Question 1

Solve the quadratic inequality. Write the solution set in interval notation.
-$( 5 + 4 x ) ^ { 2 } \geq - 4$

Accepted Answer

A)  $\left( - \infty , - \frac { 7 } { 4 } \right) \cup \left( - \frac { 3 } { 4 } , \infty \right)$ 
B)  $\varnothing$ 
C)  $\left[ - \frac { 7 } { 4 } , - \frac { 3 } { 4 } \right]$ 
D)  $( - \infty , \infty )$ 
A)  $\left( - \infty , - \frac { 7 } { 4 } \right) \cup \left( - \frac { 3 } { 4 } , \infty \right)$ 
B)  $\varnothing$ 
C)  $\left[ - \frac { 7 } { 4 } , - \frac { 3 } { 4 } \right]$ 
D)  $( - \infty , \infty )$

Question 2

A boat is 180 feet from the base of cliff. If the distance from the top of the cliff to the boat is 45 more than twice the height of the cliff. Find the height of the cliff. Round to the nearest tenth of a foot if necessary.

Accepted Answer

A)  135 ft 
B)  45 ft 
C)  75 ft 
D)  100.6 ft 
A)  135 ft 
B)  45 ft 
C)  75 ft 
D)  100.6 ft

Question 3

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { x } { x - 3 } - \frac { 1 } { x + 9 } = \frac { 10 } { x ^ { 2 } + 6 x - 27 }$$

Accepted Answer

A)  $- 9,3$ 
B)  $- 9,0,3$ 
C)  $- 3,9 , - 27$ 
D)  $- 3,0,9$ 
A)  $- 9,3$ 
B)  $- 9,0,3$ 
C)  $- 3,9 , - 27$ 
D)  $- 3,0,9$

Question 4

Solve the formula for the indicated variable.
-$S = 2 \pi r h + 2 \pi r ^ { 2 }$, for $h$

Accepted Answer

A)  $h = S - r$ 
B)  $h = \frac { S } { 2 \pi r } - 1$ 
C)  $h = \frac { S - 2 \pi r ^ { 2 } } { 2 \pi r }$ 
D)  $h = 2 \pi ( S - r )$ 
A)  $h = S - r$ 
B)  $h = \frac { S } { 2 \pi r } - 1$ 
C)  $h = \frac { S - 2 \pi r ^ { 2 } } { 2 \pi r }$ 
D)  $h = 2 \pi ( S - r )$

Question 5

Decide whether or not the equations are equivalent.
-$\begin{array} { l } 
z ^ { 2 } = 49 \
z = 7
\end{array}$

Accepted Answer

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

Question 6

Graph the solution set.
-$$| x - 2 | + 3 = 6$$

Accepted Answer

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

Question 7

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex.
-$2 y ^ { 2 } = - 5 y - 6$

Accepted Answer

A)  Two distinct irrational solutions 
B)  One rational solution (a double solution) 
C)  Two distinct nonreal complex solutions 
D)  Two distinct rational solutions 
A)  Two distinct irrational solutions 
B)  One rational solution (a double solution) 
C)  Two distinct nonreal complex solutions 
D)  Two distinct rational solutions

Question 8

The area of a square is numerically 77 more than the perimeter. Find the length of the side.

Accepted Answer

A)  44 units 
B)  11 units 
C)  242 units 
D)  61 units 
A)  44 units 
B)  11 units 
C)  242 units 
D)  61 units

Question 9

Solve the inequality. Write the solution set in interval notation.
-$| 7 - x | \geq 9$

Accepted Answer

A)  $( - \infty , - 2 ] \cup [ 16 , \infty )$ 
B)  $[ - 2,16 ]$ 
C)  $[ 16 , \infty )$ 
D)  $[ - 2 , \infty )$ 
A)  $( - \infty , - 2 ] \cup [ 16 , \infty )$ 
B)  $[ - 2,16 ]$ 
C)  $[ 16 , \infty )$ 
D)  $[ - 2 , \infty )$

Question 10

Solve the problem.
-Helen Weller invested $12,000 in an account that pays 1.25% simple interest. How much additional money must be invested in an account that pays 3.5% simple interest so that the average return on the two investments
Amounts to 2%?

Accepted Answer

A)  $9000 
B)  $6000 
C)  $8000 
D)  $12,000 
A)  $9000 
B)  $6000 
C)  $8000 
D)  $12,000

Question 11

Graph the solution set.
-$$\left| \frac { 7 x + 9 } { 8 } \right| = 1$$

Accepted Answer

A)  $\left\{ \frac { 17 } { 4 } , \frac { 1 } { 4 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 7 } \right\}$ 
C)  $\left\{ - 2 , - \frac { 5 } { 2 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 7 } , - \frac { 17 } { 7 } \right\}$ 
A)  $\left\{ \frac { 17 } { 4 } , \frac { 1 } { 4 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 7 } \right\}$ 
C)  $\left\{ - 2 , - \frac { 5 } { 2 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 7 } , - \frac { 17 } { 7 } \right\}$

Question 12

Solve and graph the inequality. Give answer in interval notation.
-$$- 3 ( 4 x - 1 ) < - 15 x + 9$$

Accepted Answer

A)  $( - 15 , \infty )$
  
B)  $( 2 , \infty )$
  
C)  $( - \infty , - 15 )$
  
D)  $( - \infty , 2 )$
  
A)  $( - 15 , \infty )$
  
B)  $( 2 , \infty )$
  
C)  $( - \infty , - 15 )$
  
D)  $( - \infty , 2 )$

Question 13

Find the sum or difference. Write the answer in standard form.
-$3 \mathrm { i } + ( - 9 - \mathrm { i } )$

Accepted Answer

A)  $9 - 2 i$ 
B)  $9 - 4 \mathrm { i }$ 
C)  $- 9 + 4 \mathrm { i }$ 
D)  $- 9 + 2 \mathrm { i }$ 
A)  $9 - 2 i$ 
B)  $9 - 4 \mathrm { i }$ 
C)  $- 9 + 4 \mathrm { i }$ 
D)  $- 9 + 2 \mathrm { i }$

Question 14

Solve the equation by completing the square.
-$$4 x ^ { 2 } - 4 x - 8 = 0$$

Accepted Answer

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

Question 15

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may
apply.
-$\sqrt { 5 }$

Accepted Answer

A)  Complex 
B)  Nonreal complex 
C)  Real, complex 
D)  Complex, pure imaginary, nonreal complex 
A)  Complex 
B)  Nonreal complex 
C)  Real, complex 
D)  Complex, pure imaginary, nonreal complex

Question 16

A ball is dropped from a cliff that is 368 feet high. The distance S (in feet) that it falls in t seconds is given by the formula S = 16t2. How many seconds (to tenths) will it take for the ball to hit the ground?

Accepted Answer

A)  18.8 sec 
B)  19.2 sec 
C)  4.8 sec 
D)  8464 sec 
A)  18.8 sec 
B)  19.2 sec 
C)  4.8 sec 
D)  8464 sec

Question 17

Graph the solution set.
-$$| - 6 + 7 x | = | 9 - 6 x |$$

Accepted Answer

A)  $\left\{ \frac { 15 } { 13 } , - 3 \right\}$ 
B)  $\left\{ 15 , - \frac { 3 } { 13 } \right\}$ 
C)  $\left\{ - \frac { 3 } { 13 } , 1 \right\}$ 
D)  $\left\{ \frac { 3 } { 13 } , 1 \right\}$ 
A)  $\left\{ \frac { 15 } { 13 } , - 3 \right\}$ 
B)  $\left\{ 15 , - \frac { 3 } { 13 } \right\}$ 
C)  $\left\{ - \frac { 3 } { 13 } , 1 \right\}$ 
D)  $\left\{ \frac { 3 } { 13 } , 1 \right\}$

Question 18

Simplify the power of i.
-$\mathrm { i } ^ { 30 }$

Accepted Answer

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

Question 19

Solve the problem.
-From a point on a river, two boats are driven in opposite directions, one at 9 miles per hour and the other at 11 miles per hour. In how many hours will they be 40 miles apart?

Accepted Answer

A)  3 hr 
B)  2 hr 
C)  1 hr 
D)  4 hr 
A)  3 hr 
B)  2 hr 
C)  1 hr 
D)  4 hr

Question 20

A flare fired from the bottom of a gorge is visible only when the flare is above the rim. If it is fired with an initial velocity of $112 \mathrm { ft } / \mathrm { sec }$, and the gorge is $192 \mathrm { ft }$ deep, during what interval can the flare be seen?
$$\left( h = - 16 t ^ { 2 } + v _ { 0 } t + h _ { 0 } \right)$$

Accepted Answer

A)  $9 < t < 10$ 
B)  $6 < t < 7$ 
C)  $3 < t < 4$ 
D)  $0 < t < 3$ 
A)  $9 < t < 10$ 
B)  $6 < t < 7$ 
C)  $3 < t < 4$ 
D)  $0 < t < 3$

Solve the quadratic inequality. Write the solution set in interval notation. - $( 5 + 4 x ) ^ { 2 } \geq - 4$

A boat is 180 feet from the base of cliff. If the distance from the top of the cliff to the boat is 45 more than twice the height of the cliff. Find the height of the cliff. Round to the nearest tenth of a foot if necessary.

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { x } { x - 3 } - \frac { 1 } { x + 9 } = \frac { 10 } { x ^ { 2 } + 6 x - 27 }$

Solve the formula for the indicated variable. - $S = 2 \pi r h + 2 \pi r ^ { 2 }$ , for $h$

Decide whether or not the equations are equivalent. - =49 z=7

Graph the solution set. - $| x - 2 | + 3 = 6$

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $2 y ^ { 2 } = - 5 y - 6$

The area of a square is numerically 77 more than the perimeter. Find the length of the side.

Solve the inequality. Write the solution set in interval notation. - $| 7 - x | \geq 9$

Solve the problem. -Helen Weller invested $12,000 in an account that pays 1.25% simple interest. How much additional money must be invested in an account that pays 3.5% simple interest so that the average return on the two investments Amounts to 2%?

Graph the solution set. - $\left| \frac { 7 x + 9 } { 8 } \right| = 1$

Solve and graph the inequality. Give answer in interval notation. - $- 3 ( 4 x - 1 ) < - 15 x + 9$

Find the sum or difference. Write the answer in standard form. - $3 \mathrm { i } + ( - 9 - \mathrm { i } )$

Solve the equation by completing the square. - $4 x ^ { 2 } - 4 x - 8 = 0$

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - $\sqrt { 5 }$

A ball is dropped from a cliff that is 368 feet high. The distance S (in feet) that it falls in t seconds is given by the formula S = 16t2. How many seconds (to tenths) will it take for the ball to hit the ground?

Graph the solution set. - $| - 6 + 7 x | = | 9 - 6 x |$

Simplify the power of i. - $\mathrm { i } ^ { 30 }$

Solve the problem. -From a point on a river, two boats are driven in opposite directions, one at 9 miles per hour and the other at 11 miles per hour. In how many hours will they be 40 miles apart?

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 quadratic inequality. Write the solution set in interval notation. - (5+4x)2≥−4( 5 + 4 x ) ^ { 2 } \geq - 4(5+4x)2≥−4

A boat is 180 feet from the base of cliff. If the distance from the top of the cliff to the boat is 45 more than twice the height of the cliff. Find the height of the cliff. Round to the nearest tenth of a foot if necessary.

Decide what values of the variable cannot possibly be solutions for the equation. - xx−3−1x+9=10x2+6x−27\frac { x } { x - 3 } - \frac { 1 } { x + 9 } = \frac { 10 } { x ^ { 2 } + 6 x - 27 }x−3x​−x+91​=x2+6x−2710​

Solve the formula for the indicated variable. - S=2πrh+2πr2S = 2 \pi r h + 2 \pi r ^ { 2 }S=2πrh+2πr2 , for hhh

Decide whether or not the equations are equivalent. - =49 z=7

Graph the solution set. - ∣x−2∣+3=6| x - 2 | + 3 = 6∣x−2∣+3=6

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - 2y2=−5y−62 y ^ { 2 } = - 5 y - 62y2=−5y−6

The area of a square is numerically 77 more than the perimeter. Find the length of the side.

Solve the inequality. Write the solution set in interval notation. - ∣7−x∣≥9| 7 - x | \geq 9∣7−x∣≥9

Solve the problem. -Helen Weller invested $12,000 in an account that pays 1.25% simple interest. How much additional money must be invested in an account that pays 3.5% simple interest so that the average return on the two investments Amounts to 2%?

Graph the solution set. - ∣7x+98∣=1\left| \frac { 7 x + 9 } { 8 } \right| = 1​87x+9​​=1

Solve and graph the inequality. Give answer in interval notation. - −3(4x−1)<−15x+9- 3 ( 4 x - 1 ) < - 15 x + 9−3(4x−1)<−15x+9

Find the sum or difference. Write the answer in standard form. - 3i+(−9−i)3 \mathrm { i } + ( - 9 - \mathrm { i } )3i+(−9−i)

Solve the equation by completing the square. - 4x2−4x−8=04 x ^ { 2 } - 4 x - 8 = 04x2−4x−8=0

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - 5\sqrt { 5 }5​

A ball is dropped from a cliff that is 368 feet high. The distance S (in feet) that it falls in t seconds is given by the formula S = 16t2. How many seconds (to tenths) will it take for the ball to hit the ground?

Graph the solution set. - ∣−6+7x∣=∣9−6x∣| - 6 + 7 x | = | 9 - 6 x |∣−6+7x∣=∣9−6x∣

Simplify the power of i. - i30\mathrm { i } ^ { 30 }i30

Solve the problem. -From a point on a river, two boats are driven in opposite directions, one at 9 miles per hour and the other at 11 miles per hour. In how many hours will they be 40 miles apart?

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 quadratic inequality. Write the solution set in interval notation. - $( 5 + 4 x ) ^ { 2 } \geq - 4$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { x } { x - 3 } - \frac { 1 } { x + 9 } = \frac { 10 } { x ^ { 2 } + 6 x - 27 }$

Solve the formula for the indicated variable. - $S = 2 \pi r h + 2 \pi r ^ { 2 }$ , for $h$

Graph the solution set. - $| x - 2 | + 3 = 6$

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $2 y ^ { 2 } = - 5 y - 6$

Solve the inequality. Write the solution set in interval notation. - $| 7 - x | \geq 9$

Graph the solution set. - $\left| \frac { 7 x + 9 } { 8 } \right| = 1$

Solve and graph the inequality. Give answer in interval notation. - $- 3 ( 4 x - 1 ) < - 15 x + 9$

Find the sum or difference. Write the answer in standard form. - $3 \mathrm { i } + ( - 9 - \mathrm { i } )$

Solve the equation by completing the square. - $4 x ^ { 2 } - 4 x - 8 = 0$

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - $\sqrt { 5 }$

Graph the solution set. - $| - 6 + 7 x | = | 9 - 6 x |$

Simplify the power of i. - $\mathrm { i } ^ { 30 }$