Question 1

Solve the polynomial equation by factoring and then using the zero product principle.
-$$20 x ^ { 3 } + 100 x ^ { 2 } + 120 x = 0$$

Accepted Answer

A)  $\{ 0 , - 2 , - 3 \}$ 
B)  $\{ - 2 , - 3 \}$ 
C)  $\{ 0,2,3 \}$ 
D)  $\left\{ - \frac { 1 } { 2 } , - 3 \right\}$ 
A)  $\{ 0 , - 2 , - 3 \}$ 
B)  $\{ - 2 , - 3 \}$ 
C)  $\{ 0,2,3 \}$ 
D)  $\left\{ - \frac { 1 } { 2 } , - 3 \right\}$

Question 2

Solve the equation.
-$$\frac { x } { 2 x + 2 } = \frac { - 2 x } { 4 x + 4 } + \frac { 2 x - 3 } { x + 1 }$$

Accepted Answer

A)  $\{ 3 \}$ 
B)  $\left\{ \frac { 3 } { 2 } \right\}$ 
C)  $\{ - 3 \}$ 
D)  $\left\{ - \frac { 12 } { 5 } \right\}$ 
A)  $\{ 3 \}$ 
B)  $\left\{ \frac { 3 } { 2 } \right\}$ 
C)  $\{ - 3 \}$ 
D)  $\left\{ - \frac { 12 } { 5 } \right\}$

Question 3

Add or subtract as indicated and write the result in standard form.
-$( - 7 + 7 i ) - 8$

Accepted Answer

A)  $- 15 + 7 \mathrm { i }$ 
B)  $15 - 7 \mathrm { i }$ 
C)  $1 + 7 \mathrm { i }$ 
D)  $1 - 7 \mathrm { i }$ 
A)  $- 15 + 7 \mathrm { i }$ 
B)  $15 - 7 \mathrm { i }$ 
C)  $1 + 7 \mathrm { i }$ 
D)  $1 - 7 \mathrm { i }$

Question 4

Solve Quadratic Equations by Completing the Square
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then
write and factor the trinomial.
-$$x ^ { 2 } + \frac { 1 } { 6 } x$$

Accepted Answer

A)  $\frac { 1 } { 144 } ; x ^ { 2 } + \frac { 1 } { 6 } x + \frac { 1 } { 144 } = \left( x + \frac { 1 } { 12 } \right) ^ { 2 }$ 
B)  $\frac { 1 } { 36 } ; x ^ { 2 } + \frac { 1 } { 6 } x + \frac { 1 } { 36 } = \left( x + \frac { 1 } { 6 } \right) ^ { 2 }$ 
C)  $\frac { 1 } { 12 } ; x ^ { 2 } + \frac { 1 } { 6 } x + \frac { 1 } { 12 } = \left( x + \frac { 1 } { 6 } \right) ^ { 2 }$ 
D)  $144 ; x ^ { 2 } + \frac { 1 } { 6 } x + 144 = ( x + 12 ) ^ { 2 }$ 
A)  $\frac { 1 } { 144 } ; x ^ { 2 } + \frac { 1 } { 6 } x + \frac { 1 } { 144 } = \left( x + \frac { 1 } { 12 } \right) ^ { 2 }$ 
B)  $\frac { 1 } { 36 } ; x ^ { 2 } + \frac { 1 } { 6 } x + \frac { 1 } { 36 } = \left( x + \frac { 1 } { 6 } \right) ^ { 2 }$ 
C)  $\frac { 1 } { 12 } ; x ^ { 2 } + \frac { 1 } { 6 } x + \frac { 1 } { 12 } = \left( x + \frac { 1 } { 6 } \right) ^ { 2 }$ 
D)  $144 ; x ^ { 2 } + \frac { 1 } { 6 } x + 144 = ( x + 12 ) ^ { 2 }$

Question 5

Solve the problem.
-The formula $P = 0.68 x ^ { 2 } - 0.047 x + 3$ models the approximate population $P$, in thousands, for a species of fish in a local pond, x years after 1997. During what year will the population reach 27,198 fish?

Accepted Answer

A)  2003 
B)  2002 
C)  2004 
D)  2005 
A)  2003 
B)  2002 
C)  2004 
D)  2005

Question 6

Solve Compound Inequalities
Solve the compound inequality. Other than $$\varnothing$$ use interval notation to express the solution set and graph the
solution set on a number line.
-$$4 < 2 x \leq 10$$

Accepted Answer

A)  $( 2,5 ]$
  
B)  $[ 2,5 )$
  
C)  $( - \infty , 2 ) \cup [ 5 , \infty )$
  
D)  $( - \infty , 2 ] \cup ( 5 , \infty )$
  
A)  $( 2,5 ]$
  
B)  $[ 2,5 )$
  
C)  $( - \infty , 2 ) \cup [ 5 , \infty )$
  
D)  $( - \infty , 2 ] \cup ( 5 , \infty )$

Question 7

Solve Linear Inequalities
Solve the linear inequality. Other than ∅, use interval notation to express the solution set and graph the solution set
on a number line.
-$$\frac { x } { 5 } - \frac { 2 } { 5 } \leq \frac { x } { 2 } + 1$$

Accepted Answer

A)  $\left[ - \frac { 14 } { 3 } , \infty \right]$
  
B)  $\left( - \infty , - \frac { 14 } { 3 } \right]$
  
C)  $\left( - \frac { 14 } { 3 } , \infty \right)$
  
D)  $\left( - \infty , - \frac { 14 } { 3 } \right)$
  
A)  $\left[ - \frac { 14 } { 3 } , \infty \right]$
  
B)  $\left( - \infty , - \frac { 14 } { 3 } \right]$
  
C)  $\left( - \frac { 14 } { 3 } , \infty \right)$
  
D)  $\left( - \infty , - \frac { 14 } { 3 } \right)$

Question 8

Solve the problem.
-A certain store has a fax machine available for use by its customers. The store charges $2.35 to send the first page and $0.70 for each subsequent page. The total price, P, for the faxing x pages can be modeled by
The formula P = 0.70(x - 1)+ 2.35. Determine the number of pages that can be faxed for $9.35.

Accepted Answer

A) 11 pages 
B) 57 pages 
C) 4 pages 
D) 13 pages 
A) 11 pages 
B) 57 pages 
C) 4 pages 
D) 13 pages

Question 9

Recognize Identities, Conditional Equations, and Inconsistent Equations
Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
-2x + 7x = 8x

Accepted Answer

A) Identity 
B) Conditional equation 
C) Inconsistent equation 
A) Identity 
B) Conditional equation 
C) Inconsistent equation

Question 10

Solve Linear Equations in One Variable
-6x - 6 = 54

Accepted Answer

A)  $\{ 10 \}$ 
B)  $\{ 54 \}$ 
C)  $\{ 58 \}$ 
D)  $\{ 15 \}$ 
A)  $\{ 10 \}$ 
B)  $\{ 54 \}$ 
C)  $\{ 58 \}$ 
D)  $\{ 15 \}$

Question 11

Solve the problem.
-A formula for the length of a diagonal from the upper corner of a box to the opposite lower corner is $\mathrm { d } = \sqrt { \mathrm { L } ^ { 2 } + \mathrm { W } ^ { 2 } + \mathrm { H } ^ { 2 } }$, where $\mathrm { L } , \mathrm { W }$, and $\mathrm { H }$ are the length, width, and height, respectively. Find the length of the diagonal of the box if the length is 20 inches, width is 14 inches, and height is 9 inches. Leave your answer in simplified radical form.

Accepted Answer

A)  $\sqrt { 677 }$ in. 
B)  $\sqrt { 86 } \mathrm { in }$. 
C)  $\sqrt { 43 }$ in. 
D)  $\sqrt { 1354 } \mathrm { in }$. 
A)  $\sqrt { 677 }$ in. 
B)  $\sqrt { 86 } \mathrm { in }$. 
C)  $\sqrt { 43 }$ in. 
D)  $\sqrt { 1354 } \mathrm { in }$.

Question 12

Solve Radical Equations
Solve the radical equation, and check all proposed solutions.
-$$\sqrt { 2 x + 3 } - \sqrt { x + 1 } = 1$$

Accepted Answer

A)  $\{ - 1,3 \}$ 
B)  $\{ 3 \}$ 
C)  $\{ - 3 , - 1 \}$ 
D)  $\varnothing$ 
A)  $\{ - 1,3 \}$ 
B)  $\{ 3 \}$ 
C)  $\{ - 3 , - 1 \}$ 
D)  $\varnothing$

Question 13

Solve the equation.
-$\frac { m + 8 } { m ^ { 2 } + 4 m + 3 } - \frac { 8 } { m ^ { 2 } + 6 m + 9 } = \frac { m - 8 } { m ^ { 2 } + 4 m + 3 }$

Accepted Answer

A)  $\{ - 5 \}$ 
B)  $\{ - 40 \}$ 
C)  $\{ 5 \}$ 
D)  $\{ - 8 \}$ 
A)  $\{ - 5 \}$ 
B)  $\{ - 40 \}$ 
C)  $\{ 5 \}$ 
D)  $\{ - 8 \}$

Question 14

Perform Operations with Square Roots of Negative Numbers
Perform the indicated operations and write the result in standard form.
-$5 \sqrt { - 81 } + 3 \sqrt { - 4 }$

Accepted Answer

A)  $51 \mathrm { i }$ 
B)  $- 51$ 
C)  51 
D)  $- 51 \mathrm { i }$ 
A)  $51 \mathrm { i }$ 
B)  $- 51$ 
C)  51 
D)  $- 51 \mathrm { i }$

Question 15

Solve Quadratic Equations by the Square Root Property
Solve the equation by the square root property.
-$$( 2 x + 2 ) ^ { 2 } = 16$$

Accepted Answer

A)  $\{ - 3,1 \}$ 
B)  $\{ 1,3 \}$ 
C)  $\{ - 9,9 \}$ 
D)  $\{ 0,1 \}$ 
A)  $\{ - 3,1 \}$ 
B)  $\{ 1,3 \}$ 
C)  $\{ - 9,9 \}$ 
D)  $\{ 0,1 \}$

Question 16

Solve Linear Equations in One Variable
-$$- 4 [ 3 x + 7 + 3 ( x + 1 ) ] = - 7 x - 5$$

Accepted Answer

A)  $\left\{ - \frac { 35 } { 17 } \right\}$ 
B)  $\left\{ \frac { 35 } { 3 } \right\}$ 
C)  $\left\{ \frac { 21 } { 17 } \right\}$ 
D)  $\{ - 7 \}$ 
A)  $\left\{ - \frac { 35 } { 17 } \right\}$ 
B)  $\left\{ \frac { 35 } { 3 } \right\}$ 
C)  $\left\{ \frac { 21 } { 17 } \right\}$ 
D)  $\{ - 7 \}$

Question 17

Solve Equations Involving Absolute Value
Solve the absolute value equation or indicate that the equation has no solution.
-$\left| x ^ { 2 } - 4 x - 4 \right| = 8$

Accepted Answer

A)  $\{ - 2,2,6 \}$ 
B)  $\{ 2,6 \}$ 
C)  $\{ - 2,2 \}$ 
D)  $\{ - 2,2 , - 6 \}$ 
A)  $\{ - 2,2,6 \}$ 
B)  $\{ 2,6 \}$ 
C)  $\{ - 2,2 \}$ 
D)  $\{ - 2,2 , - 6 \}$

Question 18

Solve the problem.
-The equation V = -2000t + 23,000 describes the value in dollars of a certain model of car after it is t years old. If a car is worth $15,000, substitute 15,000 into the equation to find the age of the car.

Accepted Answer

A) 4 years 
B) 3 years 
C) 5 years 
D) 6 years 
A) 4 years 
B) 3 years 
C) 5 years 
D) 6 years

Question 19

Solve the problem.
-When a number is subtracted from $- 7$, the absolute value of the difference is more than 3 . Use interval notation to express the set of all numbers that satisfy this condition.

Accepted Answer

A)  $( - \infty , - 10 ) \cup ( - 4 , \infty )$ 
B)  $( - \infty , - 4 ) \cup ( 10 , \infty )$ 
C)  $( - \infty , - 10 ] \cup [ - 4 , \infty )$ 
D)  $( - 10 , - 4 )$ 
A)  $( - \infty , - 10 ) \cup ( - 4 , \infty )$ 
B)  $( - \infty , - 4 ) \cup ( 10 , \infty )$ 
C)  $( - \infty , - 10 ] \cup [ - 4 , \infty )$ 
D)  $( - 10 , - 4 )$

Question 20

Solve Quadratic Equations by Completing the Square
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then
write and factor the trinomial.
-$$x ^ { 2 } + \frac { 4 } { 5 } x$$

Accepted Answer

A)  $\frac { 4 } { 25 } ; x ^ { 2 } + \frac { 4 } { 5 } x + \frac { 4 } { 25 } = \left( x + \frac { 2 } { 5 } \right) ^ { 2 }$ 
B)  $\frac { 8 } { 25 } ; x ^ { 2 } + \frac { 4 } { 5 } x + \frac { 8 } { 25 } = \left( x + \frac { 4 } { 5 } \right) ^ { 2 }$ 
C)  $\frac { 4 } { 5 } ; x ^ { 2 } + \frac { 4 } { 5 } x + \frac { 4 } { 5 } = \left( x + \frac { 2 } { 5 } \right) ^ { 2 }$ 
D)  $\frac { 2 } { 25 } ; x ^ { 2 } + \frac { 4 } { 5 } x + \frac { 2 } { 25 } = \left( x + \frac { 2 } { 5 } \right) ^ { 2 }$ 
A)  $\frac { 4 } { 25 } ; x ^ { 2 } + \frac { 4 } { 5 } x + \frac { 4 } { 25 } = \left( x + \frac { 2 } { 5 } \right) ^ { 2 }$ 
B)  $\frac { 8 } { 25 } ; x ^ { 2 } + \frac { 4 } { 5 } x + \frac { 8 } { 25 } = \left( x + \frac { 4 } { 5 } \right) ^ { 2 }$ 
C)  $\frac { 4 } { 5 } ; x ^ { 2 } + \frac { 4 } { 5 } x + \frac { 4 } { 5 } = \left( x + \frac { 2 } { 5 } \right) ^ { 2 }$ 
D)  $\frac { 2 } { 25 } ; x ^ { 2 } + \frac { 4 } { 5 } x + \frac { 2 } { 25 } = \left( x + \frac { 2 } { 5 } \right) ^ { 2 }$

Solve the polynomial equation by factoring and then using the zero product principle. - $20 x ^ { 3 } + 100 x ^ { 2 } + 120 x = 0$

Solve the equation. - $\frac { x } { 2 x + 2 } = \frac { - 2 x } { 4 x + 4 } + \frac { 2 x - 3 } { x + 1 }$

Add or subtract as indicated and write the result in standard form. - $( - 7 + 7 i ) - 8$

Solve Quadratic Equations by Completing the Square Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. - $x ^ { 2 } + \frac { 1 } { 6 } x$

Solve the problem. -The formula $P = 0.68 x ^ { 2 } - 0.047 x + 3$ models the approximate population $P$ , in thousands, for a species of fish in a local pond, x years after 1997. During what year will the population reach 27,198 fish?

Recognize Identities, Conditional Equations, and Inconsistent Equations Determine whether the equation is an identity, a conditional equation, or an inconsistent equation. -2x + 7x = 8x

Solve Linear Equations in One Variable -6x - 6 = 54

Solve Radical Equations Solve the radical equation, and check all proposed solutions. - $\sqrt { 2 x + 3 } - \sqrt { x + 1 } = 1$

Solve the equation. - $\frac { m + 8 } { m ^ { 2 } + 4 m + 3 } - \frac { 8 } { m ^ { 2 } + 6 m + 9 } = \frac { m - 8 } { m ^ { 2 } + 4 m + 3 }$

Perform Operations with Square Roots of Negative Numbers Perform the indicated operations and write the result in standard form. - $5 \sqrt { - 81 } + 3 \sqrt { - 4 }$

Solve Quadratic Equations by the Square Root Property Solve the equation by the square root property. - $( 2 x + 2 ) ^ { 2 } = 16$

Solve Linear Equations in One Variable - $- 4 [ 3 x + 7 + 3 ( x + 1 ) ] = - 7 x - 5$

Solve Equations Involving Absolute Value Solve the absolute value equation or indicate that the equation has no solution. - $\left| x ^ { 2 } - 4 x - 4 \right| = 8$

Solve the problem. -The equation V = -2000t + 23,000 describes the value in dollars of a certain model of car after it is t years old. If a car is worth $15,000, substitute 15,000 into the equation to find the age of the car.

Solve the problem. -When a number is subtracted from $- 7$ , the absolute value of the difference is more than 3 . Use interval notation to express the set of all numbers that satisfy this condition.

Solve Quadratic Equations by Completing the Square Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. - $x ^ { 2 } + \frac { 4 } { 5 } x$

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences, Induction, and Probability

Filters

Exam 1: Equations and Inequalities

Solve the polynomial equation by factoring and then using the zero product principle. - 20x3+100x2+120x=020 x ^ { 3 } + 100 x ^ { 2 } + 120 x = 020x3+100x2+120x=0

Solve the equation. - x2x+2=−2x4x+4+2x−3x+1\frac { x } { 2 x + 2 } = \frac { - 2 x } { 4 x + 4 } + \frac { 2 x - 3 } { x + 1 }2x+2x​=4x+4−2x​+x+12x−3​

Add or subtract as indicated and write the result in standard form. - (−7+7i)−8( - 7 + 7 i ) - 8(−7+7i)−8

Solve Quadratic Equations by Completing the Square Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. - x2+16xx ^ { 2 } + \frac { 1 } { 6 } xx2+61​x

Solve the problem. -The formula P=0.68x2−0.047x+3P = 0.68 x ^ { 2 } - 0.047 x + 3P=0.68x2−0.047x+3 models the approximate population PPP , in thousands, for a species of fish in a local pond, x years after 1997. During what year will the population reach 27,198 fish?

Solve Compound Inequalities Solve the compound inequality. Other than ∅\varnothing∅ use interval notation to express the solution set and graph the solution set on a number line. - 4<2x≤104 < 2 x \leq 104<2x≤10

Solve Linear Inequalities Solve the linear inequality. Other than ∅, use interval notation to express the solution set and graph the solution set on a number line. - x5−25≤x2+1\frac { x } { 5 } - \frac { 2 } { 5 } \leq \frac { x } { 2 } + 15x​−52​≤2x​+1