Deck 1: Algebra and Equations

Question 1

Determine whether the statement is true or false.

-Every rational number is an integer.

Answer 1

False

Question 2

Name the property illustrated.

- $8 \cdot 1=8$

A) Commutative property
B) Identity property
C) Associative property
D) Distributive property

Answer 2

Identity property

Question 3

Name the property illustrated.

- $(9+2)+1=(2+9)+1$

A) Distributive property
B) Identity property
C) Associative property
D) Commutative property

Answer 3

Commutative property

Question 4

Name the property illustrated.

- $1+0=1$

A) Commutative property
B) Associative property
C) Distributive property
D) Identity property

Question 5

Name the property illustrated.

- $6(x+8)=6 x+6 \cdot 8$

A) Associative property
B) Distributive property
C) Identity property
D) Commutative property

Question 6

Name the property illustrated.

- $4+3=3+4$

A) Associative property
B) Identity property
C) Distributive property
D) Commutative property

Question 7

Name the property illustrated.

- $(3 \cdot 4) \cdot 7=3 \cdot(4 \cdot 7)$

A) Commutative property
B) Identity property
C) Associative property
D) Distributive property

Question 8

Name the property illustrated.

- $7 \cdot 8=8 \cdot 7$

A) Associative property
B) Identity property
C) Distributive property
D) Commutative property

Question 9

Name the property illustrated.

- $3+(9+6)=(3+9)+6$

A) Identity property
B) Commutative property
C) Associative property
D) Distributive property

Question 10

Name the property illustrated.

- $3(8+7)=(8+7) 3$

A) Identity and associative properties
B) Distributive and associative properties
C) Associative and commutative properties
D) Commutative property

Question 11

Evaluate the expression, given x =- 2, y =3 , and a = -4.

-7x + 5y - 6a

A) 1
B) 25
C) 35
D) -52

Question 12

Evaluate the expression, given x =- 2, y =3 , and a = -4.

- $(4 x+6 y)(-3 a)$

A) -384
B) 120
C) -120
D) 0

Question 13

Evaluate the expression, given x =- 2, y =3 , and a = -4.

- $-6 a-5 y-7 x$

A) 5
B) 11
C) 23
D) 13

Question 14

Evaluate the expression, given x =- 2, y =3 , and a = -4.

- $(4+\mathrm{x})(6+\mathrm{y})(-3-\mathrm{a})$

A) 18
B) -378
C) -126
D) -18

Question 15

Evaluate the expression, given x =- 2, y =3 , and a = -4.

- $(-7 a)(-2 x-3 y)$

A) -140
B) -364
C) 140
D) 0

Question 16

Evaluate the expression, given x =- 2, y =3 , and a = -4.

- $6(x-8)+5 a^{2}$

A) 20
B) 44
C) -80
D) -140

Question 17

Evaluate the expression using order of operations.

-(7 + (-3))[3 + (5 + 2)]

A) 37
B) 40
C) 10
D) 14

Question 18

Evaluate the expression using order of operations.

- $\frac{(-7) \cdot(7+8)+(-7) \cdot 2}{(-7) \cdot(2-1)}$

A) $\frac{1}{17}$
B) $\frac{128}{7}$
C) 17
D) $\frac{120}{7}$

Question 19

Evaluate the expression using order of operations.

- $\frac{(-7) \cdot(7-7)+(-7) \cdot 6}{(-7) \cdot(4-1)}$

A) 18
B) $\frac{1}{2}$
C) $\frac{43}{21}$
D) 2

Question 20

Evaluate the expression using order of operations.

- $8[-6+4(-7+(-8))]$

A) -108
B) -528
C) 240
D) 236

Question 21

Evaluate the expression using order of operations.

- $-15+(5 \cdot 2+20) \div 5$

A) -9
B) 9
C) 5
D) -1

Question 22

Evaluate the expression using order of operations.

- $(7+3)[2+(6+7)]$

A) 21
B) 150
C) 33
D) 25

Question 23

Evaluate the expression using order of operations.

- $2[7+5(8-5)]$

A) 29
B) 68
C) 44
D) 72

Question 24

Evaluate the expression using order of operations.

- $\frac{3(4+6)-7}{2}$

A) $\frac{2}{11}$
B) $\frac{23}{2}$
C) $\frac{25}{2}$
D) $\frac{11}{2}$

Question 25

Evaluate the expression using order of operations.

- $5 \cdot 4^{2}$

A) 80
B) 400
C) 20
D) 320

Question 26

Evaluate the expression using order of operations.

- $(7+(-5))\left[4+\left(\sqrt{49}+8^{2}\right)\right]$

A) 25
B) 150
C) 23
D) 29

Question 27

Express each of the following statements in symbols, using <, >, ?, or ?.

-4 is less than 7 .

A) $4 > 7$
B) $7 < 4$
C) $4<7$
D) $4 \leq 7$

Question 28

Express each of the following statements in symbols, using <, >, ?, or ?.

--8 is greater than -11 .

A) $-8>-11$
B) $-11>-8$
C) $-8 \geq-11$
D) $-8<-11$

Question 29

Express each of the following statements in symbols, using <, >, ?, or ?.

- $x$ is less than or equal to 2 .

A) $x \geq 2$
B) $x<2$
C) $x \leq 2$
D) $2 \leq x$

Question 30

Express each of the following statements in symbols, using <, >, ?, or ?.

-y is greater than or equal to -6 .

A) $y>-6$
B) $-6 \geq y$
C) $y \leq-6$
D) $y \geq-6$

Question 31

Express each of the following statements in symbols, using <, >, ?, or ?.

- $w$ is positive.

A) w $\leq 0$
B) $w \geq 0$
C) $\mathrm{w}>0$
D) w $<0$

Question 32

Express each of the following statements in symbols, using <, >, ?, or ?.

- $s$ is negative.

A) $\mathrm{s}<0$
B) $s \geq 0$
C) $\mathrm{s} \leq 0$
D) $s>0$

Question 33

Express each of the following statements in symbols, using <, >, ?, or ?.

- $p$ is at most 33

A) $p>33$
B) p $<33$
C) $p \leq 33$
D) $p \geq 33$

Question 34

Express each of the following statements in symbols, using <, >, ?, or ?.

- $p$ is at least 45

A) p $<45$
B) $p>45$
C) $\mathrm{p} \leq 45$
D) $\mathrm{p} \geq 45$

Question 35

Insert $<,=$ , or $>$ to write a true statement.

- $\frac{1}{8}$ ____ $0.125$

A) $<$
B) >
C) $=$

Question 36

Insert $<,=$ , or $>$ to write a true statement.

- $\frac{2}{11}$ ____ $0.18$

A) $<$
B) $=$
C) $>$

Question 37

Insert $<,=$ , or $>$ to write a true statement.

- $\sqrt{28}$ ____ $\frac{2546}{416}$

A) =
B) $<$
C) $>$

Question 38

Insert $<,=$ , or $>$ to write a true statement.

--9 ____-1

A) $<$
B) =
C) >

Question 39

Graph the inequality on a number line.

- $(7$ , $\infty$ )

A)
B)
C) D)

Question 40

Graph the inequality on a number line.

- $(-\infty, 8)$

A)
B)
C) D)

Question 41

Graph the inequality on a number line.

- $[5, \infty)$

A)
B)
C) D)

Question 42

Graph the inequality on a number line.

- $(-\infty,-2]$

A)
B)
C) D)

Question 43

Graph the inequality on a number line.

- $[-3,0]$

A)
B)
C) D)

Question 44

Graph the inequality on a number line.

- $(-4, -1]$

A)
B)
C) D)

Question 45

Solve the problem.

-Kafka Inc. imports hard drives and sells them on the internet. The profit is given by the equation $\mathrm{P}=140 \mathrm{n}-6500$ , where $\mathrm{n}$ is the number of hard drives sold. Estimate the profit, to the nearest ten dollars, corresponding to the sale of 775 hard drives.

A) $\$ 101,990$
B) $\$ 102,010$
C) $\$ 102,020$
D) $\$ 102,000$

Question 46

Solve the problem.

-Kafka Inc. imports hard drives and sells them on the internet. The profit is given by the equation $\mathrm{P}=153 \mathrm{n}-7000$ , where $\mathrm{n}$ is the number of hard drives sold. How many hard drives must be sold for the company to break even? Round your answer to the units place, in other words, to the nearest number of hard drives.

A) 50 hard drives
B) 46 hard drives
C) 44 hard drives
D) 66 hard drives

Question 47

Solve the problem.

-The two charts show the weight gain of some people and the weight loss of other people. Use the information given to answer the questions below.

What is the difference between the weight gain of Bob and the weight loss of Don?

A) 1250 grams
B) -1250 grams
C) 7166 grams
D) - 7166 grams

Question 48

Solve the problem.

-The two charts show the weight gain of some people and the weight loss of other people. Use the information given to answer the questions below.

How much more weight did Don lose than Frank?

A) 3815 grams
B) 2101 grams
C) -2101 grams
D) -3815 grams

Question 49

Evaluate the expression.

- $-|-8|-|10|$

A) -18
B) -2
C) 18
D) 2

Question 50

Evaluate the expression.

- $-|-6|-|7|$

A) 1
B) -1
C) 13
D) -13

Question 51

Evaluate the expression.

- $-|-22|-|-22-19|$

A) -19
B) 19
C) -63
D) 63

Question 52

Fill in the blank with either $=,<$ , or $>$ to make the statement true.}

- $|21| \_|-21|$

A) $<$
B) $=$
C) >

Question 53

Fill in the blank with either $=,<$ , or $>$ to make the statement true.}

- $-|-1| \_|1|$

A) >
B) $<$
C) $=$

Question 54

Fill in the blank with either $=,<$ , or $>$ to make the statement true.}

- $-|4| \_|-4|$

A) $<$
B) >
C) $=$

Question 55

Fill in the blank with either $=,<$ , or $>$ to make the statement true.}

- $\mid 5$ - (-4)|_ |-5 - 4|

A) >
B) =
C) <

Question 56

Fill in the blank with either $=,<$ , or $>$ to make the statement true.}

- $|8-3| \_|3-8|$

A) <
B) >
C) $=$

Question 57

Fill in the blank with either $=,<$ , or $>$ to make the statement true.}

- $|5| \cdot|-4| \_|4(5)|$

A) >
B) <
C) $=$

Question 58

Fill in the blank with either $=,<$ , or $>$ to make the statement true.}

- $\mid 10$ - 3 |_| $10|-| 3 \mid$

A) <
B) $=$
C) >

Question 59

Use inequality symbols to rewrite the statement. Let $x$ represent the unknown.

-A Software company could lose up to $6 \%$ of its market share due to slow product delivery. Let $x$ be the market share lost.

A) $x \leq 0.06$
B) $x \geq 0.06$
C) $x \geq-0.06$
D) $x \leq-0.06$

Question 60

Use inequality symbols to rewrite the statement. Let $x$ represent the unknown.

-The market shakeout could result in as few as 5 companies remaining in business.

A) $x-5=0$
B) $x=5$
C) $x \leq 5$
D) $x \geq 5$

Question 61

Use inequality symbols to rewrite the statement. Let $x$ represent the unknown.

-Computer company $X Y Z$ can't possibly spend less than $\$ 38$ million in advertising to regain its market share.

A) $x<\$ 38$ million
B) $x>\$ 38$ million
C) $x \geq \$ 38$ million
D) $x \leq \$ 38$ million

Question 62

Use inequality symbols to rewrite the statement. Let $x$ represent the unknown.

-The new software product will cost between $\$ 295$ and $\$ 370$ per unit.

A)
B)
C) $x>\$ 295, x<\$ 370$
D) $x \leq 370$

Question 63

Use inequality symbols to rewrite the statement. Let $x$ represent the unknown.

-When a baseball player is in a slump, he may get fewer than 5 hits in 21 times at bat. Let $x$ represent the number of hits.

A)
B) $x>\frac{5}{21}$
C) $x<5$
D) $x<21$

Question 64

Use inequality symbols to rewrite the statement. Let $x$ represent the unknown.

-A plumber makes more money than $54 \%$ of the population and is better educated than $72 \%$ . Find the average status and status incongruity for this person.

A) 9 and 63
B) 9 and 37
C) 37 and 9
D) 63 and 9

Question 65

Use a calculator to evaluate the expression.

- $7^{2}$

A) 49
B) 9
C) 3
D) 14

Question 66

Use a calculator to evaluate the expression.

- $11^{2}$

A) 22
B) 242
C) 13
D) 121

Question 67

Use a calculator to evaluate the expression.

- $2^{5}$

A) 32
B) 4
C) 25
D) 10

Question 68

Use a calculator to evaluate the expression.

- $-8^{5}$

A) -40
B) 40
C) 32,768
D) $-32,768$

Question 69

Use a calculator to evaluate the expression.

- $(-4)^{4}$

A) -16
B) 256
C) -256
D) 16

Question 70

Use a calculator to evaluate the expression.

- $-4.2^{3}$

A) -12.60
B) 74.09
C) 12.60
D) -74.09

Question 71

Use a calculator to evaluate the expression.

- $(-7.3)^{2}$

A) -53.3
B) -14.6
C) 53.3
D) 14.6

Question 72

Use a calculator to evaluate the expression.

- $(-5.2)^{9}$

A) $-2,779,905.88$
B) 46.8
C) -46.8
D) $2,779,905.88$

Question 73

Use a calculator to evaluate the expression.

- $\left(\frac{1}{3}\right)^{10}$

A) 3.3333
B) 59,049
C) 0
D) 30

Question 74

Use a calculator to evaluate the expression.

- $\left(\frac{4}{3}\right)^{2}$

A) 0.444
B) 1.778
C) 2.667
D) 5.333

Question 75

Simplify. Leave answer with exponent.

- $8^{3} \cdot 8^{7}$

A) $8^{21}$
B) $64^{10}$
C) $64^{21}$
D) $8^{10}$

Question 76

Simplify. Leave answer with exponent.

- $(-2)^{3} \cdot(-2)^{4}$

A) $4^{7}$
B) $4^{12}$
C) $-2^{7}$
D) $2^{7}$

Question 77

Simplify. Leave answer with exponent.

- $(-5)^{9} \cdot(-5)^{3}$

A) $25^{27}$
B) $25^{12}$
C) $5^{12}$
D) $-5^{12}$

Question 78

Simplify. Leave answer with exponent.

- $(4 y)^{5} \cdot(4 y)^{9}$

A) $(4 y)^{14}$
B) $16 y^{14}$
C) $16 y^{45}$
D) $4 y^{45}$

Question 79

Simplify. Leave answer with exponent.

- $3^{3} \cdot 3^{3}$

A) $9^{6}$
B) $9^{9}$
C) $3^{6}$
D) $3^{9}$

Question 80

Identify the degree of the polynomial and list its coefficients.

- $6 x-5$

A) degree: 1
Coefficients: 6,5
B) degree: 6
Coefficients: 6,5
C) degree: 1
Coefficients: $6,-5$
D) degree: 0
Coefficients: $6,-5$