Question 1

Insert $$\in$$ or $\notin$ in the blank to make the statement is true.
-6 {3, 4, 5, 6}

Accepted Answer

A)  $\in$ 
B)  $\notin$ 
A)  $\in$ 
B)  $\notin$

Question 2

Perform the indicated operation and write your answer with positive integer exponents.
-$$\frac { x ^ { 2 } - 25 y ^ { - 2 } } { \left( x - 5 y ^ { - 1 } \right) \left( x + 5 y ^ { - 1 } \right) }$$

Accepted Answer

A)  $- 1$ 
B)  $\frac { y ^ { 2 } - x } { x y - 5 }$ 
C)  1 
D)  $\frac { x y ^ { 2 } } { y - x }$ 
A)  $- 1$ 
B)  $\frac { y ^ { 2 } - x } { x y - 5 }$ 
C)  1 
D)  $\frac { x y ^ { 2 } } { y - x }$

Question 3

Determine the degree of the polynomial.
-$3 t ^ { 6 } + 4 t ^ { 3 } + 6 - 2 t ^ { 2 }$

Accepted Answer

A)  4 
B)  12 
C)  11 
D)  6 
A)  4 
B)  12 
C)  11 
D)  6

Question 4

Evaluate the expression.
-(-4)1/2

Accepted Answer

A)  -2 
B)  -1 
C)  2 
D)  not a real number 
A)  -2 
B)  -1 
C)  2 
D)  not a real number

Question 5

Write the expression in lowest terms.
-$$\frac { x ^ { 3 } + 125 } { x + 5 }$$

Accepted Answer

A)  $x ^ { 2 } + 25$ 
B)  $x ^ { 2 } - 5$ 
C)  $x ^ { 2 } - 5 x + 25$ 
D)  $x ^ { 2 } - 25 x + 5$ 
A)  $x ^ { 2 } + 25$ 
B)  $x ^ { 2 } - 5$ 
C)  $x ^ { 2 } - 5 x + 25$ 
D)  $x ^ { 2 } - 25 x + 5$

Question 6

Use the distributive property to rewrite a sum as a product or the product as a sum.
-2 - 6b

Accepted Answer

A)  2(1 - 3b) 
B)  2(1 - 4b) 
C)  8b 
D)  -4b 
A)  2(1 - 3b) 
B)  2(1 - 4b) 
C)  8b 
D)  -4b

Question 7

Calculate the value mentally.
-$$\frac { 48 ^ { 1 / 2 } } { 3 ^ { 1 / 2 } }$$

Accepted Answer

A)  16 
B)  4 
C)  none of these 
D)  45 
A)  16 
B)  4 
C)  none of these 
D)  45

Question 8

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$$\frac { 3 x ^ { - 3 } } { 6 x ^ { - 6 } }$$

Accepted Answer

A)  $\frac { x ^ { 3 } } { 2 }$ 
B)  $\frac { x ^ { 3 } } { 3 }$ 
C)  $\frac { x ^ { 9 } } { 2 }$ 
D)  $\frac { x ^ { 2 } } { 2 }$ 
A)  $\frac { x ^ { 3 } } { 2 }$ 
B)  $\frac { x ^ { 3 } } { 3 }$ 
C)  $\frac { x ^ { 9 } } { 2 }$ 
D)  $\frac { x ^ { 2 } } { 2 }$

Question 9

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$$\frac { x ^ { 4 } } { x ^ { 12 } }$$

Accepted Answer

A)  $\frac { 1 } { x ^ { 16 } }$ 
B)  $x ^ { 8 }$ 
C)  $- x ^ { 8 }$ 
D)  $\frac { 1 } { x ^ { 8 } }$ 
A)  $\frac { 1 } { x ^ { 16 } }$ 
B)  $x ^ { 8 }$ 
C)  $- x ^ { 8 }$ 
D)  $\frac { 1 } { x ^ { 8 } }$

Question 10

Identify the property illustrated by the statement. Assume all variables represent real numbers.
-6 · 1 = 6

Accepted Answer

A)  Identity 
B)  Closure 
C)  Inverse 
D)  Distributive 
A)  Identity 
B)  Closure 
C)  Inverse 
D)  Distributive

Question 11

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$( - 8 x ) ^ { 0 }$

Accepted Answer

A)  8 
B)  1 
C)  0 
D)  -1 
A)  8 
B)  1 
C)  0 
D)  -1

Question 12

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt { \frac { 31 } { x ^ { 4 } } }$$

Accepted Answer

A)  $\frac { \sqrt { 31 } } { x ^ { 4 } }$ 
B)  $\frac { 31 } { x ^ { 2 } }$ 
C)  $\frac { \sqrt { 31 } } { x ^ { 2 } }$ 
D)  $\frac { \sqrt { 31 } } { x }$ 
A)  $\frac { \sqrt { 31 } } { x ^ { 4 } }$ 
B)  $\frac { 31 } { x ^ { 2 } }$ 
C)  $\frac { \sqrt { 31 } } { x ^ { 2 } }$ 
D)  $\frac { \sqrt { 31 } } { x }$

Question 13

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$$\frac { 5 - \sqrt { 2 } } { 5 + \sqrt { 2 } }$$

Accepted Answer

A)  $\frac { 23 - 10 \sqrt { 2 } } { 27 }$ 
B)  $- 1$ 
C)  $\frac { 27 - 10 \sqrt { 2 } } { 23 }$ 
D)  $\frac { 27 + 10 \sqrt { 2 } } { 23 }$ 
A)  $\frac { 23 - 10 \sqrt { 2 } } { 27 }$ 
B)  $- 1$ 
C)  $\frac { 27 - 10 \sqrt { 2 } } { 23 }$ 
D)  $\frac { 27 + 10 \sqrt { 2 } } { 23 }$

Question 14

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$$\frac { 42 a ^ { - 2 } b ^ { 4 } } { 6 a ^ { - 8 } b ^ { 7 } }$$

Accepted Answer

A)  $\frac { 7 a ^ { 6 } } { b ^ { 3 } }$ 
B)  $- \frac { a ^ { 5 } } { 7 b ^ { 4 } }$ 
C)  $- 7 a b ^ { 2 }$ 
D)  $\frac { 7 b ^ { 4 } } { a ^ { 6 } }$ 
A)  $\frac { 7 a ^ { 6 } } { b ^ { 3 } }$ 
B)  $- \frac { a ^ { 5 } } { 7 b ^ { 4 } }$ 
C)  $- 7 a b ^ { 2 }$ 
D)  $\frac { 7 b ^ { 4 } } { a ^ { 6 } }$

Question 15

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
--9

Accepted Answer

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

Question 16

Factor the trinomial, if possible.
-$$9 z ^ { 2 } + 6 z - 8$$

Accepted Answer

A)  $( 9 z + 4 ) ( z - 2 )$ 
B)  $( 3 z - 4 ) ( 3 z + 2 )$ 
C)  $( 9 z + 1 ) ( z - 8 )$ 
D)  $( 3 z + 4 ) ( 3 z - 2 )$ 
A)  $( 9 z + 4 ) ( z - 2 )$ 
B)  $( 3 z - 4 ) ( 3 z + 2 )$ 
C)  $( 9 z + 1 ) ( z - 8 )$ 
D)  $( 3 z + 4 ) ( 3 z - 2 )$

Question 17

Insert $$\in$$ or $\notin$ in the blank to make the statement is true.
-{0} {0, 6, 7, 8, 9}

Accepted Answer

A)  $\notin$ 
B)  $\in$ 
A)  $\notin$ 
B)  $\in$

Question 18

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 3 ] { 48 }$$

Accepted Answer

A)  $6 \sqrt [ 3 ] { 2 }$ 
B)  $2 \sqrt [ 3 ] { 6 }$ 
C)  6 
D)  3 
A)  $6 \sqrt [ 3 ] { 2 }$ 
B)  $2 \sqrt [ 3 ] { 6 }$ 
C)  6 
D)  3

Question 19

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-19z - 2

Accepted Answer

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

Question 20

Solve the problem.
-$$( 7 x + 10 y ) ^ { 2 }$$

Accepted Answer

A)  $7 x ^ { 2 } + 140 x y + 100 y ^ { 2 }$ 
B)  $7 x ^ { 2 } + 100 y ^ { 2 }$ 
C)  $49 x ^ { 2 } + 140 x y + 100 y ^ { 2 }$ 
D)  $49 x ^ { 2 } + 100 y ^ { 2 }$ 
A)  $7 x ^ { 2 } + 140 x y + 100 y ^ { 2 }$ 
B)  $7 x ^ { 2 } + 100 y ^ { 2 }$ 
C)  $49 x ^ { 2 } + 140 x y + 100 y ^ { 2 }$ 
D)  $49 x ^ { 2 } + 100 y ^ { 2 }$

Insert $\in$ or $\notin$ in the blank to make the statement is true. -6 {3, 4, 5, 6}

Perform the indicated operation and write your answer with positive integer exponents. - $\frac { x ^ { 2 } - 25 y ^ { - 2 } } { \left( x - 5 y ^ { - 1 } \right) \left( x + 5 y ^ { - 1 } \right) }$

Determine the degree of the polynomial. - $3 t ^ { 6 } + 4 t ^ { 3 } + 6 - 2 t ^ { 2 }$

Evaluate the expression. -(-4)1/2

Write the expression in lowest terms. - $\frac { x ^ { 3 } + 125 } { x + 5 }$

Use the distributive property to rewrite a sum as a product or the product as a sum. -2 - 6b

Calculate the value mentally. - $\frac { 48 ^ { 1 / 2 } } { 3 ^ { 1 / 2 } }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { 3 x ^ { - 3 } } { 6 x ^ { - 6 } }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { x ^ { 4 } } { x ^ { 12 } }$

Identify the property illustrated by the statement. Assume all variables represent real numbers. -6 · 1 = 6

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $( - 8 x ) ^ { 0 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 31 } { x ^ { 4 } } }$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - $\frac { 5 - \sqrt { 2 } } { 5 + \sqrt { 2 } }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { 42 a ^ { - 2 } b ^ { 4 } } { 6 a ^ { - 8 } b ^ { 7 } }$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. --9

Factor the trinomial, if possible. - $9 z ^ { 2 } + 6 z - 8$

Insert $\in$ or $\notin$ in the blank to make the statement is true. -{0} {0, 6, 7, 8, 9}

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { 48 }$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. -19z - 2

Solve the problem. - $( 7 x + 10 y ) ^ { 2 }$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 1: Review of Basic Concepts

Insert ∈\in∈ or ∉\notin∈/ in the blank to make the statement is true. -6 {3, 4, 5, 6}

Perform the indicated operation and write your answer with positive integer exponents. - x2−25y−2(x−5y−1)(x+5y−1)\frac { x ^ { 2 } - 25 y ^ { - 2 } } { \left( x - 5 y ^ { - 1 } \right) \left( x + 5 y ^ { - 1 } \right) }(x−5y−1)(x+5y−1)x2−25y−2​

Determine the degree of the polynomial. - 3t6+4t3+6−2t23 t ^ { 6 } + 4 t ^ { 3 } + 6 - 2 t ^ { 2 }3t6+4t3+6−2t2