Question 1

Write the reciprocal (or multiplicative inverse) of the number if it exists.
-0

Accepted Answer

A)  1 
B)  Undefined 
C)  $\frac { 1 } { 0 }$ 
D)  0 
A)  1 
B)  Undefined 
C)  $\frac { 1 } { 0 }$ 
D)  0

Question 2

Simplify.
-$( 3 - 8 ) ^ { 3 } - | - 4 - 5 | ^ { 2 }$

Accepted Answer

A)  44 
B)   -126 
C)   -206 
D)   -44 
A)  44 
B)   -126 
C)   -206 
D)   -44

Question 3

Write the number in standard notation.
-There are $2.365 \times 10 ^ { 6 }$ miles of highways, roads, and streets in a certain country.

Accepted Answer

A)  236,500 
B)   2,365,000 
C)   23,650,000 
D)   236,500,000 
A)  236,500 
B)   2,365,000 
C)   23,650,000 
D)   236,500,000

Question 4

Add or subtract as indicated.
- 7+(-11)

Accepted Answer

A)   -18 
B)  18 
C)   -4 
D)  4 
A)   -18 
B)  18 
C)   -4 
D)  4

Question 5

Solve.
-The algebraic expression  300+$\frac { 4000 } { x }$ represents the cost per chair (in dollars) of producing  x  chairs. Complete the table below by evaluating this expression at given values of  x .

Accepted Answer

A)  $\begin{array} { l | c | c | c | c | c } 
\text { chairs } & x & 80 & 160 & 400 & 800 \
\hline \begin{array} { l } 
\text { cost per } \
\text { chair }
\end{array} & 300 + \frac { 4000 } { x } & 350 & 313 & 310 & 303
\end{array}$ 
B)  $\begin{array} { l | c | c | c | c | c } 
\text { chairs } & x & 80 & 160 & 400 & 800 \
\hline \begin{array} { l } 
\text { cost per } \
\text { chair }
\end{array} & 300 + \frac { 4000 } { x } & 350 & 325 & 310 & 305
\end{array}$ 
C)    
D)    
A)  $\begin{array} { l | c | c | c | c | c } 
\text { chairs } & x & 80 & 160 & 400 & 800 \
\hline \begin{array} { l } 
\text { cost per } \
\text { chair }
\end{array} & 300 + \frac { 4000 } { x } & 350 & 313 & 310 & 303
\end{array}$ 
B)  $\begin{array} { l | c | c | c | c | c } 
\text { chairs } & x & 80 & 160 & 400 & 800 \
\hline \begin{array} { l } 
\text { cost per } \
\text { chair }
\end{array} & 300 + \frac { 4000 } { x } & 350 & 325 & 310 & 305
\end{array}$ 
C)    
D)

Question 6

Multiply or divide as indicated.
-$- 11 \cdot 7$

Accepted Answer

A)   -77 
B)   -177 
C)   -770 
D)   -84 
A)   -77 
B)   -177 
C)   -770 
D)   -84

Question 7

List the elements in the set.
-$| x | x$ is an integer greater than 0}

Accepted Answer

A)   {-1,-2,-3, ...} 
B)   {-1,-2,-3} 
C)   {1,2,3, ...} 
D)   {1,2,3,4} 
A)   {-1,-2,-3, ...} 
B)   {-1,-2,-3} 
C)   {1,2,3, ...} 
D)   {1,2,3,4}

Question 8

List the elements in the set.
-$\{ x \mid x$ is an integer between 4 and 8 }

Accepted Answer

A)   {5,6,7,8} 
B)   {4,5,6,7} 
C)   {4,5,6,7,8} 
D)   {5,6,7} 
A)   {5,6,7,8} 
B)   {4,5,6,7} 
C)   {4,5,6,7,8} 
D)   {5,6,7}

Question 9

Tell whether the statement is true or false.
-Every irrational number is a rational number.

Accepted Answer

A) True 
 B)False

Question 10

Insert $ \text {, or } =$ to in the space provided to form a true statement.
--44 ________-39

Accepted Answer

A)  $- 44 = - 39$ 
B)   -44-39 
A)  $- 44 = - 39$ 
B)   -44-39

Question 11

Add or subtract as indicated.
-2+5+6

Accepted Answer

A)   -13 
B)  1 
C)   -9 
D)  13 
A)   -13 
B)  1 
C)   -9 
D)  13

Question 12

Use the product rule to simplify the expression.
-$\left( 4 x ^ { 5 } \right) \left( - 9 x ^ { 7 } \right.$

Accepted Answer

A)  $36 x ^ { 12 }$ 
B)  $36 x ^ { 35 }$ 
C)  $- 36 x ^ { 12 }$ 
D)  $- 36 x ^ { 35 }$ 
A)  $36 x ^ { 12 }$ 
B)  $36 x ^ { 35 }$ 
C)  $- 36 x ^ { 12 }$ 
D)  $- 36 x ^ { 35 }$

Question 13

Write the number in scientific notation.
-1022

Accepted Answer

A)   1.022 x 101 
B)   1.022 x 104 
C)   1.022 x 10-3 
D)   1.022 x 103 
A)   1.022 x 101 
B)   1.022 x 104 
C)   1.022 x 10-3 
D)   1.022 x 103

Question 14

Simplify and write with positive exponents only.
-$\frac { x ^ { - 2 } } { x ^ { - 6 } }$

Accepted Answer

A)  $\frac { 1 } { \mathrm { x } _ { 12 } }$ 
B)  $\frac { 1 } { \mathrm { x } ^ { 4 } }$ 
C)  $x ^ { 4 }$ 
D)  $x ^ { 8 }$ 
A)  $\frac { 1 } { \mathrm { x } _ { 12 } }$ 
B)  $\frac { 1 } { \mathrm { x } ^ { 4 } }$ 
C)  $x ^ { 4 }$ 
D)  $x ^ { 8 }$

Question 15

Perform the indicated operation. Write the answer in scientific notation.
-$\frac { 24,000,000,000 } { 0.00006 }$

Accepted Answer

A)   18 x 1014 
B)   18 x 1013 
C)   4 x 1014 
D)   4 x 1013 
A)   18 x 1014 
B)   18 x 1013 
C)   4 x 1014 
D)   4 x 1013

Question 16

Write the number in standard notation.
-$8.654 \times 10 ^ { - 5 }$

Accepted Answer

A)   -865,400 
B)   0.0008654 
C)   0.000008654 
D)   0.00008654 
A)   -865,400 
B)   0.0008654 
C)   0.000008654 
D)   0.00008654

Question 17

Multiply or divide as indicated.
-$- \frac { 3 } { 8 } \div \left( - \frac { 3 } { 4 } \right)$

Accepted Answer

A)  $- \frac { 9 } { 32 }$ 
B)  2 
C)  $\frac { 1 } { 2 }$ 
D)  $- \frac { 1 } { 2 }$ 
A)  $- \frac { 9 } { 32 }$ 
B)  2 
C)  $\frac { 1 } { 2 }$ 
D)  $- \frac { 1 } { 2 }$

Question 18

Find the absolute value.
-$- \left| - \frac { 11 } { 15 } \right|$

Accepted Answer

A)  $\frac { 11 } { 15 }$ 
B)  $- \frac { 11 } { 15 }$ 
C)   -4 
D)   -26 
A)  $\frac { 11 } { 15 }$ 
B)  $- \frac { 11 } { 15 }$ 
C)   -4 
D)   -26

Question 19

Use a calculator to approximate the square root. Round to three decimal places.
-$\sqrt { 113 }$

Accepted Answer

A)   10.627 
B)   10.630 
C)   113.000 
D)   10.635 
A)   10.627 
B)   10.630 
C)   113.000 
D)   10.635

Question 20

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0.
-$\frac { \left( x ^ { a } + 3 \right) ^ { 6 } } { \left( x ^ { a - 4 } \right) ^ { 3 } }$

Accepted Answer

A)  $3 x ^ { 7 }$ 
B)  $x ^ { 9 a + 30 }$ 
C)  $x ^ { 3 a + 30 }$ 
D)  $x ^ { a } + 30$ 
A)  $3 x ^ { 7 }$ 
B)  $x ^ { 9 a + 30 }$ 
C)  $x ^ { 3 a + 30 }$ 
D)  $x ^ { a } + 30$

Write the reciprocal (or multiplicative inverse) of the number if it exists. -0

Simplify. - $( 3 - 8 ) ^ { 3 } - | - 4 - 5 | ^ { 2 }$

Write the number in standard notation. -There are $2.365 \times 10 ^ { 6 }$ miles of highways, roads, and streets in a certain country.

Add or subtract as indicated. - 7+(-11)

Multiply or divide as indicated. - $- 11 \cdot 7$

List the elements in the set. - $| x | x$ is an integer greater than 0}

List the elements in the set. - $\{ x \mid x$ is an integer between 4 and 8 }

Tell whether the statement is true or false. -Every irrational number is a rational number.

Insert $< , > \text {, or } =$ to in the space provided to form a true statement. --44 ________-39

Add or subtract as indicated. -2+5+6

Use the product rule to simplify the expression. - $\left( 4 x ^ { 5 } \right) \left( - 9 x ^ { 7 } \right.$

Write the number in scientific notation. -1022

Simplify and write with positive exponents only. - $\frac { x ^ { - 2 } } { x ^ { - 6 } }$

Perform the indicated operation. Write the answer in scientific notation. - $\frac { 24,000,000,000 } { 0.00006 }$

Write the number in standard notation. - $8.654 \times 10 ^ { - 5 }$

Multiply or divide as indicated. - $- \frac { 3 } { 8 } \div \left( - \frac { 3 } { 4 } \right)$

Find the absolute value. - $- \left| - \frac { 11 } { 15 } \right|$

Use a calculator to approximate the square root. Round to three decimal places. - $\sqrt { 113 }$

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - $\frac { \left( x ^ { a } + 3 \right) ^ { 6 } } { \left( x ^ { a - 4 } \right) ^ { 3 } }$

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Fractions

Filters

Exam 1: Real Numbers and Algebraic Expressions

Write the reciprocal (or multiplicative inverse) of the number if it exists. -0

Simplify. - (3−8)3−∣−4−5∣2( 3 - 8 ) ^ { 3 } - | - 4 - 5 | ^ { 2 }(3−8)3−∣−4−5∣2

Write the number in standard notation. -There are 2.365×1062.365 \times 10 ^ { 6 }2.365×106 miles of highways, roads, and streets in a certain country.

Add or subtract as indicated. - 7+(-11)

Solve. -The algebraic expression 300+ 4000x\frac { 4000 } { x }x4000​ represents the cost per chair (in dollars) of producing x chairs. Complete the table below by evaluating this expression at given values of x .

Multiply or divide as indicated. - −11⋅7- 11 \cdot 7−11⋅7

List the elements in the set. - ∣x∣x| x | x∣x∣x is an integer greater than 0}

List the elements in the set. - {x∣x\{ x \mid x{x∣x is an integer between 4 and 8 }