Introductory Algebra Test Bank - 840 Verified Questions

Introductory Algebra Test Bank

Course Introduction

Introductory Algebra lays the foundation for understanding algebraic concepts and operations, focusing on the manipulation of variables and expressions, solving linear equations and inequalities, and working with polynomials and factoring. This course introduces students to mathematical reasoning, problem-solving strategies, and key concepts such as exponents, ratios, and proportions. With a practical approach to algebras role in real-world scenarios, students will build critical skills necessary for success in advanced mathematics courses.

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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Page 2

Chapter 1: Section 1: Real Numbers and Their Properties

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29 Verified Questions

29 Flashcards

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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) Jim has a $112,700 home with a $58,444 mortgage. He has $7,995 in savings and an additional $5,021 in a mutual fund account. He owes $9,822 on his car and $2,143 on his credit card. What is Jim's net worth?

A) $45,265

B) $74,951

C) $55,307

D) $39,317

Answer: C

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3

Chapter 1: Section 2: Real Numbers and Their Properties

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29 Verified Questions

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Sample Questions

Q1) Simplify: 2(m - 4) - 3(-m - 7)

Answer: 5m + 13

Q2) Jim has a $147,000 home with a $98,672 mortgage. He has $8,210 in savings and an additional $9,756 in a mutual fund account. He owes $3,416 on his car and $1,146 on his credit card. What is Jim's net worth?

Answer: $61,732

Q3) Evaluate: (5)(10)

Answer: 50

Q4) Combine like terms if possible: 7z - (-12z)

Answer: 19z

Q5) Use the distributive property to factor the expression. -35p + 20

Answer: 5(-7p + 4)

Q6) A large industrial plant produces one ton of concrete every 0.75 minutes. At what rate is the facility producing concrete in tons per hour? Round to the nearest thousandth of a ton per hour.

Answer: 80.000 tons/hr

Q7) Evaluate the expression for b = -10 and c = -11: c² - 3b - 1

Answer: 150

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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) Liam invested some money in the Abernathy Fund and $8,436 more than that amount in the Carlson Fund. For the year he was in these funds, the Abernathy fund paid 8% simple interest and the Carlson Fund paid 11% simple interest. If the income from the two funds totalled $2,175.12, then how much was invested in each fund?

A) $6,564 in Abernathy and $15,000 in Carlson

B) $16,500 in Abernathy and $8,064 in Carlson

C) $8,064 in Abernathy and $16,500 in Carlson

D) $15,000 in Abernathy and $6,564 in Carlson

Answer: A

Q2) 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

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Chapter 2: Section 2: Linear Equations and Inequalities in

One Variable

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26 Verified Questions

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Sample Questions

Q1) Find an algebraic expression for the underlined quantity. The distance, given that the rate is x miles per hour and the time is 8 hours.

Q2) Solve for x.

4(x - a) - (26b - x) = a - b

Q3) James paid $234 for a DVD player that was priced originally at $260. What was the discount rate?

Q4) How many pints of a 9% cleaning solution must be mixed with 2 pints of a 13% cleaning solution to give a 11% solution?

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

-55 \(\ge\) 5y

-11 _____ y

Q7) Find y given that x = -7 and y = -4x + 5.

Q8) 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?

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Chapter 3: Section 1: Linear Equations and Inequalities in

Two Variables

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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) 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.

Q3) Does the point (2, 14) satisfy the inequality y \(\le\) 2x - 2?

A)True

B)False

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Chapter 3: Section 2: Linear Equations and Inequalities in

Two Variables

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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 5.0 hours at 49 mph, then how long will it take at 70 mph? Round to the nearest tenth of an hour.

Q2) Complete the ordered pair so that it satisfies the given equation. y = -4x + 3: (-10, ___)

Q3) 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.

Q4) 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

Q5) Tim works at a bakery and can prepare a birthday cake in 4 hours. It takes him 5 hours to prepare a wedding cake. Tim works a 40-hour week and he must bake at least as many wedding cakes as birthday cakes. Draw a graph that illustrates the number of each type of cake Tim can bake per week.

Q6) Does the point (-4, -1) satisfy the inequality y \(\le\) 6x - 5? A)True B)False

8

Q7) Find the slope and the y-intercept of the line represented by 12x + 7y = 5.

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Chapter 4: Section 1: Exponents and Polynomials

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Sample Questions

Q1) Find the quotient and the remainder. (x⁴ - 5x³ + 10)

\(\div\) (x² + 2)

A) x² - 5x - 2, 10x - 6

B) x² - 2, -5x + 14

C) x² - 5x + 2, -10x + 14

D) x² - 5x - 2, 10x + 14

Q2) Multiply. (4 + 3s)(4 - 3s)

A) 16 - 9s²

B) 9s² + 16

C) 16 - 24s + 9s²

D) 16 - 24s - 9s²

Q3) Simplify. 3p⁴·(p⁴)³

A) 3p²⁴

B) 3p⁴⁸

C) 3p¹¹

D) 3p¹⁶

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Chapter 4: Section 2: Exponents and Polynomials

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Sample Questions

Q1) State the degree of the polynomial and determine if it is a monomial, binomial, or trinomial.

x⁴

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) Multiply.

(5x - 6)²

Q4) Simplify.

5y⁴·(y⁴)⁵

Q5) The edges of a triangular homesite have lengths of 3x + 4, x, and x - 1. Write an expression for the perimeter of the property.

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

Q7) Simplify. (xy³)³

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

Q9) Multiply.

(6 + 5x)(6 - 5x)

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Chapter 5: Section 1: Factoring

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Sample Questions

Q1) Factor out the greatest common factor. (m - 4)8 + (m - 4)m

A) The polynomial is prime.

B) m² + 4m - 32

C) (m - 4)8 + m

D) (m - 4)(8 + m)

Q2) 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)

Q3) Factor the given polynomial completely. 6v²w - 48vw + 90w

A) w(6v - 30)(6v - 18)

B) 6w(v - 5)(v - 3)

C) The polynomial is prime.

D) 6w(v² - 8v + 15)

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11

Chapter 5: Section 2: Factoring

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Sample Questions

Q1) Factor completely.

8u³v - 392uv

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. If the polynomial is prime, say so. c³+ cd + 3c² + 3d

Q4) Solve the given equation. y² = 9y

Q5) Factor the given polynomial completely. x⁴+ y⁴

Q6) Factor.

8x³ - 27

Q7) Factor out the opposite of the greatest common factor. 10z³ - 2z²

Q8) Solve the given equation. x³ + 5x² - 2x - 24 = 0

Q9) Factor.

q² + 6qr + 36r²

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Chapter 6: Section 1: Rational Expressions

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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) 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

Q3) 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)

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Chapter 6: Section 2: Rational Expressions

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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) 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.

Q3) 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?

Q4) 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?

Q5) 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.

Q6) 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?

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Page 14

Chapter 7: Section 1: Systems of Linear Equations

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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) When three linear equations (each in three variables) are graphed, two of the equations are seen to be parallel planes. The system is

A) normal.

B) incomplete.

C) inconsistent.

D) dependent.

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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) 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 equations.

3x - 2y + 4z = 12

-5x - y - z = -10

-3x - 5y - 3z = -4

Q4) Solve the system of equations.

-x + 5y - 3z = 31

-4x - 5y + 4z = 6

3x - 15y + 9z = -91

Q5) Suzanne invested $14,300 in two mutual fund accounts: the Abernathy Fund and the Brice Fund. During the subsequent year, The Abernathy Fund earned 4% and the Brice account earned 5%. At the end of the year, the total interest earned was $672. How much did Suzanne invest in each fund?

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Chapter 8: Section 1: More on Inequalities

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Sample Questions

Q1) Write as a single interval if possible: [-6, \(\infty\)) \(\cup\) (-4, \(\infty\))

A) [-6, \(\infty\)) \(\cup\) (-4, \(\infty\))

B) (-6, \(\infty\))

C) [-6, \(\infty\))

D) (-4, \(\infty\))

Q2) 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 $3.50 and comes with two pieces of chicken and three rolls. The department has a total of 508 rolls and 300 pieces of chicken. How many of each type of dinners need to be sold to maximize the fire department's revenue?

A) 254 small dinners, 0 large dinners

B) 0 small dinners, 92 large dinners

C) 269 small dinners, 2 large dinners

D) 259 small dinners, 10 large dinners

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Page 17

Chapter 8: Section 2: More on Inequalities

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Sample Questions

Q1) 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

Q2) Determine if the compound inequality is true: 10 \(\le\) 10 and 10 > 0

A)True

B)False

Q3) Write as a single interval if possible: [-1, \(\infty\))\(\cup\)(4, \(\infty\))

Q4) Write as a single interval if possible: (-9, \(\infty\))\(\cup\) [13, \(\infty\))

Q5) Solve: |x - 5| = 3

Q6) 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?

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

Q8) Solve the inequality and write the solution set in interval notation. 5 < |x| - 10

18

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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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19

Chapter 9: Section 2: Radicals and Rational Exponents

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Sample Questions

Q1) The diagonal of a square measures 8 inches. What is the length of the sides?

Q2) Evaluate.

(27)^-4/3

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

Q4) Simplify.

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

Q5) Find the difference. (-5 - 10i) - (-7 - 3i)

Q6) Find all real solutions.

-10(x - 3)³ = 0

Q7) Find all real solutions. (s + 3)² - 5 = 0

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Chapter 10: Section 1: Quadratic Equations and Inequalities

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Sample Questions

Q1) Solve by factoring: x² - x - 42 = 0

A) {-7, -6}

B) {-7, 6}

C) {-6, 7}

D) {6, 7}

Q2) Solve the given inequality and express the solution in interval notation. x² + 9x \(\ge\) 0

A) (-\(\infty\), 0] \(\cup\) [9, \(\infty\))

B) [0, \(\infty\))

C) [-9, 0]

D) (-\(\infty\), -9] \(\cup\) [0, \(\infty\))

Q3) Use the discriminant to determine whether the given quadratic polynomial can be factored, then factor it if it is not prime. 10x² + 10x + 6

A) The expression is prime.

B) (x + 10)(x + 6)

C) (10x + 6)(x + 10)

D) (10x + 10)(x + 6)

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21

Chapter 10: Section 2: Quadratic Equations and Inequalities

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Sample Questions

Q1) Solve by factoring: x² - 5x - 50 = 0

Q2) Find all real solutions of the given equation. x^2/3 - 3x^1/3 - 10 = 0

Q3) The monthly profit P in dollars that Carla makes on the sale of x automobiles is determined by the formula P = x² - 6x - 7. For what values of x is her profit positive?

Q4) Graph the parabola. y = -x² + 4

Q5) Use the discriminant to determine whether the given quadratic polynomial can be factored, then factor it if it is not prime. 7x² + 7x + 9

Q6) Find all intercepts for the graph of the parabola. f(x) = 49 - x²

Q7) 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?

Q8) Find all real and imaginary solutions to the equation. t⁴ - 6561 = 0

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

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Chapter 11: Section 1: Functions

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Sample Questions

Q1) 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.

Q2) 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.

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23

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

A)True

B)False

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

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

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) 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).

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Chapter 12: Section 1: Exponential and Logarithmic Functions

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Sample Questions

Q1) Evaluate log_1/3(3.6). Round to four decimal places.

A) -0.5064

B) -1.1660

C) 1.2809

D) -0.858

Q2) Write log₈64 = 2 as an exponential equation.

A) 8² = 64

B) 8² = 8

C) 64² = 8

D) 64² = 64

Q3) Solve log₃(x² - 1) = 2 + log₃(x² + 2).

A) {-2, 1}

B) Ø

C) {19}

D) {4, 7}

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Chapter 12: Section 2: Exponential and Logarithmic Functions

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Sample Questions

Q1) Write 3⁶ = 729 as a logarithmic equation.

Q2) Solve log(x) = -4.

Q3) Write ln(s⁵) + ln(s⁶) + ln(s) as a single logarithm. Assume s represents numbers for which the logarithms are defined.

Q4) Solve -7^-5-^x = -49.

Q5) Solve log₂(x² - 2) = 2 + log₂(x² + 8).

Q6) Rewrite log(75) in terms of log(3) and log(5).

Q7) Solve log₁₂(x - 35) + log₁₂(x + 35) = 2.

Q8) Simplify ln(e⁹).

Q9) Evaluate log_1/5(6). Round to four decimal places.

Q10) Write log₆216 = 3 as an exponential equation.

Q11) Solve e^x^{+ 2} = 5.

Q13) Write log(64) in terms of log(4). Page 26

Q12) If $10,000 is deposited in an account paying 7% compounded quarterly, then what amount will be in the account after 8 years?

Q14) Write log₇(36) - log₇(6) as a single logarithm.

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Page 27

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

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Sample Questions

Q1) Rewrite the given equation in the standard form for the equation of a circle and identify its center and radius. x² - 2x + y² + 2y - 98 = 0

A) (x + 1)² + (y - 1)² = 10; (-1, 1); 10

B) (x - 1)² + (y + 1)² = 10; (1, -1); 10

C) (x - 1)² + (y + 1)² = 100; (1, -1); 10

D) (x + 1)² + (y - 1)² = 100; (-1, 1); 10

Q2) Find two complex numbers that have a sum of 12 and a product of 72.

A) 6 - 7i and 6 + 5i

B) 6 - 7i and 6 + 7i

C) 6 - 6i and 6 + 6i

D) 6 and 6

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. xy = 3 y = x

Q2) Find the center and radius for the given circle. 169 - x² = (y - 4)²

Q3) Write the standard equation for the circle with the given radius and center. Center (8, -5), radius 12

Q4) Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. (x + 1)² - y = 1

Q5) 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?

Q6) Find the midpoint and length of the line segment with the endpoints (5,9) and (8,14).

Q7) Write the given equation in the form y = a(x - h)² + k and identify the vertex, focus, and directrix. y = 6x² + 36x + 55

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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) a_n = 6n - 2

B) a_n = 7n - 3

C) a_n = 6n + 2

D) a_n = 2n - 6

Q2) 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

Q3) Write the first five terms of the arithmetic sequence whose nth term is given. a_n = -3 + (n - 2)(-3)

A) -6, -3, 0, 3, 6

B) 3, 0, -3, -6.0, -9

C) 3, 0, -3, -6, -9

D) 0, -3, -6, -9, -12

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Chapter 14: Section 2: Sequences and Series Available

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Sample Questions

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

Q2) List all terms of the finite sequence a_n = 3n + 2 for 1 n 5.

Q3) 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

Q4) 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 45^th year?

Q5) Write a formula for the nth term of the given arithmetic sequence. 1, 7, 13, 19, 25, . . .

Q6) 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.

Q7) Write the first four terms of the geometric sequence whose nth term is given. a_n = (-3)ⁿ^-1

Q8) Write a formula for the nth term of the given geometric sequence. 3, -9, 27, ... Page 31

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Chapter 15: Mathematical Problem Set

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Sample Questions

Q1) 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?

Q2) Solve the system of equations.

-0.75x + 3.5y = 3.125

0.6x + 1.5y = 1.8

Q3) Solve the given equation. y² + 6y + 8 = 0

Q4) Sarah has 15 coins (nickels, dimes, and quarters) in her piggy bank with a total value of $2.25. There are 3 more dimes than nickels. How many of each type of coin does Sarah have?

Q5) Perform the indicated operation. (s² - 5s + 5) - (s² - 4s - 6)

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) Simplify: u - 0.03(u - 300)

Q8) Find the product. (3a + 7)(a + 9)

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Chapter 16: Algebraic Equations and Problem Solving

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Sample Questions

Q1) 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)

Q2) Liam invested some money in the Abernathy Fund at 5% simple interest and twice as much at twice the rate in the Carlson Fund. If the simple-interest income from the two funds totalled $3055.75, then how much was invested in each fund?

A) $13,723 in Abernathy and $27,446 in Carlson

B) $14,323 in Abernathy and $28,646 in Carlson

C) $10,723 in Abernathy and $21,446 in Carlson

D) $12,223 in Abernathy and $24,446 in Carlson

Q3) Solve the given equation. x² + 10x + 24 = 0

A) 4, -6

B) -4, 6

C) -4, -6

D) 4, 6

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Chapter 17: Algebra and Math Problems

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Sample Questions

Q1) Use the binomial theorem to expand the given binomial. (m + 1)³

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

Q3) Raphael can load a large shipping truck in 15 hours. Working together, Raphael and Jana can load the same truck in 6 hours. How long would it take Jana to load the truck by herself?

Q4) Solve. (z - 8)^1/3 = -3

Q5) Find the sum of the given infinite geometric series. 36 + 30 + 25 + ...

Q6) If $1,300 is deposited in an account paying 11% compounded continuously, then what amount will be in the account after 3 years?

Q7) 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

Q8) Solve 3¹⁰^x^{- 8} = 9⁴^x^{- 1}.

Q9) Solve the given equation. t² + 6t + 5 = 0

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Chapter 18: Algebraic Equation Practice

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Sample Questions

Q1) Find the midpoint and length of the line segment with the endpoints (3,2) and (13,26).

A) (9, 15), 13

B) (8, 14), 13

C) (-2, -10), 26

D) (8, 14), 26

Q2) Together, Paul and Quincy weigh 357 pounds, Quincy and Ramon weigh 348 pounds, and Paul and Ramon weigh 337 pounds. How much does each weigh individually?

A) Paul = 175 lb., Quincy = 180 lb. , Ramon = 166 lb.

B) Paul = 163 lb., Quincy = 184 lb. , Ramon = 174 lb.

C) Paul = 173 lb., Quincy = 184 lb. , Ramon = 164 lb.

D) Paul = 181 lb., Quincy = 180 lb. , Ramon = 160 lb.

Q3) List all terms of the finite sequence a_n = n + 4 for 1 n 5.

A) 5, 9, 13, 17, 21

B) 4, 5, 6, 7, 8

C) 5, 6, 7, 8, 9

D) 4, 8, 12, 16, 20

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36