Deck 8: Real Numbers and Algebraic Thinking

Question 1

Decide if the number is rational or irrational.
1.41421. . .

A)Irrational
B)Rational

Answer 1

A

Question 2

Classify the following number as rational or irrational.

A) Irrational
B) Rational

Answer 2

Irrational

Question 3

Classify the following number as rational or irrational.

A) Irrational
B) Rational

Answer 3

Irrational

Question 4

Decide if the number is rational or irrational.

Question 5

Decide if the number is rational or irrational.
1.28252626. . .

A)Irrational
B)Rational

Question 6

The quotient of any two distinct irrational numbers is irrational.

Question 7

Decide if the number is rational or irrational.
0.22582259. . .

A)Rational
B)Irrational

Question 8

Decide if the number is rational or irrational.

Question 9

The sum of a rational number and an irrational number could be rational.

Question 10

Classify the following number as rational or irrational.

A) Irrational
B) Rational

Question 11

The sum of any two positive irrational numbers is an irrational number.

Question 12

Decide if the number is rational or irrational.

Question 13

Decide if the number is rational or irrational.

Question 14

Classify the following number as rational or irrational.

A) Irrational
B) Rational

Question 15

The product of a non-zero rational number and an irrational number is irrational.

Question 16

Decide if the number is rational or irrational.

Question 17

The product of any two distinct positive irrational numbers is irrational.

Question 18

Decide if the number is rational or irrational.

Question 19

Decide if the number is rational or irrational.

Question 20

The quotient of an irrational number and a nonzero rational number could be rational.

Question 21

Simplify the radical.

Question 22

If R is the set of real numbers, Q is the set of rational numbers, I is the set of integers, N is the set of natural numbers, and
S is the set of irrational numbers, list the set(s)for which a solution to the given equation exists. If a solution to the given
equation does not belong to any set, state none.

Question 23

Simplify the radical.

Question 24

Find the square root, rounded to hundredths if necessary.

Question 25

Find the square root, rounded to hundredths if necessary.

Question 26

Find the square root, rounded to hundredths if necessary.

Question 27

Find the square root, rounded to hundredths if necessary.

Question 28

If R is the set of real numbers, Q is the set of rational numbers, I is the set of integers, N is the set of natural numbers, and
S is the set of irrational numbers, list the set(s)to which the given number belongs. If the number does not belong to any,
state none.

Question 29

Arrange the following real numbers in order from greatest to least.

Question 30

Find the square root, rounded to hundredths if necessary.

Question 31

Find the square root, rounded to hundredths if necessary.

Question 32

Find the square root, rounded to hundredths if necessary.

Question 33

If R is the set of real numbers, Q is the set of rational numbers, I is the set of integers, N is the set of natural numbers, and
S is the set of irrational numbers, list the set(s)to which the given number belongs. If the number does not belong to any,
state none.

Question 34

Simplify the radical.

Question 35

Find the square root, rounded to hundredths if necessary.

Question 36

Find the square root, rounded to hundredths if necessary.

Question 37

If R is the set of real numbers, Q is the set of rational numbers, I is the set of integers, N is the set of natural numbers, and
S is the set of irrational numbers, list the set(s)to which the given number belongs. If the number does not belong to any,
state none.

Question 38

Simplify the radical.

Question 39

If R is the set of real numbers, Q is the set of rational numbers, I is the set of integers, N is the set of natural numbers, and
S is the set of irrational numbers, list the set(s)to which the given number belongs. If the number does not belong to any,
state none.

Question 40

Simplify the radical.

Question 41

If R is the set of real numbers, Q is the set of rational numbers, I is the set of integers, N is the set of natural numbers, and
S is the set of irrational numbers, list the set(s)for which a solution to the given equation exists. If a solution to the given
equation does not belong to any set, state none.

Question 42

If the following is part of a geometric sequence, find the missing terms.

Question 43

If the following is part of a geometric sequence, find the missing terms.
33 less than a number

A)33 - n
B)n + 33
C)n - 33
D)33n

Question 44

Solve for x, where x is a real number.

Question 45

If the following is part of a geometric sequence, find the missing terms.
15 times a number

Question 46

Solve for x, where x is a real number.

Question 47

If the following is part of a geometric sequence, find the missing terms.
38 less than twice a number

Question 48

Leave the answer in exponential notation.

Question 49

Solve for x, where x is a real number.

Question 50

If R is the set of real numbers, Q is the set of rational numbers, I is the set of integers, N is the set of natural numbers, and
S is the set of irrational numbers, list the set(s)for which a solution to the given equation exists. If a solution to the given
equation does not belong to any set, state none.

Question 51

If the following is part of a geometric sequence, find the missing terms.
19 times the square of a number

Question 52

Solve for x, where x is a real number.

Question 53

Solve for x, where x is a real number.

Question 54

If R is the set of real numbers, Q is the set of rational numbers, I is the set of integers, N is the set of natural numbers, and
S is the set of irrational numbers, list the set(s)for which a solution to the given equation exists. If a solution to the given
equation does not belong to any set, state none.

Question 55

If the following is part of a geometric sequence, find the missing terms.
13 more than a number

A)13n
B)13 - n
C)n - 13
D)n + 13

Question 56

Solve for x, where x is a real number.

Question 57

If R is the set of real numbers, Q is the set of rational numbers, I is the set of integers, N is the set of natural numbers, and
S is the set of irrational numbers, list the set(s)for which a solution to the given equation exists. If a solution to the given
equation does not belong to any set, state none.

Question 58

If R is the set of real numbers, Q is the set of rational numbers, I is the set of integers, N is the set of natural numbers, and
S is the set of irrational numbers, list the set(s)for which a solution to the given equation exists. If a solution to the given
equation does not belong to any set, state none.

Question 59

If the following is part of a geometric sequence, find the missing terms.
The sum of 19 and a number

A)19 - n
B)n + 19
C)19n
D)n - 19

Question 60

Leave the answer in exponential notation.

Question 61

If the following is part of a geometric sequence, find the missing terms.
Find the 15th term of the following geometric sequence:

Question 62

If the following is part of a geometric sequence, find the missing terms.

Question 63

Write an expression in terms of the given variable(s)that represents the indicated quantity.
The cost of having an electrician spend h hours at your house if the electrician charges $48 for coming to the house and $x per hour for labor

A)48h + x dollars
B)48 + x dollars
C)48 + hx dollars
D)48x + h dollars

Question 64

If the following is part of a geometric sequence, find the missing terms.
Find the 100th term of the following arithmetic sequence:

Question 65

If the following is part of a geometric sequence, find the missing terms.
Find the nth term of the following arithmetic sequence:

Question 66

If the following is part of a geometric sequence, find the missing terms.

Question 67

Write an expression in terms of the given variable(s)that represents the indicated quantity.
The amount of money in cents in a jar containing n nickels and some dimes and some quarters if there are 3 times as many dimes as nickels and twice as many quarters as dimes.

A)185x cents
B)85x cents
C)175x cents
D)110x cents

Question 68

If the following is part of a geometric sequence, find the missing terms.
Find the nth term of the following arithmetic sequence:

Question 69

If the following is part of a geometric sequence, find the missing terms.
Find the nth term of the following arithmetic sequence: 1, -1, -3, -5, -7, . . .

Question 70

Write an expression in terms of the given variable(s)that represents the indicated quantity.
Joel's total earning after 3 years if the first year his salary was s dollars, the second year it was $7000 higher, and the third year it was twice as much as the first year.

A)4s + 7000 dollars
B)3s + 7000s dollars
C)3s + 7000 dollars
D)2s + 7000 dollars

Question 71

If the following is part of a geometric sequence, find the missing terms.
The difference between the cube of a number and four times the number

Question 72

If the following is part of a geometric sequence, find the missing terms.

Question 73

If the following is part of a geometric sequence, find the missing terms.
Find the 100th term of the following arithmetic sequence: 2, -2, -6, . . .

A)-394
B)-390
C)-398
D)-402

Question 74

If the following is part of a geometric sequence, find the missing terms.
Find the nth term of the following geometric sequence:

Question 75

If the following is part of a geometric sequence, find the missing terms.

Question 76

If the following is part of a geometric sequence, find the missing terms.
Find the nth term of the following geometric sequence:

Question 77

Write an expression in terms of the given variable(s)that represents the indicated quantity.
The sum of three consecutive odd whole numbers if the least integer is x.

A)3x + 6
B)3x - 3
C)3x + 3
D)3x - 6

Question 78

Write an expression in terms of the given variable(s)that represents the indicated quantity.
For a particular event, a student pays $10 per ticket and a nonstudent pays $13 per ticket. If x students and 200 nonstudents buy tickets, find the total revenue from the sale of the tickets in terms
Of x.

A)10 + 2600x dollars
B)10x + 1300 dollars
C)10x + 2600 dollars
D)10x + 13 dollars

Question 79

Write an expression in terms of the given variable(s)that represents the indicated quantity.
The amount of bacteria after n minutes if the initial amount of bacteria is q and the amount of bacteria triples every minute.

Question 80

If the following is part of a geometric sequence, find the missing terms.
Find the 100th term of the following arithmetic sequence: