Question 1

Solve the problem.
-$$( p + 9 ) ^ { 2 }$$

Accepted Answer

A)  $p ^ { 2 } + 18 p + 81$ 
B)  $p + 81$ 
C)  $81 p ^ { 2 } + 18 p + 81$ 
D)  $p ^ { 2 } + 81$ 
A)  $p ^ { 2 } + 18 p + 81$ 
B)  $p + 81$ 
C)  $81 p ^ { 2 } + 18 p + 81$ 
D)  $p ^ { 2 } + 81$

Question 2

Solve the problem.
-$$( - 8 x - 3 ) ^ { 2 }$$

Accepted Answer

A)  $64 x ^ { 2 } + 48 x + 9$ 
B)  $- 8 x ^ { 2 } + 48 x + 9$ 
C)  $- 8 x ^ { 2 } + 9$ 
D)  $64 x ^ { 2 } + 9$ 
A)  $64 x ^ { 2 } + 48 x + 9$ 
B)  $- 8 x ^ { 2 } + 48 x + 9$ 
C)  $- 8 x ^ { 2 } + 9$ 
D)  $64 x ^ { 2 } + 9$

Question 3

Solve the problem.
-$$\frac { 18 x ^ { 7 } - 30 x ^ { 4 } } { - 6 x ^ { 7 } }$$

Accepted Answer

A)  $- 3 + 5 x ^ { 3 }$ 
B)  $18 x ^ { 7 } + \frac { 5 } { x ^ { 3 } }$ 
C)  $- 3 + \frac { 5 } { x ^ { 3 } }$ 
D)  $- 3 - 30 x ^ { 4 }$ 
A)  $- 3 + 5 x ^ { 3 }$ 
B)  $18 x ^ { 7 } + \frac { 5 } { x ^ { 3 } }$ 
C)  $- 3 + \frac { 5 } { x ^ { 3 } }$ 
D)  $- 3 - 30 x ^ { 4 }$

Question 4

Find the product. Assume variables represent positive real numbers.
-$$y ^ { 3 / 13 } \left( y ^ { 5 / 13 } - 3 y ^ { 2 / 13 } \right)$$

Accepted Answer

A)  $y ^ { 15 / 169 } - 3 y ^{6 / 169}$ 
B)  $y ^ { 8 / 13 } - 3 y ^ { 5 / 13 }$ 
C)  $y ^ { - 2 / 13 } - 3 y ^ { 1 / 13 }$ 
D)  $y ^ { 3 / 5 } - 3 y ^ { 3 / 2 }$ 
A)  $y ^ { 15 / 169 } - 3 y ^{6 / 169}$ 
B)  $y ^ { 8 / 13 } - 3 y ^ { 5 / 13 }$ 
C)  $y ^ { - 2 / 13 } - 3 y ^ { 1 / 13 }$ 
D)  $y ^ { 3 / 5 } - 3 y ^ { 3 / 2 }$

Question 5

List all the elements of set B that belong to the indicated set.
-$$B = \left\{ 15 , \sqrt { 7 } , - 13,0 , \frac { 0 } { 1 } , \sqrt { 16 } \right\}$$
Whole numbers

Accepted Answer

A)  $15 , - 13,0 , \sqrt { 16 }$ 
B)  $15,0 , \frac { 0 } { 1 } , \sqrt { 16 }$ 
C)  $15 , - 13,0$ 
D)  15,0 
A)  $15 , - 13,0 , \sqrt { 16 }$ 
B)  $15,0 , \frac { 0 } { 1 } , \sqrt { 16 }$ 
C)  $15 , - 13,0$ 
D)  15,0

Question 6

Evaluate the expression.
-$441 ^ { 1 / 2 }$

Accepted Answer

A)  10.5 
B)  84 
C)  21 
D)  42 
A)  10.5 
B)  84 
C)  21 
D)  42

Question 7

Evaluate the expression for x = -2, y = 3, and a = -4.
-$$\frac { - ( x + 3 ) ^ { 2 } - 7 y } { - 2 - a }$$

Accepted Answer

A)  10 
B)  11 
C)  $- 2$ 
D)  $- 11$ 
A)  10 
B)  11 
C)  $- 2$ 
D)  $- 11$

Question 8

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-It is recommended that a woman who is pregnant should exercise such that her heart rate does not exceed 140 beats per minute. Use absolute value notation to write an expression that describes the difference
Between the heart rate achieved by each of the following pregnant women and the recommended
Maximum heart rate. Then evaluate that expression. (i) Abigail: 123 beats per minute
(i) Abigail: $123  $ beats per minute
(ii) Mathilda: 146 beats per minute

Accepted Answer

A)  (i) Abigail: $| 140 - 123 | = - 17$
(ii) Mathilda: $| 140 - 146 | = - 6$ 
B)  (i) Abigail: $| 123 - 140 | = 17$
(ii) Mathilda: $| 146 - 140 | = 6$ 
C)  (i) Abigail: $123 - 140 = - 17$
(i) Mathilda: $146 - 140 = 6$ 
D)  (i) Abigail: $| 123 + 140 | = 263$
(ii) Mathilda: $| 146 + 140 | = 286$ 
A)  (i) Abigail: $| 140 - 123 | = - 17$
(ii) Mathilda: $| 140 - 146 | = - 6$ 
B)  (i) Abigail: $| 123 - 140 | = 17$
(ii) Mathilda: $| 146 - 140 | = 6$ 
C)  (i) Abigail: $123 - 140 = - 17$
(i) Mathilda: $146 - 140 = 6$ 
D)  (i) Abigail: $| 123 + 140 | = 263$
(ii) Mathilda: $| 146 + 140 | = 286$

Question 9

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { \frac { x } { 9 } } { \frac { 2 } { x + 6 } }$$

Accepted Answer

A)  $\frac { 2 x } { 9 ( x + 6 ) }$ 
B)  $18 x ( x + 6 )$ 
C)  $\frac { x ( x + 6 ) } { 18 }$ 
D)  $\frac { x + 6 } { 18 x }$ 
A)  $\frac { 2 x } { 9 ( x + 6 ) }$ 
B)  $18 x ( x + 6 )$ 
C)  $\frac { x ( x + 6 ) } { 18 }$ 
D)  $\frac { x + 6 } { 18 x }$

Question 10

Evaluate the expression.
-$$\left[ - \frac { 7 } { 8 } - \left( - \frac { 3 } { 4 } \right) \right] - \left( \frac { 3 } { 2 } - \frac { 9 } { 8 } \right)$$

Accepted Answer

A)  $- \frac { 1 } { 2 }$ 
B)  $- 2$ 
C)  $\frac { 1 } { 4 }$ 
D)  $- \frac { 5 } { 4 }$ 
A)  $- \frac { 1 } { 2 }$ 
B)  $- 2$ 
C)  $\frac { 1 } { 4 }$ 
D)  $- \frac { 5 } { 4 }$

Question 11

Tell whether the statement is true or false.
-$4 \notin \{ 0,2,3,5,7 \}$

Accepted Answer

A) True 
 B)False

Question 12

Identify the property illustrated by the statement. Assume all variables represent real numbers.
-(9 + 4) + 7 = (4 + 9) + 7

Accepted Answer

A)  Associative 
B)  Closure 
C)  Distributive 
D)  Commutative 
A)  Associative 
B)  Closure 
C)  Distributive 
D)  Commutative

Question 13

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$- 6 y ^ { 4 } + 9 y ^ { 3 } + - 5$

Accepted Answer

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

Question 14

Perform the indicated operations.
-$$\frac { 1 } { 6 x } - \frac { 7 } { 12 x }$$

Accepted Answer

A)  $\frac { 12 } { - 5 x }$ 
B)  $\frac { - 5 } { 12 x }$ 
C)  $\frac { - 5 } { 24 x }$ 
D)  1 
A)  $\frac { 12 } { - 5 x }$ 
B)  $\frac { - 5 } { 12 x }$ 
C)  $\frac { - 5 } { 24 x }$ 
D)  1

Question 15

Calculate the value mentally.
-$$\frac { 500 ^ { 3 / 2 } } { 5 ^ { 3 / 2 } }$$

Accepted Answer

A)  100 
B)  1,000 
C)  none of these 
D)  10 
A)  100 
B)  1,000 
C)  none of these 
D)  10

Question 16

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$- \frac { 1 } { 4 } ( 8 y )$

Accepted Answer

A)  3y 
B)  2y 
C)  -2y 
D)  -4y 
A)  3y 
B)  2y 
C)  -2y 
D)  -4y

Question 17

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 $x + 9$. Use the formula for the area of a square to write $t$ area of the largest square as a power.

Accepted Answer

A)  $( x - 9 ) ^ { 2 }$ 
B)  $x ^ { 2 } - 9 ^ { 2 }$ 
C)  $( x + 9 ) ^ { 2 }$ 
D)  $x ^ { 2 } + 9 ^ { 2 }$ 
A)  $( x - 9 ) ^ { 2 }$ 
B)  $x ^ { 2 } - 9 ^ { 2 }$ 
C)  $( x + 9 ) ^ { 2 }$ 
D)  $x ^ { 2 } + 9 ^ { 2 }$

Question 18

Perform the indicated operations.
-$$\frac { 3 } { 10 x } + \frac { 9 } { 14 x ^ { 2 } }$$

Accepted Answer

A)  $\frac { 3 ( 7 x + 15 ) } { 70 x }$ 
B)  $\frac { 3 ( 7 x + 15 ) } { 70 x ^ { 2 } }$ 
C)  $\frac { 12 } { 10 x + 14 x ^ { 2 } }$ 
D)  $\frac { 12 } { 140 x ^ { 2 } }$ 
A)  $\frac { 3 ( 7 x + 15 ) } { 70 x }$ 
B)  $\frac { 3 ( 7 x + 15 ) } { 70 x ^ { 2 } }$ 
C)  $\frac { 12 } { 10 x + 14 x ^ { 2 } }$ 
D)  $\frac { 12 } { 140 x ^ { 2 } }$

Question 19

Use set notation, and list all the elements of the set.
-$\{ 14,15,16 , \ldots , 20 \}$

Accepted Answer

A)  $\{ 14,16,18,20 \}$ 
B)  $\{ 14,15,16,17,18,19,20 \}$ 
C)  $\{ 14,15,16,17,18,19,20,21 \}$ 
D)  $\{ 14,15,17,19,20 \}$ 
A)  $\{ 14,16,18,20 \}$ 
B)  $\{ 14,15,16,17,18,19,20 \}$ 
C)  $\{ 14,15,16,17,18,19,20,21 \}$ 
D)  $\{ 14,15,17,19,20 \}$

Question 20

Evaluate the expression.
-$\text { |9| }$

Accepted Answer

A)  -9 
B)  9 
C)  0 
D)  $\pm 9$ 
A)  -9 
B)  9 
C)  0 
D)  $\pm 9$

Solve the problem. - $( p + 9 ) ^ { 2 }$

Solve the problem. - $( - 8 x - 3 ) ^ { 2 }$

Solve the problem. - $\frac { 18 x ^ { 7 } - 30 x ^ { 4 } } { - 6 x ^ { 7 } }$

Find the product. Assume variables represent positive real numbers. - $y ^ { 3 / 13 } \left( y ^ { 5 / 13 } - 3 y ^ { 2 / 13 } \right)$

List all the elements of set B that belong to the indicated set. - $B = \left\{ 15 , \sqrt { 7 } , - 13,0 , \frac { 0 } { 1 } , \sqrt { 16 } \right\}$ Whole numbers

Evaluate the expression. - $441 ^ { 1 / 2 }$

Evaluate the expression for x = -2, y = 3, and a = -4. - $\frac { - ( x + 3 ) ^ { 2 } - 7 y } { - 2 - a }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { \frac { x } { 9 } } { \frac { 2 } { x + 6 } }$

Evaluate the expression. - $\left[ - \frac { 7 } { 8 } - \left( - \frac { 3 } { 4 } \right) \right] - \left( \frac { 3 } { 2 } - \frac { 9 } { 8 } \right)$

Tell whether the statement is true or false. - $4 \notin \{ 0,2,3,5,7 \}$

Identify the property illustrated by the statement. Assume all variables represent real numbers. -(9 + 4) + 7 = (4 + 9) + 7

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $- 6 y ^ { 4 } + 9 y ^ { 3 } + - 5$

Perform the indicated operations. - $\frac { 1 } { 6 x } - \frac { 7 } { 12 x }$

Calculate the value mentally. - $\frac { 500 ^ { 3 / 2 } } { 5 ^ { 3 / 2 } }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $- \frac { 1 } { 4 } ( 8 y )$

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 $x + 9$ . Use the formula for the area of a square to write $t$ area of the largest square as a power.

Perform the indicated operations. - $\frac { 3 } { 10 x } + \frac { 9 } { 14 x ^ { 2 } }$

Use set notation, and list all the elements of the set. - $\{ 14,15,16 , \ldots , 20 \}$

Evaluate the expression. - $\text { |9| }$

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

Solve the problem. - (p+9)2( p + 9 ) ^ { 2 }(p+9)2

Solve the problem. - (−8x−3)2( - 8 x - 3 ) ^ { 2 }(−8x−3)2

Solve the problem. - 18x7−30x4−6x7\frac { 18 x ^ { 7 } - 30 x ^ { 4 } } { - 6 x ^ { 7 } }−6x718x7−30x4​

Find the product. Assume variables represent positive real numbers. - y3/13(y5/13−3y2/13)y ^ { 3 / 13 } \left( y ^ { 5 / 13 } - 3 y ^ { 2 / 13 } \right)y3/13(y5/13−3y2/13)

List all the elements of set B that belong to the indicated set. - B={15,7,−13,0,01,16}B = \left\{ 15 , \sqrt { 7 } , - 13,0 , \frac { 0 } { 1 } , \sqrt { 16 } \right\}B={15,7​,−13,0,10​,16​} Whole numbers

Evaluate the expression. - 4411/2441 ^ { 1 / 2 }4411/2

Evaluate the expression for x = -2, y = 3, and a = -4. - −(x+3)2−7y−2−a\frac { - ( x + 3 ) ^ { 2 } - 7 y } { - 2 - a }−2−a−(x+3)2−7y​

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - x92x+6\frac { \frac { x } { 9 } } { \frac { 2 } { x + 6 } }x+62​9x​​

Evaluate the expression. - [−78−(−34)]−(32−98)\left[ - \frac { 7 } { 8 } - \left( - \frac { 3 } { 4 } \right) \right] - \left( \frac { 3 } { 2 } - \frac { 9 } { 8 } \right)[−87​−(−43​)]−(23​−89​)

Tell whether the statement is true or false. - 4∉{0,2,3,5,7}4 \notin \{ 0,2,3,5,7 \}4∈/{0,2,3,5,7}