MathTV Topic - Definitions, Order of Operations, Simplifying Expressions, and Sets

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Get Ready for Statistics: Corequisites
Definitions, Order of Operations, Simplifying Expressions, and Sets

Problem 1

Write each of the following in symbols:

The sum of $x$ and $5$ is less than $2$ .
The product of $3$ and $x$ is $21$ .
The quotient of $y$ and $6$ is $4$ .
Twice the difference of $b$ and $7$ is greater than $5$ .
The difference of twice $b$ and $7$ is greater than $5$ .

Choose instructor to watch:

Mr. McKeague

Betsy

Gordon

Cynthia

Problem 2

Expand and multiply: $5^2$

Choose instructor to watch:

Preston

Katrina

Aaron

Cynthia

Problem 3

Expand and multiply: $2^5$

Choose instructor to watch:

Preston

Katrina

Aaron

Cynthia

Problem 4

Expand and multiply: $4^3$

Choose instructor to watch:

Preston

Katrina

Aaron

Cynthia

Problem 5

Simplify: $\; 5+3(2+4)$

Choose instructor to watch:

Aaron

Lauren

Anthony

Problem 6

Simplify: $\; 5\cdot 2^3-4\cdot 3^2$

Choose instructor to watch:

Aaron

Lauren

Julieta

Problem 7

Simplify: $\; 20-(2\cdot 5^2-30)$

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Katrina

Brooke

Anthony

Problem 8

Simplify: $40-20 \div 5+8$

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Katrina

Brooke

Logan

Anthony

Problem 9

Simplify the expression $\dfrac{72-68}{5}$

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Mr. McKeague

Suhas

Julieta

Problem 10

Evaluate the expression $\dfrac{23.6+16.3+18.9}{7-1}$

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Mr. McKeague

Suhas

Julieta

Problem 11

Evaluate $a^2+8a+16$ when $a$ is $0, 1, 2, 3,$ and $4$

Choose instructor to watch:

Suhas

Aaron

Mr. Martinez

Problem 12

Evaluate $\dfrac{x-\overline{x}}{s}$ if $x=186$ , $\overline{x}=135.8$ , and $s=35.2$ .

Choose instructor to watch:

Mr. McKeague

Suhas

Julieta

Problem 13

Evaluate $\dfrac{s^2}{n}$ for the given values of the variables.

$s=12$ and $n=10$
$s=4.3$ and $n=100$

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Mr. McKeague

Suhas

Julieta

Problem 14

If $A=\{\text{all college students in the US}\}$ and $B=\{\text{all college students in Boston}\}$ , then which of the following is true?

$A\subset B$
$B\subset A$

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Mr. McKeague

Suhas

Problem 15

Let $A=\{1, 3, 5\}$ , $B=\{0, 2, 4\}$ , and $C=\{1, 2, 3, \ldots\}$ . Find $A\cup B$ .

Choose instructor to watch:

Suhas

Katrina

Logan

Mr. Martinez

Problem 16

Let $A=\{1, 3, 5\}$ , $B=\{0, 2, 4\}$ , and $C=\{1, 2, 3, \ldots\}$ . Find $A\cap B$ .

Choose instructor to watch:

Mr. Perez

Katrina

Logan

Julieta

Problem 17

Let $A=\{1, 3, 5\}$ , $B=\{0, 2, 4\}$ , and $C=\{1, 2, 3, \ldots\}$ . Find $A\cap C$ .

Choose instructor to watch:

Mr. Perez

Katrina

Logan

Mr. Martinez

Problem 18

Let $A=\{1, 3, 5\}$ , $B=\{0, 2, 4\}$ , and $C=\{1, 2, 3, \ldots\}$ . Find $B\cup C$ .

Choose instructor to watch:

Mr. Perez

Katrina

Logan

Julieta

Problem 19

If $A=\{1,2,3,4,5,6\}$ , find $C=\{x \mid x\in A \text{ and } x\geq4\}$ .

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Katrina

Mr. Martinez

welcome

Welcome from Mr. McKeague.

Choose instructor to watch:

Mr. McKeague

Problem 21

Write each of the following in symbols:

Choose instructor to watch:

Mr. McKeague

Betsy

Gordon

Cynthia

Problem 22

Simplify: $\; 5+3(2+4)$

Choose instructor to watch:

Aaron

Lauren

Anthony

Problem 23

Simplify: $40-20 \div 5+8$

Choose instructor to watch:

Katrina

Brooke

Logan

Anthony

Problem 24

Simplify $(-2-3)(5-9)$

Choose instructor to watch:

Preston

Stefanie

Anthony

Problem 25

Simplify $2-5(7-4)-6$

Choose instructor to watch:

Preston

Stefanie

Winston

Julieta

Problem 26

Simplify $2(4-7)^3+(-2-3)^2$

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Preston

Stefanie

Anthony

Problem 27

Simplify: $\dfrac{-8-8}{-5-3}$

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Mr. McKeague

Matt

Anthony

Problem 28

Simplify: $\dfrac{-5(-4)+2(-3)}{2(-1)-5}$

Choose instructor to watch:

Mr. McKeague

Anthony

Problem 29

Find the value of the expression $3x+4y+5$ when $x$ is $6$ and $y$ is $7$

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Aaron

Mr. Martinez

Problem 30

Locate the numbers $-4.5$ , $-0.75$ , $\dfrac{1}{2}$ , $\sqrt{2}$ , $\pi$ , and $4.1$ on the real number line.

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Mr. Perez

Katrina

Logan

Mr. Martinez

Problem 31

Write $\lvert 5\rvert$ without absolute value symbols.

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Aaron

Mr. Martinez

Problem 32

Write $\lvert -2\rvert$ without absolute value symbols

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Aaron

Cynthia

Problem 33

Write $-\lvert -3\rvert$ without absolute value symbols

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Aaron

Cynthia

Problem 34

Simplify $5(4x)$ by using the associative property.

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Betsy

Logan

Cynthia

Problem 35

Simplify $\dfrac{1}{4}(4a)$ by using the associative property.

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Betsy

Logan

Mr. Martinez

Problem 36

Apply the distributive property to $\dfrac{1}{2}(3x+6)$ and then simplify the result.

Choose instructor to watch:

Julieta

Betsy

Logan

Julieta

Problem 37

Simplify: $\,2(3y+4)+2$

Choose instructor to watch:

Betsy

Logan

Mr. Martinez

Problem 38

Apply the distributive property to $a\left(1+\dfrac{1}{a}\right)$ and then simplify the result.

Choose instructor to watch:

Betsy

Logan

Cynthia

Problem 39

Apply the distributive property to $3\left(\dfrac{1}{3}x+5\right)$ and then simplify the result.

Choose instructor to watch:

Betsy

Logan

Mr. Martinez

Problem 40

Apply the distributive property to $6\left(\dfrac{1}{3}x+\dfrac{1}{2}y\right)$ and then simplify the result.

Choose instructor to watch:

Betsy

Logan

Cynthia

Problem 41

Use the distributive property to combine similar terms for the expression $3x+5x$ .

Choose instructor to watch:

Betsy

Logan

Mr. Martinez

Problem 42

Use the distributive property to combine similar terms for the expression $3y+y$

Choose instructor to watch:

Betsy

Logan

Cynthia

Problem 43

Simplify: $7x+4+6x+3$

Choose instructor to watch:

Stefanie

Katrina

Logan

Julieta

Problem 44

Simplify: $4+3(2y+5)+8y$

Choose instructor to watch:

Stefanie

Katrina

Cynthia

Mr. Martinez

Problem 45

Simplify: $3(2y-1)+y$

Choose instructor to watch:

Stefanie

Katrina

Anthony

Problem 46

Simplify: $8-3(4x-2)+5x$

Choose instructor to watch:

Mr. McKeague

Stefanie

Anthony

David

Problem 47

Simplify: $5(2a+3)-(6a-4)$

Choose instructor to watch:

Stefanie

Katrina

Anthony

Problem 48

Let $A=\{1, 3, 5\}$ , $B=\{0, 2, 4\}$ , and $C=\{1, 2, 3, \ldots\}$ . Find $A\cup B$ .

Choose instructor to watch:

Suhas

Katrina

Logan

Mr. Martinez

Problem 49

Let $A=\{1, 3, 5\}$ , $B=\{0, 2, 4\}$ , and $C=\{1, 2, 3, \ldots\}$ . Find $A\cap B$ .

Choose instructor to watch:

Mr. Perez

Katrina

Logan

Julieta

Problem 50

Let $A=\{1, 3, 5\}$ , $B=\{0, 2, 4\}$ , and $C=\{1, 2, 3, \ldots\}$ . Find $A\cap C$ .

Choose instructor to watch:

Mr. Perez

Katrina

Logan

Mr. Martinez

Problem 51

Let $A=\{1, 3, 5\}$ , $B=\{0, 2, 4\}$ , and $C=\{1, 2, 3, \ldots\}$ . Find $B\cup C$ .

Choose instructor to watch:

Mr. Perez

Katrina

Logan

Julieta

Problem 52

For the set $\left\{-5, \,-3.5, \,0, \,\frac{3}{4}, \,\sqrt{3}, \,\sqrt{5}, \,9\right\}$ , list:

whole numbers
integers
rational numbers
irrational numbers
real numbers

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Mr. Perez

Katrina

Mr. Martinez

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