Precalculus Test Preparation

Course Introduction

Precalculus serves as a foundational course that prepares students for the study of calculus by covering essential mathematical concepts and skills. The course focuses on functions and their properties, including polynomial, rational, exponential, logarithmic, and trigonometric functions. Students learn to analyze, graph, and apply these functions to solve real-world problems. Additional topics such as sequences, series, complex numbers, and conic sections are also explored to strengthen algebraic and analytical thinking. Emphasis is placed on developing problem-solving abilities and mathematical reasoning, laying the groundwork for success in subsequent calculus 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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Chapter 1: Section 1: Real Numbers and Their Properties

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Sample Questions

Q1) Translate the given sentence into an equation: "The product of n - 8 and n - 12 is 5."

A) (n - 8)(n - 12) = 5

B) (n - 8)(n - 12)(5)

C) n - 8n - 12 = 5

D) (n - 8) + (n - 12) = 5

Answer: A

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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Chapter 1: Section 2: Real Numbers and Their Properties

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Sample Questions

Q1) Translate the given sentence into an equation: "The product of n + 14 and n + 7 is 1."

Answer: (n + 14)(n + 7) = 1

Q2) Evaluate: (5)(10)

Answer: 50

Q3) Use the appropriate properties to evaluate 1822(4·10 - 40).

Answer: 0

Q4) Evaluate: (6 - 2)(5 - 12)

Answer: -28

Q5) Translate the verbal expression into an algebraic expression: The difference of p and the square of a Answer: p - a2

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

Q7) Evaluate: 0 $\div$ 2

Answer: 0

Q8) Convert to a percent and a fraction: 0.7

Answer: 70%, 11ea9079_e301_cd10_aec7_0df6f8cf357c_TB3543_11

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Chapter 2: Section 1: Linear Equations and Inequalities in

One Variable

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Sample Questions

Q1) 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

Q2) The length of a rectangle must be 6 centimeters more than the width, and the perimeter must be at least 36 centimeters. What is the range of values for the width?

A) At least 6 centimeters

B) At least 12 centimeters

C) No more than 12 centimeters

D) At most 6 centimeters

Answer: A

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Chapter 2: Section 2: Linear Equations and Inequalities in

One Variable

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Sample Questions

Q1) How many pints of a 9% cleaning solution must be mixed with 2 pints of a 13% cleaning solution to give a 11% solution?

Q2) Write the appropriate inequality symbol in the blank so that the two inequalities are equivalent.

-55 $\ge$ 5y -11 _____ y

Q3) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. 13y + 4y = 12y

Q4) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. p - 8 = p + 8

Q5) Solve and write your solution in interval notation. -17 < 28 - 9n $\le$ 1

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

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

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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) 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

Q3) A playground equipment manufacturer plans to spend $300,000 on a new facility plus $160 for each swing set made.The formula C = 160n + 300,000 gives the cost in dollars to manufacture n swing sets. What is the marginal cost of the nth swing set? [Hint - the marginal cost of the nth swing set is the difference in cost of producing n + 1 swing sets and n swing sets).

A) $170

B) $160

C) $300,000

D) $320

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Chapter 3: Section 2: Linear Equations and Inequalities in

Two Variables

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Sample Questions

Q1) Find the equation (in standard form) of the line through (2, 0) and (4, -1).

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 9 hours.

Q3) 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.

Q4) 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).

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

Page 8

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Chapter 4: Section 1: Exponents and Polynomials

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Sample Questions

Q1) A shipping carton has a length of 2x + 3, width of 3x, and a height of x. Write an expression for the volume of the box.

A) 5x3 + 9x2

B) 6x3 + 9x

C) 6x2 + 9x

D) 6x3 + 9x2

Q2) Find the product. -5y7·2y2

A) -10y9

B) -10y14

C) -5y7.2y2

D) -3y9

Q3) Simplify. (st5)6

A) st11

B) st30

C) s6t11

D) s6t30

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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) Simplify. (xy3)3

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

Q4) Perform the computation. (3 $\times$10-14)2

Q5) Perform the indicated operation. (-4m - 7) + (m2 + 7m + 6)

Q6) The edges of a triangular homesite have lengths of 3x + 4, x, and x - 1. Write an expression for the perimeter of the property.

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

Q8) Find the product. -10t5·2t7

Q9) Find the product. (5w2 - 4)(5w2 - 1)

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Chapter 5: Section 1: Factoring

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Sample Questions

Q1) Factor the polynomial below completely, given that the binomial following it is a factor of the polynomial. n3 + 4n2 - 9n - 36, n + 3

A) (n + 3)(n2 - 7n - 12)

B) (n + 3)(n + 3)(n - 4)

C) (n + 3)(n2 + n - 12)

D) (n + 3)(n - 3)(n + 4)

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. 36u2 - 12u + 1

A) The expression is prime.

B) (6u - 1)2

C) (6u - 1)(6u + 1)

D) (6u + 1)2

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Chapter 5: Section 2: Factoring

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Sample Questions

Q1) Factor.

q2 + 6qr + 36r2

Q2) Factor.

uvw + 9u + 5vw + 45

Q3) Factor the given polynomial completely. z6 + 2z3 - 3

Q4) Find the prime factorization. 115

Q5) Find the greatest common factor of the given terms. 8qr, 28rs, 12qs

Q6) Solve the given equation.

x3 + 5x2 - 2x - 24 = 0

Q7) Factor.

9y2 - 100

Q8) Factor the polynomial below completely, given that the binomial following it is a factor of the polynomial.

u3 + 2u2 - 11u - 12, u - 3

Q9) 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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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) 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

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Chapter 6: Section 2: Rational Expressions

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Sample Questions

Q1) Find the least common multiple of the given terms. q2 + 7q - 30, q2 + 20q + 100

Q2) 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?

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) 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.

Q5) 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?

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

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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) 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

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Chapter 7: Section 2: Systems of Linear Equations

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Sample Questions

Q1) Solve the system of equations.

-3.5x + 3y = -5.375

-0.875x - 0.5y = 0.53125

Q2) Solve the system of equations.

-x + 5y - 3z = 31

-4x - 5y + 4z = 6

3x - 15y + 9z = -91

Q3) 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?

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) 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

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

A)True B)False

Q3) Solve: |x - 10| = 8

A) {2, 18}

B) {-18, 18}

C) {2}

D) {18}

Q4) 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

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Chapter 8: Section 2: More on Inequalities

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Sample Questions

Q1) 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

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) 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.

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

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

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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. -10(x - 3)3 = 0

Q2) Evaluate.

(27)-4/3

Q3) Simplify.

492/3 $\div$ 491/6

Q4) Find all real solutions. (s + 3)2 - 5 = 0

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

Q6) Find all real solutions. (u - 2)-1/3 = 1

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

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Chapter 10: Section 1: Quadratic Equations and Inequalities

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Sample Questions

Q1) Complete the ordered pair so that it satisfies the given equation. y = x210x - 5, (-10, )

A) (-10, 195)

B) (-10, 194)

C) (-10, 200)

D) (-10, 196)

Q2) Find the imaginary solutions: x2 - 18x + 117 = 0

A) {9 + 6i, 9 - 6i}

B) {9 + 6i}

C) {-9 - 6i, 9 + 6i}

D) {9 + 6i, -9 + 6i}

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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Sample Questions

Q1) 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?

Q2) Solve by factoring: x2 - 5x - 50 = 0

Q3) Find all real and imaginary solutions to the equation. x-2 - 3x-1 + 5 = 0

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

Q5) Write a quadratic equation that has the solutions 8 and 1.

Q6) Find b2 - 4ac and the number of real solutions for the given equation. x2 - 2x + 1 = 0

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

Q8) Complete the ordered pair so that it satisfies the given equation. y = x2 + 4x + 2, (4, )

Q9) Graph the parabola. y = -x2 + 4

Page 22

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

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Chapter 11: Section 1: Functions

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Sample Questions

Q1) 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)}

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

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

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

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

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

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Chapter 11: Section 2: Functions

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Sample Questions

Q1) Let f(x) = -2x - 4 and g(x) = x2 + 10x. Find (f ·g)(4).

Q2) 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

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

Q4) 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).

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

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

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Chapter 12: Section 1: Exponential and Logarithmic Functions

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Sample Questions

Q1) Simplify ln(e12).

A) 12

B) -12

C) e

D) 12 ln(e12)

Q2) Write log864 = 2 as an exponential equation.

A) 82 = 64

B) 82 = 8

C) 642 = 8

D) 642 = 64

Q3) Write 25 = 32 as a logarithmic equation.

A) log25 = 32

B) log232 = 2

C) log532 = 2

D) log232 = 5

Q4) Write log9(28) - log9(7) as a single logarithm.

A) 935

B) The logarithms cannot be combined.

C) log9(4)

D) log9(35)

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Chapter 12: Section 2: Exponential and Logarithmic Functions

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Sample Questions

Q1) Solve -7-5-x = -49.

Q2) Solve log12(x - 35) + log12(x + 35) = 2.

Q3) Solve ex + 2 = 5.

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

Q5) If $10,000 is deposited in an account paying 7% compounded quarterly, then what amount will be in the account after 8 years?

Q6) Evaluate log1/5(6). Round to four decimal places.

Q7) Write log7(36) - log7(6) as a single logarithm.

Q8) Simplify ln(e9).

Q9) Write log(64) in terms of log(4).

Q10) Write 36 = 729 as a logarithmic equation.

Q11) Write log6216 = 3 as an exponential equation.

Q13) Rewrite log(75) in terms of log(3) and log(5). Page 26

Q12) Solve log2(x2 - 2) = 2 + log2(x2 + 8).

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Page 27

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) 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

Q3) 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

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

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Sample Questions

Q1) 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

Q2) Write the given equation in the form y = a(x - h)2 + k and identify the vertex, focus, and directrix.

y = 6x2 + 36x + 55

Q3) Find two complex numbers that have a sum of -14 and a product of 58.

Q4) Solve the given system of equations.

xy = 3

y = x

Q5) Solve the given system of equations.

y = x2 + 4

-7x + y = -6

Q6) Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola.

(x + 9)2 + 3y2 = 1

Page 29

Q7) Find the midpoint and length of the line segment with the endpoints (5,9) and (8,14).

Q8) Find the distance between (-10, 1) and (-12, 2).

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Chapter 14: Section 1: Sequences and Series Available

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Q1) Write the first five terms of the arithmetic sequence whose nth term is given. an = -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

Q2) 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

Q3) Suppose a deposit of $500 is made at the beginning of each year for 15 years into an account that pays 9% compounded annually. What is the amount of this annuity at the end of the 15th year?

A) $16,501.70

B) $18,486.85

C) $13,009.59

D) $16,001.70

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Chapter 14: Section 2: Sequences and Series Available

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Sample Questions

Q1) List all terms of the finite sequence an = 3n + 2 for 1 n 5.

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

Q4) Write a formula for the nth term of the given arithmetic sequence. 1, 7, 13, 19, 25, . . .

Q5) Use the binomial theorem to write out the first four terms of the given binomial. (x2 + 1)22

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

Q8) Write the first four terms of the geometric sequence whose nth term is given. an = (-3)n-1

Q9) Write the first five terms of the arithmetic sequence whose nth term is given. an = -1 + (n + 1)(2) Page 32

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Chapter 15: Mathematical Problem Set

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Sample Questions

Q1) Factor completely. If the polynomial is prime, say so. 9q2 + 8q + 2

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

Q4) 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.

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

Q6) Simplify: u - 0.03(u - 300)

Q7) Find the product. (3a + 7)(a + 9)

Q8) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. 4x - x = 3x

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Chapter 16: Algebraic Equations and Problem Solving

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Q1) The temperature T of a gas sample varies jointly as the pressure P and the volume V. If the temperature is 297 kelvin when the volume is 4.6 liters and the pressure is 1.2 atmospheres, then what is its temperature if the gas is compressed to 1.5 liters at 2.9 atmospheres? Round your answer to the nearest tenth of a kelvin. [The unit "kelvin" is simply a temperature unit related to the Celsius degree. The exact relationship between the two plays no part in the solution of this problem.]

A) 230.8 kelvin

B) 234.0 kelvin

C) 198.9 kelvin

D) 242.9 kelvin

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

A) Length 22 yd, width 14 yd

B) Length 40 yd, width 24 yd

C) Length 18 yd, width 14 yd

D) Length 20 yd, width 12 yd

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Chapter 17: Algebra and Math Problems

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Q1) Find the inverse of the given function and include any domain restrictions. f (x) = (x - 4)2

Q2) Factor: 125x3 + 27

Q3) List all terms of the finite sequence an = n + 6 for 1 n 5.

Q4) Together, Paul and Quincy weigh 333 pounds, Quincy and Ramon weigh 326 pounds, and Paul and Ramon weigh 325 pounds. How much does each weigh individually?

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) 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

Q7) The owner of a hobby store bought a case of 9-volt batteries for $70.00. He marked the price up such that his profit was $2.80 per battery. After selling 20 batteries, the store owner had recovered his cost. How many 9-volt batteries are in a case?

Q8) Solve the given equation. t2 + 6t + 5 = 0

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Chapter 18: Algebraic Equation Practice

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Q1) Find all real solutions of the given equation. (x2 - x)239(x2 - x) - 126 = 0

A) {-7, 6}

B) {-7, 3, 6}

C) {-6, -3, 7}

D) {-6, 7}

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 an = 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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