Question 1

Find the sum or difference.
-$( 6 r - 5 ) ( 6 r + 5 )$

Accepted Answer

A)  $36 r ^ { 2 } - 25$ 
B)  $36 + 60 r - 25 r ^ { 2 }$ 
C)  $36 r ^ { 2 } - 60 r - 25$ 
D)  $6 r ^ { 2 } - 25$ 
A)  $36 r ^ { 2 } - 25$ 
B)  $36 + 60 r - 25 r ^ { 2 }$ 
C)  $36 r ^ { 2 } - 60 r - 25$ 
D)  $6 r ^ { 2 } - 25$

Question 2

Decide whether the expression has been simplified correctly.
-$x ^ { 4 } \cdot x ^ { 2 } = x ^ { 6 }$

Accepted Answer

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

Question 3

Find the sum or difference.
-$$\frac { y ^ { 2 } + 18 y + 81 } { y + 9 }$$

Accepted Answer

A)  $y ^ { 2 } + 9$ 
B)  $y + \frac { 9 } { v + 9 }$ 
C)  $y + 9$ 
D)  $y - 9$ 
A)  $y ^ { 2 } + 9$ 
B)  $y + \frac { 9 } { v + 9 }$ 
C)  $y + 9$ 
D)  $y - 9$

Question 4

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$- ( - 2 ) ^ { - 6 }$$

Accepted Answer

A)  $\frac { 1 } { 64 }$ 
B)  64 
C)  $- \frac { 1 } { 64 }$ 
D)  $- 64$ 
A)  $\frac { 1 } { 64 }$ 
B)  64 
C)  $- \frac { 1 } { 64 }$ 
D)  $- 64$

Question 5

Insert   in the blank to make the statement true.
-

Accepted Answer

A)  $\subseteq$ 
B)  $\nsubseteq$ 
A)  $\subseteq$ 
B)  $\nsubseteq$

Question 6

Find the sum or difference.
-$$( x + 11 y ) ( x - 4 y )$$

Accepted Answer

A)  $x ^ { 2 } + 7 x y + 7 y ^ { 2 }$ 
B)  $x + 7 x y - 44 y$ 
C)  $x ^ { 2 } + 4 x y - 44 y ^ { 2 }$ 
D)  $x ^ { 2 } + 7 x y - 44 y ^ { 2 }$ 
A)  $x ^ { 2 } + 7 x y + 7 y ^ { 2 }$ 
B)  $x + 7 x y - 44 y$ 
C)  $x ^ { 2 } + 4 x y - 44 y ^ { 2 }$ 
D)  $x ^ { 2 } + 7 x y - 44 y ^ { 2 }$

Question 7

Find the product or quotient.
-$$\frac { 2 x ^ { 2 } } { 4 } \div \frac { x ^ { 3 } } { 24 }$$

Accepted Answer

A)  $\frac { x } { 12 }$ 
B)  $\frac { 12 } { x }$ 
C)  $\frac { 12 x ^ { 2 } } { x ^ { 3 } }$ 
D)  $\frac { 48 x ^ { 2 } } { 4 x ^ { 3 } }$ 
A)  $\frac { x } { 12 }$ 
B)  $\frac { 12 } { x }$ 
C)  $\frac { 12 x ^ { 2 } } { x ^ { 3 } }$ 
D)  $\frac { 48 x ^ { 2 } } { 4 x ^ { 3 } }$

Question 8

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-A manufacturer's cost is given b $C = 400 n ^ { 1 / 3 } + 1300$ , where C is the cost in dollars and n is the number of parts produced. Find the cost when 216 parts are produced.

Accepted Answer

A)  $2500 
B)  $7180 
C)  $3700 
D)  $67 
A)  $2500 
B)  $7180 
C)  $3700 
D)  $67

Question 9

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { \frac { 37 } { x ^ { 4 } } }$

Accepted Answer

A)  $\frac { 37 } { x ^ { 2 } }$ 
B)  $\frac { \sqrt { 37 } } { x }$ 
C)  $\frac { \sqrt { 37 } } { x ^ { 2 } }$ 
D)  $\frac { \sqrt { 37 } } { x ^ { 4 } }$ 
A)  $\frac { 37 } { x ^ { 2 } }$ 
B)  $\frac { \sqrt { 37 } } { x }$ 
C)  $\frac { \sqrt { 37 } } { x ^ { 2 } }$ 
D)  $\frac { \sqrt { 37 } } { x ^ { 4 } }$

Question 10

Factor the polynomial by substitution.
-$6 y ^ { 4 } + 5 y ^ { 2 } - 6$

Accepted Answer

A)  $\left( 6 y ^ { 2 } - 2 \right) \left( y ^ { 2 } + 3 \right)$ 
B)  $\left( 3 y ^ { 2 } - 2 \right) \left( 2 y ^ { 2 } + 3 \right)$ 
C)  $( 2 y - 3 ) ( 3 y + 2 )$ 
D)  $\left( 3 y ^ { 2 } + 1 \right) \left( 2 y ^ { 2 } - 6 \right)$ 
A)  $\left( 6 y ^ { 2 } - 2 \right) \left( y ^ { 2 } + 3 \right)$ 
B)  $\left( 3 y ^ { 2 } - 2 \right) \left( 2 y ^ { 2 } + 3 \right)$ 
C)  $( 2 y - 3 ) ( 3 y + 2 )$ 
D)  $\left( 3 y ^ { 2 } + 1 \right) \left( 2 y ^ { 2 } - 6 \right)$

Question 11

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-If the lengths of the sides of a square are tripled, by what factor will the area change?

Accepted Answer

A)  9 
B)  6 
C)  27 
D)  3 
A)  9 
B)  6 
C)  27 
D)  3

Question 12

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$\frac { 5 \sqrt { x } } { \sqrt { x } - 5 \sqrt { y } }$

Accepted Answer

A)  $\frac { 5 \sqrt { x } ( \sqrt { x } + 5 \sqrt { y } ) } { x - 5 y }$ 
B)  $\frac { 5 \sqrt { x } ( \sqrt { x } + 5 \sqrt { y } ) } { x + 5 y }$ 
C)  $\frac { 5 \sqrt { x } ( \sqrt { x } + 5 \sqrt { y } ) } { x - 25 y }$ 
D)  $\frac { 5 \sqrt { x } ( \sqrt { x } - 5 \sqrt { y } ) } { x + 25 y }$ 
A)  $\frac { 5 \sqrt { x } ( \sqrt { x } + 5 \sqrt { y } ) } { x - 5 y }$ 
B)  $\frac { 5 \sqrt { x } ( \sqrt { x } + 5 \sqrt { y } ) } { x + 5 y }$ 
C)  $\frac { 5 \sqrt { x } ( \sqrt { x } + 5 \sqrt { y } ) } { x - 25 y }$ 
D)  $\frac { 5 \sqrt { x } ( \sqrt { x } - 5 \sqrt { y } ) } { x + 25 y }$

Question 13

Write the expression in lowest terms.
-$$\frac { 4 y + 16 } { 3 y + 12 }$$

Accepted Answer

A)  $\frac { 4 } { 3 }$ 
B)  1 
C)  $\frac { y + 4 } { y + 12 }$ 
D)  $y + 4$ 
A)  $\frac { 4 } { 3 }$ 
B)  1 
C)  $\frac { y + 4 } { y + 12 }$ 
D)  $y + 4$

Question 14

Evaluate the expression.
-Let $x = - 19 , y = - 18$. Evaluate $| 21 x |$.

Accepted Answer

A)  399 
B)  $- 342$ 
C)  $- 399$ 
D)  342 
A)  399 
B)  $- 342$ 
C)  $- 399$ 
D)  342

Question 15

Insert   in the blank to make the statement true.
-

Accepted Answer

A)  $\nsubseteq$ 
B)  $\subseteq$ 
A)  $\nsubseteq$ 
B)  $\subseteq$

Question 16

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 $x$ : $y =$ $\frac { 0.50 x } { 100.5 - x }$. How many hours of study are needed to score $86 ?$

Accepted Answer

A)  5.58 hr 
B)  29.70 hr 
C)  2.97 hr 
D)  100.91 hr 
A)  5.58 hr 
B)  29.70 hr 
C)  2.97 hr 
D)  100.91 hr

Question 17

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers.
-$( 5 x ) ^ { 0 }$

Accepted Answer

A)  1 
B)  $5 x$ 
C)  0 
D)  5 
A)  1 
B)  $5 x$ 
C)  0 
D)  5

Question 18

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$\frac { \left( 3 x ^ { 5 } y ^ { 6 } \right) ^ { 4 } } { 9 x y ^ { 2 } }$

Accepted Answer

A)  $9 \mathrm { x } ^ { 19 } \mathrm { y } ^ { 22 }$ 
B)  $\frac { x ^ { 19 } y ^ { 22 } } { 3 }$ 
C)  $9 \mathrm { x } ^ { 8 } \mathrm { y } ^ { 8 }$ 
D)  $\frac { x ^ { 8 } y ^ { 8 } } { 3 }$ 
A)  $9 \mathrm { x } ^ { 19 } \mathrm { y } ^ { 22 }$ 
B)  $\frac { x ^ { 19 } y ^ { 22 } } { 3 }$ 
C)  $9 \mathrm { x } ^ { 8 } \mathrm { y } ^ { 8 }$ 
D)  $\frac { x ^ { 8 } y ^ { 8 } } { 3 }$

Question 19

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 3 ] { 729 x ^ { 4 } y ^ { 5 } }$$

Accepted Answer

A)  $3 x ^ { 2 } y ^ { 2 } \sqrt [ 3 ] { x ^ { 2 } }$ 
B)  $9 x y \sqrt [ 3 ] { x y ^ { 2 } }$ 
C)  $9 x y ^ { 2 } \sqrt [ 3 ] { x y }$ 
D)  $9 x y \sqrt [ 3 ] { x y }$ 
A)  $3 x ^ { 2 } y ^ { 2 } \sqrt [ 3 ] { x ^ { 2 } }$ 
B)  $9 x y \sqrt [ 3 ] { x y ^ { 2 } }$ 
C)  $9 x y ^ { 2 } \sqrt [ 3 ] { x y }$ 
D)  $9 x y \sqrt [ 3 ] { x y }$

Question 20

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 $x + 2$, which means that the area of the largest square is $( x + 2 ) ^ { 2 }$. 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)  $x ^ { 2 } - 2 x + 4$ 
B)  $x ^ { 2 } + 4 x + 4$ 
C)  $x ^ { 2 } + 2 x + 4$ 
D)  $x ^ { 2 } + x + 4$ 
A)  $x ^ { 2 } - 2 x + 4$ 
B)  $x ^ { 2 } + 4 x + 4$ 
C)  $x ^ { 2 } + 2 x + 4$ 
D)  $x ^ { 2 } + x + 4$

Find the sum or difference. - $( 6 r - 5 ) ( 6 r + 5 )$

Decide whether the expression has been simplified correctly. - $x ^ { 4 } \cdot x ^ { 2 } = x ^ { 6 }$

Find the sum or difference. - $\frac { y ^ { 2 } + 18 y + 81 } { y + 9 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $- ( - 2 ) ^ { - 6 }$

Insert in the blank to make the statement true. -

Find the sum or difference. - $( x + 11 y ) ( x - 4 y )$

Find the product or quotient. - $\frac { 2 x ^ { 2 } } { 4 } \div \frac { x ^ { 3 } } { 24 }$

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers. -A manufacturer's cost is given b $C = 400 n ^ { 1 / 3 } + 1300$ , where C is the cost in dollars and n is the number of parts produced. Find the cost when 216 parts are produced.

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 37 } { x ^ { 4 } } }$

Factor the polynomial by substitution. - $6 y ^ { 4 } + 5 y ^ { 2 } - 6$

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers. -If the lengths of the sides of a square are tripled, by what factor will the area change?

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - $\frac { 5 \sqrt { x } } { \sqrt { x } - 5 \sqrt { y } }$

Write the expression in lowest terms. - $\frac { 4 y + 16 } { 3 y + 12 }$

Evaluate the expression. -Let $x = - 19 , y = - 18$ . Evaluate $| 21 x |$ .

Insert in the blank to make the statement true. -

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 $x$ : $y =$ $\frac { 0.50 x } { 100.5 - x }$ . How many hours of study are needed to score $86 ?$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $( 5 x ) ^ { 0 }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { \left( 3 x ^ { 5 } y ^ { 6 } \right) ^ { 4 } } { 9 x y ^ { 2 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { 729 x ^ { 4 } y ^ { 5 } }$

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 1: Review of Basic Concepts

Find the sum or difference. - (6r−5)(6r+5)( 6 r - 5 ) ( 6 r + 5 )(6r−5)(6r+5)

Decide whether the expression has been simplified correctly. - x4⋅x2=x6x ^ { 4 } \cdot x ^ { 2 } = x ^ { 6 }x4⋅x2=x6

Find the sum or difference. - y2+18y+81y+9\frac { y ^ { 2 } + 18 y + 81 } { y + 9 }y+9y2+18y+81​

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - −(−2)−6- ( - 2 ) ^ { - 6 }−(−2)−6

Insert in the blank to make the statement true. -

Find the sum or difference. - (x+11y)(x−4y)( x + 11 y ) ( x - 4 y )(x+11y)(x−4y)

Find the product or quotient. - 2x24÷x324\frac { 2 x ^ { 2 } } { 4 } \div \frac { x ^ { 3 } } { 24 }42x2​÷24x3​

Simplify the expression. Assume all variables represent positive real numbers. - 37x4\sqrt { \frac { 37 } { x ^ { 4 } } }x437​​

Factor the polynomial by substitution. - 6y4+5y2−66 y ^ { 4 } + 5 y ^ { 2 } - 66y4+5y2−6

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers. -If the lengths of the sides of a square are tripled, by what factor will the area change?

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - 5xx−5y\frac { 5 \sqrt { x } } { \sqrt { x } - 5 \sqrt { y } }x​−5y​5x​​

Write the expression in lowest terms. - 4y+163y+12\frac { 4 y + 16 } { 3 y + 12 }3y+124y+16​

Evaluate the expression. -Let x=−19,y=−18x = - 19 , y = - 18x=−19,y=−18 . Evaluate ∣21x∣| 21 x |∣21x∣ .

Insert in the blank to make the statement true. -

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - (5x)0( 5 x ) ^ { 0 }(5x)0

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - (3x5y6)49xy2\frac { \left( 3 x ^ { 5 } y ^ { 6 } \right) ^ { 4 } } { 9 x y ^ { 2 } }9xy2(3x5y6)4​

Simplify the expression. Assume all variables represent positive real numbers. - 729x4y53\sqrt [ 3 ] { 729 x ^ { 4 } y ^ { 5 } }3729x4y5​

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Find the sum or difference. - $( 6 r - 5 ) ( 6 r + 5 )$

Decide whether the expression has been simplified correctly. - $x ^ { 4 } \cdot x ^ { 2 } = x ^ { 6 }$

Find the sum or difference. - $\frac { y ^ { 2 } + 18 y + 81 } { y + 9 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $- ( - 2 ) ^ { - 6 }$

Find the sum or difference. - $( x + 11 y ) ( x - 4 y )$

Find the product or quotient. - $\frac { 2 x ^ { 2 } } { 4 } \div \frac { x ^ { 3 } } { 24 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 37 } { x ^ { 4 } } }$

Factor the polynomial by substitution. - $6 y ^ { 4 } + 5 y ^ { 2 } - 6$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - $\frac { 5 \sqrt { x } } { \sqrt { x } - 5 \sqrt { y } }$

Write the expression in lowest terms. - $\frac { 4 y + 16 } { 3 y + 12 }$

Evaluate the expression. -Let $x = - 19 , y = - 18$ . Evaluate $| 21 x |$ .

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $( 5 x ) ^ { 0 }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { \left( 3 x ^ { 5 } y ^ { 6 } \right) ^ { 4 } } { 9 x y ^ { 2 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { 729 x ^ { 4 } y ^ { 5 } }$