Remedial Mathematics Practice Exam - 840 Verified Questions

Remedial Mathematics Practice Exam

Course Introduction

Remedial Mathematics is designed to strengthen foundational mathematical skills for students who require additional support before undertaking college-level math courses. This course covers basic arithmetic operations, fractions, decimals, percentages, elementary algebra, and problem-solving strategies. Emphasis is placed on building confidence and proficiency in applying mathematical concepts to real-life situations, preparing students for more advanced mathematical studies and improving overall numeracy skills.

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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2

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) Evaluate the expression for b = 14 and c = 7: c² + 6b + 6

A) -41

B) 139

C) 97

D) -29

Answer: B

Q3) 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

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Chapter 1: Section 2: Real Numbers and Their Properties

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Sample Questions

Q1) Evaluate: 23 + (-24)

Answer: -1

Q2) Perform the indicated operation: 4 - (-12)

Answer: 16

Q3) Use the commutative and associative properties of multiplication and exponential notation to rewrite the given product. v²(v·13)(vw)

Answer: 13v⁴w

Q4) Determine the value of |-2|.

Answer: 2

Q5) 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

Q6) 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

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Chapter 2: Section 1: Linear Equations and Inequalities in

One Variable

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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) Find three consecutive integers whose sum is 81.

A) 25, 26, 27

B) 26, 28, 30

C) 26, 27, 28

D) 27, 28, 29

Answer: C

Q3) Write the appropriate inequality symbol in the blank so that the two inequalities are equivalent. 39 \(\ge\) 3r

13 _____ r

A) 13 \(\le\)0 r

B) 13 \(\ge\) r

C) 13 \(\lt\) r

D) 13 \(\gt\) r

Answer: B

Page 5

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Chapter 2: Section 2: Linear Equations and Inequalities in

One Variable

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Sample Questions

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

Q2) 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?

Q3) 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?

Q4) Find three consecutive integers whose sum is 216.

Q5) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity.

13y + 4y = 12y

Q6) Solve.

0.2n + 2.4 = 0.6n

Q7) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity.

80 - 5(t + 4) = 0

Page 6

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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) 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

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Chapter 3: Section 2: Linear Equations and Inequalities in

Two Variables

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Sample Questions

Q1) Find the x- and y-intercepts of x + 3y + 2 = 0 and use these intercepts to graph the equation.

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

Q5) Graph the line through (-1, 3) with slope -2.

Q6) Graph the equation y = -3x + 1.

Q7) Find the equation (in standard form) of the line through (2, 0) and (4, -1).

Q8) Find the slope of the line that contains the points (-11,2) and (8,-12).

Q9) Find the slope and the y-intercept of the line represented by 12x + 7y = 5.

Page 8

Q10) 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

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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 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

Q3) Multiply. (-4r - 9)²

A) 16r² + 72r + 81

B) -4r² + 72r + 81

C) 16r² + 81

D) 16r² + 36r + 81

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10

Chapter 4: Section 2: Exponents and Polynomials

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Sample Questions

Q1) The edges of a triangular homesite have lengths of 3x + 4, x, and x - 1. Write an expression for the perimeter of the property.

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

Q4) Find the product. -10t⁵·2t⁷

Q5) Find the product. (5w² - 4)(5w² - 1)

Q6) Write in scientific notation. 957 \(\times\)10³

Q7) Find the quotient and the remainder. (x⁴ - x³ + 5) \(\div\) (x² + 2)

Q8) Perform the indicated operation. (t - 5) - (5t - 8)

Q9) Perform the computation. (3 \(\times\)10^-14)²

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Chapter 5: Section 1: Factoring

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Sample Questions

Q1) 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)

Q2) 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)

Q3) Solve the given equation. w² = 8w

A) 8

B) 64

C) 0, 8

D) 8, -8

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Chapter 5: Section 2: Factoring

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Sample Questions

Q1) Factor.

uvw + 9u + 5vw + 45

Q2) Factor out the greatest common factor. (y - 6)4 + (y - 6)y

Q3) Factor.

9z² - 6z + 1

Q4) Factor the given polynomial completely. z⁶ + 2z³ - 3

Q5) Factor out the opposite of the greatest common factor. 10z³ - 2z²

Q6) Factor.

9y² - 100

Q7) Solve the given equation. x³ + 5x² - 2x - 24 = 0

Q8) Factor.

8x³ - 27

Q9) Solve the given equation. y² = 9y

Q10) Factor.

tu + 5u - 7t - 35

Page 13

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Page 14

Chapter 6: Section 1: Rational Expressions

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Sample Questions

Q1) Brandi bought a total of 6 lb of flounder and shrimp and paid $16 for the flounder and $16 for the shrimp. If the price per pound of the shrimp is twice that of the flounder, how many pounds of each did she buy?

A) 3 lb shrimp and 3 lb flounder

B) 1 lb shrimp and 5 lb flounder

C) 2 lb shrimp and 4 lb flounder

D) 4 lb shrimp and 2 lb flounder

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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15

Chapter 6: Section 2: Rational Expressions

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Sample Questions

Q1) 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?

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) 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?

Q4) 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?

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

Q6) 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?

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Chapter 7: Section 1: 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 224. Fred's score was 4 more than Tiger's, and Nancy's score was 6 more than Fred's. What was each person's score?

A) Fred = 74 ; Tiger = 70 ; Nancy = 80

B) Fred = 71 ; Tiger = 67 ; Nancy = 77

C) Fred = 76 ; Tiger = 72 ; Nancy = 82

D) Fred = 70 ; Tiger = 74 ; Nancy = 80

Q2) 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)}

Q3) 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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Page 17

Chapter 7: Section 2: Systems of Linear Equations

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Sample Questions

Q1) Solve the system of equations.

-x + 5y - 3z = 31

-4x - 5y + 4z = 6

3x - 15y + 9z = -91

Q2) Solve the system of linear equations by the substitution method.

-5x = -2y + 9

5x + 5y = -30

Q3) 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?

Q4) Solve the system of equations.

-3.5x + 3y = -5.375

-0.875x - 0.5y = 0.53125

Q5) 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?

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Chapter 8: Section 1: More on Inequalities

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Sample Questions

Q1) Solve: |x - 10| = 8

A) {2, 18}

B) {-18, 18}

C) {2}

D) {18}

Q2) Solve: -4 - |-11 - x| = -10

A) {-19, -3}

B) {-17, -5}

C) {-16, -2}

D) {-16, -4}

Q3) Trisha needs to adjust her cholesterol level to a target value of 150. She recalls that her cholesterol level differed from her target value by 16 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.

A) 118 or 134

B) 129 or 161

C) 134 or 166

D) 144 or 176

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19

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

Q3) 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

Q4) 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?

Q5) Solve: |x - 5| = 3

Q6) Solve: 12 - |-13 - x| = 2

Page 20

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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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Chapter 9: Section 2: Radicals and Rational Exponents

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Sample Questions

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

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

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

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

Q7) Evaluate. (27)^-4/3

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22

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) Solve by factoring: x² - x - 42 = 0

A) {-7, -6}

B) {-7, 6}

C) {-6, 7}

D) {6, 7}

Q3) 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

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23

Chapter 10: Section 2: Quadratic Equations and Inequalities

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Sample Questions

Q1) Solve by completing the square. 2x² - 5x + 1 = 0

Q2) 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?

Q3) Find all real solutions of the given equation. x^2/3 - 3x^1/3 - 10 = 0

Q4) Find all real and imaginary solutions to the equation. x^-2 - 3x^-1 + 5 = 0

Q5) Solve: (q - 6)² = 36

Q6) 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) = 0.02x² - 3x + 217.5. What number of batteries per hour minimizes the cost?

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) Graph the parabola. y = -x² + 4

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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) 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)

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25

Chapter 11: Section 2: Functions

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Sample Questions

Q1) Determine whether the given function is invertible. If it is invertible, then find its inverse. {(-5,4),(-1,1),(-13,5)}

Q2) How are the graphs of f(x) = x² and g(x) = x² + 7 related?

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

Q4) Determine whether f(x) = 2x and g(x) = 0.5x are inverses of each other. A)True

B)False

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

Q6) 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

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

Q8) Give the correct domain and range of the relation . {(-5, 4), (5, 4)}

26

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Chapter 12: Section 1: Exponential and Logarithmic Functions

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Sample Questions

Q1) 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)

Q2) Solve log₃(x² - 1) = 2 + log₃(x² + 2).

A) {-2, 1}

B) Ø

C) {19}

D) {4, 7}

Q3) Solve -8^-6-^x = -64.

A) {-8}

B) {0}

C) {-6}

D) {-7}

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Page 27

Chapter 12: Section 2: Exponential and Logarithmic Functions

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Sample Questions

Q1) Solve e^x^{+ 2} = 5.

Q2) Write ln(s⁵) + ln(s⁶) + ln(s) as a single logarithm. Assume s represents numbers for which the logarithms are defined.

Q3) Evaluate log_1/5(6). Round to four decimal places.

Q4) Write log₇(36) - log₇(6) as a single logarithm.

Q5) Solve log(x) = -4.

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

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

Q8) Write log(64) in terms of log(4).

Q9) Solve log₁₂(x - 35) + log₁₂(x + 35) = 2.

Q10) Write log₆216 = 3 as an exponential equation.

Q11) Simplify ln(e⁹).

Q13) Solve -7^-5-^x = -49. Page 28

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

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Sample Questions

Q1) Write the given equation in the form y = a(x - h)² + k and identify the vertex, focus, and directrix. y = 6x² + 36x + 55

Q2) Find the distance between (-10, 1) and (-12, 2).

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

(x + 9)² - y² = 1

Q4) Solve the given system of equations. x² + y² = 25 y = x² - 5

Q5) 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

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

-7x + y = -6

Q7) Solve the given system of equations. xy = 3

y = x

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Chapter 14: Section 1: Sequences and Series Available

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Sample Questions

Q1) 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

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

A) 1, -6, 36, -216

B) 0, -6, 36, -216

C) 1, 6, 36, 216

D) -6, 36, -216, 1296

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

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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. c_n = (-1)ⁿ(-4n + 3)²

Q3) Find r for the geometric sequence that has a₁ = 3 and a₄ = 192.

Q4) Use the binomial theorem to expand the given binomial. (b + 2)⁴

Q5) Write a formula for the nth term of the given geometric sequence. 3, -9, 27, ...

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, ...

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

Q8) List all terms of the finite sequence a_n = 3n + 2 for 1 n 5. Page 34

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Chapter 15: Mathematical Problem Set

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Sample Questions

Q1) Solve the given equation.

y² + 6y + 8 = 0

Q2) 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?

Q3) Find the equation (in standard form) of the line through (3, -7) and (5, -8).

Q4) Factor completely. If the polynomial is prime, say so.

9q² + 8q + 2

Q5) Solve and write your answer in interval notation. y + 6 < 7y - 36

Q6) Factor.

125x³ + 27

Q7) Determine whether 14 is a solution of 11x + 5 = 149.

A)True

B)False

Q8) 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?

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

Q10) Simplify: u - 0.03(u - 300)

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Chapter 16: Algebraic Equations and Problem Solving

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Sample Questions

Q1) 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

Q2) Factor the given polynomial completely. If the polynomial is prime, say so. y³- 8y² - 9y + 72

A) y(y + 3)(y - 8)

B) (y - 3)(y + 3)(y - 8)

C) The polynomial is prime. D) (y - 3)²(y - 8)

Q3) Find the product. (3b + 5)(b + 6)

A) b²+ 23b + 30

B) 3b²+ 23b + 30

C) 3b²+ 11b + 30

D) b²+ 9b + 18

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Chapter 17: Algebra and Math Problems

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Sample Questions

Q1) Solve 3¹⁰^x^{- 8} = 9⁴^x^{- 1}.

Q2) Use the binomial theorem to expand the given binomial. (m + 1)³

Q3) Write a formula for the nth term of the given arithmetic sequence. 6, 10, 14, 18, 22, . . .

Q4) The formulas

b = 0.03t + 2.13 and m = 0.22t + 1.12

give an approximate model for the yearly average price b of a bushel of barley and m of a bushel of millet over the past five years, where t is the number of years since 1994. What is the first year in which the price of barley exceeded $2.19/bu and the price of millet exceeded $2.00/bu? Show your work.

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

Q6) 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

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Chapter 18: Algebraic Equation Practice

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Sample Questions

Q1) 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 108 2\(\times\)4's and 180 1\(\times\)6's in his inventory. If tables sell for $50 and swings sell for $30, how many of each item should Conrad make in order to maximize his revenue?

A) 15 picnic tables and 10 porch swings

B) 0 picnic tables and 30 porch swings

C) 18 picnic tables and 0 porch swings

D) 12 picnic tables and 12 porch swings

Q2) Find the product. (2a + 6)(10a + 1)

A) 20a²+ 22a + 6

B) 20a²+ 19a + 6

C) 20a²+ 6a + 62

D) 20a²+ 62a + 6

Q3) Solve. (z + 4)^1/3 = -4

A) {-68, 68}

B) {-60}

C) {-68}

D) {-68, -60}

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