Question 1

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

Question 2

Solve the equation.
-$$\left| x ^ { 2 } + 9 \right| = | 6 x |$$

Accepted Answer

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

Question 3

Solve the problem.
-An experienced accountant can prepare a tax return in 13 hours. A novice accountant can do the job in 18 hours. How long will it take them to do the job working together?

Accepted Answer

A)  $\frac { 1 } { 31 } \mathrm { hr }$ 
B)  $\frac { 234 } { 31 } \mathrm { hr }$ 
C)  $\frac { 1 } { 234 } \mathrm { hr }$ 
D)  $\frac { 234 } { 5 } \mathrm { hr }$ 
A)  $\frac { 1 } { 31 } \mathrm { hr }$ 
B)  $\frac { 234 } { 31 } \mathrm { hr }$ 
C)  $\frac { 1 } { 234 } \mathrm { hr }$ 
D)  $\frac { 234 } { 5 } \mathrm { hr }$

Question 4

Solve the problem.
-The profit made when $t$ units are sold, $t > 0$, is given by $\mathrm { P } = \mathrm { t } ^ { 2 } - 27 \mathrm { t } + 170$. Determine the number of units to be sold in order for $\mathrm { P } > 0$ (a profit is made).

Accepted Answer

A) $t = 17$ or $t = 10$ B) $t > 17$ or $t < 10$ C) $\mathrm { t } = 27$ D) $17 < \mathrm { t } < 10$ A) $t = 17$ or $t = 10$ B) $t > 17$ or $t < 10$ C) $\mathrm { t } = 27$ D) $17 < \mathrm { t } < 10$

Question 5

Solve the problem.
-Kevin invested part of his $5000 bonus in a certificate of deposit that paid 2% annual simple interest, and the remainder in a mutual fund that paid 4% annual simple interest. If his total
Interest for that year was $110, how much did Kevin invest in the mutual fund?

Accepted Answer

A)  $4879.00 
B)  $500.00 
C)  $610.00 
D)  $4989.00 
A)  $4879.00 
B)  $500.00 
C)  $610.00 
D)  $4989.00

Question 6

Solve the equation.
-$$\left( x ^ { 2 } - 3 \right) ^ { 1 / 2 } - ( x + 3 ) ^ { 1 / 2 } = 0$$

Accepted Answer

A)  $\{ - 3,3 \}$ 
B)  $\{ 2,3 \}$ 
C)  $\{ - 2,3 \}$ 
D)  $\{ - 3 \}$ 
A)  $\{ - 3,3 \}$ 
B)  $\{ 2,3 \}$ 
C)  $\{ - 2,3 \}$ 
D)  $\{ - 3 \}$

Question 7

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

Accepted Answer

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

Question 8

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$12 ( x - 1 ) = 6 ( 2 x - 1 ) - 6$$

Accepted Answer

A)  Conditional; $\{ - 12 \}$ 
B)  Contradiction; $\varnothing$ 
C)  Identity;{all real numbers} 
D)  Conditional; $\{ 0 \}$ 
A)  Conditional; $\{ - 12 \}$ 
B)  Contradiction; $\varnothing$ 
C)  Identity;{all real numbers} 
D)  Conditional; $\{ 0 \}$

Question 9

Solve the problem.
-A square lawn has an area of 2450 square feet. A sprinkler placed at the center of the lawn sprays a water in a circular pattern that just covers the lawn. What is the radius of the circle?

Accepted Answer

A)  24.75 ft 
B)  70 ft 
C)  35 ft 
D)  49.5 ft 
A)  24.75 ft 
B)  70 ft 
C)  35 ft 
D)  49.5 ft

Question 10

Solve the equation.
-$$\sqrt [ 4 ] { x - 2 } + 10 = 0$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ 5000 \}$ 
C)  $\{ - 5000 \}$ 
D)  $\{ 5 \}$ 
A)  $\varnothing$ 
B)  $\{ 5000 \}$ 
C)  $\{ - 5000 \}$ 
D)  $\{ 5 \}$

Question 11

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may
apply.
-π

Accepted Answer

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

Question 12

Solve the problem.
-A circular hole is filled with concrete to make a footing for a load-bearing pier. The hole measures 15 inches across and requires 1.9 bags of concrete in order to fill it to ground level. What is the
Depth of the hole? Round your answer to the nearest inch. (One bag of concrete, when mixed with
The appropriate amount of water, makes 1800 in.3 of material.)

Accepted Answer

A)  23 in. 
B)  16 in. 
C)  19 in. 
D)  25 in. 
A)  23 in. 
B)  16 in. 
C)  19 in. 
D)  25 in.

Question 13

Simplify the power of i.
-$\mathrm { i } 76$

Accepted Answer

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

Question 14

Solve the problem.
-Your company uses the quadratic model $y = - 4.5 x ^ { 2 } + 150 x$ 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 22?

Accepted Answer

A)  1122 customers 
B)  561 customers 
C)  $- 528$ customers 
D)  3201 customers 
A)  1122 customers 
B)  561 customers 
C)  $- 528$ customers 
D)  3201 customers

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

Solve the equation. - $\left| x ^ { 2 } + 9 \right| = | 6 x |$

Solve the problem. -An experienced accountant can prepare a tax return in 13 hours. A novice accountant can do the job in 18 hours. How long will it take them to do the job working together?

Solve the problem. -The profit made when $t$ units are sold, $t > 0$ , is given by $\mathrm { P } = \mathrm { t } ^ { 2 } - 27 \mathrm { t } + 170$ . Determine the number of units to be sold in order for $\mathrm { P } > 0$ (a profit is made).

Solve the problem. -Kevin invested part of his $5000 bonus in a certificate of deposit that paid 2% annual simple interest, and the remainder in a mutual fund that paid 4% annual simple interest. If his total Interest for that year was $110, how much did Kevin invest in the mutual fund?

Solve the equation. - $\left( x ^ { 2 } - 3 \right) ^ { 1 / 2 } - ( x + 3 ) ^ { 1 / 2 } = 0$

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

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $12 ( x - 1 ) = 6 ( 2 x - 1 ) - 6$

Solve the problem. -A square lawn has an area of 2450 square feet. A sprinkler placed at the center of the lawn sprays a water in a circular pattern that just covers the lawn. What is the radius of the circle?

Solve the equation. - $\sqrt [ 4 ] { x - 2 } + 10 = 0$

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. -π

Simplify the power of i. - $\mathrm { i } 76$

Solve the problem. -Your company uses the quadratic model $y = - 4.5 x ^ { 2 } + 150 x$ 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 22?

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

Review of Basic Concepts

Filters

Exam 1: Equations and Inequalities