Deck 1: Fundamentals

Question 1

State whether the inequality is true or false. $- \frac { 1 } { 10 } > - \frac { 1 } { 100 }$

Answer 1

False

Question 2

Perform the indicated operation. $\frac { 1 } { 4 } + \frac { 1 } { 12 }$

A) $\frac { 1 } { 16 }$
B) $\frac { 1 } { 48 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 1 } { 3 }$
E) $3$

Answer 2

$\frac { 1 } { 3 }$

Question 3

Write the following statement in terms of inequalities. $Z$ is greater than or equal to $- 1$ .

A) $z \leq - 1$
B) $z \geq - 1$
C) $z < - 1$
D) $z > - 1$
E) $z = 0$

Answer 3

$z \geq - 1$

Question 4

Perform the indicated operation. $\frac { 1 } { 6 } \div \frac { 2 } { 3 }$

A) $- \frac { 1 } { 2 }$
B) $\frac { 2 } { 18 }$
C) $\frac { 1 } { 18 }$
D) $\frac { 1 } { 3 }$
E) $\frac { 1 } { 4 }$

Question 5

Perform the indicated operations.

Question 6

State whether the inequality is true or false. $\frac { 22 } { 7 } > \pi$

Question 7

Write the following statement in terms of inequalities. $x$ is negative.

A) $x > 0$
B) $x < 0$
C) $x \geq 0$
D) $x \leq 0$
E) $x = 0$

Question 8

Use properties of real numbers to write $- r ( s - 2 )$ without parentheses.

A) $- 2 r + 2 s$
B) $- r S + 2$
C) $rs + 2 r$
D) $- r s + 2 r$
E) $- rs- 2 r$

Question 9

Perform the indicated operations.

Question 10

Use the properties of real numbers to write the expression without parentheses. $2 x \left( a - b - 2 c + \frac { d } { 2 } \right)$

A) $x a - x b - 2 x c + x d$
B) $2 x a - 2 x b - x c + 4 x d$
C) $x a - 2 x b - 4 x c + x d$
D) $2 x a - 2 x b - 4 x c + x d$
E) $2 x a - x b - 2 x c + 2 x d$

Question 11

State the property of real numbers being used. $$x + 4 = 4 + x$$

A) Commutative Property for addition
B) Commutative Property for multiplication
C) Associative Property for addition
D) Associative Property for multiplication
E) Distributive Property

Question 12

State the property of real numbers being used. $$2 ( x + 5 y ) = 2 x + 10 y$$

A) Commutative Property for addition
B) Commutative Property for multiplication
C) Associative Property for addition
D) Associative Property for multiplication
E) Distributive Property

Question 13

Perform the indicated operations.

Question 14

State whether the inequality is true or false. $- \sqrt { 2 } < - 1.41$

Question 15

Perform the indicated operations.

Question 16

Perform the indicated operation(s) and simplify. $\frac { 1 } { 5 } \div \left[ \frac { 1 } { 4 } \left( \frac { 1 } { 2 } + \frac { 1 } { 3 } \right) \right]$

A) $\frac { 3 } { 2 }$
B) $\frac { 25 } { 24 }$
C) $1$
D) $\frac { 2 } { 3 }$
E) $\frac { 24 } { 25 }$

Question 17

Use properties of real numbers to write $12 ( z / 4 )$ without parentheses.

A) $\frac { 1 } { 4 } Z$
B) $\frac { 1 } { 12 } z$
C) $48 z$
D) $12 z$
E) $3 z$

Question 18

Use properties of real numbers to write $3 ( 2 a + b )$ without parentheses.

A) $6 a + 6 b$
B) $3 + 2 a b$
C) $6 a - b$
D) $6 a + 3 b$
E) $6 a - 3 b$

Question 19

State the property of real numbers being used. $$3 x y = y x 3$$

A) Commutative Property for addition
B) Commutative Property for multiplication
C) Associative Property for addition
D) Associative Property for multiplication
E) Distributive Property

Question 20

Perform the indicated operation(s) and simplify. $\frac { 1 } { 4 } + 5 \left( \frac { 1 } { 4 } \cdot \frac { 1 } { 5 } \right) - \frac { 3 } { 4 }$

A) $- \frac { 3 } { 4 }$
B) $\frac { 3 } { 4 }$
C) $\frac { 1 } { 25 }$
D) $- \frac { 1 } { 4 }$
E) $\frac { 1 } { 4 }$

Question 21

Evaluate $( 32 ) ^ { - 0.2 }$

A) $2$
B) $\frac { 1 } { 2 }$
C) $16$
D) $\frac { 1 } { 4 }$
E) $\frac { 1 } { 1024 }$

Question 22

Evaluate the expression.

Question 23

Evaluate each expression.
(a)
(b)
(c)

Question 24

Evaluate the expression. $4 ^ { - 3 }$

A) $- \frac { 1 } { 256 }$
B) $- \frac { 1 } { 64 }$
C) $\frac { 1 } { 64 }$
D) $\frac { 1 } { 256 }$
E) $\frac { 1 } { 512 }$

Question 25

Evaluate the expression.

Question 26

Express the repeating decimal as a fraction.

Question 27

Find the set $A \cup B$ if $A = \left\{ - 3 , - 2,0 , \frac { 1 } { 3 } , \frac { 2 } { 3 } , 6,9 \right\}$ and $B = \left\{ 0 , \frac { 1 } { 3 } , \frac { 2 } { 3 } \right\}$

A) $\left( 0 , - 2 , - 3,6,9 , \frac { 1 } { 3 } , \frac { 2 } { 3 } \right)$
B) $\left( 0 , - 2,3,6,9 , \frac { - 1 } { 3 } , \frac { 2 } { 3 } \right)$
C) $\left\{ 0,2 , - 3,6,9 , \frac { 1 } { 3 } , \frac { - 2 } { 3 } \right\}$
D) $\{ 0 , - 2 , - 3,6 , - 9 \}$
E) $\left\{ 0 , - 2 , - 3,6,9 , \frac { 2 } { 3 } \right)$

Question 28

Evaluate $\left( \frac { 1 } { 4 } \right) ^ { - 2 } \left( \frac { 1 } { 2 } \right) ^ { - 4 }$

A) $\frac { 1 } { 64 }$
B) $\frac { 1 } { 256 }$
C) $64$
D) $\frac { - 1 } { 4 }$
E) $256$

Question 29

Write the statement in terms of inequalities. The distance from x to 3 is at most $6$ .

A) $| x - 3 | \leq 6$
B) $| x - 3 | \geq 6$
C) $| x - 3 | < 6$
D) $| x - 6 | \leq 3$
E) $| x - 6 | \geq 3$

Question 30

Express the repeating decimal as a fraction.

Question 31

Simplify $a b ^ { 3 } c ^ { 2 } \left( \frac { 2 a ^ { 2 } b } { c ^ { 4 } } \right) ^ { - 1 }$ and eliminate any negative exponents.

A)
$b ^ { 2 } c ^ { 6 }$
B)
$\frac { b ^ { 6 } c ^ { 2 } } { 2 a ^ { 2 } }$
C)
$\frac { 2 b ^ { 2 } c ^ { 6 } } { 3 a }$
D)
$\frac { b ^ { 2 } c ^ { 6 } } { 2 a }$
E)
$2 b ^ { 2 } c ^ { 6 }$

Question 32

Evaluate the expression.

Question 33

Simplify $\frac { x ^ { 1 / 3 } y ^ { 1 / 3 } } { ( x y ) ^ { - 2 / 3 } }$ and eliminate any negative exponents.

A) $x y$
B) $( x y ) ^ { -2 / 3 }$
C) $( x y ) ^ { 1 / 3 }$
D) $y$
E) $x ^ { 1 / 3 } y$

Question 34

Evaluate each expression.
(a)
(b)
(c)

Question 35

Find the distance between and .

Question 36

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

A) $\frac { 9 } { 4 }$
B) $\frac { 4 } { 9 }$
C) $\frac { - 9 } { 4 }$
D) $\frac { 1 } { 4 }$
E) $1$

Question 37

Find $A \cup B$ if $A = \{ x \mid x > \pi \}$ and $B = \{ x \mid - 1 < x < \pi \}$ .

A) $\varnothing$
B) $\{ x \mid x > - 1 \text { and } x \neq \pi \}$
C) $\{ x \mid - 1 < x < \pi \}$
D) $\{ x \mid - \pi < x \leq 1 \}$
E) $\{ x \mid x > - \pi \}$

Question 38

Evaluate $- 2 ^ { 3 }$

A) $- 16$
B) $- 8$
C) $- 4$
D) $8$
E) $16$

Question 39

Express the repeating decimal as a fraction.

Question 40

Evaluate $( 512 ) ^ { - \frac { 1 } { 9 } }$

A) $\frac { 1 } { 4 }$
B) $\frac { 1 } { 2 }$
C) $16$
D) $\frac { 1 } { 16 }$
E) $256$

Question 41

Simplify the expression. Assume the letters denote any real numbers.

Question 42

Write the number in the statement in scientific notation. The distance to the edge of the observable universe is about m.

Question 43

Write in scientific notation.

Question 44

Simplify the expression and eliminate any negative exponents(s).
Assume that all letters denote positive numbers.

Question 45

Find the sum, difference, or product.

Question 46

Simplify the expression. Assume the letters denote any real numbers.

Question 47

A sealed warehouse measuring m wide, m long and 6 m high, is filled with pure oxygen. One cubic meter contains 1000 L, and 22.4 L of any gas contains molecules. How many molecules of oxygen are there in the room?

Question 48

Simplify the expression and eliminate any negative exponents(s).
Assume that all letters denote positive numbers.

Question 49

Perform the indicated operations and simplify. $3 ( 3 x - 4 ) - 5 ( x - 1 )$

A) $4 x - 13$
B) $2 x - 13$
C) $4 x - 7$
D) $2 x + 13$
E) $2 x + 29$

Question 50

Rationalize the denominator.

Question 51

Simplify the expression. Assume the letters denote any real numbers.

Question 52

Write the number in the statement in scientific notation:
The mass of a proton is kg.

Question 53

Rationalize the denominator.

Question 54

Simplify the expression. Assume the letters denote any real numbers.

Question 55

Which of the numbers and is smaller?

Question 56

Write in scientific notation.

Question 57

Simplify the expression .

Question 58

Use scientific notation, laws of exponents, and a calculator to perform the indicated operations. State your answer correct to the number of significant digits indicated by the data.

Question 59

Simplify the expression and eliminate any negative exponents(s).
Assume that all letters denote positive numbers.

Question 60

Perform the indicated operations and simplify. $\left( - 2 x ^ { 3 } + 6 x ^ { 2 } - 4 x + 8 \right) + \left( 3 x ^ { 3 } + x - 4 \right)$

A) $2 x ^ { 3 } + 6 x ^ { 2 } + 3 x + 5$
B) $2 x ^ { 3 } + 6 x ^ { 2 } + 3 x + 12$
C) $2 x ^ { 3 } + 6 x ^ { 2 } + 3 x - 1$
D) $x ^ { 3 } + 6 x ^ { 2 } + 3 x - 4$
E) $x ^ { 3 } + 6 x ^ { 2 } - 3 x + 4$

Question 61

Perform the indicated operations and simplify. $\left( x + \frac { 1 } { y ^ { 2 } } \right) ^ { 3 }$

A) $x ^ { 3 } + \frac { 3 x ^ { 2 } } { y ^ { 2 } } + \frac { 3 x } { y ^ { 4 } } + \frac { 1 } { y ^ { 6 } }$
B) $x ^ { 3 } + \frac { 3 x ^ { 2 } } { y ^ { 2 } } + \frac { x } { y ^ { 2 } } + \frac { 1 } { y ^ { 6 } }$
C) $x ^ { 3 } + \frac { 3 x ^ { 2 } } { y } + \frac { 3 x ^ { 2 } } { y ^ { 4 } } + \frac { 3 } { y ^ { 3 } }$
D) $x ^ { 3 } + \frac { 3 x ^ { 2 } } { y } + \frac { 1 } { y ^ { 6 } }$
E) $x ^ { 3 } + \frac { 1 } { y ^ { 6 } }$

Question 62

Factor the expression. $x ^ { 2 } + 7 x - 8$

A) $( x - 4 ) ( x + 2 )$
B) $( x + 4 ) ( x + 2 )$
C) $( x - 8 ) ( x - 1 )$
D) $( x + 8 ) ( x - 1 )$
E) $( x + 4 ) ( x - 2 )$

Question 63

Perform the indicated operations and simplify. $\left( \alpha x ^ { 2 } - y ^ { 2 } \right) \left( \alpha x ^ { 2 } + y ^ { 2 } \right)$

A) $a ^ { 2 } x ^ { 2 } - y ^ { 2 }$
B) $a ^ { 2 } x ^ { 4 } + a x ^ { 2 } y ^ { 2 } - y ^ { 4 }$
C) $a ^ { 2 } x ^ { 4 } - y ^ { 4 }$
D) $a ^ { 2 } x ^ { 4 } - a x ^ { 2 } y ^ { 2 } - y ^ { 4 }$
E) $a ^ { 2 } x ^ { 4 } + y ^ { 4 }$

Question 64

Perform the indicated operations and simplify. $( 2 u - v ) ( 2 u + v )$

A) $4 u ^ { 2 } - v ^ { 2 }$
B) $8 u ^ { 2 } + 4 v ^ { 2 }$
C) $16 u ^ { 2 } + 4 v ^ { 2 }$
D) $16 u ^ { 2 } + 2 v ^ { 2 }$
E) $16 u ^ { 2 } - 4 v ^ { 2 }$

Question 65

Perform the indicated operations and simplify. $\left( 1 - x ^ { 2 / 3 } \right) \left( 2 + x ^ { 1 / 3 } \right)$

A) $2 + \sqrt [ 3 ] { x } - 2 ( \sqrt [ 3 ] { x } ) ^ { 3 } + x$
B) $1 + \sqrt [ 3 ] { x } - ( \sqrt [ 3 ] { x } ) ^ { 2 } - x$
C) $2 + \sqrt [ 3 ] { x } - \sqrt [ 3 ] { x } - x ^ { 2 }$
D) $2 + \sqrt [ 3 ] { x } - 2 ( \sqrt [ 3 ] { x } ) ^ { 2 } - x$
E) $2 + \sqrt [ 3 ] { x } + 2 ( \sqrt [ 3 ] { x } ) ^ { 2 }$

Question 66

Factor the expression. $x ^ { 2 } ( x - 5 ) ^ { 3 } + x ^ { 3 } ( x - 5 ) ^ { 2 }$

A) $x ( 2 x + 5 ) ( x - 5 ) ^ { 2 }$
B) $x ^ { 2 } ( 2 x + 5 ) ( x - 5 ) ^ { 2 }$
C) $x ( 2 x - 5 ) ^ { 2 } ( x - 5 ) ^ { 2 }$
D) $x ^ { 2 } ( 5 x - 5 ) ( 2 x - 5 )$
E) $x ^ { 2 } ( 2 x - 5 ) ( x - 5 ) ^ { 2 }$

Question 67

Factor the expression. $y ^ { 2 } + x y - 2 x ^ { 2 }$

A) $- ( 2 x + x y ) ( y - 2 x )$
B) $- ( 2 x + y ) ( x - y )$
C) $( 2 x - y ) ( x - y )$
D) $( 2 x + y ) ( x + y )$
E) $- ( 2 x + y ) ( x - 2 y )$

Question 68

Multiply the algebraic expressions using a Special Product Formula and simplify.

Question 69

Factor out the common factor.

Question 70

Multiply the algebraic expressions using a Special Product Formula and simplify.

Question 71

Factor the expression. $x ( n - y ) + ( x - 1 ) ( y - n )$

A) $xn - y$
B) $x + ( x - 1 ) ( y - n )$
C) $n - y$
D) $x + y$
E) $x y$

Question 72

Multiply the algebraic expressions using a Special Product Formula and simplify.

Question 73

Use a Factoring Formula to factor the expression.

Question 74

Multiply the algebraic expressions using a Special Product Formula and simplify.

Question 75

Find the sum, difference, or product.

Question 76

Multiply the algebraic expressions using the FOIL method and simplify.

Question 77

Factor the expression. $x ^ { 2 } + 8 x + 15$

A)
$( x + 3 ) ( x + 5 )$
B)
$( x - 3 ) ( x + 5 )$
C)
$( x - 3 ) ( x - 5 )$
D)
$( x + 3 ) ( x - 5 )$
E)
$( - x - 3 ) ( x - 5 )$

Question 78

Perform the indicated operations and simplify. $( t + 3 ) ( 2 t - 1 ) - 3 ( t + 2 )$

A) $2 t ^ { 2 } + 6 t + 4$
B) $2 t ^ { 2 } + 2 t - 9$
C) $2 t ^ { 2 } - 2 t - 10$
D) $2 t ^ { 2 } - 3 t - 5$
E) $2 t ^ { 2 } + 5 t + 4$

Question 79

Factor the expression. $6 x ^ { 2 } + 13 x + 6$

A) $( 2 x + 3 ) ^ { 2 }$
B) $( x + 3 ) ( 6 x + 2 )$
C) $( 2 x + 1 ) ( 3 x + 6 )$
D) $( 6 x + 1 ) ( x + 6 )$
E) $( 2 x + 3 ) ( 3 x + 2 )$

Question 80

Perform the indicated operations and simplify. $\left( x ^ { 2 } - b ^ { 2 } y ^ { 2 } \right) \left( x ^ { 2 } - c x y + a y ^ { 2 } \right)$

A) $x ^ { 4 } - c x ^ { 3 } y + a x ^ { 2 } y ^ { 2 } - b ^ { 2 } y ^ { 2 } x ^ { 2 } + b ^ { 2 } c y ^ { 3 } x - a b ^ { 2 } y ^ { 4 }$
B) $x ^ { 4 } - x ^ { 3 } c y + x ^ { 2 } a y ^ { 2 } + b ^ { 2 } y ^ { 3 } c x - b ^ { 2 } y ^ { 4 } a$
C) $x ^ { 2 } - x ^ { 3 } y + x ^ { 2 } a y ^ { 2 } - b ^ { 2 } y ^ { 3 } c x - a b ^ { 2 } y ^ { 4 }$
D) $a ^ { 2 } x ^ { 4 } - a x ^ { 2 } y ^ { 2 } - y ^ { 4 }$
E) $x ^ { 4 } - c x ^ { 3 } y + a x ^ { 2 } y ^ { 2 } - c y ^ { 3 } x - a b ^ { 2 } y ^ { 4 }$