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Elementary Algebra Test Bank

Course Introduction

Elementary Algebra introduces students to the fundamental concepts and operations of algebra, focusing on the basic principles that form the foundation for higher-level mathematics. Topics include variables, expressions, linear equations and inequalities, exponents, polynomials, factoring, and graphing on the coordinate plane. Students will develop problem-solving skills and learn to apply algebraic techniques to real-world situations, preparing them for advanced mathematical courses and everyday quantitative reasoning.

Recommended Textbook

Elementary and Intermediate Algebra 4th Edition by Mark Dugopolski Emeritus

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32 Chapters

840 Verified Questions

840 Flashcards

Source URL: https://quizplus.com/study-set/3927 Page 2

Chapter 1: Section 1: Real Numbers and Their Properties

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29 Verified Questions

29 Flashcards

Source URL: https://quizplus.com/quiz/78323

Sample Questions

Q1) A large industrial plant produces one ton of concrete every 0.80 minutes. At what rate is the facility producing concrete in tons per hour? Round to the nearest thousandth of a ton per hour.

A) 84.523 tons/hr

B) 61.112 tons/hr

C) 0.021 tons/hr

D) 75.000 tons/hr

Answer: D

Q2) Evaluate: 21 + (-23)

A) -44

B) 44

C) -2

D) 2

Answer: C

Q3) Evaluate: 0 $\div$ 5

A) 0

B) 1

C) Undefined

D) 5

Answer: A

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Chapter 1: Section 2: Real Numbers and Their Properties

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29 Verified Questions

29 Flashcards

Source URL: https://quizplus.com/quiz/78322

Sample Questions

Q1) Evaluate: (6 - 2)(5 - 12)

Answer: -28

Q2) Evaluate the expression for b = -10 and c = -11: c2 - 3b - 1

Answer: 150

Q3) Write the interval of real numbers in interval notation. The set of real numbers less than -7

Answer: (- , -7)

Q4) Evaluate: 23 + (-24) Answer: -1

Q5) Evaluate: (5)(10) Answer: 50

Q6) Evaluate: 7 - 3 · |3 - (52 - 2)| Answer: -53

Q7) Convert to a percent and a fraction: 0.7

Answer: 70%, 11ea9079_e301_cd10_aec7_0df6f8cf357c_TB3543_11

Q8) Use the commutative and associative properties of multiplication and exponential notation to rewrite the given product. v2(v·13)(vw)

Answer: 13v4w

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Chapter 2: Section 1: Linear Equations and Inequalities in

One Variable

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26 Verified Questions

26 Flashcards

Source URL: https://quizplus.com/quiz/78311

Sample Questions

Q1) James paid $285 for a DVD player that was priced originally at $300. What was the discount rate?

A) 3%

B) 10%

C) 7%

D) 5%

Answer: D

Q2) Lori built a dog lot for her dog, Chollie, by fencing in a rectangular area of her yard. If Chollie's lot required 52 feet of fence and the length is 2 feet longer than the width, then what are the length and width of Chollie's dog lot?

A) 6 feet long and 20 feet wide

B) 18 feet long and 8 feet wide

C) 10 feet long and 16 feet wide

D) 14 feet long and 12 feet wide

Answer: D

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Chapter 2: Section 2: Linear Equations and Inequalities in

One Variable

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26 Verified Questions

26 Flashcards

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Sample Questions

Q1) Write the appropriate inequality symbol in the blank so that the two inequalities are equivalent.

-55 $\ge$ 5y

-11 _____ y

Q2) Lori built a dog lot for her dog, Chollie, by fencing in a rectangular area of her yard. If Chollie's lot required 60 feet of fence and the length is 10 feet longer than the width, then what are the length and width of Chollie's dog lot?

Q3) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity.

80 - 5(t + 4) = 0

Q4) Cab drivers in Metro City charge $5 per mile plus a fixed charge of $2 for the tip. If a tourist pays $37 for a cab ride, then how many miles was the cab ride?

Q5) The length of a rectangle must be 8 centimeters more than the width, and the perimeter must be at least 36 centimeters. What is the range of values for the width?

Q6) How many pints of a 9% cleaning solution must be mixed with 2 pints of a 13% cleaning solution to give a 11% solution?

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Chapter 3: Section 1: Linear Equations and Inequalities in

Two Variables

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26 Verified Questions

26 Flashcards

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Sample Questions

Q1) The time to drive from Gotham City to Farmville varies inversely with the average speed. If the drive takes 6.2 hours at 42 mph, then how long will it take at 63 mph? Round to the nearest tenth of an hour.

A) 4.1 hours

B) 3.5 hours

C) 3.2 hours

D) 3.7 hours

Q2) 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 7 hours.

A) C = 40t + 50; $330

B) C = 40t; $280

C) C = 40t + 40; $320

D) C = 50t + 40; $390

Q3) If s varies inversely as x and s = 4 when x = -4, then find s when x = 2.

A) -8

B) 4

C) -16

D) -2

Page 7

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Chapter 3: Section 2: Linear Equations and Inequalities in

Two Variables

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25 Verified Questions

25 Flashcards

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Sample Questions

Q1) A playground equipment manufacturer plans to spend $300,000 on a new facility plus $140 for each swing set made.The formula C = 140n + 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).

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

Q3) Line l goes through (1, 3) and is parallel to the line through (4, 3) and (-3, 1). Find the slope of l.

Q4) Graph the equation y = -3x + 1.

Q5) 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.

Q6) Find the equation (in standard form) of the line through (2, 0) and (4, -1).

Q7) The budget deficit for Central City can be modeled by the equation D = 0.5n + 6.5 where n is the number of years since 1990 and D is the deficit in millions of dollars. Graph the equation for n ranging from 0 to 20.

Q8) Graph the line through (-1, 3) with slope -2.

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Chapter 4: Section 1: Exponents and Polynomials

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28 Verified Questions

28 Flashcards

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Sample Questions

Q1) Multiply. (-4r - 9)2

A) 16r2 + 72r + 81

B) -4r2 + 72r + 81

C) 16r2 + 81

D) 16r2 + 36r + 81

Q2) State the degree of the polynomial and determine if it is a monomial, binomial, or trinomial. -14x3

A) 3, monomial

B) -14, binomial

C) -14, monomial

D) 3, binomial

Q3) Find the indicated value of the polynomial. P(x) = 0.6x3 + 0.7x2 - 3.4, P(-0.1)

A) -3.4064

B) -3.3936

C) -3.464

D) 3.3924

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Page 9

Chapter 4: Section 2: Exponents and Polynomials

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28 Verified Questions

28 Flashcards

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Sample Questions

Q1) 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.

Q2) Find the product. (5w2 - 4)(5w2 - 1)

Q3) Expand the binomial. (n - 2)3

Q4) Find the indicated value of the polynomial. P(x) = -4.1x3 - 1.2x2 - 1.1, P(0.8)

Q5) Multiply. (5x - 6)2

Q6) Find the product. -10t5·2t7

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

Q8) Find the quotient and the remainder. (x4 - x3 + 5) $\div$ (x2 + 2)

Q9) Find the product. (n + 2)(n - 3)(n + 4)

Q10) Simplify. -(11)0

Page 10

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Chapter 5: Section 1: Factoring

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25 Verified Questions

25 Flashcards

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Sample Questions

Q1) Factor completely. b3r3 - 12b2r2 + 36br

A) br(br - 6)2

B) r(b3r - 6b2)

C) br(b2r2 - 12br + 36)

D) br(br - 6)(br + 6)

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. c4 + d4

A) c2d2(c2 - d2)

B) (c - d)2(c + d)2

C) The polynomial is prime.

D) (c - d)(c + d)(c2 + d2)

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Page 12

Chapter 5: Section 2: Factoring

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25 Verified Questions

25 Flashcards

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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 - 62t + 188. How many seconds elapse before the marble hits the ground?

Q2) Factor.

uvw + 9u + 5vw + 45

Q3) Factor the given polynomial completely. x4 + y4

Q4) Factor.

9y2 - 100

Q5) Factor the given polynomial completely. z6 + 2z3 - 3

Q6) Factor the polynomial below completely, given that the binomial following it is a factor of the polynomial. u3 + 2u2 - 11u - 12, u - 3

Q7) Factor the given polynomial completely. If the polynomial is prime, say so. 7w2 - 24w - 16

Q8) Factor the given polynomial completely. If the polynomial is prime, say so. c3 + cd + 3c2 + 3d

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Chapter 6: Section 1: Rational Expressions

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25 Verified Questions

25 Flashcards

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Sample Questions

Q1) 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

Q2) Find the least common multiple of the given terms. r2 - 8r - 9, r2 - 18r + 81

A) (r - 9)

B) (r + 1)(r - 9)

C) (r + 1)(r - 9)2

D) (r + 1)(r - 9)(r + 9)

Q3) Cora can paddle her canoe 14 miles in the same time that Susan's motorboat covers 42 miles. If Susan's boat travels 14 mph faster than Cora's canoe, then how fast is Susan's boat?

A) 23 mph

B) 21 mph

C) 7 mph

D) 22 mph

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Chapter 6: Section 2: Rational Expressions

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25 Verified Questions

25 Flashcards

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Sample Questions

Q1) 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?

Q2) 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.

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) 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.

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) A large pump can fill a 78,000 gallon reservoir in 8 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?

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Page 15

Chapter 7: Section 1: Systems of Linear Equations

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17 Verified Questions

17 Flashcards

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Sample Questions

Q1) Suzanne invested $18,100 in two mutual fund accounts: the Abernathy Fund and the Brice Fund. During the subsequent year, The Abernathy Fund earned 11% and the Brice account earned 6%. At the end of the year, the total interest earned was $1,391. How much did Suzanne invest in each fund?

A) $6,600 in the Abernathy Fund, $11,500 in the Brice Fund

B) $5,100 in the Abernathy Fund, $13,000 in the Brice Fund

C) $6,100 in the Abernathy Fund, $12,000 in the Brice Fund

D) $6,600 in the Abernathy Fund, $11,700 in the Brice Fund

Q2) Solve the system of equations. 0.5x + 2y = 1.25

-0)875x + 1.5y = 2.8125

A) {(-1, 1.5)}

B) {(0, 1)}

C) {(0, 3)}

D) {(-1.5, 1)}

Q3) When the graphs of two independent linear equations (each in three variables) intersect, the intersection is

A) a line.

B) a plane.

C) a point.

D) None of these.

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Chapter 7: Section 2: Systems of Linear Equations

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15 Verified Questions

15 Flashcards

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Sample Questions

Q1) Solve the system of equations.

-3.5x + 3y = -5.375

-0.875x - 0.5y = 0.53125

Q2) Fred, Tiger, and Nancy play a round of golf together. Their combined score is 226. Fred's score was 5 more than Tiger's, and Nancy's score was 9 more than Fred's. What was each person's score?

Q3) 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

Q4) Cashews sell for $5 per pound and peanuts sell for $2 per pound. How many pounds of each would you use to make 15 pounds of a mixture that sells for $3.20 per pound?

Q5) Solve the system of linear equations by the substitution method.

-5x = -2y + 9

5x + 5y = -30

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Page 17

Chapter 8: Section 1: More on Inequalities

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23 Verified Questions

23 Flashcards

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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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22 Verified Questions

22 Flashcards

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Sample Questions

Q1) Write as a single interval if possible: [-1, $\infty$)$\cup$(4, $\infty$)

Q2) Solve: |x - 5| = 3

Q3) Determine if the compound inequality is true: 10 $\le$ 10 and 10 > 0

A)True

B)False

Q4) 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

Q5) The Belew's Creek Volunteer Fire Department is having a community chicken dinner in order to raise funds. Patrons have a choice between two sizes of dinners. The small dinner costs $2.50 and comes with one piece of chicken and two rolls. The large dinner costs $4.00 and comes with two pieces of chicken and three rolls. The department has a total of 568 rolls and 300 pieces of chicken. How many of each type of dinners need to be sold to maximize the fire department's revenue?

Q6) Write as a single interval if possible: (-9, $\infty$)$\cup$ [13, $\infty$)

Q7) Solve: 12 - |-13 - x| = 2

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Chapter 9: Section 1: Radicals and Rational Exponents

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25 Verified Questions

25 Flashcards

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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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Chapter 9: Section 2: Radicals and Rational Exponents

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25 Verified Questions

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Sample Questions

Q1) Find all real solutions. (s + 3)2 - 5 = 0

Q2) The diagonal of a square measures 8 inches. What is the length of the sides?

Q3) Find all real solutions. -10(x - 3)3 = 0

Q4) Find all real solutions. (u - 2)-1/3 = 1

Q5) Simplify.

492/3 $\div$ 491/6

Q6) Find the difference. (-5 - 10i) - (-7 - 3i)

Q7) Evaluate. (27)-4/3

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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) 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

Q3) Find b2 - 4ac and the number of real solutions for the given equation. x2 + 3x + 4 = 0

A) -7, 2

B) 25, 0

C) -7, 0

D) 25, 2

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Chapter 10: Section 2: Quadratic Equations and Inequalities

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25 Verified Questions

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Sample Questions

Q1) Solve the inequality. Graph the solution set. x2 - 8x + 12 < 0

Q2) Terrence paddles his canoe upstream a distance of 6 miles. He completes the return trip in 30 minutes less that the upstream journey. If the current flows at 4 miles per hour, what is Terrence's speed in still water?

Q3) Graph the parabola. y = -x2 + 4

Q4) Complete the ordered pair so that it satisfies the given equation. y = x2 + 4x + 2, (4, )

Q5) Find all real solutions of the given equation. (x2 + 1)2 - 11(x2 + 1) = -10

Q6) Solve using the quadratic formula: 3x2 + 5x - 1 = 0

Q7) Solve by factoring: x2 - 5x - 50 = 0

Q8) Find the vertex for the graph of the parabola. f(x) = x2 - 5

Q9) Write a quadratic equation that has the solutions 8 and 1.

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

Q11) Solve by completing the square. 2x2 - 5x + 1 = 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) For the given polynomial, find the x-intercepts and determine the behavior of the graph of the polynomial at each x-intercept. Match your result to the correct answer below. f(x) = x2 + 7x + 12

A) Crosses at (-4, 0) and (3, 0)

B) Crosses at (4, 0) and (-3, 0)

C) Crosses at (4, 0) and (3, 0)

D) Crosses at (-4, 0) and (-3, 0)

Q3) Determine whether f(x) = 5x and g(x) = 0.2x are inverses of each other.

A)True

B)False

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Chapter 11: Section 2: Functions

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Sample Questions

Q1) 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).

Q2) Give the correct domain and range of the relation . {(-5, 4), (5, 4)}

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

Q4) Determine whether the given function is invertible. If it is invertible, then find its inverse.

{(-5,4),(-1,1),(-13,5)}

Q5) How are the graphs of f(x) = (x + 4)2 and g(x) = -(x + 4)2 related?

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

A)True

B)False

Q7) Let f(x) = -2x - 4 and g(x) = x2 + 10x. Find (f ·g)(4).

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

A)True

B)False

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Chapter 12: Section 1: Exponential and Logarithmic

Functions

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Sample Questions

Q1) Write log864 = 2 as an exponential equation.

A) 82 = 64

B) 82 = 8

C) 642 = 8

D) 642 = 64

Q2) Write ln(r2) + ln(r4) + ln(r) as a single logarithm. Assume r represents numbers for which the logarithms are defined.

A) ln(r5)

B) ln(r7)

C) The logarithms cannot be combined.

D) ln(r8)

Q3) Solve log7(x - 24) + log7(x + 24) = 2.

A) {26}

B) {-25}

C) {25}

D) {27}

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Chapter 12: Section 2: Exponential and Logarithmic Functions

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Sample Questions

Q1) Write ln(s5) + ln(s6) + ln(s) as a single logarithm. Assume s represents numbers for which the logarithms are defined.

Q2) Rewrite log(75) in terms of log(3) and log(5).

Q3) Evaluate log1/5(6). Round to four decimal places.

Q4) Solve ex + 2 = 5.

Q5) Simplify ln(e9).

Q6) If $10,000 is deposited in an account paying 7% compounded quarterly, then what amount will be in the account after 8 years?

Q7) Solve log2(x2 - 2) = 2 + log2(x2 + 8).

Q8) Solve log12(x - 35) + log12(x + 35) = 2.

Q9) Write log6216 = 3 as an exponential equation.

Q10) Solve log(x) = -4.

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

Q12) Write log(64) in terms of log(4).

Q13) Write log7(36) - log7(6) as a single logarithm. Page 28

Q14) Write 36 = 729 as a logarithmic equation.

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Page 29

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

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Sample Questions

Q1) 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

Q2) 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)}

Q3) Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. (x + 8)2 - y = 1

A) Ellipse

B) Circle

C) Hyperbola

D) Parabola

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

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Sample Questions

Q1) Graph both equations of the system on the same coordinate axes. Use elimination to find all points of intersection.

y = 1 - x2

x2 + 4y2 = 4

Q2) Solve the given system of equations.

x2 + y2 = 25

y = x2 - 5

Q3) Which, if any, of the ordered pairs (3, 4), (-1, 7), (-3, -1), and (8, -5) satisfy the system of inequalities?

x2 + y2 25

y < x2

Q4) Find two complex numbers that have a sum of -14 and a product of 58.

Q5) Rewrite the given equation in the standard form for the equation of a circle and identify its center and radius.

x2 - 18x + y2 + 6y - 10 = 0

Q6) Write the standard equation for the circle with the given radius and center. Center (8, -5), radius 12

Q7) Find the center and radius for the given circle. 169 - x2 = (y - 4)2

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Chapter 14: Section 1: Sequences and Series Available

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Q1) Write a formula for the nth term of the given arithmetic sequence. 4, 10, 16, 22, 28, . . .

A) an = 6n - 2

B) an = 7n - 3

C) an = 6n + 2

D) an = 2n - 6

Q2) Write the first four terms of the geometric sequence whose nth term is given. an = (-6)n-1

A) 1, -6, 36, -216

B) 0, -6, 36, -216

C) 1, 6, 36, 216

D) -6, 36, -216, 1296

Q3) 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

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Chapter 14: Section 2: Sequences and Series Available

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Q1) 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 80% efficient, what percent of the original material remains if a can is recycled 3 times? Round to the nearest tenth of a percent.

Q2) List the first four terms of the given sequence and match your result to the correct answer below. cn = (-1)n(-4n + 3)2

Q3) Suppose a deposit of $2000 is made at the beginning of each year for 45 years into an account that pays 11% compounded annually. What is the amount of this annuity at the end of the 45th year?

Q4) Use the binomial theorem to write out the first four terms of the given binomial. (x2 + 1)22

Q5) Write the given series in summation notation. Use the index i, and let i begin at 1. ln(6) + ln(7) + ln(8)

Q6) Use the binomial theorem to expand the given binomial. (b + 2)4

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

Page 33

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Chapter 15: Mathematical Problem Set

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Q1) Does the point (5, -12) satisfy the inequality y $\ge$ 15x + 12?

Q2) A triangle has sides of length x inches, x + 1 inches, and x + 2 inches and its perimeter is given by x + (x + 1) + (x + 2) = 42 inches. Find the measures of the sides by solving the perimeter equation.

Q3) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity.

4x - x = 3x

Q4) The length of a rectangular painting is 5 feet greater than the width. If the perimeter is 22 feet, then what are the length and the width?

Q5) Solve the given equation.

y2 + 6y + 8 = 0

Q6) Solve the system of equations.

-0.75x + 3.5y = 3.125

0.6x + 1.5y = 1.8

Q7) Find the equation (in standard form) of the line through (3, -7) and (5, -8).

Q8) Solve and write your answer in interval notation. y + 6 < 7y - 36

Q9) Factor the given polynomial completely. If the polynomial is prime, say so. y3 - 6y2 - 9y + 54

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Chapter 16: Algebraic Equations and Problem Solving

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Q1) Perform the indicated operation. (p2 - p - 1) - (p2 + 4p + 5)

A) -5p + 4

B) 2p2 - 5p - 6

C) -5p + 6

D) -5p - 6

Q2) Solve and write your answer in interval notation. p - 3 < 3p - 13

A) (- , 3)

B) (6, )

C) (5, )

D) (3, )

Q3) Frank rides his bike 10 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 6 miles and the distance from his home to the park is 2 miles, what is Frank's walking speed?

A) 7 mph

B) 6 mph

C) 6.5 mph

D) 5 mph

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Chapter 17: Algebra and Math Problems

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Q1) Write the given equation in the form y = a(x - h)2 + k and identify the vertex, focus, and directrix. Show your work. y = 2x2 - 5x + 2

Q2) Find the product. (3a + 4)(2a + 1)

Q3) Find the sum of the given infinite geometric series. 36 + 30 + 25 + ...

Q4) Write a formula for the nth term of the given arithmetic sequence. 6, 10, 14, 18, 22, . . .

Q5) The pH of a solution is defined by pH = -log10[H+] where [H+] is the hydrogen ion concentration in moles per liter. To the nearest hundredth, what is the pH of a cup of coffee in which [H+] = 2.1$\times$10-8 mol/L?

Q6) Write a formula for the nth term of the given geometric sequence. 1, 6, 36, 216, 1296, . . .

Q7) Find the inverse of the given function and include any domain restrictions. f (x) = (x - 4)2

Q8) Solve the given system of equations. y = x2 y = 5

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Chapter 18: Algebraic Equation Practice

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Q1) For the given polynomial, find the x-intercepts and determine the behavior of the graph of the polynomial at each x-intercept. f(x) = x3 - 10x2

A) Crosses at (10, 0) and at (-10, 0) but does not cross at (0, 0)

B) Crosses at (10, 0) but does not cross at (0, 0)

C) Crosses at (10, 0)

D) Crosses at (10, 0) and at (0, 0)

Q2) Factor. 64y3 - 125z3

A) (4y + 5z)(16y2 - 20yz + 25z2)

B) (4y - 5z)(16y2 + 20yz + 25z2)

C) (4y - 5z)(4y2 + 20yz + 5z2)

D) (4y - 5z)(16y2 - 20yz + 25z2)

Q3) Find four consecutive integers whose sum is 226.

A) 55, 57, 59, 61

B) 56, 57, 58, 59

C) 55, 56, 57, 58

D) 54, 55, 56, 57

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