Question 1

Find the sum or difference.
-$( 7 p - 1 ) \left( 49 p ^ { 2 } + 7 p + 1 \right)$

Accepted Answer

A)  $343 p ^ { 3 } - 1$ 
B)  $49 p ^ { 3 } - 1$ 
C)  $343 p ^ { 3 } + 56 p ^ { 2 } - 1$ 
D)  $343 p ^ { 3 } + 1$ 
A)  $343 p ^ { 3 } - 1$ 
B)  $49 p ^ { 3 } - 1$ 
C)  $343 p ^ { 3 } + 56 p ^ { 2 } - 1$ 
D)  $343 p ^ { 3 } + 1$

Question 2

Evaluate the expression.
-$( 9 + ( - 2 ) ) [ 7 + ( 4 + 8 ) ]$

Accepted Answer

A)  89 
B)  26 
C)  133 
D)  22 
A)  89 
B)  26 
C)  133 
D)  22

Question 3

Factor out the greatest common factor. Simplify the factors, if possible.
-$6 x ^ { 2 } - 4 x y - 15 x y + 10 y ^ { 2 }$

Accepted Answer

A)  $( 2 x + 5 y ) ( 3 x - 2 y )$ 
B)  $( 6 x - 5 y ) ( x - 2 y )$ 
C)  $( 2 x - 5 y ) ( 3 x - 2 y )$ 
D)  $( 2 x - 5 ) ( 3 x - 2 )$ 
A)  $( 2 x + 5 y ) ( 3 x - 2 y )$ 
B)  $( 6 x - 5 y ) ( x - 2 y )$ 
C)  $( 2 x - 5 y ) ( 3 x - 2 y )$ 
D)  $( 2 x - 5 ) ( 3 x - 2 )$

Question 4

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$10 y ^ { 7 } + 1$

Accepted Answer

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

Question 5

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { \frac { 2 } { p ^ { 2 } - 16 } + p } { \frac { 1 } { p - 4 } }$$

Accepted Answer

A)  $\frac { 2 + p ^ { 3 } - 16 p } { p + 4 }$ 
B)  $\frac { 2 + p ^ { 3 } + 16 p } { p }$ 
C)  $\frac { 1 } { p ^ { 2 } - 4 }$ 
D)  $\frac { 2 + p ^ { 2 } - 16 p } { p + 16 }$ 
A)  $\frac { 2 + p ^ { 3 } - 16 p } { p + 4 }$ 
B)  $\frac { 2 + p ^ { 3 } + 16 p } { p }$ 
C)  $\frac { 1 } { p ^ { 2 } - 4 }$ 
D)  $\frac { 2 + p ^ { 2 } - 16 p } { p + 16 }$

Question 6

Factor out the greatest common factor. Simplify the factors, if possible.
-$15 x ^ { 2 } + 18 x y + 20 x y + 24 y ^ { 2 }$

Accepted Answer

A)  $( 3 x - 4 y ) ( 5 x + 6 y )$ 
B)  $( 3 x + 4 ) ( 5 x + 6 )$ 
C)  $( 3 x + 4 y ) ( 5 x + 6 y )$ 
D)  $( 15 x + 4 y ) ( x + 6 y )$ 
A)  $( 3 x - 4 y ) ( 5 x + 6 y )$ 
B)  $( 3 x + 4 ) ( 5 x + 6 )$ 
C)  $( 3 x + 4 y ) ( 5 x + 6 y )$ 
D)  $( 15 x + 4 y ) ( x + 6 y )$

Question 7

Determine the degree of the polynomial.
-$4 t ^ { 6 } + 5 t ^ { 3 } + 4 - 3 t ^ { 2 }$

Accepted Answer

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

Question 8

Find the sum or difference.
-$$( m + 3 ) ( m - 3 )$$

Accepted Answer

A)  $m ^ { 2 } - 6 m + 9$ 
B)  $m ^ { 2 } - 9$ 
C)  $m ^ { 2 } - 6$ 
D)  $m ^ { 2 } - 6 m - 9$ 
A)  $m ^ { 2 } - 6 m + 9$ 
B)  $m ^ { 2 } - 9$ 
C)  $m ^ { 2 } - 6$ 
D)  $m ^ { 2 } - 6 m - 9$

Question 9

Decide whether the statement is true or false. If false, correct the statement so it is true.
-$| - 3 | = | 3 |$

Accepted Answer

A) True 
 B)False

Question 10

Write in exponential form. Assume all variables are positive real numbers.
-$- \sqrt { 72 \mathrm {~m} ^ { 11 } }$

Accepted Answer

A)  $- 72 \mathrm {~m} ^ { 11 / 2 }$ 
B)  $72 m^{2 / 11}$ 
C) $-5184 m^{2 / 11}$ 
D)  $- 72 ^ { 1 / 2 } \mathrm {~m} ^ { 11 / 2 }$ 
A)  $- 72 \mathrm {~m} ^ { 11 / 2 }$ 
B)  $72 m^{2 / 11}$ 
C) $-5184 m^{2 / 11}$ 
D)  $- 72 ^ { 1 / 2 } \mathrm {~m} ^ { 11 / 2 }$

Question 11

Use these sets to find the following. Identify any disjoint sets.
-Let $\mathrm { U } = \{ 5,6,7,8,9,10,11,12,13,14,15 \} , \mathrm { M } = \{ 5,7,9,11 \} , \mathrm { N } = \{ 6,8,10,12,14 \} , \mathrm { Q } = \{ 5,7,9,11,13,15 \}$, and $\mathrm { R } = \{ 5,6,7,8 \}$
$( \mathrm { N } \cup \mathrm { R } ) \cap \mathrm { Q }$

Accepted Answer

A)  $\{ 5,7 \}$ 
B)  $\varnothing ; N$ and $R$ are disjoint sets. 
C)  $\{ 7 \}$ 
D)  $\{ 5 \}$ 
A)  $\{ 5,7 \}$ 
B)  $\varnothing ; N$ and $R$ are disjoint sets. 
C)  $\{ 7 \}$ 
D)  $\{ 5 \}$

Question 12

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { 1 } { h } \left( \frac { 1 } { ( x + h ) ^ { 2 } + 6 } - \frac { 1 } { x ^ { 2 } + 6 } \right)$$

Accepted Answer

A)  $\frac { 2 x + h } { \left( ( x + h ) ^ { 2 } + 6 \right) \left( x ^ { 2 } + 6 \right) }$ 
B)  $\frac { 2 x } { \left( ( x + h ) ^ { 2 } + 6 \right) }$ 
C)  $\frac { - 2 x - h } { \left( ( x + h ) ^ { 2 } + 6 \right) \left( x ^ { 2 } + 6 \right) }$ 
D)  $\frac { - 2 x + h } { ( x + h ) ^ { 2 } \left( x ^ { 2 } + 6 \right) }$ 
A)  $\frac { 2 x + h } { \left( ( x + h ) ^ { 2 } + 6 \right) \left( x ^ { 2 } + 6 \right) }$ 
B)  $\frac { 2 x } { \left( ( x + h ) ^ { 2 } + 6 \right) }$ 
C)  $\frac { - 2 x - h } { \left( ( x + h ) ^ { 2 } + 6 \right) \left( x ^ { 2 } + 6 \right) }$ 
D)  $\frac { - 2 x + h } { ( x + h ) ^ { 2 } \left( x ^ { 2 } + 6 \right) }$

Question 13

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$3 ^ { - 3 }$

Accepted Answer

A)  $- 9$ 
B)  $- \frac { 1 } { 27 }$ 
C)  $\frac { 1 } { 27 }$ 
D)  $- 27$ 
A)  $- 9$ 
B)  $- \frac { 1 } { 27 }$ 
C)  $\frac { 1 } { 27 }$ 
D)  $- 27$

Question 14

List all the elements of set B that belong to the indicated set.
-$$B = \left\{ 14 , \sqrt { 7 } , - 14,0 , \frac { 0 } { 1 } , \sqrt { 25 } \right\}$$
Integers

Accepted Answer

A)  14,0 
B)  $14 , - 14,0$ 
C)  $14 , - 14,0 , \frac { 0 } { 1 } , \sqrt { 25 }$ 
D)  $14,0 , \sqrt { 25 }$ 
A)  14,0 
B)  $14 , - 14,0$ 
C)  $14 , - 14,0 , \frac { 0 } { 1 } , \sqrt { 25 }$ 
D)  $14,0 , \sqrt { 25 }$

Question 15

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$\frac { x ^ { 2 } } { x ^ { 18 } }$

Accepted Answer

A)  $x ^ { 16 }$ 
B)  $\frac { 1 } { x ^ { 20 } }$ 
C)  $\frac { 1 } { x ^ { 16 } }$ 
D)  $- \mathrm { x } ^ { 16 }$ 
A)  $x ^ { 16 }$ 
B)  $\frac { 1 } { x ^ { 20 } }$ 
C)  $\frac { 1 } { x ^ { 16 } }$ 
D)  $- \mathrm { x } ^ { 16 }$

Question 16

Identify the property illustrated by the statement. Assume all variables represent real numbers.
-$2 + 9 = 9 + 2$

Accepted Answer

A)  Identity 
B)  Commutative 
C)  Associative 
D)  Inverse 
A)  Identity 
B)  Commutative 
C)  Associative 
D)  Inverse

Question 17

Simplify the expression. Assume all variables represent nonzero real numbers.
-$$68 \cdot 6 ^ { 5 }$$

Accepted Answer

A)  640 
B)  3640 
C)  1213 
D)  613 
A)  640 
B)  3640 
C)  1213 
D)  613

Question 18

Use the distributive property to rewrite a sum as a product or the product as a sum.
-$$- ( - 5 y + 8 k )$$

Accepted Answer

A)  $5 y + 8 k$ 
B)  $- 5 y - 8 k$ 
C)  $5 y - 8 k$ 
D)  $- 5 y + 8 k$ 
A)  $5 y + 8 k$ 
B)  $- 5 y - 8 k$ 
C)  $5 y - 8 k$ 
D)  $- 5 y + 8 k$

Question 19

Evaluate the expression.
-$\left( \frac { 16 } { 25 } \right) ^ { - 1 / 2 }$

Accepted Answer

A)  $\frac { 8 } { 25 }$ 
B)  not a real number 
C)  $\frac { 5 } { 4 }$ 
D)  $\frac { 4 } { 5 }$ 
A)  $\frac { 8 } { 25 }$ 
B)  not a real number 
C)  $\frac { 5 } { 4 }$ 
D)  $\frac { 4 } { 5 }$

Question 20

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt { \frac { 500 } { 216 } }$$

Accepted Answer

A)  $\frac { \sqrt { 4 } } { 6 }$ 
B)  $\frac { 5 } { \sqrt { 216 } }$ 
C)  $\frac { 6 } { 5 }$ 
D)  $\frac { 5 \sqrt { 30 } } { 18 }$ 
A)  $\frac { \sqrt { 4 } } { 6 }$ 
B)  $\frac { 5 } { \sqrt { 216 } }$ 
C)  $\frac { 6 } { 5 }$ 
D)  $\frac { 5 \sqrt { 30 } } { 18 }$

Find the sum or difference. - $( 7 p - 1 ) \left( 49 p ^ { 2 } + 7 p + 1 \right)$

Evaluate the expression. - $( 9 + ( - 2 ) ) [ 7 + ( 4 + 8 ) ]$

Factor out the greatest common factor. Simplify the factors, if possible. - $6 x ^ { 2 } - 4 x y - 15 x y + 10 y ^ { 2 }$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $10 y ^ { 7 } + 1$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { \frac { 2 } { p ^ { 2 } - 16 } + p } { \frac { 1 } { p - 4 } }$

Factor out the greatest common factor. Simplify the factors, if possible. - $15 x ^ { 2 } + 18 x y + 20 x y + 24 y ^ { 2 }$

Determine the degree of the polynomial. - $4 t ^ { 6 } + 5 t ^ { 3 } + 4 - 3 t ^ { 2 }$

Find the sum or difference. - $( m + 3 ) ( m - 3 )$

Decide whether the statement is true or false. If false, correct the statement so it is true. - $| - 3 | = | 3 |$

Write in exponential form. Assume all variables are positive real numbers. - $- \sqrt { 72 \mathrm {~m} ^ { 11 } }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { 1 } { h } \left( \frac { 1 } { ( x + h ) ^ { 2 } + 6 } - \frac { 1 } { x ^ { 2 } + 6 } \right)$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $3 ^ { - 3 }$

List all the elements of set B that belong to the indicated set. - $B = \left\{ 14 , \sqrt { 7 } , - 14,0 , \frac { 0 } { 1 } , \sqrt { 25 } \right\}$ Integers

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { x ^ { 2 } } { x ^ { 18 } }$

Identify the property illustrated by the statement. Assume all variables represent real numbers. - $2 + 9 = 9 + 2$

Simplify the expression. Assume all variables represent nonzero real numbers. - $68 \cdot 6 ^ { 5 }$

Use the distributive property to rewrite a sum as a product or the product as a sum. - $- ( - 5 y + 8 k )$

Evaluate the expression. - $\left( \frac { 16 } { 25 } \right) ^ { - 1 / 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 500 } { 216 } }$

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. - (7p−1)(49p2+7p+1)( 7 p - 1 ) \left( 49 p ^ { 2 } + 7 p + 1 \right)(7p−1)(49p2+7p+1)

Evaluate the expression. - (9+(−2))[7+(4+8)]( 9 + ( - 2 ) ) [ 7 + ( 4 + 8 ) ](9+(−2))[7+(4+8)]

Factor out the greatest common factor. Simplify the factors, if possible. - 6x2−4xy−15xy+10y26 x ^ { 2 } - 4 x y - 15 x y + 10 y ^ { 2 }6x2−4xy−15xy+10y2

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - 10y7+110 y ^ { 7 } + 110y7+1

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 2p2−16+p1p−4\frac { \frac { 2 } { p ^ { 2 } - 16 } + p } { \frac { 1 } { p - 4 } }p−41​p2−162​+p​

Factor out the greatest common factor. Simplify the factors, if possible. - 15x2+18xy+20xy+24y215 x ^ { 2 } + 18 x y + 20 x y + 24 y ^ { 2 }15x2+18xy+20xy+24y2

Determine the degree of the polynomial. - 4t6+5t3+4−3t24 t ^ { 6 } + 5 t ^ { 3 } + 4 - 3 t ^ { 2 }4t6+5t3+4−3t2

Find the sum or difference. - (m+3)(m−3)( m + 3 ) ( m - 3 )(m+3)(m−3)

Decide whether the statement is true or false. If false, correct the statement so it is true. - ∣−3∣=∣3∣| - 3 | = | 3 |∣−3∣=∣3∣

Write in exponential form. Assume all variables are positive real numbers. - −72 m11- \sqrt { 72 \mathrm {~m} ^ { 11 } }−72 m11​

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 1h(1(x+h)2+6−1x2+6)\frac { 1 } { h } \left( \frac { 1 } { ( x + h ) ^ { 2 } + 6 } - \frac { 1 } { x ^ { 2 } + 6 } \right)h1​((x+h)2+61​−x2+61​)

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 3−33 ^ { - 3 }3−3

List all the elements of set B that belong to the indicated set. - B={14,7,−14,0,01,25}B = \left\{ 14 , \sqrt { 7 } , - 14,0 , \frac { 0 } { 1 } , \sqrt { 25 } \right\}B={14,7​,−14,0,10​,25​} Integers

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - x2x18\frac { x ^ { 2 } } { x ^ { 18 } }x18x2​

Identify the property illustrated by the statement. Assume all variables represent real numbers. - 2+9=9+22 + 9 = 9 + 22+9=9+2

Simplify the expression. Assume all variables represent nonzero real numbers. - 68⋅6568 \cdot 6 ^ { 5 }68⋅65

Use the distributive property to rewrite a sum as a product or the product as a sum. - −(−5y+8k)- ( - 5 y + 8 k )−(−5y+8k)

Evaluate the expression. - (1625)−1/2\left( \frac { 16 } { 25 } \right) ^ { - 1 / 2 }(2516​)−1/2

Simplify the expression. Assume all variables represent positive real numbers. - 500216\sqrt { \frac { 500 } { 216 } }216500​​