Question 1

Evaluate the expression.
-$125 ^ { 1 / 3 }$

Accepted Answer

A)  625 
B)  1875 
C)  5 
D)  15 
A)  625 
B)  1875 
C)  5 
D)  15

Question 2

Solve the problem. Round to two decimal places unless otherwise indicated.
-In the following formula, $y$ is the minimum number of hours of studying required to attain a test score of $x : y = \frac { 0.37 x } { 100.5 - x }$. How many hours of study are needed to score 87 ?

Accepted Answer

A)  $23.80 \mathrm { hr }$ 
B)  $101.07 \mathrm { hr }$ 
C)  $2.38 \mathrm { hr }$ 
D)  $6.03 \mathrm { hr }$ 
A)  $23.80 \mathrm { hr }$ 
B)  $101.07 \mathrm { hr }$ 
C)  $2.38 \mathrm { hr }$ 
D)  $6.03 \mathrm { hr }$

Question 3

Factor the trinomial, if possible.
-$49 m ^ { 2 } + 126 m + 81$

Accepted Answer

A)  $( 7 m + 9 ) ( 7 m - 9 )$ 
B)  $( 7 m - 9 ) ^ { 2 }$ 
C)  $( 7 m + 9 ) ^ { 2 }$ 
D)  $( 7 m - 10 ) ^ { 2 }$ 
A)  $( 7 m + 9 ) ( 7 m - 9 )$ 
B)  $( 7 m - 9 ) ^ { 2 }$ 
C)  $( 7 m + 9 ) ^ { 2 }$ 
D)  $( 7 m - 10 ) ^ { 2 }$

Question 4

Write the expression in lowest terms.
-$\frac { 22 k ^ { 2 } } { 25 k }$

Accepted Answer

A)  $\frac { 11 } { 12 } \mathrm { k }$ 
B)  $\frac { 22 } { 25 } k$ 
C)  $\frac { 22 } { 25 }$ 
D)  $\frac { 11 } { 12 }$ 
A)  $\frac { 11 } { 12 } \mathrm { k }$ 
B)  $\frac { 22 } { 25 } k$ 
C)  $\frac { 22 } { 25 }$ 
D)  $\frac { 11 } { 12 }$

Question 5

Find the product.
-$$( 9 p + 10 ) ( 9 p - 10 )$$

Accepted Answer

A)  $81 p ^ { 2 } - 100$ 
B)  $81 p ^ { 2 } + 180 p - 100$ 
C)  $\mathrm { p } ^ { 2 } - 100$ 
D)  $81 p ^ { 2 } - 180 p - 100$ 
A)  $81 p ^ { 2 } - 100$ 
B)  $81 p ^ { 2 } + 180 p - 100$ 
C)  $\mathrm { p } ^ { 2 } - 100$ 
D)  $81 p ^ { 2 } - 180 p - 100$

Question 6

Find the domain of the expression.
-$$\frac { a - 9 } { - 8 + a }$$

Accepted Answer

A)  all real numbers 
B)  $\{ a \mid a \neq 8 \}$ 
C)  $\{ a \mid a \neq - 8 \}$ 
D)  $\{ a \mid a \neq 9 \}$ 
A)  all real numbers 
B)  $\{ a \mid a \neq 8 \}$ 
C)  $\{ a \mid a \neq - 8 \}$ 
D)  $\{ a \mid a \neq 9 \}$

Question 7

Solve the problem.
-The cost of manufacturing clocks is given by c = 49(n + 36)1/2, where c is the cost in dollars and n is the number produced. What is the cost when no clocks are produced?

Accepted Answer

A)  $49 
B)  $294 
C)  $42 
D)  $1764 
A)  $49 
B)  $294 
C)  $42 
D)  $1764

Question 8

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$z ^ { - 2 / 5 } \cdot z ^ { 3 / 5 }$

Accepted Answer

A)  $z ^ { 6 / 5 }$ 
B)  $z ^ { 1 / 5 }$ 
C)  $z ^ { 5 / 6 }$ 
D)  $\mathrm { z } ^ { - 1 / 5 }$ 
A)  $z ^ { 6 / 5 }$ 
B)  $z ^ { 1 / 5 }$ 
C)  $z ^ { 5 / 6 }$ 
D)  $\mathrm { z } ^ { - 1 / 5 }$

Question 9

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers.
-$\frac { 5 } { 3 } \left( \frac { 2 } { 5 } y - \frac { 3 } { 10 } x + \frac { 4 } { 5 } \right)$

Accepted Answer

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

Question 10

Find the product.
-$$( 11 a + 4 c ) ( 11 a - 4 c )$$

Accepted Answer

A)  $11 a ^ { 2 } - 4 c ^ { 2 }$ 
B)  $121 a ^ { 2 } - 88 a c - 16 c ^ { 2 }$ 
C)  $121 a ^ { 2 } - 16 c ^ { 2 }$ 
D)  $121 a ^ { 2 } + 88 a c - 16 c ^ { 2 }$ 
A)  $11 a ^ { 2 } - 4 c ^ { 2 }$ 
B)  $121 a ^ { 2 } - 88 a c - 16 c ^ { 2 }$ 
C)  $121 a ^ { 2 } - 16 c ^ { 2 }$ 
D)  $121 a ^ { 2 } + 88 a c - 16 c ^ { 2 }$

Question 11

Evaluate the expression.
-Let $x = 2 , y = 3$. Evaluate $| 6 x - 7 y |$.

Accepted Answer

A)  9 
B)  $- 9$ 
C)  $- 33$ 
D)  33 
A)  9 
B)  $- 9$ 
C)  $- 33$ 
D)  33

Question 12

Evaluate the expression.
-$$| - 12 |$$

Accepted Answer

A)  12 
B)  $- 12$ 
C)  0 
D)  $\pm 12$ 
A)  12 
B)  $- 12$ 
C)  0 
D)  $\pm 12$

Question 13

Factor by any method.
-$1000 c ^ { 3 } + 27$

Accepted Answer

A)  $( 1000 c + 3 ) \left( c ^ { 2 } - 30 c + 9 \right)$ 
B)  $( 10 c - 3 ) \left( 100 c ^ { 2 } + 30 c + 9 \right)$ 
C)  $( 10 c + 3 ) \left( 100 c ^ { 2 } - 30 c + 9 \right)$ 
D)  $( 10 c + 3 ) \left( 100 c ^ { 2 } + 9 \right)$ 
A)  $( 1000 c + 3 ) \left( c ^ { 2 } - 30 c + 9 \right)$ 
B)  $( 10 c - 3 ) \left( 100 c ^ { 2 } + 30 c + 9 \right)$ 
C)  $( 10 c + 3 ) \left( 100 c ^ { 2 } - 30 c + 9 \right)$ 
D)  $( 10 c + 3 ) \left( 100 c ^ { 2 } + 9 \right)$

Question 14

Provide an appropriate response.
-Consider the following figure, which is a square divided into two squares and two rectangles.   The length of each side of the large square is $x + 7$, which means that the area of the largest square is $( x + 7 ) ^ { 2 }$. Use the formulas for the area of a square and the area of a rectangle to write the area of the largest square as a trinomial that represents the sum of the areas of the four figures that comprise it.

Accepted Answer

A)  $x ^ { 2 } + 14 x + 49$ 
B)  $x ^ { 2 } - 2 x + 49$ 
C)  $x ^ { 2 } + x + 49$ 
D)  $x ^ { 2 } + 7 x + 49$ 
A)  $x ^ { 2 } + 14 x + 49$ 
B)  $x ^ { 2 } - 2 x + 49$ 
C)  $x ^ { 2 } + x + 49$ 
D)  $x ^ { 2 } + 7 x + 49$

Question 15

Decide whether the expression has been simplified correctly.
-$$\left( x ^ { 3 } \right) ^ { 2 } = x ^ { 6 }$$

Accepted Answer

A)  Not simplified correctly 
B)  Simplified correctly 
A)  Not simplified correctly 
B)  Simplified correctly

Question 16

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
--23

Accepted Answer

A)  None of these 
B)  Trinomial 
C)  Monomial 
D)  Binomial 
A)  None of these 
B)  Trinomial 
C)  Monomial 
D)  Binomial

Question 17

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 3 ] { 175 } \cdot \sqrt [ 3 ] { 25 }$

Accepted Answer

A)  $10 \sqrt [ 3 ] { 15 }$ 
B)  $5 \sqrt [ 3 ] { 35 }$ 
C)  $10 \sqrt [ 3 ] { 35 }$ 
D)  $5 \sqrt [ 3 ] { 25 }$ 
A)  $10 \sqrt [ 3 ] { 15 }$ 
B)  $5 \sqrt [ 3 ] { 35 }$ 
C)  $10 \sqrt [ 3 ] { 35 }$ 
D)  $5 \sqrt [ 3 ] { 25 }$

Question 18

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt { \frac { 2 } { 3 } } - \sqrt { \frac { 72 } { 108 } }$$

Accepted Answer

A)  0 
B)  $- 1$ 
C)  $- 6$ 
D)  $- \frac { 1 } { 6 }$ 
A)  0 
B)  $- 1$ 
C)  $- 6$ 
D)  $- \frac { 1 } { 6 }$

Question 19

Determine which property of absolute value justifies the statement.
-$$| x + y | \leq | x | + | y |$$

Accepted Answer

A)  Property 5 : the sum of the absolute values of two numbers is less than or equal to the absolute value of their sum (the triangle inequality). 
B)  Property 4: the sum of two numbers is less than or equal to the absolute value of the sum of the numbers. 
C)  Property 5: the absolute value of the sum of two numbers is less than or equal to the sum of their absolute values (the triangle inequality). 
D)  Property 4: the absolute value of the sum of the numbers is less than or equal to the sum of the two numbers. 
A)  Property 5 : the sum of the absolute values of two numbers is less than or equal to the absolute value of their sum (the triangle inequality). 
B)  Property 4: the sum of two numbers is less than or equal to the absolute value of the sum of the numbers. 
C)  Property 5: the absolute value of the sum of two numbers is less than or equal to the sum of their absolute values (the triangle inequality). 
D)  Property 4: the absolute value of the sum of the numbers is less than or equal to the sum of the two numbers.

Question 20

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 6 ] { \frac { t ^ { 5 } } { 15,625 } }$

Accepted Answer

A)  $\frac { t } { 5 }$ 
B)  $\sqrt { \frac { 6 \mathrm { t } ^ { 5 } } { 15,625 } }$ 
C)  $\frac { \sqrt [ 6 ] { t } } { 5 }$ 
D)  $\frac { \sqrt [ 6 ] { \mathrm { t } ^ { 5 } } } { 5 }$ 
A)  $\frac { t } { 5 }$ 
B)  $\sqrt { \frac { 6 \mathrm { t } ^ { 5 } } { 15,625 } }$ 
C)  $\frac { \sqrt [ 6 ] { t } } { 5 }$ 
D)  $\frac { \sqrt [ 6 ] { \mathrm { t } ^ { 5 } } } { 5 }$

Evaluate the expression. - $125 ^ { 1 / 3 }$

Solve the problem. Round to two decimal places unless otherwise indicated. -In the following formula, $y$ is the minimum number of hours of studying required to attain a test score of $x : y = \frac { 0.37 x } { 100.5 - x }$ . How many hours of study are needed to score 87 ?

Factor the trinomial, if possible. - $49 m ^ { 2 } + 126 m + 81$

Write the expression in lowest terms. - $\frac { 22 k ^ { 2 } } { 25 k }$

Find the product. - $( 9 p + 10 ) ( 9 p - 10 )$

Find the domain of the expression. - $\frac { a - 9 } { - 8 + a }$

Solve the problem. -The cost of manufacturing clocks is given by c = 49(n + 36)1/2, where c is the cost in dollars and n is the number produced. What is the cost when no clocks are produced?

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $z ^ { - 2 / 5 } \cdot z ^ { 3 / 5 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { 5 } { 3 } \left( \frac { 2 } { 5 } y - \frac { 3 } { 10 } x + \frac { 4 } { 5 } \right)$

Find the product. - $( 11 a + 4 c ) ( 11 a - 4 c )$

Evaluate the expression. -Let $x = 2 , y = 3$ . Evaluate $| 6 x - 7 y |$ .

Evaluate the expression. - $| - 12 |$

Factor by any method. - $1000 c ^ { 3 } + 27$

Decide whether the expression has been simplified correctly. - $\left( x ^ { 3 } \right) ^ { 2 } = x ^ { 6 }$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. --23

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { 175 } \cdot \sqrt [ 3 ] { 25 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 2 } { 3 } } - \sqrt { \frac { 72 } { 108 } }$

Determine which property of absolute value justifies the statement. - $| x + y | \leq | x | + | y |$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 6 ] { \frac { t ^ { 5 } } { 15,625 } }$

Equations and Inequalities

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Inverse, Exponential, and Logarithmic Functions

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Exam 12: Review of Basic Concepts

Evaluate the expression. - 1251/3125 ^ { 1 / 3 }1251/3

Factor the trinomial, if possible. - 49m2+126m+8149 m ^ { 2 } + 126 m + 8149m2+126m+81

Write the expression in lowest terms. - 22k225k\frac { 22 k ^ { 2 } } { 25 k }25k22k2​

Find the product. - (9p+10)(9p−10)( 9 p + 10 ) ( 9 p - 10 )(9p+10)(9p−10)

Find the domain of the expression. - a−9−8+a\frac { a - 9 } { - 8 + a }−8+aa−9​