Module 1 Problem Sets

The correct answer is b. The base is 2 (the number of outcomes) and the exponent is 4 (the number of flips). 2⁴ = 2 x 2 x 2 x 2 = 16.

A coin is flipped 4 times. How many different outcomes are there? a) 8 b) 16 c) 32 d) 64

The correct answer is c. The base is 6 (the number of outcomes) and the exponent is 3 (the number of rolls). 6³ = 6 x 6 x 6 = 216.

A die is rolled three times. How many different outcomes are there? a) 18 b) 36 c) 216 d) 648

The correct answer is c. The estimated number of miles is 15 + 12 + 22 + 21 = 70 miles.

A runner runs 14.5 miles, 12.25 miles, 21.75 miles, and 20.8 miles. What is an accurate estimate for the total number of miles? a) 65 b) 67 c) 70 d) 74

The correct answer is c. The base is 10 and the exponent is 5. 10⁵ = 10 x 10 x 10 x 10 x 10 = 100,000.

Calculate the following: The distance between two planets is 10⁵ kilometers. What is the actual distance? a) 10 b) 10,000 c) 100,000 d) 100,000,000

The correct answer is b. √3 is only a real number. Its complete decimal expansion goes on forever without repeating.

Please complete the following to make a true statement: √3 is a(an) a) integer. b) only a real number. c) rational number. d) whole number.

The correct answer is a. (-3)⁴ = -3 x -3 x -3 x -3 = 81.

Please evaluate the following exponential expression: (-3)⁴ a) -81 b) -12 c) 12 d) 81

The correct answer is d. 10³ = 10 x 10 x 10 = 1,000.

Please evaluate the following exponential expression: 10³ a) 10 b) 30 c) 300 d) 1,000

The correct answer is a. A negative times a negative is a positive product. A positive times a negative is a negative product. -6 x -5 x -4 = 30 x -4 = -120

Please evaluate the following expression :-6 x -5 x -4 a) -120 b) -100 c) 100 d) 120

The correct answer is b. Exponents should be calculated first, then we can add and subtract from left to right. 4² - 8 + 10 = 16 - 8 + 10 = 8 + 10 = 18

Please evaluate the following expression using order of operations: 4² - 8 + 10 a) 10 b) 18 c) 26 d) 34

The correct answer is b. First, evaluate the parenthesis, then evaluate the exponent, and lastly complete the addition. 8 + (6-3)² = 8 + (3)² = 8 + 9 = 17

Please evaluate the following expression using order of operations: 8 + (6-3)² a) 14 b) 17 c) 31 d) 35

The correct answer is d. (-4)² = -4 · -4 = 16.

Please evaluate the following expression: (-4)² a) -16 b) -8 c) 8 d) 16

The correct answer is d. First, evaluate the parenthesis, then evaluate the exponent, then, the multiplication, and lastly the subtraction. (7-3)² x 2 - 12 = (4)² x 2 - 12 = 16 x 2 - 12 = 32 - 12 = 20

Please evaluate the following expression: (7-3)² x 2 - 12 a) 3 b) 4 c) 19 d) 20

The correct answer is d. A negative times a negative is a positive product. -14 x -7 = 98.

Please evaluate the following expression: -14 x -7 a) -98 b) -78 c) 78 d) 98

The correct answer is a. -18 + (-10) - 4 = -28 - 4 = -32

Please evaluate the following expression: -18 + (-10) - 4 a) -32 b) -24 c) -12 d) -4

The correct answer is b. A negative divided by a positive is a negative quotient. -36 ÷ 3 = -12.

Please evaluate the following expression: -36 ÷ 3 a) -13 b) -12 c) 12 d) 13

The correct answer is c. 12 x 15 = 180.

Please evaluate the following expression: 12 x 15 a) 160 b) 170 c) 180 d) 190

The correct answer is a. 14 - 21 + (-3) = -7 + (-3) = -10

Please evaluate the following expression: 14 - 21 + (-3) a) -10 b) -4 c) 4 d) 10

The correct answer is b. 18 - 9 + 22 - 15 = 9 + 22 - 15 = 31 - 15 = 16.

Please evaluate the following expression: 18 - 9 + 22-15 a) 14 b) 16 c) 24 d) 26

The correct answer is d. 18 x 7 = 126.

Please evaluate the following expression: 18 x 7 a) 74 b) 76 c) 124 d) 126

The correct answer is d. The exponent is first, the solve from left to right. 20 - 11 + 2³ = 20 - 11 + 8 = 9 + 8 = 17

Please evaluate the following expression: 20 - 11 + 2³ a) 1 b) 3 c) 15 d) 17

The correct answer is c. 24 - (-15)- 17 = 24+15-17 = 39-17 = 22

Please evaluate the following expression: 24 - (-15)- 17 a) -26 b) -22 c) 22 d) 26

The correct answer is a. First, evaluate the parenthesis, then evaluate the exponent. Next, complete the division. Finally, complete the addition. 25 ÷ (3 + 2)² + 20 = 25 ÷ (5)² + 20 = 25 ÷ 25 + 20 = 1 + 20 = 21

Please evaluate the following expression: 25 ÷ (3 + 2)² + 20 a) 21 b) 30 c) 45 d) 57

The correct answer is c. The order of operations is 3 x 12 ÷ 2 - 6 = 36 ÷ 2 - 6 = 18 - 6 = 12

Please evaluate the following expression: 3 x 12 ÷ 2-6 a) 0 b) 6 c) 12 d) 18

The correct answer is d. 32 + 19 = 51.

Please evaluate the following expression: 32 + 19 a) 40 b) 41 c) 50 d) 51

The correct answer is b. 42 - 16 + 21 - 17 = 26 + 21 - 17 = 47 - 17 = 30

Please evaluate the following expression: 42 - 16 + 21 - 17 a) 28 b) 30 c) 38 d) 42

The correct answer is a. 51 - 18 = 33.

Please evaluate the following expression: 51 - 18 a) 33 b) 37 c) 43 d) 47

The correct answer is c. 64 ÷ 4 = 16.

Please evaluate the following expression: 64 ÷ 4 a) 4 b) 8 c) 16 d) 32

The correct answer is a. Solve from left to right. 83 - 31 - 13 - 8 = 52 - 13 - 8 = 39 - 8 = 31

Please evaluate the following expression: 83 - 31 - 13 - 8 a) 31 b) 33 c) 37 d) 39

The correct answer is b. 84 - 27 = 57.

Please evaluate the following expression: 84 - 27 a) 53 b) 57 c) 63 d) 67

The correct answer is a. √144 = 12.

Please evaluate the following expression: √144 a) 12 b) 13 c) 14 d) 15

The correct answer is b. √225 = 15.

Please evaluate the following expression: √225 a) 14 b) 15 c) 16 d) 17

The correct answer is d. √81 = 9.

Please evaluate the following expression: √81 a) 6 b) 7 c) 8 d) 9

The correct answer is c. -10 is a number with no decimal or fractional component and is an integer. If a number is an integer, it is also rational, because it can be written as a fraction, and it is real, because it can be placed on a number line.

-10 belongs to which set(s) of numbers? a) real b) real, rational c) real, rational, integer d) real, rational, integer, whole

The correct answer is d. 37 beds can be estimated at 40, which ensures that there will be more than enough sheets. 41 can be estimated at 40, which is lower than the reality but not by much. (Estimating 40 for 37 left more room.) Each of the beds will be changed twice: (40 + 40) × 2

Cori is in charge of ordering bed linens for two floors. The first floor has 37 beds, and the second floor has 41. Each bed is generally changed twice a day. What is a good estimate of the total number of sheet sets she will need each day? a) 35 × 2 b) (35 + 35) × 2 c) (35 + 40) × 2 d) (40 + 40) × 2

The correct answer is c. All values greater than -5 are true for the inequality. Greater than is denoted by a parenthesis and denotes that the value alongside it, in this example -5, is not to be included. The infinity symbol is always paired with a parenthesis, rather than a bracket. Therefore, (-5, ∞) is the interval notation.

Display x is greater than -5 using interval notation. a) (-∞, -5) b) (-∞, -5] c) (-5, ∞) d) [-5, ∞)

The correct answer is b. All values less than or equal to 4 are true for the inequality. Less than or equal to is denoted by a bracket and denotes that the value alongside it, in this example 4, is to be included. Also, the infinity symbol is always paired with a parenthesis rather than a bracket. Therefore, (-∞, 4] is the interval notation.

Display x less than or equal to 4 using interval notation. a) (-∞, 4) b) (-∞, 4] c) (4, ∞) d) [4, ∞)

The correct answer is b. All values greater than -8 and less than or equal to 8 are true. Less than or equal to is denoted by a bracket and denotes that the value alongside it, in this example 8, is to be included. Greater than to is denoted by a parenthesis and denotes that the value alongside it, in this example -8, is not to be included. Therefore, (-8, 8] is the interval notation.

Display -8 is less than x, x is less than or equal to 8 using interval notation. a) (-8, 8) b) (-8, 8] c) [-8, 8) d) [-8, 8]

The correct answer is a. A is the greatest number because it is to the right on the number line.

On the number line below, which letter is the greatest value? a) A b) B c) C d) D

The correct answer is d. -5000 is to the left of 0. Therefore, it is less than 0.

Please complete the following statement so that it is true: -5000 is a) greater than -3,000. b) greater than 0. c) less than -7,000. d) less than 0.

The correct answer is b. -250 lies to the right of -300 on a number line, and, therefore, it is greater than -300.

Please complete the following to make a true statement: -250 is a) greater than -200. b) greater than -300. c) less than -400. d) less than -500.

The correct answer is c. 4.4444 . . . is a repeating decimal and a rational number because it can be written as a fraction.

Please complete the following to make a true statement: 4.4444 . . . is a(an) a) integer. b) only a real number. c) rational number. d) whole number.

The correct answer is a. -4.5 is greater than -5 but is less than -4.

Select the true statement from the following: a) -4.5 is between -4 and -5. b) -3.8 is between -3 and -2. c) -2.3 is between -2 and -1. d) -1.2 is between -1 and 0.

The correct answer is c. 0.34 is greater than 0.335, but it is less than 0.35.

Select the true statement from the following: a) 0.15 is between 0.138 and 0.149. b) 0.22 is between 0.23 and 0.24. c) 0.34 is between 0.335 and 0.35. d) 0.46 is between 0.465 and 0.468.

The correct answer is d. 8,500 is greater than 8,485 but is less than 8,510.

Select the true statement from the following: a) 2,500 is between 2,450 and 2,475. b) 4,500 is between 4,510 and 4,535. c) 6,500 is between 6,470 and 6,495. d) 8,500 is between 8,485 and 8,510.

The correct answer is b. The approximate sum is 5 + 15 + 10 + 20 + 10, which is 60 minutes.

This week, your commutes into work have taken 4, 14, 12, 17, and 8 minutes. What is an accurate estimate for the the number of minutes you have spent driving? a) 45 b) 60 c) 65 d) 70

The correct answer is b. 113 has only two factors, 1 and 113, and so it is a prime number.

Which number is a prime number? a) 111 b) 113 c) 115 d) 117

The correct answer is c. 23 has only two factors, 1 and 23, and so it is a prime number.

Which number is a prime number? a) 21 b) 22 c) 23 d) 24

The correct answer is d. All of the positive factors of 105 include 1, 3, 5, 7, 15, 21, 35, 105.

What are all of the positive factors of 105? a) 1, 105 b) 1, 3, 35, 105 c) 1, 3, 5, 21, 35, 105 d) 1, 3, 5, 7, 15, 21, 35, 105

The correct answer is c. All of the positive factors of 72 include 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

What are all of the positive factors of 72? a) 1, 2, 4, 18, 36, 72 b) 1, 2, 4, 8, 12, 18, 24, 36, 72 c) 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 d) 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 32, 36, 48, 72

The correct answer is b. All of the positive factors of 80 include 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.

What are all of the positive factors of 80? a) 1, 2, 40, 80 b) 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 c) 1, 2, 4, 10, 20, 40, 50, 60, 80 d) 1, 2, 4, 5, 10, 20, 40, 50, 60, 80

The correct answer is c. 6 is the largest number that divides both into 30 and 48.

What is the greatest common factor of 30 and 48? a) 2 b) 4 c) 6 d) 8

The correct answer is a. 12 is the largest number that evenly divides both into 36 and 84.

What is the greatest common factor of 36 and 84? a) 12 b) 16 c) 18 d) 24

The correct answer is b. 20 is the largest number that divides both into 60 and 80.

What is the greatest common factor of 60 and 80? a) 10 b) 20 c) 30 d) 40

The correct answer is d. The prime factorization is 2 x 2 x 3 x 3.

What is the prime factorization of 36? a) 2 x 3 b) 2 x 2 x 3 c) 2 x 3 x 3 d) 2 x 2 x 3 x 3

The correct answer is b. The prime factorization is 2 x 2 x 13.

What is the prime factorization of 52? a) 2 x 13 b) 2 x 2 x 13 c) 2 x 2 x 2 x 13 d) 2 x 2 x 2 x 2 x 13

The correct answer is c. The prime factorization is 2 x 5 x 7.

What is the prime factorization of 70? a) 3 x 7 b) 5 x 7 c) 2 x 5 x 7 d) 3 x 5 x 7

The correct answer is c. 77 has factors of 1, 7, 11, and 77, so it is a composite number.

Which number is a composite number? a) 71 b) 73 c) 77 d) 79

The correct answer is a. The number of student in a school can be counted because it is a whole number, and therefore, it is discrete.

Which set of data is discrete? a) Number of students in a school b) The height of a maple tree c) The weight of a football player d) Distance between two towns

The correct answer is c. The number of adults in a household contains gaps and is discrete.

Which set of data is discrete? a) Speed of a car b) Weight of a dog c) Adults in a household d) Time to go to bed

The correct answer is c. The set of real numbers contains no gaps and is continuous.

Which set of numbers is continuous? a) integer b) rational c) real d) whole