Question 1

Write the inequality in interval notation.
-$7 > x \geq - 5$

Accepted Answer

A)  $( - 5,7 )$ 
B)  $[ - 5,7 )$ 
C)  $[ - 5,7 ]$ 
D)  $( - 5,7 ]$ 
A)  $( - 5,7 )$ 
B)  $[ - 5,7 )$ 
C)  $[ - 5,7 ]$ 
D)  $( - 5,7 ]$

Question 2

If an amount of money, called the principal, P, is deposited into an account that earns interest at a rate r, compounded annually, then in two years that investment will grow to an amount A, given by the formula $A = P ( 1 + r ) ^ { 2 }$ If a principal amount of $5500 grows to $6415.20 in two years, what is the interest rate?

Accepted Answer

A)  6% 
B)  10% 
C)  9% 
D)  8% 
A)  6% 
B)  10% 
C)  9% 
D)  8%

Question 3

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { x + 24 } { 7 } = \frac { 5 x - 4 } { x }$$

Accepted Answer

A)  $\left\{ \frac { 28 } { 9 } \right\}$ 
B)  $\left\{ \frac { 30 } { 17 } \right\}$ 
C)  $\{ 4,7 \}$ 
D)  $\{ - 4 , - 7 \}$ 
A)  $\left\{ \frac { 28 } { 9 } \right\}$ 
B)  $\left\{ \frac { 30 } { 17 } \right\}$ 
C)  $\{ 4,7 \}$ 
D)  $\{ - 4 , - 7 \}$

Question 4

Solve the problem.
-An airplane leaves Los Angeles for Denver at a speed of 450 mph. Thirty minutes later, a plane going from Denver to Los Angeles leaves Denver, which is 850 miles from Los Angeles, at a speed of 470 mph. When they
Meet, how far are they from Denver?

Accepted Answer

A)  319 mi 
B)  111 mi 
C)  277 mi 
D)  55 mi 
A)  319 mi 
B)  111 mi 
C)  277 mi 
D)  55 mi

Question 5

Find the values of a, b, and c for which the quadratic equation $a x ^ { 2 } + b x + c = 0$ 0 has the given numbers as solutions. Then
use those values to write a quadratic equation.
-8,5

Accepted Answer

A)  $x ^ { 2 } + 40 x + 13 = 0$ 
B)  $x ^ { 2 } + 13 x + 40 = 0$ 
C)  $x ^ { 2 } + 40 x - 13 = 0$ 
D)  $x ^ { 2 } - 13 x + 40 = 0$ 
A)  $x ^ { 2 } + 40 x + 13 = 0$ 
B)  $x ^ { 2 } + 13 x + 40 = 0$ 
C)  $x ^ { 2 } + 40 x - 13 = 0$ 
D)  $x ^ { 2 } - 13 x + 40 = 0$

Question 6

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\sqrt { x + 6 } + \sqrt { 2 - x } = 4$$

Accepted Answer

A)  $\{ \sqrt { 31 } , - 2 \}$ 
B)  $\{ 0 \}$ 
C)  $\{ - 2 \}$ 
D)  $\{ 2 , - 2 \}$ 
A)  $\{ \sqrt { 31 } , - 2 \}$ 
B)  $\{ 0 \}$ 
C)  $\{ - 2 \}$ 
D)  $\{ 2 , - 2 \}$

Question 7

Solve the cubic equation using factoring and the quadratic formula.
-$$x ^ { 2 } = 36$$

Accepted Answer

A)  $\pm \sqrt { 6 }$ 
B)  $\pm i \sqrt { 6 }$ 
C)  $\pm 6 \mathrm { i }$ 
D)  $\pm 6$ 
A)  $\pm \sqrt { 6 }$ 
B)  $\pm i \sqrt { 6 }$ 
C)  $\pm 6 \mathrm { i }$ 
D)  $\pm 6$

Question 8

Your company uses the quadratic model y $y = - 4.5 x ^ { 2 } + 150 x$ 150x to represent the average number of new customers who will be signed on (x) weeks after the release of your new service. How many new customers can you
Expect to gain in week 8?

Accepted Answer

A)  456 customers 
B)  1164 customers 
C)  312 customers 
D)  912 customers 
A)  456 customers 
B)  1164 customers 
C)  312 customers 
D)  912 customers

Question 9

Solve the cubic equation using factoring and the quadratic formula.
-$$x ^ { 3 } + 8 = 0$$

Accepted Answer

A)  $\{ - 2,1 \pm i \sqrt { 6 } \}$ 
B)  $\{ - 2 , - 1 \pm \sqrt { 5 } \}$ 
C)  $\{ - 2,1 \pm i \sqrt { 3 } \}$ 
D)  $\{ - 2 , \pm 2 i \}$ 
A)  $\{ - 2,1 \pm i \sqrt { 6 } \}$ 
B)  $\{ - 2 , - 1 \pm \sqrt { 5 } \}$ 
C)  $\{ - 2,1 \pm i \sqrt { 3 } \}$ 
D)  $\{ - 2 , \pm 2 i \}$

Question 10

Determine whether or not the equation is linear.
-$$7 [ - 5 x + 2 - 6 ( x + 1 ) ] = 3 x - 6$$

Accepted Answer

A)  $\left\{ - \frac { 5 } { 8 } \right\}$ 
B)  $\left\{ - \frac { 11 } { 40 } \right\}$ 
C)  $\left\{ - \frac { 22 } { 5 } \right\}$ 
D)  $\{ - 10 \}$ 
A)  $\left\{ - \frac { 5 } { 8 } \right\}$ 
B)  $\left\{ - \frac { 11 } { 40 } \right\}$ 
C)  $\left\{ - \frac { 22 } { 5 } \right\}$ 
D)  $\{ - 10 \}$

Question 11

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 4 } { x - 9 } + \frac { 9 } { x + 6 } = \frac { 7 } { x ^ { 2 } - 3 x - 54 }$$

Accepted Answer

A)  $\left\{ - \frac { 11 } { 2 } \right\}$ 
B)  $\left\{ \frac { 28 } { 3 } \right\}$ 
C)  $\varnothing$ 
D)  $\left\{ \frac { 64 } { 13 } \right\}$ 
A)  $\left\{ - \frac { 11 } { 2 } \right\}$ 
B)  $\left\{ \frac { 28 } { 3 } \right\}$ 
C)  $\varnothing$ 
D)  $\left\{ \frac { 64 } { 13 } \right\}$

Question 12

Solve the inequality. Write the solution set in interval notation.
-$$x ^ { 2 } ( x + 16 ) ^ { 2 } < 0$$

Accepted Answer

A)  $( - \infty , - 4 ] \cup [ 0,4 ]$ 
B)  $\varnothing$ 
C)  $( - \infty , \infty )$ 
D)  $[ - 4,0 ] \cup [ 4 , \infty )$ 
A)  $( - \infty , - 4 ] \cup [ 0,4 ]$ 
B)  $\varnothing$ 
C)  $( - \infty , \infty )$ 
D)  $[ - 4,0 ] \cup [ 4 , \infty )$

Question 13

Solve the equation using the quadratic formula.
-$$( 2 x - 1 ) ( x + 1 ) = 3$$

Accepted Answer

A)  $\left\{ \frac { - 1 \pm \sqrt { 33 } } { 4 } \right\}$ 
B)  $\left\{ \frac { 1 \pm \sqrt { 33 } } { 4 } \right\}$ 
C)  $\left\{ \frac { - 1 \pm \sqrt { 57 } } { 2 } \right\}$ 
D)  $\left\{ \frac { 1 \pm \sqrt { 33 } } { 2 } \right\}$ 
A)  $\left\{ \frac { - 1 \pm \sqrt { 33 } } { 4 } \right\}$ 
B)  $\left\{ \frac { 1 \pm \sqrt { 33 } } { 4 } \right\}$ 
C)  $\left\{ \frac { - 1 \pm \sqrt { 57 } } { 2 } \right\}$ 
D)  $\left\{ \frac { 1 \pm \sqrt { 33 } } { 2 } \right\}$

Question 14

Solve the inequality. Write the solution set in interval notation.
-$$| 7 x - 7 | + 4 < 7$$

Accepted Answer

A)  $\varnothing$ 
B)  $\left( - \infty , \frac { 4 } { 7 } \right)$ 
C)  $\left( - \infty , \frac { 4 } { 7 } \right) \cup \left( \frac { 10 } { 7 } , \infty \right)$ 
D)  $\left( \frac { 4 } { 7 } , \frac { 10 } { 7 } \right)$ 
A)  $\varnothing$ 
B)  $\left( - \infty , \frac { 4 } { 7 } \right)$ 
C)  $\left( - \infty , \frac { 4 } { 7 } \right) \cup \left( \frac { 10 } { 7 } , \infty \right)$ 
D)  $\left( \frac { 4 } { 7 } , \frac { 10 } { 7 } \right)$

Question 15

If a rocket is propelled upward from ground level, its height in meters after $t$ seconds is given by $\mathrm { h } = - 9.8 \mathrm { t } ^ { 2 } + 98 \mathrm { t }$. During what interval of time will the rocket be higher than $235.2 \mathrm {~m}$ ?

Accepted Answer

A)  $4 < t < 6$ 
B)  $8 < t < 10$ 
C)  $6 < t < 8$ 
D)  $0 < t < 4$ 
A)  $4 < t < 6$ 
B)  $8 < t < 10$ 
C)  $6 < t < 8$ 
D)  $0 < t < 4$

Question 16

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 6 } { x + 5 } = 1 - \frac { 1 } { x - 5 }$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ 0 , - 5 \}$ 
C)  $\{ 1,5 \}$ 
D)  $\{ 0,7 \}$ 
A)  $\varnothing$ 
B)  $\{ 0 , - 5 \}$ 
C)  $\{ 1,5 \}$ 
D)  $\{ 0,7 \}$

Question 17

Multiply or divide, as indicated. Simplify the answer.
-$\frac { \sqrt { - 8 } } { \sqrt { 72 } }$

Accepted Answer

A)  $\frac { 1 } { 3 }$ 
B)  $- \frac { 1 } { 3 }$ 
C)  $- \frac { 1 } { 3 } \mathrm { i }$ 
D)  $\frac { 1 } { 3 } \mathrm { i }$ 
A)  $\frac { 1 } { 3 }$ 
B)  $- \frac { 1 } { 3 }$ 
C)  $- \frac { 1 } { 3 } \mathrm { i }$ 
D)  $\frac { 1 } { 3 } \mathrm { i }$

Question 18

Solve the cubic equation using factoring and the quadratic formula.
-$$x ^ { 2 } = - 25$$

Accepted Answer

A)  $\pm \sqrt { 5 }$ 
B)  $\pm 5 \mathrm { i }$ 
C)  $\pm 5$ 
D)  $\pm i \sqrt { 5 }$ 
A)  $\pm \sqrt { 5 }$ 
B)  $\pm 5 \mathrm { i }$ 
C)  $\pm 5$ 
D)  $\pm i \sqrt { 5 }$

Question 19

Solve the problem.
-In a chemistry class, 3 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

Accepted Answer

A)  3 L 
B)  2.5 L 
C)  1.5 L 
D)  0.5 L 
A)  3 L 
B)  2.5 L 
C)  1.5 L 
D)  0.5 L

Question 20

Decide whether or not the equations are equivalent.
-$\begin{array} { l } 
\frac { x + 1 } { 5 } = \frac { 4 } { 5 } \
x + 2 = 5
\end{array}$

Accepted Answer

A)  Equivalent 
B)  Not equivalent 
A)  Equivalent 
B)  Not equivalent

Write the inequality in interval notation. - $7 > x \geq - 5$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { x + 24 } { 7 } = \frac { 5 x - 4 } { x }$

Solve the problem. -An airplane leaves Los Angeles for Denver at a speed of 450 mph. Thirty minutes later, a plane going from Denver to Los Angeles leaves Denver, which is 850 miles from Los Angeles, at a speed of 470 mph. When they Meet, how far are they from Denver?

Find the values of a, b, and c for which the quadratic equation $a x ^ { 2 } + b x + c = 0$ 0 has the given numbers as solutions. Then use those values to write a quadratic equation. -8,5

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { x + 6 } + \sqrt { 2 - x } = 4$

Solve the cubic equation using factoring and the quadratic formula. - $x ^ { 2 } = 36$

Your company uses the quadratic model y $y = - 4.5 x ^ { 2 } + 150 x$ 150x to represent the average number of new customers who will be signed on (x) weeks after the release of your new service. How many new customers can you Expect to gain in week 8?

Solve the cubic equation using factoring and the quadratic formula. - $x ^ { 3 } + 8 = 0$

Determine whether or not the equation is linear. - $7 [ - 5 x + 2 - 6 ( x + 1 ) ] = 3 x - 6$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 4 } { x - 9 } + \frac { 9 } { x + 6 } = \frac { 7 } { x ^ { 2 } - 3 x - 54 }$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } ( x + 16 ) ^ { 2 } < 0$

Solve the equation using the quadratic formula. - $( 2 x - 1 ) ( x + 1 ) = 3$

Solve the inequality. Write the solution set in interval notation. - $| 7 x - 7 | + 4 < 7$

If a rocket is propelled upward from ground level, its height in meters after $t$ seconds is given by $\mathrm { h } = - 9.8 \mathrm { t } ^ { 2 } + 98 \mathrm { t }$ . During what interval of time will the rocket be higher than $235.2 \mathrm {~m}$ ?

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 6 } { x + 5 } = 1 - \frac { 1 } { x - 5 }$

Multiply or divide, as indicated. Simplify the answer. - $\frac { \sqrt { - 8 } } { \sqrt { 72 } }$

Solve the cubic equation using factoring and the quadratic formula. - $x ^ { 2 } = - 25$

Solve the problem. -In a chemistry class, 3 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

Decide whether or not the equations are equivalent. - = x+2=5

Review of Basic Concepts

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 2: Equations and Inequalities

Write the inequality in interval notation. - 7>x≥−57 > x \geq - 57>x≥−5

Decide what values of the variable cannot possibly be solutions for the equation. - x+247=5x−4x\frac { x + 24 } { 7 } = \frac { 5 x - 4 } { x }7x+24​=x5x−4​

Solve the problem. -An airplane leaves Los Angeles for Denver at a speed of 450 mph. Thirty minutes later, a plane going from Denver to Los Angeles leaves Denver, which is 850 miles from Los Angeles, at a speed of 470 mph. When they Meet, how far are they from Denver?

Find the values of a, b, and c for which the quadratic equation ax2+bx+c=0a x ^ { 2 } + b x + c = 0ax2+bx+c=0 0 has the given numbers as solutions. Then use those values to write a quadratic equation. -8,5

Decide what values of the variable cannot possibly be solutions for the equation. - x+6+2−x=4\sqrt { x + 6 } + \sqrt { 2 - x } = 4x+6​+2−x​=4

Solve the cubic equation using factoring and the quadratic formula. - x2=36x ^ { 2 } = 36x2=36

Your company uses the quadratic model y y=−4.5x2+150xy = - 4.5 x ^ { 2 } + 150 xy=−4.5x2+150x 150x to represent the average number of new customers who will be signed on (x) weeks after the release of your new service. How many new customers can you Expect to gain in week 8?

Solve the cubic equation using factoring and the quadratic formula. - x3+8=0x ^ { 3 } + 8 = 0x3+8=0

Determine whether or not the equation is linear. - 7[−5x+2−6(x+1)]=3x−67 [ - 5 x + 2 - 6 ( x + 1 ) ] = 3 x - 67[−5x+2−6(x+1)]=3x−6

Decide what values of the variable cannot possibly be solutions for the equation. - 4x−9+9x+6=7x2−3x−54\frac { 4 } { x - 9 } + \frac { 9 } { x + 6 } = \frac { 7 } { x ^ { 2 } - 3 x - 54 }x−94​+x+69​=x2−3x−547​

Solve the inequality. Write the solution set in interval notation. - x2(x+16)2<0x ^ { 2 } ( x + 16 ) ^ { 2 } < 0x2(x+16)2<0

Solve the equation using the quadratic formula. - (2x−1)(x+1)=3( 2 x - 1 ) ( x + 1 ) = 3(2x−1)(x+1)=3

Solve the inequality. Write the solution set in interval notation. - ∣7x−7∣+4<7| 7 x - 7 | + 4 < 7∣7x−7∣+4<7

If a rocket is propelled upward from ground level, its height in meters after ttt seconds is given by h=−9.8t2+98t\mathrm { h } = - 9.8 \mathrm { t } ^ { 2 } + 98 \mathrm { t }h=−9.8t2+98t . During what interval of time will the rocket be higher than 235.2 m235.2 \mathrm {~m}235.2 m ?

Decide what values of the variable cannot possibly be solutions for the equation. - 6x+5=1−1x−5\frac { 6 } { x + 5 } = 1 - \frac { 1 } { x - 5 }x+56​=1−x−51​

Multiply or divide, as indicated. Simplify the answer. - −872\frac { \sqrt { - 8 } } { \sqrt { 72 } }72​−8​​

Solve the cubic equation using factoring and the quadratic formula. - x2=−25x ^ { 2 } = - 25x2=−25