Question 1

Match between columns
                        Premises: integer

Accepted Answer

The Answer of {..., -3, -2, -1, 0, 1, 2, is...

Question 2

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

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

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 5

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

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

A) true 
B) false

Question 11

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

Accepted Answer

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 12

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

Accepted Answer

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 13

Subtract. $$44.5$$
$24.1$

Accepted Answer

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

Question 14

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 $x = - \sqrt { a }$ .

Accepted Answer

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 15

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

Accepted Answer

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 16

Evaluate. $- 6 ^ { 2 } + 6 ^ { 2 }$

Accepted Answer

The answer of Evaluate. \(- 6 ^ { 2 }...

Question 17

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 18

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

Accepted Answer

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 19

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

Accepted Answer

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

Question 20

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

Accepted Answer

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

Exam 1: Basic Concepts and Properties

Match each description below with the letter of the correct number set.

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

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

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

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

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

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

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

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

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

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

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

Subtract. $44.5$ $24.1$

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 $x = - \sqrt { a }$ .

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

Evaluate. $- 6 ^ { 2 } + 6 ^ { 2 }$

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

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

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

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

Exam 1: Basic Concepts and Properties

Match each description below with the letter of the correct number set.

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

Simplify the numerical expression. −(15) −2- \left( \frac { 1 } { 5 } \right) ^ { - 2 }−(51​) −2

Find the sum. 6111+9256 \frac { 1 } { 11 } + 9 \frac { 2 } { 5 }6111​+952​

Simplify the numerical expression. 104⋅10−510 ^ { 4 } \cdot 10 ^ { - 5 }104⋅10−5

Simplify the expression. 683623\frac{6^{\frac{8}{3}}}{6^{\frac{2}{3}}}632​638​​

List the elements in the set that are composite numbers. {−5,0,23,1,2,2,9}\left\{ - 5,0 , \frac { 2 } { 3 } , 1 , \sqrt { 2 } , 2,9 \right\}{−5,0,32​,1,2​,2,9}

Multiply. −9.4⋅5.9⋅(−3.1) - 9.4 \cdot 5.9 \cdot ( - 3.1 ) −9.4⋅5.9⋅(−3.1)

Simplify the expression. (213323) 3\left( 2 \frac { 1 } { 3 } 3 ^ { \frac { 2 } { 3 } } \right) ^ { 3 }(231​332​) 3

If x is any nonzero real number, then x−5=1x5x ^ { - 5 } = \frac { 1 } { x ^ { 5 } }x−5=x51​ .

Find the sum. 1613+5\frac { 16 } { 13 } + 51316​+5

List the numbers in the set that are natural numbers. {−5,−1,−45,0,1,1312,2,6,3.75,6,8}\left\{ - 5 , - 1 , - \frac { 4 } { 5 } , 0,1 , \frac { 13 } { 12 } , 2 , \sqrt { 6 } , 3.75,6,8 \right\}{−5,−1,−54​,0,1,1213​,2,6​,3.75,6,8}

Subtract. 44.544.544.5 24.124.124.1

Solve the quadratic equation. 2(x+8) 2−5=32 ( x + 8 ) ^ { 2 } - 5 = 32(x+8) 2−5=3 Use the following property: For any real number DDD , x2=ax ^ { 2 } = ax2=a if and only if x=ax = \sqrt { a }x=a​ or x=−ax = - \sqrt { a }x=−a​ .

Simplify the expression. (125216) 43\left( \frac { 125 } { 216 } \right) ^ { \frac { 4 } { 3 } }(216125​) 34​

Evaluate. −62+62- 6 ^ { 2 } + 6 ^ { 2 }−62+62

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

Simplify the expression. (−3z2−4z+7) +(2z2+2z−1) −(4z2−20z+9) \left( - 3 z ^ { 2 } - 4 z + 7 \right) + \left( 2 z ^ { 2 } + 2 z - 1 \right) - \left( 4 z ^ { 2 } - 20 z + 9 \right) (−3z2−4z+7) +(2z2+2z−1) −(4z2−20z+9)

Find the value of the expression (12) 7\left( \frac { 1 } { 2 } \right) ^ { 7 }(21​) 7 .

Simplify the fraction to lowest terms. 47\frac { 4 } { 7 }74​

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

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

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

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

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

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

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

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

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

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

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

Subtract. $44.5$ $24.1$

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 $x = - \sqrt { a }$ .

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

Evaluate. $- 6 ^ { 2 } + 6 ^ { 2 }$

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

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

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

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