Algebra Fundamentals Textbook Exam Questions - 840 Verified Questions

Algebra Fundamentals

Textbook Exam Questions

Course Introduction

Algebra Fundamentals introduces students to the foundational concepts and techniques of algebra, emphasizing the use of variables, expressions, and equations to represent and solve mathematical problems. Topics include simplifying algebraic expressions, solving linear equations and inequalities, working with polynomials, exploring functions and their graphs, and applying algebraic reasoning to real-world scenarios. The course is designed to build essential problem-solving skills, foster logical thinking, and provide a solid base for subsequent study in mathematics and related disciplines.

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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Sample Questions

Q1) Evaluate: (-7 + 6)(-11 - 9)

A) 20

B) -82

C) 2

D) 260

Answer: A

Q2) 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

Q3) Determine the value of |-3|.

A) -3 or 3

B) 3

C) The expression is undefined.

D) -3

Answer: B

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Chapter 1: Section 2: Real Numbers and Their Properties

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Sample Questions

Q1) Use the distributive property to factor the expression. -35p + 20

Answer: 5(-7p + 4)

Q2) Evaluate: 7 - 3 · |3 - (5² - 2)| Answer: -53

Q3) Evaluate: 23 + (-24) Answer: -1

Q4) Translate the verbal expression into an algebraic expression: The difference of p and the square of a Answer: p - a²

Q5) Evaluate: (6 - 2)(5 - 12) Answer: -28

Q6) Evaluate: 11 - 14 + 10 - 15 Answer: -8

Q7) Write the interval of real numbers in interval notation. The set of real numbers less than -7 Answer: (- , -7)

Q8) Simplify: 2(m - 4) - 3(-m - 7) Answer: 5m + 13

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Chapter 2: Section 1: Linear Equations and Inequalities in

One Variable

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Sample Questions

Q1) Solve for x. 8(x - a) - (28b - x) = a - b

A) x = 4a + 3b

B) x = 4a + 4b

C) x = a + 3b

D) x = a + 4b

Answer: C

Q2) Cab drivers in Metro City charge $4 per mile plus a fixed charge of $2 for the tip. If a tourist pays $46 for a cab ride, then how many miles was the cab ride?

A) 10 miles

B) 13 miles

C) 14 miles

D) 11 miles

Answer: D

Q3) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. s + 6s = 7s

A) Ø, inconsistent

B) All real numbers, identity

C) {0}, conditional

Answer: B

5

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Chapter 2: Section 2: Linear Equations and Inequalities in

One Variable

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Sample Questions

Q1) Solve for x.

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

Q2) Translate into an algebraic expression. 35 decreased by the quotient of x and 10

Q3) Solve.

0.2n + 2.4 = 0.6n

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) 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.

Q6) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity.

13y + 4y = 12y

Q7) 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?

Q8) Solve and write your solution in interval notation. -17 < 28 - 9n \(\le\) 1

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Chapter 3: Section 1: Linear Equations and Inequalities in

Two Variables

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Sample Questions

Q1) Does the point (2, 14) satisfy the inequality y \(\le\) 2x - 2?

A)True

B)False

Q2) 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

Q3) Complete the ordered pair so that it satisfies the given equation. y = 7x - 13: (4, ___)

A) (4, 16)

B) (4, 28)

C) (4, 15)

D) (4, 41)

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Chapter 3: Section 2: Linear Equations and Inequalities in

Two Variables

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Sample Questions

Q1) Complete the ordered pair so that it satisfies the given equation. y = -4x + 3: (-10, ___)

Q2) Gotham City's budget deficit was $4.5 million in 1991 and $4.6 million in 2000. Find the slope of the line through (1991, 4.5) and (2000, 4.6) and interpret your result.

Q3) 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.

Q4) Find the slope and the y-intercept of the line represented by 12x + 7y = 5.

Q5) Does the point (-4, -1) satisfy the inequality y \(\le\) 6x - 5?

A)True

B)False

Q6) Line l goes through (1, 3) and is parallel to the line through (4, 3) and (-3, 1). Find the slope of l.

Q7) Find the slope of the line that contains the points (-11,2) and (8,-12).

Q8) 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.

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Chapter 4: Section 1: Exponents and Polynomials

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Sample Questions

Q1) Multiply. (4 + 3s)(4 - 3s)

A) 16 - 9s²

B) 9s² + 16

C) 16 - 24s + 9s²

D) 16 - 24s - 9s²

Q2) Simplify. 3p⁴·(p⁴)³

A) 3p²⁴

B) 3p⁴⁸

C) 3p¹¹

D) 3p¹⁶

Q3) Simplify. (st⁵)⁶

A) st¹¹

B) st³⁰

C) s⁶t¹¹

D) s⁶t³⁰

Q4) Find the product. (x + 2)(x - 3)(x + 6)

A) x³+ 15x² + 12x - 36

B) x³+ 5x² + 12x + 36

C) x³+ 11x² + 36x + 36

D) x³+ 5x² - 12x - 36

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Chapter 4: Section 2: Exponents and Polynomials

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Sample Questions

Q1) Find the product. (n + 2)(n - 3)(n + 4)

Q2) What is the coefficient of x³ in the polynomial -11x³ + 13x²?

Q3) Perform the indicated operation. (t - 5) - (5t - 8)

Q4) Perform the indicated operation. (-4m - 7) + (m² + 7m + 6)

Q5) Find the product. -10t⁵·2t⁷

Q6) Find the indicated value of the polynomial. P(x) = -4.1x³ - 1.2x² - 1.1, P(0.8)

Q7) Find the product. (5w² - 4)(5w² - 1)

Q8) Expand the binomial. (n - 2)³

Q9) 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.

Q10) Simplify.

5y⁴·(y⁴)⁵ Page 10

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Chapter 5: Section 1: Factoring

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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) Factor. 16r² - 25

A) The expression is prime.

B) (4r - 5)²

C) (4r - 5)(4r + 5)

D) (16r - 5)(16r + 5)

Q3) Factor. vw - 9w - 2v + 18

A) (v - 9)(w - 2)

B) The expression is prime.

C) (v + 9)(w + 2)

D) (v - 2)(w - 9)

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Page 12

Chapter 5: Section 2: Factoring

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Sample Questions

Q1) Factor the given polynomial completely. If the polynomial is prime, say so. c³+ cd + 3c² + 3d

Q2) Factor out the opposite of the greatest common factor. 10z³ - 2z²

Q3) Find the prime factorization. 115

Q4) Factor the given polynomial completely. 7p²q - 28pq + 21q

Q5) Find the greatest common factor for the given numbers. 36, 80, 120

Q6) Factor out the greatest common factor. -63q²r² - 45q²r + 54qr²

Q7) Factor the polynomial below completely, given that the binomial following it is a factor of the polynomial. u³ + 2u² - 11u - 12, u - 3

Q8) Factor completely. 8u³v - 392uv

Q9) Factor. 9y² - 100

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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) 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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Sample Questions

Q1) 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?

Q2) 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?

Q3) 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.

Q4) 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?

Q5) Find the least common multiple of the given terms. q² + 7q - 30, q² + 20q + 100

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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Chapter 7: Section 1: Systems of Linear Equations

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Sample Questions

Q1) Solve the system of linear equations by the substitution method. 8x = -3y - 15

5x - 8y = 40

A) {(-2, -4)}

B) {(0, -5)}

C) No solution. The system is inconsistent.

D) {(2, -2)}

Q2) Solve the system of equations. -3x + 3y - 4z = -58

5x + 2y - z = 1

-4x - 3y + 3z = 23

A) {(4, -4, 2)}

B) {(1, -6, 7)}

C) {(4, -6, 7)}

D) {(-6, 6, 5)}

Q3) 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)}

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Page 16

Chapter 7: Section 2: Systems of Linear Equations

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Sample Questions

Q1) 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?

Q2) 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?

Q3) Solve the system of equations.

-x + 5y - 3z = 31

-4x - 5y + 4z = 6

3x - 15y + 9z = -91

Q4) 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 3 is 17 times the probability of successfully rolling a total of 3. The total probability (probability of failing to roll a 3 + probability of successfully rolling a 3) is 1. What is the probability of rolling a 3?

Q5) 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?

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Chapter 8: Section 1: More on Inequalities

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Sample Questions

Q1) Determine whether the absolute value inequality is equivalent to the inequality following it: |4 - x| < 14, 4 - x < 14 and -(4 - x) < 14

A)True

B)False

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

Q3) Determine if the compound inequality is true: 4 \(\le\) 4 and 4 > 0

A)True

B)False

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Chapter 8: Section 2: More on Inequalities

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Sample Questions

Q1) Trisha needs to adjust her cholesterol level to a target value of 170. She recalls that her cholesterol level differed from her target value by 6 units, but does not recall whether she is above or below the target value. Use an absolute value equation to find the possible values for Trisha's cholesterol level.

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) Graph the solution set for the following system of inequalities and identify each vertex of the region.

x \(\ge\) 0, y \(\ge\) 0

2x + y \(\ge\) 4

2x + 3y \(\ge\) 7

Q4) Solve: 12 - |-13 - x| = 2

Q5) Kara works at a bakery and can prepare a birthday cake in 4 hours. It takes her 5 hours to prepare a wedding cake. Kara works a 40-hour week and she must bake more wedding cakes than birthday cakes. Draw a graph that illustrates the number of each type of cake Kara can bake per week.

Q6) Write as a single interval if possible: [-1, \(\infty\))\(\cup\)(4, \(\infty\))

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

Q2) Find all real solutions. (s + 3)² - 5 = 0

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

Q4) The diagonal of a square measures 8 inches. What is the length of the sides?

Q5) Simplify.

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

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

Q7) Find the difference. (-5 - 10i) - (-7 - 3i)

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Chapter 10: Section 1: Quadratic Equations and Inequalities

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Sample Questions

Q1) A battery manufacturing plant spends C dollars per hour to produce "D"-size batteries. An efficiency consultant has determined that C is related to the number of batteries produced per hour, x, according to the equation C(x) = 0.01x²2.4x + 224. What number of batteries per hour minimizes the cost?

A) 224 batteries

B) 130 batteries

C) 80 batteries

D) 120 batteries

Q2) 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

Q3) Solve: (x - 7)² = 100

A) {-3, 17}

B) {3, 17}

C) {-3, 3}

D) {17, 17}

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Chapter 10: Section 2: Quadratic Equations and Inequalities

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Sample Questions

Q1) Find all real and imaginary solutions to the equation. t⁴ - 6561 = 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) Write a quadratic equation that has the solutions 8 and 1.

Q4) Find b² - 4ac and the number of real solutions for the given equation. x² - 2x + 1 = 0

Q5) 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?

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

Q7) Find all real solutions of the given equation. (x² + 1)² - 11(x² + 1) = -10

Q8) Solve by completing the square. 2x² - 5x + 1 = 0

Q9) Solve: (q - 6)² = 36

Page 23

Q10) Complete the ordered pair so that it satisfies the given equation. y = x² + 4x + 2, (4, )

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Chapter 11: Section 1: Functions

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Sample Questions

Q1) 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)

Q2) Determine whether the given function is invertible. If it is invertible, then find its inverse. Match your results to the correct answer below. {(-10,-13),(-8,-2),(1,-7)}

A) No

B) Yes ; {(-13,-10),(-2,-8),(-7,1)}

C) Yes ; {(-10,13),(-8,2),(1,7)}

D) Yes ; {(10,13),(8,2),(-1,7)}

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

A)True

B)False

Q2) Determine whether the given function is invertible. If it is invertible, then find its inverse.

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

Q3) How are the graphs of f(x) = (x + 4)² and g(x) = -(x + 4)² 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) 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).

Q6) How are the graphs of f(x) = x² and g(x) = x² + 7 related?

Q7) Determine whether the relation |2x| = |-8y| is a function.

A)True B)False

Q8) Let f(x) = -2x - 4 and g(x) = x² + 10x. Find (f ·g)(4).

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Chapter 12: Section 1: Exponential and Logarithmic Functions

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Sample Questions

Q1) Solve -8^-6-^x = -64.

A) {-8}

B) {0}

C) {-6}

D) {-7}

Q2) Write log₈64 = 2 as an exponential equation.

A) 8² = 64

B) 8² = 8

C) 64² = 8

D) 64² = 64

Q3) Solve log(x) = 1.

A) {10}

B) {1}

C) no solution

D) {0.1}

Q4) Write 2⁵ = 32 as a logarithmic equation.

A) log₂5 = 32

B) log₂32 = 2

C) log₅32 = 2

D) log₂32 = 5

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Chapter 12: Section 2: Exponential and Logarithmic Functions

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Q1) Solve log₁₂(x - 35) + log₁₂(x + 35) = 2.

Q2) Write log(64) in terms of log(4).

Q3) Solve log₂(x² - 2) = 2 + log₂(x² + 8).

Q4) Write ln(s⁵) + ln(s⁶) + ln(s) as a single logarithm. Assume s represents numbers for which the logarithms are defined.

Q5) Evaluate log_1/5(6). Round to four decimal places.

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

Q7) Solve log(x) = -4.

Q8) Simplify ln(e⁹).

Q9) Write log₇(36) - log₇(6) as a single logarithm.

Q10) Solve e^x^{+ 2} = 5.

Q11) If $10,000 is deposited in an account paying 7% compounded quarterly, then what amount will be in the account after 8 years?

Q12) Write 3⁶ = 729 as a logarithmic equation.

Q13) Write log₆216 = 3 as an exponential equation. Page 27

Q14) Solve -7^-5-^x = -49.

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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. 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)}

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Page 29

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

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Q1) Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola.

(x + 9)² + 3y² = 1

Q2) Solve the given system of equations.

y = x² + 4

-7x + y = -6

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

(x + 5)² + y² = 1

Q4) 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?

Q5) 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

Q6) 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) List the first four terms of the given sequence and match your result to the correct answer below. c_n = (-1)ⁿ(-2n + 3)²

A) 1, -1, 9, -25

B) 1, -1, 1, -9

C) 1, -9, 25, -49

D) -1, 1, -9, 25

Q2) 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%

Q3) Write a formula for the nth term of the given geometric sequence. 3, -6, 12, ...

A) a_n = -3(2)ⁿ^-1

B) a_n = 3(-2)ⁿ⁺¹

C) a_n = 3(-2)ⁿ^-1

D) a_n = 3(-2)ⁿ

Page 31

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Chapter 14: Section 2: Sequences and Series Available

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21 Verified Questions

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Sample Questions

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.

c_n = (-1)ⁿ(-4n + 3)²

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

Q4) List all terms of the given finite sequence and match your result to the correct answer below.

c_n = (-2)^n-³ for 3 \(\le\) n \(\le\) 7

Q5) 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?

Q6) 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, ...

Page 32

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Chapter 15: Mathematical Problem Set

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Sample Questions

Q1) Perform the indicated operation. (s² - 5s + 5) - (s² - 4s - 6)

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

Q4) Factor.

125x³ + 27

Q5) Find the product. (3a + 7)(a + 9)

Q6) Find the equation (in standard form) of the line through (3, -7) and (5, -8).

Q7) Factor completely. If the polynomial is prime, say so. 9q² + 8q + 2

Q8) 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?

Q9) Does the point (5, -12) satisfy the inequality y \(\ge\) 15x + 12?

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Chapter 16: Algebraic Equations and Problem Solving

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Sample Questions

Q1) Solve the system of equations. 0.25x + 3.5y = -3.6875

-1)4x - 2.5y = 3.55

A) {(-0.75, -1)}

B) {(0.75, -1)}

C) {(-0.25, -0.5)}

D) {(0.75, 1)}

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

A) (- , 3)

B) (6, )

C) (5, )

D) (3, )

Q3) 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

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34

Chapter 17: Algebra and Math Problems

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Sample Questions

Q1) Find four consecutive integers whose sum is 138.

Q2) Factor: 125x³ + 27

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

Q4) 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

Q5) Find the midpoint and length of the line segment with the endpoints (2,2) and (12,26).

Q6) Solve the given equation. t² + 6t + 5 = 0

Q7) 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

Q8) Which, if any, of the ordered pairs (1, 2), (-1, 4), (-1, -1), and (5, -3) satisfy the system of inequalities? x - y > 0 4x² + y² 4

Q9) Find the inverse of the given function and include any domain restrictions. f (x) = (x - 4)²

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Chapter 18: Algebraic Equation Practice

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Sample Questions

Q1) Simplify: y - (6y + 5)

A) 7y - 5

B) -5y + 5

C) -5y - 5

D) 7y + 5

Q2) 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

Q3) 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)

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Page 36