 21.6999

Exercise 1.E.12 Decimals and Percents

Convert to a decimal.

  1. 7.2%
  2. 538%
  3. 147%
  4. 2712%
Answer

1. 0.072

3. 1.47

Exercise 1.E.13 Decimals and Percents

Convert to a percent.

  1. 0.055
  2. 1.75
  3. 910
  4. 56
  5. 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?
  6. A retail outlet is offering 12% off the original $39.99 price of tennis shoes. What is the price after the discount?
  7. If an item costs $129.99, then what is the total after adding 714% sales tax?
  8. 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

Exercise 1.E.14 Exponents and Square Roots

Simplify.

  1. 82
  2. (5)2
  3. 42
  4. (3)2
  5. (29)2
  6. (123)2
  7. 33
  8. (4)3
  9. (25)3
  10. (16)3
  11. (2)4
  12. (1)5
  13. 49
  14. 225
  15. 225
  16. 121
  17. 350
  18. 412
  19. 49
  20. 825
  21. Calculate the area of a square with sides measuring 3 centimeters. (A=s2)
  22. Calculate the volume of a cube with sides measuring 3 centimeters. (V=s3)
  23. Determine the length of the diagonal of a square with sides measuring 3 centimeters.
  24. 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. 152

19. 23

21. 9 square centimeters

23. 32 centimeters

Exercise 1.E.15 Order of Operations

Simplify.

  1. 5(2)72
  2. 142+2(3)2
  3. 2+3(624)3
  4. 53(834)2
  5. 23+6(324)+(3)2
  6. 5240÷5(2)2(4)
  7. 34[29(3)24]2
  8. (12)234÷91613
  9. 23(632)24552
  10. (2862)210273(2(5)37)
  11. 85|34(2)4|
  12. |14||352|
Answer

1. 59

3. 22

5. 31

7. 3

9. 5

11. 12

Exercise 1.E.16 Order of Operations

Find the distance between the given numbers on a number line.

  1. 14 and 22
  2. 42 and 2
  3. 78 and 15
  4. 512 and 114
Answer

1. 36 units

3. 4340 units

Sample Exam

Exercise 1.E.17
  1. List three integers greater than 10.
  2. Determine the unknown(s): |?|=13.
  3. Fill in the blank with <,=, or  : |100|_92.
  4. Convert to a fraction: 3313%
  5. Convert to a percent: 234.
  6. Reduce: 75225.
Answer

1. {5,0,5} (answers may vary)

3. <

5. 275%

Exercise 1.E.18

Calculate the following.

  1. a. (7)2; b. (7)2; c. 72
  2. a. (3)3; b. (3)3; c. 33
  3. a. |10|; b. |10|; c. |10|
Answer

1. a. 49; b. 49; c. 49

3. a. 10; b. 10; c. 10

Exercise 1.E.19

Simplify.

  1. ((1))
  2. 23+15310
  3. 10(12)+(8)20
  4. 8(4)(3)÷2
  5. 12(45)÷1415
  6. 351223
  7. 4520÷52
  8. 107(38)52
  9. 3+2|22(1)|+(2)2
  10. 13[52(7|2|)+152÷3]
  11. 116
  12. 372
Answer

2. 1730

4. 48

6. 1130

8. 20

10. 10

12. 182

Exercise 1.E.20
  1. Subtract 2 from the sum of 8 and 10.
  2. Subtract 10 from the product of 8 and 10.
  3. A student earns 9,8,10,7, and 8 points on the first 5 chemistry quizzes. What is her quiz average?
  4. 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


This page titled 1.E: Review Exercises and Sample Exam is shared under a not declared license and was authored, remixed, and/or curated by Anonymous via source content that was edited to the style and standards of the LibreTexts platform.

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