Question 1

Simplify the expression using the order of operations.
-$$| 9 - 19 | \cdot - 8 \div ( - 4 )$$

Accepted Answer

A) -320 
B) 20 
C) -20 
D) 320 
A) -320 
B) 20 
C) -20 
D) 320

Question 2

Rationalize the denominator. Assume all variables represent positive real numbers.
-$\frac { \sqrt { 81 } } { \sqrt { 10 } }$

Accepted Answer

A)  109 
B)  $\frac { 9 \sqrt { 10 } } { 10 }$ 
C)  $\frac { 81 \sqrt { 10 } } { 10 }$ 
D)  $9 \sqrt { 10 }$ 
A)  109 
B)  $\frac { 9 \sqrt { 10 } } { 10 }$ 
C)  $\frac { 81 \sqrt { 10 } } { 10 }$ 
D)  $9 \sqrt { 10 }$

Question 3

Completely factor the polynomial or state that the polynomial is prime.
-$$( x + 6 ) ^ { 2 } - 7 ( x + 6 ) + 10$$

Accepted Answer

A)  $\left( x ^ { 2 } + 6 x - 2 \right) \left( x ^ { 2 } + 6 x - 5 \right)$ 
B)  $( x + 4 ) ( x + 1 )$ 
C)  $\left( x ^ { 2 } - 6 x + 2 \right) \left( x ^ { 2 } - 6 x + 5 \right)$ 
D)  $( x + 8 ) ( x + 11 )$ 
A)  $\left( x ^ { 2 } + 6 x - 2 \right) \left( x ^ { 2 } + 6 x - 5 \right)$ 
B)  $( x + 4 ) ( x + 1 )$ 
C)  $\left( x ^ { 2 } - 6 x + 2 \right) \left( x ^ { 2 } - 6 x + 5 \right)$ 
D)  $( x + 8 ) ( x + 11 )$

Question 4

Given the set sketched on the number line, identify the type of interval (open, closed, half-open, open infinite, closed infinite), write the set using set-builder notation, and write the set using interval notation.
-

Accepted Answer

A)  closed interval; $\{ x \mid - 9 \leq x \leq - 3 \} ; [ - 9 , - 3 ]$ 
B)  half-open interval; $\{ x \mid - 9 < x \leq - 3 \} ; ( - 9 , - 3 ]$ 
C)  half-open interval; $\{ x \mid - 9 \leq x < - 3 \} ; [ - 9 , - 3 )$ 
D)  open interval; $\{ x \mid - 9 < x < - 3 \} ; ( - 9 , - 3 )$ 
A)  closed interval; $\{ x \mid - 9 \leq x \leq - 3 \} ; [ - 9 , - 3 ]$ 
B)  half-open interval; $\{ x \mid - 9 < x \leq - 3 \} ; ( - 9 , - 3 ]$ 
C)  half-open interval; $\{ x \mid - 9 \leq x < - 3 \} ; [ - 9 , - 3 )$ 
D)  open interval; $\{ x \mid - 9 < x < - 3 \} ; ( - 9 , - 3 )$

Question 5

Write the expression using exponential notation. Then identify the base and the exponent.
-$( - 3 x ) \cdot ( - 3 x ) \cdot ( - 3 x ) \cdot ( - 3 x )$

Accepted Answer

A)  $- 3 x ^ { 4 }$
base: $- 3 x$
exponent: 4 
B)  $- 3 x ^ { 4 }$
base: $3 \mathrm { x }$
exponent: 4 
C)  $( - 3 x ) ^ { 4 }$
base: $3 x$
exponent: 4 
D)  $( - 3 x ) ^ { 4 }$
base: $- 3 x$
exponent: 4 
A)  $- 3 x ^ { 4 }$
base: $- 3 x$
exponent: 4 
B)  $- 3 x ^ { 4 }$
base: $3 \mathrm { x }$
exponent: 4 
C)  $( - 3 x ) ^ { 4 }$
base: $3 x$
exponent: 4 
D)  $( - 3 x ) ^ { 4 }$
base: $- 3 x$
exponent: 4

Question 6

Factor out the greatest common factor.
-$$x ( x + 14 ) + 8 ( x + 14 )$$

Accepted Answer

A)  $14 x ( x + 8 )$ 
B)  $( x + 14 ) ( x + 8 )$ 
C)  $8 x ( x + 14 )$ 
D)  $\left( x ^ { 2 } + 14 x \right) + ( 8 x + 112 )$ 
A)  $14 x ( x + 8 )$ 
B)  $( x + 14 ) ( x + 8 )$ 
C)  $8 x ( x + 14 )$ 
D)  $\left( x ^ { 2 } + 14 x \right) + ( 8 x + 112 )$

Question 7

List all the elements of B that belong to the given set.
-$$B = \left\{ 11 , \sqrt { 8 } , - 6,0 , \frac { 0 } { 4 } , \sqrt { 9 } , 0.68 , - 8 \pi , 0.999 \ldots \right\}$$
Rational numbers

Accepted Answer

A)  $\left\{ 11 , - 6,0 , \frac { 0 } { 4 } , \sqrt { 9 } , 0.68,0.999 \ldots \right\}$ 
B)  $\left\{ 11 , - 6,0 , \frac { 0 } { 4 } , 0.68 \right\}$ 
C)  $\left\{ 11 , - 6,0 , \frac { 0 } { 4 } , \sqrt { 9 } , 0.68 , - 8 \pi , 0.999 \ldots \right\}$ 
D)  $\left\{ 11 , - 6,0 , \frac { 0 } { 4 } , 0.68,0.999 \ldots \right\}$ 
A)  $\left\{ 11 , - 6,0 , \frac { 0 } { 4 } , \sqrt { 9 } , 0.68,0.999 \ldots \right\}$ 
B)  $\left\{ 11 , - 6,0 , \frac { 0 } { 4 } , 0.68 \right\}$ 
C)  $\left\{ 11 , - 6,0 , \frac { 0 } { 4 } , \sqrt { 9 } , 0.68 , - 8 \pi , 0.999 \ldots \right\}$ 
D)  $\left\{ 11 , - 6,0 , \frac { 0 } { 4 } , 0.68,0.999 \ldots \right\}$

Question 8

Perform the indicated operations and simplify the result. Leave the answer in factored form.
-$$\frac { \frac { 7 } { x } + 1 } { \frac { 7 } { x } - 1 }$$

Accepted Answer

A)  $\frac { x ^ { 2 } } { x ^ { 2 } + 7 }$ 
B)  7 
C)  $x ^ { 2 } + 7$ 
D)  $\frac { 7 + x } { 7 - x }$ 
A)  $\frac { x ^ { 2 } } { x ^ { 2 } + 7 }$ 
B)  7 
C)  $x ^ { 2 } + 7$ 
D)  $\frac { 7 + x } { 7 - x }$

Question 9

Rationalize the denominator. Assume all variables represent positive real numbers.
-$\frac { 7 - \sqrt { 2 } } { 7 + \sqrt { 2 } }$

Accepted Answer

A)  $\frac { 47 - 14 \sqrt { 2 } } { 51 }$ 
B)  1 
C)  $\frac { 51 - 14 \sqrt { 2 } } { 47 }$ 
D)  $\frac { 51 + 14 \sqrt { 2 } } { 47 }$ 
A)  $\frac { 47 - 14 \sqrt { 2 } } { 51 }$ 
B)  1 
C)  $\frac { 51 - 14 \sqrt { 2 } } { 47 }$ 
D)  $\frac { 51 + 14 \sqrt { 2 } } { 47 }$

Question 10

Simplify the expression using the order of operations.
-$$- 2 - ( - 7 + 9 \cdot 9 - 2 )$$

Accepted Answer

A) -88 
B) -74 
C) -78 
D) 70 
A) -88 
B) -74 
C) -78 
D) 70

Question 11

Perform the indicated operations and simplify the result. Leave the answer in factored form.
-$$\frac { 6 - x } { x - 2 } - \frac { 2 x - 1 } { 2 - x }$$

Accepted Answer

A)  $\frac { x + 7 } { x - 2 }$ 
B)  $- \frac { x + 5 } { x - 2 }$ 
C)  $\frac { x + 5 } { x - 2 }$ 
D)  $- \frac { x + 7 } { x - 2 }$ 
A)  $\frac { x + 7 } { x - 2 }$ 
B)  $- \frac { x + 5 } { x - 2 }$ 
C)  $\frac { x + 5 } { x - 2 }$ 
D)  $- \frac { x + 7 } { x - 2 }$

Question 12

Completely factor the polynomial or state that the polynomial is prime.
-$x ^ { 2 } + 7 x - 8$

Accepted Answer

A)  prime 
B)  $( x + 1 ) ( x + 1 )$ 
C)  $( x + 1 ) ( x + 8 )$ 
D)  $( x - 1 ) ( x + 8 )$ 
A)  prime 
B)  $( x + 1 ) ( x + 1 )$ 
C)  $( x + 1 ) ( x + 8 )$ 
D)  $( x - 1 ) ( x + 8 )$

Question 13

Simplify the radical expression. Assume all variables represent positive real numbers.
-$\sqrt { 6 x ^ { 2 } } + 2 \sqrt { 96 x ^ { 2 } } + 6 \sqrt { 96 x ^ { 2 } }$

Accepted Answer

A)  $33 x \sqrt { 135 }$ 
B)  $8 \times \sqrt { 6 }$ 
C)  $33 x \sqrt { 6 }$ 
D)  $8 \times \sqrt { 135 }$ 
A)  $33 x \sqrt { 135 }$ 
B)  $8 \times \sqrt { 6 }$ 
C)  $33 x \sqrt { 6 }$ 
D)  $8 \times \sqrt { 135 }$

Question 14

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers.
-8 4/3

Accepted Answer

A)  128 
B)  64 
C)  32 
D)  16 
A)  128 
B)  64 
C)  32 
D)  16

Question 15

Find the intersection of the given intervals.
-$[ - 6 , \infty ) \cap ( - \infty , - 4 ]$

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $( - \infty , - 4 ]$ 
C)  $[ - 6 , \infty )$ 
D)  $[ - 6 , - 4 ]$ 
A)  $( - \infty , \infty )$ 
B)  $( - \infty , - 4 ]$ 
C)  $[ - 6 , \infty )$ 
D)  $[ - 6 , - 4 ]$

Question 16

Write the given set in interval notation and graph the set on a number line.
-$$\left\{ x \mid - \frac { 1 } { 2 } < x \leq 3 \right\}$$

Accepted Answer

A)  $\left[ - \frac { 1 } { 2 } , 3 \right]$
  
B)  $\left[ - \frac { 1 } { 2 } , 3 \right)$
  
C)  $\left[ - \frac { 1 } { 2 } , 3 \right]$
  
D)  $\left[ - \frac { 1 } { 2 } , 3 \right]$
  
A)  $\left[ - \frac { 1 } { 2 } , 3 \right]$
  
B)  $\left[ - \frac { 1 } { 2 } , 3 \right)$
  
C)  $\left[ - \frac { 1 } { 2 } , 3 \right]$
  
D)  $\left[ - \frac { 1 } { 2 } , 3 \right]$

Question 17

Given the set sketched on the number line, identify the type of interval (open, closed, half-open, open infinite, closed infinite), write the set using set-builder notation, and write the set using interval notation.
-

Accepted Answer

A)  open interval; $\{ x \mid - 3 < x < 2 \} ; ( - 3,2 )$ 
B)  half-open interval; $\{ \mathrm { x } \mid - 3 \leq \mathrm { x } < 2 \} ; [ - 3,2 )$ 
C)  half-open interval; $\{ x \mid - 3 < x \leq 2 \} ; ( - 3,2 ]$ 
D)  closed interval; $\{ x \mid - 3 \leq x \leq 2 \} ; [ - 3,2 ]$ 
A)  open interval; $\{ x \mid - 3 < x < 2 \} ; ( - 3,2 )$ 
B)  half-open interval; $\{ \mathrm { x } \mid - 3 \leq \mathrm { x } < 2 \} ; [ - 3,2 )$ 
C)  half-open interval; $\{ x \mid - 3 < x \leq 2 \} ; ( - 3,2 ]$ 
D)  closed interval; $\{ x \mid - 3 \leq x \leq 2 \} ; [ - 3,2 ]$

Question 18

Factor out the greatest common factor.
-$$x ^ { 2 } ( x - 8 ) - ( x - 8 )$$

Accepted Answer

A)  $( x - 8 ) \left( x ^ { 2 } - 1 \right)$ 
B)  $x ^ { 2 } ( x - 8 )$ 
C)  $( x - 8 ) \left( x ^ { 2 } + 1 \right)$ 
D)  $\left( x ^ { 3 } - 8 x ^ { 2 } \right) - ( x - 8 )$ 
A)  $( x - 8 ) \left( x ^ { 2 } - 1 \right)$ 
B)  $x ^ { 2 } ( x - 8 )$ 
C)  $( x - 8 ) \left( x ^ { 2 } + 1 \right)$ 
D)  $\left( x ^ { 3 } - 8 x ^ { 2 } \right) - ( x - 8 )$

Question 19

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form.
-$$( x + 10 ) ( x - 10 )$$

Accepted Answer

A)  $x ^ { 2 } + 20 x - 100$ 
B)  $x ^ { 2 } - 20 x - 100$ 
C)  $x ^ { 2 } - 20$ 
D)  $x ^ { 2 } - 100$ 
A)  $x ^ { 2 } + 20 x - 100$ 
B)  $x ^ { 2 } - 20 x - 100$ 
C)  $x ^ { 2 } - 20$ 
D)  $x ^ { 2 } - 100$

Question 20

Determine whether the expression is a polynomial. If it is a polynomial, give its degree.
-$$- 6 y ^ { 6 } - \sqrt { 2 }$$

Accepted Answer

A) polynomial; degree 6 
B) polynomial; degree 2 
C) polynomial; degree -6 
D) not a polynomial 
A) polynomial; degree 6 
B) polynomial; degree 2 
C) polynomial; degree -6 
D) not a polynomial

Simplify the expression using the order of operations. - $| 9 - 19 | \cdot - 8 \div ( - 4 )$

Rationalize the denominator. Assume all variables represent positive real numbers. - $\frac { \sqrt { 81 } } { \sqrt { 10 } }$

Completely factor the polynomial or state that the polynomial is prime. - $( x + 6 ) ^ { 2 } - 7 ( x + 6 ) + 10$

Given the set sketched on the number line, identify the type of interval (open, closed, half-open, open infinite, closed infinite), write the set using set-builder notation, and write the set using interval notation. -

Write the expression using exponential notation. Then identify the base and the exponent. - $( - 3 x ) \cdot ( - 3 x ) \cdot ( - 3 x ) \cdot ( - 3 x )$

Factor out the greatest common factor. - $x ( x + 14 ) + 8 ( x + 14 )$

List all the elements of B that belong to the given set. - $B = \left\{ 11 , \sqrt { 8 } , - 6,0 , \frac { 0 } { 4 } , \sqrt { 9 } , 0.68 , - 8 \pi , 0.999 \ldots \right\}$ Rational numbers

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { \frac { 7 } { x } + 1 } { \frac { 7 } { x } - 1 }$

Rationalize the denominator. Assume all variables represent positive real numbers. - $\frac { 7 - \sqrt { 2 } } { 7 + \sqrt { 2 } }$

Simplify the expression using the order of operations. - $- 2 - ( - 7 + 9 \cdot 9 - 2 )$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 6 - x } { x - 2 } - \frac { 2 x - 1 } { 2 - x }$

Completely factor the polynomial or state that the polynomial is prime. - $x ^ { 2 } + 7 x - 8$

Simplify the radical expression. Assume all variables represent positive real numbers. - $\sqrt { 6 x ^ { 2 } } + 2 \sqrt { 96 x ^ { 2 } } + 6 \sqrt { 96 x ^ { 2 } }$

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. -8^4/3

Find the intersection of the given intervals. - $[ - 6 , \infty ) \cap ( - \infty , - 4 ]$

Write the given set in interval notation and graph the set on a number line. - $\left\{ x \mid - \frac { 1 } { 2 } < x \leq 3 \right\}$ $Write the given set in interval notation and graph the set on a number line. - \left\{ x \mid - \frac { 1 } { 2 } < x \leq 3 \right\}$

Given the set sketched on the number line, identify the type of interval (open, closed, half-open, open infinite, closed infinite), write the set using set-builder notation, and write the set using interval notation. -

Factor out the greatest common factor. - $x ^ { 2 } ( x - 8 ) - ( x - 8 )$

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form. - $( x + 10 ) ( x - 10 )$

Determine whether the expression is a polynomial. If it is a polynomial, give its degree. - $- 6 y ^ { 6 } - \sqrt { 2 }$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Filters

Exam 10: Math Exercises: Sets, Intervals, Absolute Value, and Properties

Simplify the expression using the order of operations. - ∣9−19∣⋅−8÷(−4)| 9 - 19 | \cdot - 8 \div ( - 4 )∣9−19∣⋅−8÷(−4)

Rationalize the denominator. Assume all variables represent positive real numbers. - 8110\frac { \sqrt { 81 } } { \sqrt { 10 } }10​81​​

Completely factor the polynomial or state that the polynomial is prime. - (x+6)2−7(x+6)+10( x + 6 ) ^ { 2 } - 7 ( x + 6 ) + 10(x+6)2−7(x+6)+10

Given the set sketched on the number line, identify the type of interval (open, closed, half-open, open infinite, closed infinite), write the set using set-builder notation, and write the set using interval notation. -

Write the expression using exponential notation. Then identify the base and the exponent. - (−3x)⋅(−3x)⋅(−3x)⋅(−3x)( - 3 x ) \cdot ( - 3 x ) \cdot ( - 3 x ) \cdot ( - 3 x )(−3x)⋅(−3x)⋅(−3x)⋅(−3x)

Factor out the greatest common factor. - x(x+14)+8(x+14)x ( x + 14 ) + 8 ( x + 14 )x(x+14)+8(x+14)

List all the elements of B that belong to the given set. - B={11,8,−6,0,04,9,0.68,−8π,0.999…}B = \left\{ 11 , \sqrt { 8 } , - 6,0 , \frac { 0 } { 4 } , \sqrt { 9 } , 0.68 , - 8 \pi , 0.999 \ldots \right\}B={11,8​,−6,0,40​,9​,0.68,−8π,0.999…} Rational numbers

Perform the indicated operations and simplify the result. Leave the answer in factored form. - 7x+17x−1\frac { \frac { 7 } { x } + 1 } { \frac { 7 } { x } - 1 }x7​−1x7​+1​

Rationalize the denominator. Assume all variables represent positive real numbers. - 7−27+2\frac { 7 - \sqrt { 2 } } { 7 + \sqrt { 2 } }7+2​7−2​​

Simplify the expression using the order of operations. - −2−(−7+9⋅9−2)- 2 - ( - 7 + 9 \cdot 9 - 2 )−2−(−7+9⋅9−2)

Perform the indicated operations and simplify the result. Leave the answer in factored form. - 6−xx−2−2x−12−x\frac { 6 - x } { x - 2 } - \frac { 2 x - 1 } { 2 - x }x−26−x​−2−x2x−1​

Completely factor the polynomial or state that the polynomial is prime. - x2+7x−8x ^ { 2 } + 7 x - 8x2+7x−8

Simplify the radical expression. Assume all variables represent positive real numbers. - 6x2+296x2+696x2\sqrt { 6 x ^ { 2 } } + 2 \sqrt { 96 x ^ { 2 } } + 6 \sqrt { 96 x ^ { 2 } }6x2​+296x2​+696x2​

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. -8 4/3

Find the intersection of the given intervals. - [−6,∞)∩(−∞,−4][ - 6 , \infty ) \cap ( - \infty , - 4 ][−6,∞)∩(−∞,−4]

Write the given set in interval notation and graph the set on a number line. - {x∣−12<x≤3}\left\{ x \mid - \frac { 1 } { 2 } < x \leq 3 \right\}{x∣−21​<x≤3}

Given the set sketched on the number line, identify the type of interval (open, closed, half-open, open infinite, closed infinite), write the set using set-builder notation, and write the set using interval notation. -

Factor out the greatest common factor. - x2(x−8)−(x−8)x ^ { 2 } ( x - 8 ) - ( x - 8 )x2(x−8)−(x−8)

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form. - (x+10)(x−10)( x + 10 ) ( x - 10 )(x+10)(x−10)

Determine whether the expression is a polynomial. If it is a polynomial, give its degree. - −6y6−2- 6 y ^ { 6 } - \sqrt { 2 }−6y6−2​

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Filters

Simplify the expression using the order of operations. - $| 9 - 19 | \cdot - 8 \div ( - 4 )$

Rationalize the denominator. Assume all variables represent positive real numbers. - $\frac { \sqrt { 81 } } { \sqrt { 10 } }$

Completely factor the polynomial or state that the polynomial is prime. - $( x + 6 ) ^ { 2 } - 7 ( x + 6 ) + 10$

Write the expression using exponential notation. Then identify the base and the exponent. - $( - 3 x ) \cdot ( - 3 x ) \cdot ( - 3 x ) \cdot ( - 3 x )$

Factor out the greatest common factor. - $x ( x + 14 ) + 8 ( x + 14 )$

List all the elements of B that belong to the given set. - $B = \left\{ 11 , \sqrt { 8 } , - 6,0 , \frac { 0 } { 4 } , \sqrt { 9 } , 0.68 , - 8 \pi , 0.999 \ldots \right\}$ Rational numbers

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { \frac { 7 } { x } + 1 } { \frac { 7 } { x } - 1 }$

Rationalize the denominator. Assume all variables represent positive real numbers. - $\frac { 7 - \sqrt { 2 } } { 7 + \sqrt { 2 } }$

Simplify the expression using the order of operations. - $- 2 - ( - 7 + 9 \cdot 9 - 2 )$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 6 - x } { x - 2 } - \frac { 2 x - 1 } { 2 - x }$

Completely factor the polynomial or state that the polynomial is prime. - $x ^ { 2 } + 7 x - 8$

Simplify the radical expression. Assume all variables represent positive real numbers. - $\sqrt { 6 x ^ { 2 } } + 2 \sqrt { 96 x ^ { 2 } } + 6 \sqrt { 96 x ^ { 2 } }$

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. -8^4/3

Find the intersection of the given intervals. - $[ - 6 , \infty ) \cap ( - \infty , - 4 ]$

Write the given set in interval notation and graph the set on a number line. - $\left\{ x \mid - \frac { 1 } { 2 } < x \leq 3 \right\}$ $Write the given set in interval notation and graph the set on a number line. - \left\{ x \mid - \frac { 1 } { 2 } < x \leq 3 \right\}$

Factor out the greatest common factor. - $x ^ { 2 } ( x - 8 ) - ( x - 8 )$

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form. - $( x + 10 ) ( x - 10 )$

Determine whether the expression is a polynomial. If it is a polynomial, give its degree. - $- 6 y ^ { 6 } - \sqrt { 2 }$