Question 1

Solve the equation by completing the square.
-$$x ^ { 2 } + 8 x = 3$$

Accepted Answer

A)  $\{ - 4 \pm 1 \sqrt { 19 } \}$ 
B)  $\{ 4 + \sqrt { 19 } \}$ 
C)  $\{ - 1 \pm \sqrt { 19 } \}$ 
D)  $\{ - 4 \pm \sqrt { 19 } \}$ 
A)  $\{ - 4 \pm 1 \sqrt { 19 } \}$ 
B)  $\{ 4 + \sqrt { 19 } \}$ 
C)  $\{ - 1 \pm \sqrt { 19 } \}$ 
D)  $\{ - 4 \pm \sqrt { 19 } \}$

Question 2

Solve the equation.
-$$\sqrt [ 3 ] { 5 x ^ { 2 } - 3 x - 8 } = \sqrt [ 3 ] { 5 x ^ { 2 } + 10 x + 9 }$$

Accepted Answer

A)  $\left\{ - \frac { 13 } { 17 } \right\}$ 
B)  $\left\{ \frac { 13 } { 17 } \right\}$ 
C)  $\left\{ - \frac { 17 } { 13 } \right\}$ 
D)  $\left\{ \frac { 17 } { 13 } \right\}$ 
A)  $\left\{ - \frac { 13 } { 17 } \right\}$ 
B)  $\left\{ \frac { 13 } { 17 } \right\}$ 
C)  $\left\{ - \frac { 17 } { 13 } \right\}$ 
D)  $\left\{ \frac { 17 } { 13 } \right\}$

Question 3

Solve the equation.
-$$( 10 + x ) ^ { 1 / 2 } + ( 11 - 5 x ) ^ { 1 / 2 } = - 1$$

Accepted Answer

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

Question 4

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

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 5

Indicate whether the statement is true always, sometimes, or never.
-The sum of two imaginary numbers is an imaginary number.

Accepted Answer

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

Question 6

Solve the problem.
-Find two consecutive integers whose product is 6.

Accepted Answer

A)  2,3 
B)  $- 2 , - 3$ 
C)  2,3 or $- 2 , - 3$ 
D)  $2 , - 3$ 
A)  2,3 
B)  $- 2 , - 3$ 
C)  2,3 or $- 2 , - 3$ 
D)  $2 , - 3$

Question 7

Solve the problem.
-Find the corresponding Celsius temperature for a temperature of $143 ^ { \circ } \mathrm { F }$. Round to the nearest tenth, if necessary.

Accepted Answer

A)  $199.8 ^ { \circ } \mathrm { C }$ 
B)  $75.9 ^ { \circ } \mathrm { C }$ 
C)  $61.7 ^ { \circ } \mathrm { C }$ 
D)  $289.4 ^ { \circ } \mathrm { C }$ 
A)  $199.8 ^ { \circ } \mathrm { C }$ 
B)  $75.9 ^ { \circ } \mathrm { C }$ 
C)  $61.7 ^ { \circ } \mathrm { C }$ 
D)  $289.4 ^ { \circ } \mathrm { C }$

Question 8

Solve the equation.
-$$\frac { 5 } { x ^ { 2 } - 4 } - \frac { 3 } { x ^ { 2 } + 5 x + 6 } = \frac { 3 } { x ^ { 2 } + x - 6 }$$

Accepted Answer

A)  $\{ 7 \}$ 
B)  $\left\{ \frac { 27 } { 5 } \right\}$ 
C)  $\{ - 3 , - 2,2 \}$ 
D)  $\{ 15 \}$ 
A)  $\{ 7 \}$ 
B)  $\left\{ \frac { 27 } { 5 } \right\}$ 
C)  $\{ - 3 , - 2,2 \}$ 
D)  $\{ 15 \}$

Question 9

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$5 ( 4 x - 4 ) - 20 x + 20 = 0$$

Accepted Answer

A)  Conditional; $\{ 0 \}$ 
B)  Contradiction; $\varnothing$ 
C)  Conditional; $\{ 4 \}$ 
D)  Identity; {all real numbers } 
A)  Conditional; $\{ 0 \}$ 
B)  Contradiction; $\varnothing$ 
C)  Conditional; $\{ 4 \}$ 
D)  Identity; {all real numbers }

Question 10

Simplify the power of i.
-$\mathrm { i } ^{94}$

Accepted Answer

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

Question 11

Indicate whether the statement is true always, sometimes, or never.
-To find the quotient $$\frac { 3 + 7 i } { 3 - 7 i }$$ multiply numerator and denominator by 3 + 7i.

Accepted Answer

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

Question 12

Solve the problem.
-An airplane flies from Metro City to Gotham with a tailwind that increases its normal speed by 100 mph. On the return trip, the plane must fly against this wind, which decreases its normal
Speed by the same amount. The flight from Metro City takes 3.71 hours and the return trip takes
8)67 hours. How far is it from Metro City to Gotham?

Accepted Answer

A)  1500 mi 
B)  1600 mi 
C)  1300 mi 
D)  1420 mi 
A)  1500 mi 
B)  1600 mi 
C)  1300 mi 
D)  1420 mi

Question 13

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.
-$$5 y ^ { 2 } = - 4 y - 5$$

Accepted Answer

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

Question 14

Solve the inequality. Write the solution set in interval notation.
-$$\left| \frac { 5 } { 2 } - \frac { 1 } { 3 } x \right| < \frac { 2 } { 5 }$$

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $\left( - \infty , - \frac { 87 } { 10 } \right) \cup \left( \frac { 63 } { 10 } , \infty \right)$ 
C)  $\left( - \infty , \frac { 63 } { 10 } \right) \cup \left( \frac { 87 } { 10 } , \infty \right)$ 
D)  $\left( \frac { 63 } { 10 } , \frac { 87 } { 10 } \right)$ 
A)  $( - \infty , \infty )$ 
B)  $\left( - \infty , - \frac { 87 } { 10 } \right) \cup \left( \frac { 63 } { 10 } , \infty \right)$ 
C)  $\left( - \infty , \frac { 63 } { 10 } \right) \cup \left( \frac { 87 } { 10 } , \infty \right)$ 
D)  $\left( \frac { 63 } { 10 } , \frac { 87 } { 10 } \right)$

Question 15

Write the number in standard form a + bi.
-$\frac { 6 - \sqrt { - 20 } } { 2 }$

Accepted Answer

A)  $3 - \mathrm { i } \sqrt { 10 }$ 
B)  $3 - \mathrm { i } \sqrt { 5 }$ 
C)  $3 - 2 \mathrm { i } \sqrt { 5 }$ 
D)  $3 + i \sqrt { 10 }$ 
A)  $3 - \mathrm { i } \sqrt { 10 }$ 
B)  $3 - \mathrm { i } \sqrt { 5 }$ 
C)  $3 - 2 \mathrm { i } \sqrt { 5 }$ 
D)  $3 + i \sqrt { 10 }$

Question 16

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$2 [ 3 - ( 6 - 5 x ) ] - x = - 12 + 3 ( 2 + 3 x )$

Accepted Answer

A)  Conditional; $\{ 12 \}$ 
B)  Conditional; $\{ - 6 \}$ 
C)  Identity; {all real numbers } 
D)  Contradiction; $\varnothing$ 
A)  Conditional; $\{ 12 \}$ 
B)  Conditional; $\{ - 6 \}$ 
C)  Identity; {all real numbers } 
D)  Contradiction; $\varnothing$

Question 17

Solve the problem.
-An airplane leaves Los Angeles for Denver at a speed of 420 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 520 mph. When they meet, how far are they from Denver?

Accepted Answer

A)  307 mi 
B)  123 mi 
C)  354 mi 
D)  61 mi 
A)  307 mi 
B)  123 mi 
C)  354 mi 
D)  61 mi

Question 18

Solve the equation.
-$72 x ^ { - 2 } - 33 x ^ { - 1 } = 54$

Accepted Answer

A)  $\left\{ \frac { 8 } { 9 } , - \frac { 3 } { 2 } \right\}$ 
B)  $\left\{ \frac { 9 } { 8 } , \frac { 2 } { 3 } \right\}$ 
C)  $\left\{ - \frac { 9 } { 8 } , - \frac { 2 } { 3 } \right\}$ 
D)  $\left\{ \frac { 9 } { 8 } , - \frac { 2 } { 3 } \right\}$ 
A)  $\left\{ \frac { 8 } { 9 } , - \frac { 3 } { 2 } \right\}$ 
B)  $\left\{ \frac { 9 } { 8 } , \frac { 2 } { 3 } \right\}$ 
C)  $\left\{ - \frac { 9 } { 8 } , - \frac { 2 } { 3 } \right\}$ 
D)  $\left\{ \frac { 9 } { 8 } , - \frac { 2 } { 3 } \right\}$

Question 19

Solve the problem.
-Don James wants to invest $55,000 to earn $1336 per year. He can invest in B-rated bonds paying 3.8% per year or in a Certificate of Deposit (CD) paying 1.2% per year. How much money should
Be invested in each to realize exactly $1336 in interest per year?

Accepted Answer

A)  $27,000 in B-rated bonds and $28,000 in a CD 
B)  $29,000 in B-rated bonds and $26,000 in a CD 
C)  $26,000 in B-rated bonds and $29,000 in a CD 
D)  $28,000 in B-rated bonds and $27,000 in a CD 
A)  $27,000 in B-rated bonds and $28,000 in a CD 
B)  $29,000 in B-rated bonds and $26,000 in a CD 
C)  $26,000 in B-rated bonds and $29,000 in a CD 
D)  $28,000 in B-rated bonds and $27,000 in a CD

Question 20

Solve the equation.
-$$| 3 x - 2 | = | 8 x - 11 |$$

Accepted Answer

A)  $\left\{ \frac { 13 } { 5 } , 1 \right\}$ 
B)  $\left\{ - \frac { 13 } { 5 } , 1 \right\}$ 
C)  $\left\{ - \frac { 9 } { 11 } , - \frac { 13 } { 5 } \right\}$ 
D)  $\left\{ \frac { 9 } { 5 } , \frac { 13 } { 11 } \right\}$ 
A)  $\left\{ \frac { 13 } { 5 } , 1 \right\}$ 
B)  $\left\{ - \frac { 13 } { 5 } , 1 \right\}$ 
C)  $\left\{ - \frac { 9 } { 11 } , - \frac { 13 } { 5 } \right\}$ 
D)  $\left\{ \frac { 9 } { 5 } , \frac { 13 } { 11 } \right\}$

Solve the equation by completing the square. - $x ^ { 2 } + 8 x = 3$

Solve the equation. - $\sqrt [ 3 ] { 5 x ^ { 2 } - 3 x - 8 } = \sqrt [ 3 ] { 5 x ^ { 2 } + 10 x + 9 }$

Solve the equation. - $( 10 + x ) ^ { 1 / 2 } + ( 11 - 5 x ) ^ { 1 / 2 } = - 1$

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

Indicate whether the statement is true always, sometimes, or never. -The sum of two imaginary numbers is an imaginary number.

Solve the problem. -Find two consecutive integers whose product is 6.

Solve the problem. -Find the corresponding Celsius temperature for a temperature of $143 ^ { \circ } \mathrm { F }$ . Round to the nearest tenth, if necessary.

Solve the equation. - $\frac { 5 } { x ^ { 2 } - 4 } - \frac { 3 } { x ^ { 2 } + 5 x + 6 } = \frac { 3 } { x ^ { 2 } + x - 6 }$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $5 ( 4 x - 4 ) - 20 x + 20 = 0$

Simplify the power of i. - $\mathrm { i } ^{94}$

Indicate whether the statement is true always, sometimes, or never. -To find the quotient $\frac { 3 + 7 i } { 3 - 7 i }$ multiply numerator and denominator by 3 + 7i.

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. - $5 y ^ { 2 } = - 4 y - 5$

Solve the inequality. Write the solution set in interval notation. - $\left| \frac { 5 } { 2 } - \frac { 1 } { 3 } x \right| < \frac { 2 } { 5 }$

Write the number in standard form a + bi. - $\frac { 6 - \sqrt { - 20 } } { 2 }$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $2 [ 3 - ( 6 - 5 x ) ] - x = - 12 + 3 ( 2 + 3 x )$

Solve the problem. -An airplane leaves Los Angeles for Denver at a speed of 420 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 520 mph. When they meet, how far are they from Denver?

Solve the equation. - $72 x ^ { - 2 } - 33 x ^ { - 1 } = 54$

Solve the problem. -Don James wants to invest $55,000 to earn $1336 per year. He can invest in B-rated bonds paying 3.8% per year or in a Certificate of Deposit (CD) paying 1.2% per year. How much money should Be invested in each to realize exactly $1336 in interest per year?

Solve the equation. - $| 3 x - 2 | = | 8 x - 11 |$

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

Solve the equation by completing the square. - x2+8x=3x ^ { 2 } + 8 x = 3x2+8x=3

Solve the equation. - 5x2−3x−83=5x2+10x+93\sqrt [ 3 ] { 5 x ^ { 2 } - 3 x - 8 } = \sqrt [ 3 ] { 5 x ^ { 2 } + 10 x + 9 }35x2−3x−8​=35x2+10x+9​

Solve 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