Question 1

Solve the formula for the indicated variable.
-$\mathrm { R } = \mathrm { nE } - \mathrm { nr }$, for $\mathrm { n }$

Accepted Answer

A)  $n = \frac { R } { E - r }$ 
B)  $n = R - E + r$ 
C)  $n = R + n r - E$ 
D)  $n = \frac { R + n r } { E }$ 
A)  $n = \frac { R } { E - r }$ 
B)  $n = R - E + r$ 
C)  $n = R + n r - E$ 
D)  $n = \frac { R + n r } { E }$

Question 2

Use these equations to convert between the two systems. $C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32$ Round answer to the nearest tenth of a degree if necessary.
-A square plywood platform has a perimeter which is 7 times the length of a side, decreased by 18. Find the length of a side.

Accepted Answer

A)  9 
B)  1 
C)  6 
D)  3 
A)  9 
B)  1 
C)  6 
D)  3

Question 3

The high temperature on December 12 in Hilton Head, $\mathrm { SC }$ ranges from $33 ^ { \circ } \mathrm { F }$ to $89 ^ { \circ } \mathrm { F }$. Using $\mathrm { F }$ as the variable, write an absolute value inequality that corresponds to this range.

Accepted Answer

A)  $| F - 28 | \leq 61$ 
B)  $| F - 33 | \ll 56$ 
C)  $| \mathrm { F } - 56 | \leq 33$ 
D)  $| F - 61 | \leq 28$ 
A)  $| F - 28 | \leq 61$ 
B)  $| F - 33 | \ll 56$ 
C)  $| \mathrm { F } - 56 | \leq 33$ 
D)  $| F - 61 | \leq 28$

Question 4

Find the product. Write the answer in standard form.
-$$( 8 - 4 i ) ( 7 + 5 i )$$

Accepted Answer

A)  $- 20 \mathrm { i } ^ { 2 } + 12 \mathrm { i } - 56$ 
B)  $76 + 12 \mathrm { i }$ 
C)  $76 - 12 \mathrm { i }$ 
D)  $36 - 68 \mathrm { i }$ 
A)  $- 20 \mathrm { i } ^ { 2 } + 12 \mathrm { i } - 56$ 
B)  $76 + 12 \mathrm { i }$ 
C)  $76 - 12 \mathrm { i }$ 
D)  $36 - 68 \mathrm { i }$

Question 5

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { 8 } { ( x + 4 ) ^ { 2 } } < 0$$

Accepted Answer

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

Question 6

Find the quotient. Write the answer in standard form.
-$$\frac { 5 - 5 i } { 4 + 2 i }$$

Accepted Answer

A)  $\frac { 1 } { 2 } - \frac { 3 } { 2 } i$ 
B)  $15 + 5 i$ 
C)  $\frac { 5 } { 2 } + \frac { 1 } { 4 } i$ 
D)  $\frac { 1 } { 12 } + \frac { 1 } { 4 } \mathrm { i }$ 
A)  $\frac { 1 } { 2 } - \frac { 3 } { 2 } i$ 
B)  $15 + 5 i$ 
C)  $\frac { 5 } { 2 } + \frac { 1 } { 4 } i$ 
D)  $\frac { 1 } { 12 } + \frac { 1 } { 4 } \mathrm { i }$

Question 7

A ball is thrown downward from a window in a tall building. Its position at time t in seconds is $s = 16 t ^ { 2 } + 32 t$ where s is in feet. How long (to the nearest tenth) will it take the ball to fall 133 feet?

Accepted Answer

A)  1.9 sec 
B)  4.4 sec 
C)  2.9 sec 
D)  2.1 sec 
A)  1.9 sec 
B)  4.4 sec 
C)  2.9 sec 
D)  2.1 sec

Question 8

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.
-$$- 4 , - 5$$

Accepted Answer

A)  $x ^ { 2 } + 20 x + 9 = 0$ 
B)  $x ^ { 2 } + 9 x + 20 = 0$ 
C)  $x ^ { 2 } - 9 x + 20 = 0$ 
D)  $x ^ { 2 } + 20 x - 9 = 0$ 
A)  $x ^ { 2 } + 20 x + 9 = 0$ 
B)  $x ^ { 2 } + 9 x + 20 = 0$ 
C)  $x ^ { 2 } - 9 x + 20 = 0$ 
D)  $x ^ { 2 } + 20 x - 9 = 0$

Question 9

Find two consecutive integers whose product is 20.

Accepted Answer

A)  4,5 or $- 4 , - 5$ 
B)  $4 , - 5$ 
C)  $- 4 , - 5$ 
D)  4,5 
A)  4,5 or $- 4 , - 5$ 
B)  $4 , - 5$ 
C)  $- 4 , - 5$ 
D)  4,5

Question 10

Solve the problem.
-Your home state uses a linear model y $y = 45 ( x - 70 ) + 1610$ to predict the number of vacationers (y) as compared to the average temperature for that week (x). Find the number of vacationers predicted for a week with an
Average temperature of 60 degrees.

Accepted Answer

A)  7460 vacationers 
B)  4240 vacationers 
C)  72,000 vacationers 
D)  1160 vacationers 
A)  7460 vacationers 
B)  4240 vacationers 
C)  72,000 vacationers 
D)  1160 vacationers

Question 11

Decide what values of the variable cannot possibly be solutions for the equation.
-$\sqrt [ 3 ] { 4 + 6 x } - \sqrt [ 3 ] { 1 - 8 x } = 0$

Accepted Answer

A)  $\left\{ \frac { 14 } { 3 } \right\}$ 
B)  $\left\{ - \frac { 3 } { 14 } \right\}$ 
C)  $\left\{ \frac { 3 } { 14 } \right\}$ 
D)  $\left\{ - \frac { 14 } { 3 } \right\}$ 
A)  $\left\{ \frac { 14 } { 3 } \right\}$ 
B)  $\left\{ - \frac { 3 } { 14 } \right\}$ 
C)  $\left\{ \frac { 3 } { 14 } \right\}$ 
D)  $\left\{ - \frac { 14 } { 3 } \right\}$

Question 12

The profit made when $t$ units are sold, $t > 0$, is given by $P = t ^ { 2 } - 30 t + 200$. Determine the number of units to be sold in order for $\mathrm { P } > 0$ (a profit is made).

Accepted Answer

A)  $20  20$ or $t < 10$ 
A)  $20  20$ or $t < 10$

Question 13

Solve the equation by the zero-factor property.
-$$35 x ^ { 2 } + 43 x + 12 = 0$$

Accepted Answer

A)  $\left\{ - \frac { 5 } { 4 } , - \frac { 3 } { 7 } \right\}$ 
B)  $\left\{ \frac { 4 } { 5 } , \frac { 3 } { 7 } \right\}$ 
C)  $\left\{ \frac { 5 } { 4 } , \frac { 7 } { 3 } \right\}$ 
D)  $\left\{ - \frac { 4 } { 5 } , - \frac { 3 } { 7 } \right\}$ 
A)  $\left\{ - \frac { 5 } { 4 } , - \frac { 3 } { 7 } \right\}$ 
B)  $\left\{ \frac { 4 } { 5 } , \frac { 3 } { 7 } \right\}$ 
C)  $\left\{ \frac { 5 } { 4 } , \frac { 7 } { 3 } \right\}$ 
D)  $\left\{ - \frac { 4 } { 5 } , - \frac { 3 } { 7 } \right\}$

Question 14

Decide what values of the variable cannot possibly be solutions for the equation.
-$$( 10 + x ) ^ { 1 / 2 + ( 11 - 5 x ) ^ { 1 / 2 } = - 1 }$$

Accepted Answer

A)  $\left\{ - 1 , \frac { 10 } { 9 } \right\}$ 
B)  $\varnothing$ 
C)  $\{ 0 \}$ 
D)  $\{ 1 \}$ 
A)  $\left\{ - 1 , \frac { 10 } { 9 } \right\}$ 
B)  $\varnothing$ 
C)  $\{ 0 \}$ 
D)  $\{ 1 \}$

Question 15

Solve the quadratic inequality. Write the solution set in interval notation.
-$$x ^ { 2 } + 7 x \leq - 12$$

Accepted Answer

A)  $( - \infty , 3 ] \cup [ 4 , \infty )$ 
B)  $( 3,4 )$ 
C)  $[ 3,4 ]$ 
D)  $[ - 4 , - 3 ]$ 
A)  $( - \infty , 3 ] \cup [ 4 , \infty )$ 
B)  $( 3,4 )$ 
C)  $[ 3,4 ]$ 
D)  $[ - 4 , - 3 ]$

Question 16

Indicate whether the statement is true always, sometimes, or never.
-The product of a pair of complex conjugates is a real number.

Accepted Answer

A)  Never 
B)  Sometimes 
C)  Always 
A)  Never 
B)  Sometimes 
C)  Always

Question 17

Indicate whether the statement is true always, sometimes, or never.
-A complex number is an imaginary number.

Accepted Answer

A)  Always 
B)  Never 
C)  Sometimes 
A)  Always 
B)  Never 
C)  Sometimes

Question 18

Solve for y.
-$$7 x + 9 = 5 y - 9$$

Accepted Answer

A)  $y = 7 x + 18$ 
B)  $y = \frac { 7 x - 18 } { 5 }$ 
C)  $y = 7 x - 18$ 
D)  $y = \frac { 7 x + 18 } { 5 }$ 
A)  $y = 7 x + 18$ 
B)  $y = \frac { 7 x - 18 } { 5 }$ 
C)  $y = 7 x - 18$ 
D)  $y = \frac { 7 x + 18 } { 5 }$

Question 19

Solve for y.
-$$10 y + x ^ { 2 } = x + 8$$

Accepted Answer

A)  $y = x + 8 - x ^ { 2 }$ 
B)  $y = x ^ { 2 } - x - 8$ 
C)  $y = \frac { x + 8 - x ^ { 2 } } { 10 }$ 
D)  $y = \frac { x ^ { 2 } - x - 8 } { 10 }$ 
A)  $y = x + 8 - x ^ { 2 }$ 
B)  $y = x ^ { 2 } - x - 8$ 
C)  $y = \frac { x + 8 - x ^ { 2 } } { 10 }$ 
D)  $y = \frac { x ^ { 2 } - x - 8 } { 10 }$

Question 20

Graph the solution set.
-$| 5 x - 2 | = | 2 x - 3 |$

Accepted Answer

A)  $\left\{ - \frac { 5 } { 3 } , 1 \right\}$ 
B)  $\left\{ - \frac { 1 } { 7 } , \frac { 5 } { 3 } \right\}$ 
C)  $\left\{ \frac { 5 } { 3 } , 1 \right\}$ 
D)  $\left\{ - \frac { 1 } { 3 } , \frac { 5 } { 7 } \right\}$ 
A)  $\left\{ - \frac { 5 } { 3 } , 1 \right\}$ 
B)  $\left\{ - \frac { 1 } { 7 } , \frac { 5 } { 3 } \right\}$ 
C)  $\left\{ \frac { 5 } { 3 } , 1 \right\}$ 
D)  $\left\{ - \frac { 1 } { 3 } , \frac { 5 } { 7 } \right\}$

Solve the formula for the indicated variable. - $\mathrm { R } = \mathrm { nE } - \mathrm { nr }$ , for $\mathrm { n }$

The high temperature on December 12 in Hilton Head, $\mathrm { SC }$ ranges from $33 ^ { \circ } \mathrm { F }$ to $89 ^ { \circ } \mathrm { F }$ . Using $\mathrm { F }$ as the variable, write an absolute value inequality that corresponds to this range.

Find the product. Write the answer in standard form. - $( 8 - 4 i ) ( 7 + 5 i )$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { 8 } { ( x + 4 ) ^ { 2 } } < 0$

Find the quotient. Write the answer in standard form. - $\frac { 5 - 5 i } { 4 + 2 i }$

A ball is thrown downward from a window in a tall building. Its position at time t in seconds is $s = 16 t ^ { 2 } + 32 t$ where s is in feet. How long (to the nearest tenth) will it take the ball to fall 133 feet?

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. - $- 4 , - 5$

Find two consecutive integers whose product is 20.

Solve the problem. -Your home state uses a linear model y $y = 45 ( x - 70 ) + 1610$ to predict the number of vacationers (y) as compared to the average temperature for that week (x). Find the number of vacationers predicted for a week with an Average temperature of 60 degrees.

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 3 ] { 4 + 6 x } - \sqrt [ 3 ] { 1 - 8 x } = 0$

The profit made when $t$ units are sold, $t > 0$ , is given by $P = t ^ { 2 } - 30 t + 200$ . Determine the number of units to be sold in order for $\mathrm { P } > 0$ (a profit is made).

Solve the equation by the zero-factor property. - $35 x ^ { 2 } + 43 x + 12 = 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $( 10 + x ) ^ { 1 / 2 + ( 11 - 5 x ) ^ { 1 / 2 } = - 1 }$

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } + 7 x \leq - 12$

Indicate whether the statement is true always, sometimes, or never. -The product of a pair of complex conjugates is a real number.

Indicate whether the statement is true always, sometimes, or never. -A complex number is an imaginary number.

Solve for y. - $7 x + 9 = 5 y - 9$

Solve for y. - $10 y + x ^ { 2 } = x + 8$

Graph the solution set. - $| 5 x - 2 | = | 2 x - 3 |$

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

Solve the formula for the indicated variable. - R=nE−nr\mathrm { R } = \mathrm { nE } - \mathrm { nr }R=nE−nr , for n\mathrm { n }n

The high temperature on December 12 in Hilton Head, SC\mathrm { SC }SC ranges from 33∘F33 ^ { \circ } \mathrm { F }33∘F to 89∘F89 ^ { \circ } \mathrm { F }89∘F . Using F\mathrm { F }F as the variable, write an absolute value inequality that corresponds to this range.

Find the product. Write the answer in standard form. - (8−4i)(7+5i)( 8 - 4 i ) ( 7 + 5 i )(8−4i)(7+5i)

Solve the rational inequality. Write the solution set in interval notation. - 8(x+4)2<0\frac { 8 } { ( x + 4 ) ^ { 2 } } < 0(x+4)28​<0

Find the quotient. Write the answer in standard form. - 5−5i4+2i\frac { 5 - 5 i } { 4 + 2 i }4+2i5−5i​

A ball is thrown downward from a window in a tall building. Its position at time t in seconds is s=16t2+32ts = 16 t ^ { 2 } + 32 ts=16t2+32t where s is in feet. How long (to the nearest tenth) will it take the ball to fall 133 feet?

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. - −4,−5- 4 , - 5−4,−5

Find two consecutive integers whose product is 20.

Decide what values of the variable cannot possibly be solutions for the equation. - 4+6x3−1−8x3=0\sqrt [ 3 ] { 4 + 6 x } - \sqrt [ 3 ] { 1 - 8 x } = 034+6x​−31−8x​=0

The profit made when ttt units are sold, t>0t > 0t>0 , is given by P=t2−30t+200P = t ^ { 2 } - 30 t + 200P=t2−30t+200 . Determine the number of units to be sold in order for P>0\mathrm { P } > 0P>0 (a profit is made).

Solve the equation by the zero-factor property. - 35x2+43x+12=035 x ^ { 2 } + 43 x + 12 = 035x2+43x+12=0

Decide what values of the variable cannot possibly be solutions for the equation. - (10+x)1/2+(11−5x)1/2=−1( 10 + x ) ^ { 1 / 2 + ( 11 - 5 x ) ^ { 1 / 2 } = - 1 }(10+x)1/2+(11−5x)1/2=−1

Solve the quadratic inequality. Write the solution set in interval notation. - x2+7x≤−12x ^ { 2 } + 7 x \leq - 12x2+7x≤−12

Indicate whether the statement is true always, sometimes, or never. -The product of a pair of complex conjugates is a real number.

Indicate whether the statement is true always, sometimes, or never. -A complex number is an imaginary number.

Solve for y. - 7x+9=5y−97 x + 9 = 5 y - 97x+9=5y−9

Solve for y. - 10y+x2=x+810 y + x ^ { 2 } = x + 810y+x2=x+8

Graph the solution set. - ∣5x−2∣=∣2x−3∣| 5 x - 2 | = | 2 x - 3 |∣5x−2∣=∣2x−3∣

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

Solve the formula for the indicated variable. - $\mathrm { R } = \mathrm { nE } - \mathrm { nr }$ , for $\mathrm { n }$

The high temperature on December 12 in Hilton Head, $\mathrm { SC }$ ranges from $33 ^ { \circ } \mathrm { F }$ to $89 ^ { \circ } \mathrm { F }$ . Using $\mathrm { F }$ as the variable, write an absolute value inequality that corresponds to this range.

Find the product. Write the answer in standard form. - $( 8 - 4 i ) ( 7 + 5 i )$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { 8 } { ( x + 4 ) ^ { 2 } } < 0$

Find the quotient. Write the answer in standard form. - $\frac { 5 - 5 i } { 4 + 2 i }$

A ball is thrown downward from a window in a tall building. Its position at time t in seconds is $s = 16 t ^ { 2 } + 32 t$ where s is in feet. How long (to the nearest tenth) will it take the ball to fall 133 feet?

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. - $- 4 , - 5$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 3 ] { 4 + 6 x } - \sqrt [ 3 ] { 1 - 8 x } = 0$

The profit made when $t$ units are sold, $t > 0$ , is given by $P = t ^ { 2 } - 30 t + 200$ . Determine the number of units to be sold in order for $\mathrm { P } > 0$ (a profit is made).

Solve the equation by the zero-factor property. - $35 x ^ { 2 } + 43 x + 12 = 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $( 10 + x ) ^ { 1 / 2 + ( 11 - 5 x ) ^ { 1 / 2 } = - 1 }$

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } + 7 x \leq - 12$

Solve for y. - $7 x + 9 = 5 y - 9$

Solve for y. - $10 y + x ^ { 2 } = x + 8$

Graph the solution set. - $| 5 x - 2 | = | 2 x - 3 |$