Deck 1: Basic Concepts and Properties

Question 1

Write the equation in $x = a$ form. $- 2 x + 13 = 15$

A) $x = 4$
B) $x = - 1$
C) $x = - 4$
D) $x = 1$
E) $x = - 3$

Answer 1

$x = - 1$

Question 2

Evaluate the expression. $$3.5 + | 6.1 + ( - 3.4 ) |$$

A)8.9
B)9.7
C)6.2
D)7.3
E)10.6

Answer 2

6.2

Question 3

Simplify the numerical expression. $$( 5 - 8 ) ^ { 2 }$$

A)9
B)8
C)-9
D)11
E)-5

Answer 3

9

Question 4

Perform the multiplication. Simplify the result when possible. $$\frac { 5 } { 32 } \cdot \frac { 36 } { 5 }$$

A) $\frac { 7 } { 6 }$
B) 9
$$8$$
C) $\frac { 5 } { 6 }$
D) $\frac { 6 } { 5 }$
E) $\frac { 8 } { 7 }$

Question 5

List the numbers in the set that are natural numbers. $$\left\{ - 5 , - 1 , - \frac { 4 } { 5 } , 0,1 , \frac { 13 } { 12 } , 2 , \sqrt { 6 } , 3.75,6,8 \right\}$$

A) $1,2,6,8$
B) $- 5 , - 1 , - \frac { 4 } { 5 } , 0,1 , \frac { 13 } { 12 } , 2,3.75,6,8$
C) $- 5 , - 1 , - \frac { 4 } { 5 } , 0,1,2,3.75,6,8$
D) $- 5 , - 1 , - \frac { 4 } { 5 } , 0,1 , \frac { 13 } { 12 } , 2 , \sqrt { 6 } , 3.75,6,8$
E) $- 5 , - 1,0,1,2,3.75,6,8$

Question 6

Simplify the numerical expression. $$- \left( \frac { 1 } { 5 } \right) ^ { - 2 }$$

A) $- \frac { 1 } { 5 }$
B)5
C)36
D) $- \frac { 1 } { 25 }$
E)-25

Question 9

Graph the set on the number line. $$[ - 3 , \infty )$$

A)
B)
C)
D)
E)

Question 10

The set of __________ numbers is {1, 2, 3, 4, ... }.

A)irrational
B)integer
C)natural
D)whole
E)negative

Question 11

Solve the quadratic equation. $2 ( x + 8 ) ^ { 2 } - 5 = 3$ Use the following property: For any real number $D$ , $x ^ { 2 } = a$ if and only if $x = \sqrt { a }$ or $x = - \sqrt { a }$ .

A)x = -10 or x = -9
B)x = 0
C)x = -6 or x = -10
D)x = 1 or x = -3
E)x = -1 or x = -13

Question 12

Find the value of the expression. $$- | - 35 |$$

A)- 35
B)35
C)80
D)- 80
E)0

Question 13

Find the absolute value. $$| 20 - 12 |$$

A)8
B)10
C)-10
D)0
E)-8

Question 14

Find the sum. $$\sqrt { 27 } + \sqrt { 75 }$$

A) $5 \sqrt { 4 }$
B) $7 \sqrt { 3 }$
C) $3 \sqrt { 7 }$
D) $8 \sqrt { 3 }$
E) $3 \sqrt { 8 }$

Question 15

Find the sum. $$6 \frac { 1 } { 11 } + 9 \frac { 2 } { 5 }$$

A) $3 \frac { 2 } { 5 }$
B) $53 \frac { 38 } { 55 }$
C) $15 \frac { 2 } { 5 }$
D) $3 \frac { 27 } { 55 }$
E) $15 \frac { 27 } { 55 }$

Question 16

Simplify the numerical expression. $$3 ^ { - 3 }$$

A) $\frac { 1 } { 9 }$
B) $- 27$
C) $\frac { 1 } { 27 }$
D) $27$
E) $\frac { 1 } { 10 }$

Question 17

Solve the quadratic equation. $n ^ { 2 } - 22 = 0$ Use the following property: For any real number a , $x ^ { 2 } = a$ if and only if $x = \sqrt { a }$ or $x = - \sqrt { a }$ .

A) $\{ \sqrt { 22 } \}$
B) $\{ 11.0 \}$
C) $\{ \sqrt { 22 } , - \sqrt { 22 } \}$
D) $\{ - \sqrt { 22 } \}$
E) $\{ 22,0 \}$

Question 18

Graph the set on the number line. $$\{ x \mid 3 < x < 6 \}$$

A)
B)
C)
D)
E)

Question 19

Graph the set on the number line. $$( - \infty , - 5 ] \cup [ 6 , \infty )$$

A)
B)
C)
D)
E)

Question 20

Find the sum. $$( - 0.2 ) + 0.9$$

A)0.7
B)1.2
C)0.8
D)0.5
E)1.3

Question 21

Simplify the numerical expression. $$4 ( 0.1 ) ^ { 2 } - 4 ( 0.1 ) + 0.2$$

A)-3.16
B)-2.16
C)-0.16
D)-5.16
E)0.84

Question 22

Simplify the numerical expression. $$( - 2 ) ^ { 2 } - 4 ( - 2 ) ( 4 ) - ( - 5 ) ^ { 2 }$$

A)19
B)16
C)11
D)5
E)9

Question 23

If x is any nonzero real number, then $x ^ { - 5 } = \frac { 1 } { x ^ { 5 } }$ .

A)true
B)false

Question 24

Simplify the expression. $$\left( 2 \frac { 1 } { 3 } 3 ^ { \frac { 2 } { 3 } } \right) ^ { 3 }$$

A) $36$
B) $6$
C) $11$
D) $18$
E) $12$

Question 25

Find the difference. $$18 \frac { 3 } { 6 } - 11 \frac { 2 } { 30 }$$

A) $7 \frac { 5 } { 6 }$
B) $6 \frac { 17 } { 30 }$
C) $7 \frac { 13 } { 30 }$
D) $29 \frac { 13 } { 30 }$
E) $7 \frac { 17 } { 30 }$

Question 26

Subtract. $$44.5$$
$24.1$

A)20.2
B)21.4
C)20.4
D)20.5
E)19.4

Question 27

Evaluate the expression. $$5 \cdot 10 ^ { 3 } + 5 \cdot 10 ^ { 2 } + 8 \cdot 10 ^ { 1 } + 5$$

A)5,685
B)5,585
C)5,590
D)5,574
E)5,583

Question 28

Simplify the expression. $\frac{6^{\frac{8}{3}}}{6^{\frac{2}{3}}}$

A) $216$
B) $1$
C) $6$
D) $\frac { 1 } { 6 }$
E) $36$

Question 29

Write the quotient as the quotient of two radicals and simplify. $$\sqrt { \frac { 169 } { 144 } }$$

A) $\frac { 5 } { 12 }$
B) $\frac { 12 } { 5 }$
C) $\frac { 13 } { 12 }$
D) $\frac { 12 } { 13 }$
E) $\frac { 169 } { 12 }$

Question 30

What number is the base in the expression ?

Question 31

Simplify the expression. $$9 \frac { 1 } { 2 }$$

A) $\frac { 1 } { 3 }$
B) $5$
C) $\frac { 1 } { 12 }$
D) $1$
E) $3$

Question 32

Evaluate the expression. $$( 4.26 ) ^ { 2 } - ( 4.62 ) ^ { 2 } - ( 0.16 ) ^ { 2 }$$

A)- 6.8
B)- 1.5
C)- 4.3
D)- 3.2
E)- 0.4

Question 33

Simplify the numerical expression. $$2 ^ { 7 } 2 ^ { - 4 }$$

A)2,048
B) $\frac { 1 } { 16 }$
C)8
D) $- \frac { 1 } { 16 }$
E)16

Question 34

Simplify the numerical expression. $$\left( \frac { 3 ^ { - 1 } } { 5 ^ { - 2 } } \right) ^ { - 1 }$$

A) $\frac { 9 } { 25 }$
B) $\frac { 3 } { 25 }$
C) $\frac { 25 } { 9 }$
D) $\frac { 25 } { 3 }$

Question 35

Dividing a decimal by $10 ^ { 3 }$ is equivalent to multiplying it by which number?

A) $10 ^ { - 1.5 }$
B) $10 ^ { 6 }$
C) $10 ^ { - 3 }$
D) $10 ^ { 1.5 }$
E) $10 ^ { 3 }$

Question 36

Evaluate.

Question 37

Multiply. $$- 9.4 \cdot 5.9 \cdot ( - 3.1 )$$

A)171.926
B)166.606
C)-17.1926
D)-171.926
E)17.1926

Question 38

Divide. $$( - 58.45 ) \div ( - 7 )$$

A)8.85
B)8.3
C)9.35
D)8.25
E)8.35

Question 39

Match the statement below with the corresponding property of real numbers. $8 + ( - 8 )$

A)Associative property of addition
B)Commutative property of addition
C)Commutative property of multiplication
D)Additive inverse property

Question 40

Simplify the expression. $$\left( \frac { 125 } { 216 } \right) ^ { \frac { 4 } { 3 } }$$

A) $\frac { 5 } { 6 }$
B) $\frac { 3,125 } { 7,776 }$
C) $\frac { 625 } { 1,296 }$
D) $\frac { 1,296 } { 625 }$
E) $\frac { 627 } { 1,298 }$

Question 41

Let y = $8$ and z = $4$ . Write the phrase as an algebraic expression, and evaluate it. z less than y

A) $y - z ; 5$
B) $y - z ; 4$
C) $y + z$
D) $y + z ; 4$
E) $y - z ; - 4$

Question 42

Is the statement correct? The set of primes together with the set of composites is the set of natural numbers.

A)yes
B)no

Question 43

Find the LCM of 2, 3, and 10.

A)60
B)150
C)30
D)90

Question 44

Find the value of the expression $\left( \frac { 1 } { 2 } \right) ^ { 7 }$ .

A) $\frac { 1 } { 128 }$
B) $\frac { 1 } { 64 }$
C) $\frac { 1 } { 512 }$
D) $\frac { 1 } { 256 }$
E) $\frac { 1 } { 1,024 }$

Question 45

Evaluate the expression. $$2 \cdot 10 ^ { 3 } + 2 \cdot 10 ^ { 2 } + 6 \cdot 10 ^ { 1 } + 6$$

A)2,366
B)2,266
C)2,271
D)2,255
E)2,264

Question 46

Simplify the numerical expression. $$10 ^ { 4 } \cdot 10 ^ { - 5 }$$

A)1,000
B) $\frac { 1 } { 100 }$
C) $\frac { 1 } { 1,000 }$
D) $\frac { 1 } { 10 }$
E)10

Question 47

Find the LCM of 20 and 16.

A)80
B)500
C)25
D)320

Question 48

List the elements in the set that are composite numbers. $$\left\{ - 5,0 , \frac { 2 } { 3 } , 1 , \sqrt { 2 } , 2,9 \right\}$$

A) $0,1,2,9$
B) $9$
C) $2$
D) $1,9$
E) $1,2,9$

Question 49

Simplify the algebraic expression by removing parentheses and combining similar terms. 5(- x - 1)- 3(5 x + 1)- 4( x + 3)

A)-24 x - 20
B)-22 x - 20
C)-22 x - 16
D)22 x + 20
E)-24 x - 16

Question 50

Find the LCM and the GCF of 100 and 120.

A)120, 20
B)600, 40
C)600, 20
D)12,000, 40

Question 51

Multiply and simplify where possible. $$\sqrt { 27 } \sqrt { 33 }$$

A) $11 \sqrt { 11 }$
B) $3 \sqrt { 11 }$
C) $9 \sqrt { 11 }$
D) $11 \sqrt { 3 }$
E) $27 \sqrt { 11 }$

Question 52

Use the change of base formula to identify the expression that is equivalent to $\log _ { 5 } 8$ .

A) $\frac { \log 8 } { \log 5 }$
B) $\frac { \log 5 } { \log 8 }$
C) $\frac { \ln 5 } { \ln 8 }$
D) $5 \log 8$

Question 53

A prime number is a natural number that is larger than 1 and can only be divided exactly by itself and 1. Which of the following sets of numbers contains only prime numbers?

A){ 31, 29, 35 }
B){ 25, 11, 31 }
C){ 19, 29, 31 }
D){ 11, 19, 12 }
E){ 19, 15, 29 }

Question 54

Simplify the algebraic expression by removing parentheses and combining similar terms. $$4 ( x + 1 ) + 6 ( x + 4 )$$

A) $10 x - 28$
B) $10 x + 28$
C) $28 x - 10$
D) $28 x + 10$
E) $10 x - 7$

Question 55

Simplify the expression. $$\left( - 3 z ^ { 2 } - 4 z + 7 \right) + \left( 2 z ^ { 2 } + 2 z - 1 \right) - \left( 4 z ^ { 2 } - 20 z + 9 \right)$$

A) $- 5 z ^ { 2 } + 18 z - 3$
B) $9 z ^ { 2 } + 26 z - 3$
C) $- 5 z ^ { 2 } + 18 z - 17$
D) $- 5 z ^ { 2 } + 26 z - 17$
E)none of these

Question 56

Let x , y , and z represent three real numbers. Write an algebraic expression to denote the product of z , x , and y .

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

Question 57

Simplify the fraction to lowest terms. $\frac { 4 } { 7 }$

A) $0.4$
B) $\frac { 2 } { 7 }$
C) $\frac { 2 } { 4 }$
D) $\frac { 7 } { 4 }$
E)Does not simplify further.

Question 58

What number is the base in the expression ?

Question 59

Write the following statement as a mathematical expression. Five is less than thirty-seven.

A) $5 \geq 37$
B) $5 = 37$
C) $5 \leq 37$
D) $5 < 37$
E) $5 > 37$

Question 60

Evaluate.

Question 61

Simplify the fraction to lowest terms. $$\frac { 56 } { 7 }$$

A) $\frac { 1 } { 7 }$
B) $7$
C) $\frac { 1 } { 8 }$
D) $8$
E) $\frac { 7 } { 56 }$

Question 62

Perform the operation. $$\frac { 2 } { 7 } \left( - \frac { 35 } { 2 } \right)$$

A) $2$
B) $- 5$
C) $- 2$
D) $5$
E)none of these

Question 63

Multiply and reduce your answer to lowest terms. $$- \frac { 38 } { 2 } \cdot \frac { 7 } { 19 } \cdot \frac { 1 } { 14 }$$

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

Question 64

Evaluate the expression.

Question 65

Simplify the fraction to lowest terms. $$\frac { 96 } { 156 }$$

A) $\frac { 8 } { 14 }$
B) $\frac { 24 } { 39 }$
C) $\frac { 8 } { 13 }$
D) $\frac { 32 } { 52 }$
E)Does not simplify further.

Question 66

Find the quotient. $$\frac { 2 } { 7 } \div \left( - \frac { 7 } { 5 } \right)$$

A) $\frac { 15 } { 47 }$
B) $- \frac { 11 } { 54 }$
C) $- \frac { 13 } { 46 }$
D) $- \frac { 8 } { 52 }$
E) $- \frac { 10 } { 49 }$

Question 67

Evaluate the expression. $$\left( 1 - \frac { 1 } { 3 } \right) ^ { 2 } + \left( 1 + \frac { 1 } { 3 } \right) ^ { 2 }$$

A) $2 \frac { 2 } { 9 }$
B) $\frac { 1 } { 9 }$
C) $3 \frac { 2 } { 9 }$
D) $1 \frac { 2 } { 9 }$
E) $1 \frac { 1 } { 9 }$

Question 68

Simplify the complex fraction.

Question 69

Find the sum. $\frac { 16 } { 13 } + 5$

A) $6 \frac { 3 } { 13 }$
B) $5 \frac { 3 } { 13 }$
C) $5 \frac { 4 } { 13 }$
D) $6 \frac { 4 } { 13 }$
E) $65 \frac { 3 } { 13 }$

Question 70

Subtract as indicated, and express your answer in lowest terms. $$- \frac { 2 } { 13 } - \frac { 3 } { 65 }$$

A) $- \frac { 1 } { 5 }$
B) $\frac { 1 } { 4 }$
C) $\frac { 1 } { 5 }$
D) $\frac { 4 } { 5 }$
E) $- \frac { 4 } { 5 }$

Question 71

Perform the addition. Simplify the result when possible. $$\frac { 4 } { 7 } + \frac { 4 } { 7 }$$

A) $\frac { 8 } { 9 }$
B) $\frac { 8 } { 7 }$
C) $\frac { 8 } { 11 }$
D) $\frac { 7 } { 8 }$
E) $\frac { 8 } { 49 }$

Question 72

Find the quotient. $$\left( - \frac { 3 } { 7 } \right) \div \left( - \frac { 7 } { 14 } \right)$$

A) $\frac { 6 } { 49 }$
B) $- \frac { 6 } { 7 }$
C) $\frac { 6 } { 7 }$
D) $- \frac { 2 } { 7 }$
E) $\frac { 2 } { 7 }$

Question 73

Find the quotient. $$\frac { 1 } { 5 } \div \frac { 11 } { 2 }$$

A) $\frac { 3 } { 58 }$
B) $\frac { 2 } { 55 }$
C) $\frac { 1 } { 15 }$
D) $\frac { 5 } { 58 }$
E) $\frac { 1 } { 8 }$