College Algebra Practice Questions - 840 Verified Questions

College Algebra Practice Questions

Course Introduction

College Algebra is a foundational mathematics course designed to prepare students for higher-level math and related disciplines. The course covers essential algebraic concepts, including linear, quadratic, polynomial, rational, exponential, and logarithmic functions. Students learn to solve equations and inequalities, analyze functions and their graphs, and apply algebraic problem-solving techniques to real-world scenarios. Emphasis is placed on developing critical thinking skills, mathematical reasoning, and the ability to communicate mathematical ideas effectively, providing a solid groundwork for future coursework in mathematics, science, engineering, and business fields.

Recommended Textbook

Elementary and Intermediate Algebra 4th Edition by Mark Dugopolski Emeritus

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32 Chapters

840 Verified Questions

840 Flashcards

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Chapter 1: Section 1: Real Numbers and Their Properties

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29 Verified Questions

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Sample Questions

Q1) Simplify: -10(s - 2) - 4(-s - 11)

A) -14s - 24

B) -6s + 64

C) -6s - 24

D) -14s + 64

Answer: B

Q2) If a golf ball is dropped from a tall building, the distance it has fallen in feet is given by 16t², where t is the time in seconds since the ball was dropped. How far has the ball fallen after 4 seconds?

A) 256 ft

B) 80 ft

C) 144 ft

D) 64 ft

Answer: A

Q3) Write as a product without exponents: 8⁴

A) 8 + 8 + 8 + 8

B) 4·8

C) 8·8·8·8

D) None of these.

Answer: C

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Chapter 1: Section 2: Real Numbers and Their Properties

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Sample Questions

Q1) Use the commutative and associative properties of multiplication and exponential notation to rewrite the given product. v²(v·13)(vw)

Answer: 13v⁴w

Q2) If a golf ball is dropped from a tall building, the distance it has fallen in feet is given by 16t², where t is the time in seconds since the ball was dropped. How far has the ball fallen after 7 seconds?

Answer: 784 ft

Q3) Write as a product without exponents: 12⁴

Answer: 12·12·12·12

Q4) Evaluate: 0 \(\div\) 2

Answer: 0

Q5) Evaluate: 7 - 3 · |3 - (5² - 2)|

Answer: -53

Q6) Evaluate: 23 + (-24)

Answer: -1

Q7) Combine like terms if possible: 7z - (-12z)

Answer: 19z

Page 4

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Chapter 2: Section 1: Linear Equations and Inequalities in

One Variable

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26 Verified Questions

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Sample Questions

Q1) Solve. 0.8q + 0.7 = 0.9q

A) {7}

B) {70}

C) {10}

D) {9}

Answer: A

Q2) Ferdinand sold his algebra textbook using an internet auction site that charges a commission of 8% of the selling price. After the commission was paid, Ferdinand received $22.40. If x represents the selling price, then x satisfies x - 0.08x = 22.40. Solve this equation to find the selling price.

A) $24.35

B) $21.82

C) $27.34

D) $28.97

Answer: A

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Chapter 2: Section 2: Linear Equations and Inequalities in

One Variable

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Sample Questions

Q1) Find three consecutive integers whose sum is 216.

Q2) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. 13y + 4y = 12y

Q3) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. u + 5u = 6u

Q4) Find y given that x = -7 and y = -4x + 5.

Q5) Mark and Brenda wish to get $135,240 for their home. The real estate agent's commission is 8% of the selling price. What should the selling price be?

Q6) Carol drove for 3 hours on a two-lane state road. She then increased her speed by 20 miles per hour on the freeway and drove for 5 more hours. If the total trip was 420 miles, then what was her speed on the freeway?

Q7) At a 30% discount rate, Jack's discount was more than $12 on the jacket he purchased. Write an inequality to describe this situation using p for the original price of the jacket.

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Q8) How many pints of a 9% cleaning solution must be mixed with 2 pints of a 13% cleaning solution to give a 11% solution?

Chapter 3: Section 1: Linear Equations and Inequalities in

Two Variables

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Sample Questions

Q1) Gotham City's budget deficit was $6.2 million in 1993 and $2.4 million in 1998. Find the slope of the line through (1993, 6.2) and (1998, 2.4) and interpret your result.

A) -0.760 slope; the slope of the deficit is decreasing by $0.760 million per year

B) -0.760 slope; the deficit is increasing by $0.760 million per year

C) -0.760 slope; the deficit is decreasing by $0.760 million per year

D) -0.760 slope; the deficit decreased by $0.760 million during the period between 1993 and 1998.

Q2) A playground equipment manufacturer plans to spend $300,000 on a new facility plus $160 for each swing set made.The formula C = 160n + 300,000 gives the cost in dollars to manufacture n swing sets. What is the marginal cost of the nth swing set? [Hint

- the marginal cost of the nth swing set is the difference in cost of producing n + 1 swing sets and n swing sets).

A) $170

B) $160

C) $300,000

D) $320

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Chapter 3: Section 2: Linear Equations and Inequalities in

Two Variables

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Sample Questions

Q1) Line l goes through (1, 3) and is parallel to the line through (4, 3) and (-3, 1). Find the slope of l.

Q2) Find the slope of the line that contains the points (-11,2) and (8,-12).

Q3) The price of a 2-hour plumbing repair job is $130 and the price of a 5-hour job is $250. Write an equation for the cost C of a t-hour repair job and use the equation to find the cost of a repair job lasting 9 hours.

Q4) Complete the ordered pair so that it satisfies the given equation. y = -4x + 3: (-10, ___)

Q5) Write a formula that expresses the relationship described below. P varies jointly as x and y and P = -8 when x = -2 and y = 7

Q6) The time to drive from Gotham City to Farmville varies inversely with the average speed. If the drive takes 5.0 hours at 49 mph, then how long will it take at 70 mph? Round to the nearest tenth of an hour.

Q7) Find the x- and y-intercepts of x + 3y + 2 = 0 and use these intercepts to graph the equation.

Q8) Graph the equation y = -3x + 1.

Q9) Write a formula that expresses the relationship described below. Use k as a constant of variation. P varies directly with T Page 8

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Page 9

Chapter 4: Section 1: Exponents and Polynomials

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Sample Questions

Q1) Simplify. (st⁵)⁶

A) st¹¹

B) st³⁰

C) s⁶t¹¹

D) s⁶t³⁰

Q2) Find the product. (4t² + 1)(6t² - 3)

A) 24t⁴ - 12t² - 3

B) 24t⁴ + 6t² - 3

C) 24t⁴ - 6t² - 3

D) 24t⁴ - 6t² + 3

Q3) Find the product. (q² + 3q - 7)(-5q - 7)

A) -5q³ - 22q² + 14q + 49

B) -5q³ - 22q² + 14q - 49

C) -5q³ + 22q² + 14q + 49

D) -5q³ - 22q² - 14q + 49

Q4) Multiply. (-4r - 9)²

A) 16r² + 72r + 81

B) -4r² + 72r + 81

C) 16r² + 81

D) 16r² + 36r + 81

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Chapter 4: Section 2: Exponents and Polynomials

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Sample Questions

Q1) Multiply. (6 + 5x)(6 - 5x)

Q2) A shipping carton has a length of x - 2, width of 4x, and a height of x. Write an expression for the volume of the box.

Q3) State the degree of the polynomial and determine if it is a monomial, binomial, or trinomial.

x⁴

Q4) What is the coefficient of x³ in the polynomial -11x³ + 13x²?

Q5) Simplify.

5y⁴·(y⁴)⁵

Q6) Perform the indicated operation. (t - 5) - (5t - 8)

Q7) Perform the indicated operation. (-4m - 7) + (m² + 7m + 6)

Q8) Find the product. (5w² - 4)(5w² - 1)

Q9) Expand the binomial. (n - 2)³

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Chapter 5: Section 1: Factoring

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Sample Questions

Q1) Audrey uses a slingshot to shoot a marble from a window. The height of the marble h(t) in feet at time t seconds is given by the function h(t) = -16t² - 54t + 306.

How many seconds elapse before the marble hits the ground?

A) 6 sec

B) 5 sec

C) 3 sec

D) 4 sec

Q2) Find the greatest common factor of the given terms. 6wx, 14xy, 10wy

A) 2wx

B) 1

C) 2wxy

D) 2

Q3) Factor the given polynomial completely. If the polynomial is prime, say so. w² - 8w

A) The polynomial is prime.

B) w(w - 8)

C) w(w² - 8w)

D) (w - 8)(w + 8)

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Chapter 5: Section 2: Factoring

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Sample Questions

Q1) Factor the given polynomial completely. z⁶ + 2z³ - 3

Q2) Audrey uses a slingshot to shoot a marble from a window. The height of the marble h(t) in feet at time t seconds is given by the function h(t) = -16t² - 62t + 188. How many seconds elapse before the marble hits the ground?

Q3) Factor the given polynomial completely.

x⁴+ y⁴

Q4) Factor out the greatest common factor. (y - 6)4 + (y - 6)y

Q5) Factor.

uvw + 9u + 5vw + 45

Q6) Find the greatest common factor for the given numbers. 36, 80, 120

Q7) Factor.

q² + 6qr + 36r²

Q8) Factor.

8x³ - 27

Q9) Factor completely.

8u³v - 392uv

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Chapter 6: Section 1: Rational Expressions

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Sample Questions

Q1) A large pump can fill a 73,000 gallon reservoir in 7 hours. Working together, the large pump and a smaller one can fill the reservoir in 6 hours. How long would it take the smaller pump to fill the reservoir by itself?

A) 41 hours

B) 42 hours

C) 44 hours

D) 43 hours

Q2) Among 100 college students, 45 said they study 11 or more hours per week while the rest said they did not. What is the ratio of those students who study at least 11 hours per week to those that do not?

A) 9 to 11

B) 20 to 11

C) 9 to 20

D) 11 to 9

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Chapter 6: Section 2: Rational Expressions

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Sample Questions

Q1) David hires a septic system contractor to dig trenches for his new septic tank. The cost to hire the contractor is a fixed cost of $250 plus an additional $80 per hour. Write an expression which describes the average cost of an x-hour job.

Q2) Chris prepares a 10-pound mixture of cashews and peanuts. He paid $18 for the cashews and $14 for the peanuts. If cashews cost three times more than peanuts, then how many pounds of cashews did he use?

Q3) Among 100 college students, 40 said they study 11 or more hours per week while the rest said they did not. What is the ratio of those students who study at least 11 hours per week to those that do not?

Q4) Find the least common multiple of the given terms. q² + 7q - 30, q² + 20q + 100

Q5) Cora can paddle her canoe 8 miles in the same time that Susan's motorboat covers 28 miles. If Susan's boat travels 10 mph faster than Cora's canoe, then how fast is Susan's boat?

Q6) Jimbo biked 50 miles at x mph. He then increased his speed by 5 mph and biked another 40 miles. Write a rational expression for Jimbo's total travel time.

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Page 15

Chapter 7: Section 1: Systems of Linear Equations

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Sample Questions

Q1) For Monday morning's staff meeting, Jim bought 2 bags of bagels and 3 packages of cream cheese and paid $11.50 (excluding sales tax). For Friday's meeting, he bought 4 bags of bagels and 2 packages of cream cheese and paid $13.00 (again, excluding sales tax). How much do bags of bagels and packages of cream cheese cost?

A) $1.75 per bag for bagels, $2.75 per package for cream cheese

B) $3.25 per bag for bagels, $2.50 per package for cream cheese

C) $2.00 per bag for bagels, $2.50 per package for cream cheese

D) $2.50 per bag for bagels, $2.00 per package for cream cheese

Q2) When rolling a pair of dice, the probability of getting a particular total is not very high. For example, the probability of failing to roll a total of 7 is 5 times the probability of successfully rolling a total of 7. The total probability (probability of failing to roll a 7 + probability of successfully rolling a 7) is 1. What is the probability of rolling a 7?

A) 1 in 6

B) 1 in 18

C) 1 in 9

D) None of these.

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Chapter 7: Section 2: Systems of Linear Equations

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Sample Questions

Q1) Solve the system of linear equations by the substitution method.

-5x = -2y + 9

5x + 5y = -30

Q2) Solve the system of equations.

-x + 5y - 3z = 31

-4x - 5y + 4z = 6

3x - 15y + 9z = -91

Q3) For Monday morning's staff meeting, Jim bought 2 bags of bagels and 3 packages of cream cheese and paid $9.00 (excluding sales tax). For Friday's meeting, he bought 4 bags of bagels and 2 packages of cream cheese and paid $10.00 (again, excluding sales tax). How much do bags of bagels and packages of cream cheese cost?

Q4) Solve the system of linear equations by the substitution method. Then, state whether the system is independent, dependent, or inconsistent. 4x - 3y = 4

12x - 9y = 12

Q5) Solve the system of equations.

-3.5x + 3y = -5.375

-0.875x - 0.5y = 0.53125

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Chapter 8: Section 1: More on Inequalities

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Sample Questions

Q1) Solve: -4 - |-11 - x| = -10

A) {-19, -3}

B) {-17, -5}

C) {-16, -2}

D) {-16, -4}

Q2) Carla wants to purchase insurance for her landscaping business. She determines that she needs at least $137,500 of property coverage and at least $159,500 of liability coverage. In order to gain this amount of coverage, she can purchase any combination of insurance plans A and B from two different insurance companies. For each dollar she spends on Plan A, she gets $250 of property coverage and $300 of liability coverage. Plan B provides $260 of property coverage and $290 of liability coverage for each dollar of premium paid. How much should she spend on each plan to minimize her insurance cost?

A) $290 for Plan A and $250 for Plan B

B) $550 for Plan A and $0 for Plan B

C) $250 for Plan A and $290 for Plan B

D) $320 for Plan A and $300 for Plan B

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Page 18

Chapter 8: Section 2: More on Inequalities

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Sample Questions

Q1) Carla wants to purchase insurance for her landscaping business. She determines that she needs at least $137,500 of property coverage and at least $137,800 of liability coverage. In order to gain this amount of coverage, she can purchase any combination of insurance plans A and B from two different insurance companies. For each dollar she spends on Plan A, she gets $250 of property coverage and $280 of liability coverage. Plan B provides $290 of property coverage and $260 of liability coverage for each dollar of premium paid. How much should she spend on each plan to minimize her insurance cost?

Q2) Determine which of the ordered pairs (3, 2), (-3, 4), (-1, -5), and (1, -6) satisfy the compound inequality.

y < -x + 2 or y > 2x - 4

Q3) Solve: |x - 5| = 3

Q4) Solve the inequality and write the solution set in interval notation.

5 < |x| - 10

Q5) Determine whether the absolute value inequality is equivalent to the inequality following it:

|-2 - x| < 14, -2 - x < 14 and -(-2 - x) < 14

A)True

B)False

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Chapter 9: Section 1: Radicals and Rational Exponents

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Sample Questions

Q1) Find the difference. (1 + 4i) - (-7 + 7i)

A) -6 - 3i

B) 8 + 11i

C) -6 + 11i

D) 8 - 3i

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20

Chapter 9: Section 2: Radicals and Rational Exponents

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Sample Questions

Q1) Find the difference. (-5 - 10i) - (-7 - 3i)

Q2) Find all real solutions. -10(x - 3)³ = 0

Q3) Find all real solutions. (u - 2)^-1/3 = 1

Q4) Simplify.

49^2/3 \(\div\) 49^1/6

Q5) Find all real solutions. (s + 3)² - 5 = 0

Q6) Evaluate. (27)^-4/3

Q7) The diagonal of a square measures 8 inches. What is the length of the sides?

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21

Chapter 10: Section 1: Quadratic Equations and Inequalities

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Sample Questions

Q1) Solve: (x - 7)² = 100

A) {-3, 17}

B) {3, 17}

C) {-3, 3}

D) {17, 17}

Q2) The monthly profit P in dollars that Carla makes on the sale of x automobiles is determined by the formula P = x² + 3x - 54. For what values of x is her profit positive?

A) 6, 7, ...

B) 1, 2, ..., 7

C) 7, 8, ...

D) 1, 2, ..., 6

Q3) Write a quadratic equation that has the solutions -10 and 3.

A) x² + 7x - 30 = 0

B) x² + 30 = 0

C) x² - 60x - 30 = 0

D) x² + 60x - 30 = 0

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Chapter 10: Section 2: Quadratic Equations and Inequalities

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Sample Questions

Q1) Complete the ordered pair so that it satisfies the given equation. y = x² + 4x + 2, (4, )

Q2) Find all real and imaginary solutions to the equation. x^-2 - 3x^-1 + 5 = 0

Q3) Find all intercepts for the graph of the parabola. f(x) = 49 - x²

Q4) Find the vertex for the graph of the parabola. f(x) = x² - 5

Q5) Solve the inequality. Graph the solution set. x² - 8x + 12 < 0

Q6) Find all real solutions of the given equation. x^2/3 - 3x^1/3 - 10 = 0

Q7) Use the discriminant to determine whether the given quadratic polynomial can be factored, then factor it if it is not prime. 7x² + 7x + 9

Q8) Solve: (q - 6)² = 36

Q9) Find all real solutions of the given equation. (x² + 1)² - 11(x² + 1) = -10

Q10) Find all real and imaginary solutions to the equation. t⁴ - 6561 = 0 Page 23

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Page 24

Chapter 11: Section 1: Functions

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Sample Questions

Q1) How are the graphs of f(x) = x² and g(x) = x² + 6 related?

A) The graph of g(x) is the same as that of f(x), but translated upward by 6 units.

B) The graph of g(x) is the same as that of f(x), but translated downward by 6 units.

C) The graph of g(x) is the same as that of f(x), but translated 6 units to the right.

D) The graph of g(x) is the same as that of f(x), but translated 6 units to the left.

Q2) How are the graphs of f(x) = (x + 10)² and g(x) = -(x + 10)² related?

A) The graph of g(x) is the same as that of f(x), but reflected about the x-axis.

B) The graph of g(x) is the same as that of f(x), but translated upward by 10 units.

C) The graph of g(x) is the same as that of f(x), but translated 10 units to the left.

D) The graph of g(x) is the same as that of f(x), but translated 10 units to the right.

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Chapter 11: Section 2: Functions

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Sample Questions

Q1) Give the correct domain and range of the relation . {(-5, 4), (5, 4)}

Q2) How are the graphs of f(x) = (x + 4)² and g(x) = -(x + 4)² related?

Q3) How are the graphs of f(x) = x² and g(x) = x² + 7 related?

Q4) For the given polynomial, find the x-intercepts and determine the behavior of the graph of the polynomial at each x-intercept. f(x) = x² + 2x - 3

Q5) Let f(x) = -2x - 4 and g(x) = x² + 10x. Find (f ·g)(4).

Q6) Determine whether the relation |2x| = |-8y| is a function.

A)True B)False

Q7) A gas station charges $1.67 per gallon for regular gasoline. Write an expression for the cost c(g) as a function of the number of gallons g and use this function to determine c(13).

Q8) Determine whether f(x) = 2x and g(x) = 0.5x are inverses of each other.

A)True

B)False

26

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Chapter 12: Section 1: Exponential and Logarithmic Functions

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Sample Questions

Q1) Solve log₇(x - 24) + log₇(x + 24) = 2.

A) {26}

B) {-25}

C) {25}

D) {27}

Q2) Write 2⁵ = 32 as a logarithmic equation.

A) log₂5 = 32

B) log₂32 = 2

C) log₅32 = 2

D) log₂32 = 5

Q3) If $7,000 is deposited in an account paying 5% compounded quarterly, then what amount will be in the account after 5 years?

A) $9,122.26

B) $6,998.26

C) $8,974.26

D) $18,573.08

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Chapter 12: Section 2: Exponential and Logarithmic Functions

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Sample Questions

Q1) Write log₇(36) - log₇(6) as a single logarithm.

Q2) Solve log₂(x² - 2) = 2 + log₂(x² + 8).

Q3) Rewrite log(75) in terms of log(3) and log(5).

Q4) If $10,000 is deposited in an account paying 7% compounded quarterly, then what amount will be in the account after 8 years?

Q5) Write 3⁶ = 729 as a logarithmic equation.

Q6) Write log(64) in terms of log(4).

Q7) Solve e^x^{+ 2} = 5.

Q8) Write log₆216 = 3 as an exponential equation.

Q9) Solve log(x) = -4.

Q10) Evaluate log_1/5(6). Round to four decimal places.

Q11) Solve -7^-5-^x = -49.

Page 28

Q12) Solve log₁₂(x - 35) + log₁₂(x + 35) = 2.

Q13) Simplify ln(e⁹).

Q14) Write ln(s⁵) + ln(s⁶) + ln(s) as a single logarithm. Assume s represents numbers for which the logarithms are defined.

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Chapter 13: Section 1: Nonlinear Systems and the Conic Sections

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Sample Questions

Q1) Solve the given system of equations. x² + y² = 625

Y = x² - 25

A) {(0, -25)}

B) {(-7, 24), (7, 24)}

C) {(0,-25), (-7, 26), (7, 26)}

D) {(0, -25), (-7, 24), (7, 24)}

Q2) Write the standard equation for the circle with the given radius and center. Center (-10, -2), radius 5

A) (x - 10)² + (y - 2)² = 25

B) (x - 10)² + (y - 2)² = 5

C) (x + 10)² + (y + 2)² = 5

D) (x + 10)² + (y + 2)² = 25

Q3) Solve the given system of equations. y = x² - 10

5x + y = 4

A) {(2, 14), (-7, 59)}

B) {(2, -6), (-7, 39)}

C) {(2, 4), (-7, 49)}

D) {(2, -6), (-7, 49)}

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Chapter 13: Section 2: Nonlinear Systems and the Conic Sections

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Q1) Solve the given system of equations. x² + y² = 25 y = x² - 5

Q2) Pump A can either fill or empty a tank in the same amount of time. If pump A and pump B are working together, the tank can be filled in 36 minutes. When pump A is draining the tank while pump B is filling it, the tank fills in 180 minutes. How long would it take either pump working alone to fill the tank?

Q3) Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola.

(x + 9)² + 3y² = 1

Q4) Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola.

(x + 9)² - y² = 1

Q5) Write the standard equation for the circle with the given radius and center. Center (8, -5), radius 12

Q6) Solve the given system of equations. y = x² + 4

-7x + y = -6

31

Q7) Find the distance between (-10, 1) and (-12, 2).

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Chapter 14: Section 1: Sequences and Series Available

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Q1) Use the binomial theorem to expand the given binomial. (t + 2)⁴

A) t⁴ + 8t³ + 12t² + 8t + 2

B) t⁴ + 8t³ + 24t² + 32t + 16

C) 2t⁴ + 16t³ + 48t² + 16t + 2

D) t⁴ + 2t³ + 4t² + 8t + 16

Q2) Find the common difference of an arithmetic sequence if the first term is -9 and the seventh term is -39.

A) -4

B) 3

C) -6

D) -5

Q3) Each time an aluminum beverage can is recycled, some amount of the material is lost due to a variety of reasons. If each recycling step is 90% efficient, what percent of the original material remains if a can is recycled 6 times? Round to the nearest tenth of a percent.

A) 63.2%

B) 56.5%

C) 57.9%

D) 53.1%

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Chapter 14: Section 2: Sequences and Series Available

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Q1) List the first four terms of the given sequence and match your result to the correct answer below.

c_n = (-1)ⁿ(-4n + 3)²

Q2) Use the binomial theorem to expand the given binomial. (b + 2)⁴

Q3) Use the binomial theorem to write out the first four terms of the given binomial. (x² + 1)²²

Q4) Write the first four terms of the geometric sequence whose nth term is given. a_n = (-3)ⁿ^-1

Q5) Write a formula for the general term of the given sequence and match your result to the correct answer below. -4, -3, -2, -1, 0, ...

Q6) Write the given series in summation notation. Use the index i, and let i begin at 1. ln(6) + ln(7) + ln(8)

Q7) List all terms of the finite sequence a_n = 3n + 2 for 1 n 5.

Q8) Write a formula for the nth term of the given arithmetic sequence. 1, 7, 13, 19, 25, . . .

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Chapter 15: Mathematical Problem Set

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Q1) Factor the given polynomial completely. If the polynomial is prime, say so. y³- 6y² - 9y + 54

Q2) Factor.

125x³ + 27

Q3) Liam invested some money in the Abernathy Fund at 7% simple interest and twice as much at twice the rate in the Carlson Fund. If the simple-interest income from the two funds totalled $5036.85, then how much was invested in each fund?

Q4) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. 4x - x = 3x

Q5) Determine whether 14 is a solution of 11x + 5 = 149. A)True B)False

Q6) Frank rides his bike 6 mph faster than he walks. He can bike from home to work in the same amount of time that it takes him to walk from home to the park. If the distance from Frank's home to work is 9 miles and the distance from his home to the park is 3 miles, what is Frank's walking speed?

Q7) Solve and write your answer in interval notation. y + 6 < 7y - 36

Page 34

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Chapter 16: Algebraic Equations and Problem Solving

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Q1) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. 8x - x = 7x

A) All real numbers, identity

B) {1}, conditional

C) Ø, inconsistent

Q2) A rectangular corral has a perimeter of 64 yards. Its length is 8 yards more than its width. What are the dimensions of the corral?

A) Length 22 yd, width 14 yd

B) Length 40 yd, width 24 yd

C) Length 18 yd, width 14 yd

D) Length 20 yd, width 12 yd

Q3) Factor. 64x³ + 1

A) The expression is prime.

B) (4x + 1)(16x² + 4x - 1)

C) (4x - 1)(16x² + 4x + 1)

D) (4x + 1)(16x² - 4x + 1)

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Chapter 17: Algebra and Math Problems

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Q1) Find four consecutive integers whose sum is 138.

Q2) Solve the inequality. Graph the solution set. x² + 6x + 5 0

Q3) Conrad builds picnic tables and porch swings which he sells at flea markets. A picnic table requires six 2\(\times\)4's and nine 1\(\times\)6's. A swing uses three 2\(\times\)4's and six 1\(\times\)6's. Conrad currently has 120 2\(\times\)4's and 198 1\(\times\)6's in his inventory. If tables sell for $60 and swings sell for $25, how many of each items should Conrad make in order to maximize his revenue?

Q4) If $1,300 is deposited in an account paying 11% compounded continuously, then what amount will be in the account after 3 years?

Q5) Floyd's chemistry lab manual instructs him to weigh out 20 grams of sodium carbonate. Floyd remembers that his sample's mass differed from the 20-gram target amount by 0.36 grams, but does not recall whether he weighed out more or less than the requested amount. Use an absolute value equation to find the possible values for Floyd's sample.

Q6) Find the midpoint and length of the line segment with the endpoints (2,2) and (12,26).

Q7) Write ln(x⁵) - ln(x²) as a single logarithm.

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Chapter 18: Algebraic Equation Practice

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Q1) Raphael can load a large shipping truck in 12 hours. Working together, Raphael and Jana can load the same truck in 3 hours. How long would it take Jana to load the truck by herself?

A) 3 hours

B) 5 hours

C) 6 hours

D) 4 hours

Q2) Write a formula for the nth term of the given arithmetic sequence. 9, 14, 19, 24, 29, . . .

A) a_n = 5n + 4

B) a_n = 4n - 5

C) a_n = 5n - 4

D) a_n = 6n - 5

Q3) Find the sum of the given infinite geometric series. 16 + 12 + 9 + ...

A) "64"

B) "\(\infty\)"

C) "68"

D) "60"

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