Precalculus Practice Questions - 840 Verified Questions

Precalculus Practice Questions

Course Introduction

Precalculus is a foundational mathematics course designed to prepare students for the study of calculus. It covers a range of essential topics such as algebraic functions, polynomial and rational functions, exponential and logarithmic functions, trigonometry, complex numbers, vectors, and basic analytic geometry. The course emphasizes the development of problem-solving skills and mathematical reasoning, enabling students to manipulate and analyze functions, understand their properties, and apply their knowledge to real-world scenarios. By establishing a strong mathematical foundation, precalculus helps students transition with confidence into calculus and other higher-level math 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) Use the commutative and associative properties of multiplication and exponential notation to rewrite the given product. r²(r·10)(rs)

A) 10r³s

B) 10r⁴s²

C) 10rs

D) 10r⁴s

Answer: D

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

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3

Chapter 1: Section 2: Real Numbers and Their Properties

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Sample Questions

Q1) Combine like terms if possible: 7z - (-12z)

Answer: 19z

Q2) Write as a product without exponents: 12⁴

Answer: 12·12·12·12

Q3) Perform the indicated operation: 4 - (-12)

Answer: 16

Q4) Evaluate the expression for b = -10 and c = -11: c² - 3b - 1

Answer: 150

Q5) Evaluate: 7 - 3 · |3 - (5² - 2)|

Answer: -53

Q6) Evaluate: (5)(10)

Answer: 50

Q7) Convert to a percent and a fraction: 0.7

Answer: 70%, 11ea9079_e301_cd10_aec7_0df6f8cf357c_TB3543_11

Q8) 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 7 seconds?

Answer: 784 ft

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Chapter 2: Section 1: Linear Equations and Inequalities in

One Variable

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Sample Questions

Q1) 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

Q2) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. v - 11 = v + 11

A) Ø, inconsistent

B) All real numbers, identity

C) {0}, conditional

Answer: A

Q3) Solve and write your solution in interval notation. -21 < 33 - 9x \(\le\) -3

A) [4, 6)

B) Ø

C) [2, 6)

D) (2, 6]

Answer: A

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Chapter 2: Section 2: Linear Equations and Inequalities in

One Variable

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Sample Questions

Q1) 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?

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

-55 \(\ge\) 5y

-11 _____ y

Q3) Solve for x. 4(x - a) - (26b - x) = a - b

Q4) Solve and write your solution in interval notation. -17 < 28 - 9n \(\le\) 1

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

80 - 5(t + 4) = 0

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

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

Q8) Translate into an algebraic expression. 35 decreased by the quotient of x and 10

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

A)True

B)False

Q3) 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

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

Q3) Find the x- and y-intercepts of x + 3y + 2 = 0 and use these intercepts to graph the equation.

Q4) Does the point (-4, -1) satisfy the inequality y \(\le\) 6x - 5? A)True B)False

Q5) Complete the ordered pair so that it satisfies the given equation. y = -4x + 3: (-10, ___)

Q6) Write a formula that expresses the relationship described below. Use k as a constant of variation. P varies directly with T

Q7) Graph the line through (-1, 3) with slope -2.

Q8) 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

Q9) Find the slope of the line that contains the points (-11,2) and (8,-12). Page 8

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Page 9

Chapter 4: Section 1: Exponents and Polynomials

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Sample Questions

Q1) Simplify. 3p⁴·(p⁴)³

A) 3p²⁴

B) 3p⁴⁸

C) 3p¹¹

D) 3p¹⁶

Q2) Find the product. (4t² + 1)(6t² - 3)

A) 24t⁴ - 12t² - 3

B) 24t⁴ + 6t² - 3

C) 24t⁴ - 6t² - 3

D) 24t⁴ - 6t² + 3

Q3) Expand the binomial. (s + 3)³

A) s³ + 9s² + 27s + 9

B) s³ + 9s² + 27s + 27

C) s³ + 9s² - 27s + 27

D) s³ + 27

Q4) Find the product. -5y⁷·2y²

A) -10y⁹

B) -10y¹⁴

C) -5y⁷.2y²

D) -3y⁹

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Chapter 4: Section 2: Exponents and Polynomials

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Sample Questions

Q1) Find the quotient and the remainder. (x⁴ - x³ + 5) \(\div\) (x² + 2)

Q2) Multiply. (6 + 5x)(6 - 5x)

Q3) Perform the computation. (3 \(\times\)10^-14)²

Q4) Write in scientific notation. 957 \(\times\)10³

Q5) Simplify. 5y⁴·(y⁴)⁵

Q6) Find the product. (x² + 5x - 2)(-x - 8)

Q7) Simplify. (xy³)³

Q8) State the degree of the polynomial and determine if it is a monomial, binomial, or trinomial. x⁴

Q9) Find the product. -10t⁵·2t⁷

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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. 125x³ - 27

A) (5x - 3)(25x² - 15x + 9)

B) (5x + 3)(25x² - 30x + 9)

C) (5x + 3)(25x² - 15x + 9)

D) (5x - 3)(25x² + 15x + 9)

Q3) Solve the given equation. v³ - 3v² - 13v + 15 = 0

A) -3, 1, 5

B) 3, -1

C) 1, 5

D) 3, 1, -5

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Chapter 5: Section 2: Factoring

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Sample Questions

Q1) Factor completely.

8u³v - 392uv

Q2) Factor the given polynomial completely. z⁶ + 2z³ - 3

Q3) 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?

Q4) Find the prime factorization. 115

Q5) Factor the given polynomial completely. x⁴+ y⁴

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

Q7) Factor. 8x³ - 27

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

Q9) Factor out the opposite of the greatest common factor. 10z³ - 2z²

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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) 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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14

Chapter 6: Section 2: Rational Expressions

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Sample Questions

Q1) 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.

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) 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) 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) 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 7 is 5 times the probability of successfully rolling a total of 7. The total probability (probability of failing to roll a 7 + probability of successfully rolling a 7) is 1. What is the probability of rolling a 7?

A) 1 in 6

B) 1 in 18

C) 1 in 9

D) None of these.

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

-0)875x + 1.5y = 2.8125

A) {(-1, 1.5)}

B) {(0, 1)}

C) {(0, 3)}

D) {(-1.5, 1)}

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16

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.

3x - 2y + 4z = 12

-5x - y - z = -10

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

Q3) Solve the system of linear equations by the substitution method. Then, state whether the system is independent, dependent, or inconsistent.

4x - 3y = 4

12x - 9y = 12

Q4) Solve the system of linear equations by the substitution method.

-5x = -2y + 9

5x + 5y = -30

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: -4 - |-11 - x| = -10

A) {-19, -3}

B) {-17, -5}

C) {-16, -2}

D) {-16, -4}

Q2) Solve the inequality and write the solution set in interval notation. 3 < |x| - 2

A) (-\(\infty\), -5) \(\cup\) (5, \(\infty\))

B) (-\(\infty\), -5) \(\cap\) (5, \(\infty\))

C) (-5, 5)

D) (5, \(\infty\))

Q3) Solve: |x - 10| = 8

A) {2, 18}

B) {-18, 18}

C) {2}

D) {18}

Q4) 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) Solve: |x - 5| = 3

Q2) Solve the inequality and write the solution set in interval notation.

5 < |x| - 10

Q3) Solve: 12 - |-13 - x| = 2

Q4) Determine whether the absolute value inequality is equivalent to the inequality following it:

|-2 - x| < 14, -2 - x < 14 and -(-2 - x) < 14

A)True

B)False

Q5) Write as a single interval if possible: [-1, \(\infty\))\(\cup\)(4, \(\infty\))

Q6) Determine if the compound inequality is true: 10 \(\le\) 10 and 10 > 0 A)True

B)False

Q7) 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?

Page 19

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

Q3) Evaluate. (27)^-4/3

Q4) Simplify.

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

Q5) Find all real solutions. (u - 2)^-1/3 = 1

Q6) Find all real solutions. -10(x - 3)³ = 0

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) Find all real solutions of the given equation. (x² + 1)²18(x² + 1) = -17

A) {5, 3}

B) {0, 5, 3}

C) {0, ±4}

D) {±16}

Q2) Complete the ordered pair so that it satisfies the given equation. y = x² - 10x - 5, (-10, )

A) (-10, 195)

B) (-10, 194)

C) (-10, 200)

D) (-10, 196)

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

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

Q4) 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?

Q5) Solve the given inequality and express the solution in interval notation. x² - 4x \(\ge\) 0

Q6) Complete the ordered pair so that it satisfies the given equation. y = x² + 4x + 2, (4, )

Q7) Graph the parabola. y = -x² + 4

Q8) Solve by factoring: x² - 5x - 50 = 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) 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) = (x + 4)² and g(x) = -(x + 4)² related?

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

Q4) Let f(x) = -2x - 4 and g(x) = x² + 10x. Find (f ·g)(4).

Q5) 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

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

Q7) Give the correct domain and range of the relation . {(-5, 4), (5, 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).

25

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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 log₇(x - 24) + log₇(x + 24) = 2.

A) {26}

B) {-25}

C) {25}

D) {27}

Q3) Write log(16) in terms of log(4).

A) 2log(4)

B) The expression cannot be written in terms of log(4).

C) log(4) + 2

D) log₂(4)

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Chapter 12: Section 2: Exponential and Logarithmic Functions

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Sample Questions

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

Q2) Write log₇(36) - log₇(6) as a single logarithm.

Q3) Solve log(x) = -4.

Q4) Write log(64) in terms of log(4).

Q5) Solve e^x^{+ 2} = 5.

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

Q7) Write 3⁶ = 729 as a logarithmic equation.

Q8) Write ln(s⁵) + ln(s⁶) + ln(s) as a single logarithm. Assume s represents numbers for which the logarithms are defined.

Q9) Solve log₂(x² - 2) = 2 + log₂(x² + 8).

Q10) Write log₆216 = 3 as an exponential equation.

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) Simplify ln(e⁹).

Q13) Evaluate log_1/5(6). Round to four decimal places. 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) 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) 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

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

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Sample Questions

Q1) Find the distance between (-10, 1) and (-12, 2).

Q2) Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola.

(x + 1)² - y = 1

Q3) Solve the given system of equations. x² + y² = 25 y = x² - 5

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

Q6) 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

Page 30

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) 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%

Q2) List all terms of the finite sequence a_n = 6n + 2 for 1 n 5.

A) 8, 14, 20, 26, 32

B) 8, 10, 12, 14, 16

C) 9, 10, 11, 12, 13

D) 1, 2, 3, 4, 5

Q3) Write a formula for the general term of the given sequence and match your result to the correct answer below. -2, -1, 0, 1, 2, ...

A) a_n = (-1)ⁿ(n - 3)

B) a_n = n - 3

C) a_n = -n - 3

D) a_n = n + 3

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Chapter 14: Section 2: Sequences and Series Available

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

Q2) 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, ...

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

Q4) List all terms of the finite sequence a_n = 3n + 2 for 1 n 5.

Q5) Find r for the geometric sequence that has a₁ = 3 and a₄ = 192.

Q6) Write the given series in summation notation. Use the index i, and let i begin at 1. ln(6) + ln(7) + ln(8)

Q7) Write a formula for the nth term of the given arithmetic sequence. 1, 7, 13, 19, 25, . . .

Q8) Write the first five terms of the arithmetic sequence whose nth term is given. a_n = -1 + (n + 1)(2)

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Chapter 15: Mathematical Problem Set

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Q1) 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?

Q2) Does the point (5, -12) satisfy the inequality y \(\ge\) 15x + 12?

Q3) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. 4x - x = 3x

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

A)True

B)False

Q6) 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?

Q7) Simplify: u - 0.03(u - 300)

Page 33

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Chapter 16: Algebraic Equations and Problem Solving

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Q1) 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) = 12 inches. Find the measures of the sides by solving the perimeter equation.

A) 3 inches, 5 inches, 7 inches

B) 3 inches, 3 inches, 3 inches

C) 4 inches, 5 inches, 6 inches

D) 3 inches, 4 inches, 5 inches

Q2) 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

Q3) Determine whether 13 is a solution of -3x - 15 = -24.

A)True

B)False

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Chapter 17: Algebra and Math Problems

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Q1) Factor: 125x³ + 27

Q2) Write a formula for the nth term of the given geometric sequence. 1, 6, 36, 216, 1296, . . .

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 13 seconds?

Q4) 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?

Q5) 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 120 2\(\times\)4's and 198 1\(\times\)6's in his inventory. If tables sell for $60 and swings sell for $25, how many of each items should Conrad make in order to maximize his revenue?

Q6) Solve 3¹⁰^x^{- 8} = 9⁴^x^{- 1}.

Q7) List all terms of the finite sequence a_n = n + 6 for 1 n 5.

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Chapter 18: Algebraic Equation Practice

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Q1) 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)

Q2) Find four consecutive integers whose sum is 226.

A) 55, 57, 59, 61

B) 56, 57, 58, 59

C) 55, 56, 57, 58

D) 54, 55, 56, 57

Q3) Write ln(x¹⁰) - ln(x⁶) as a single logarithm.

A) ln(x⁴)

B) The logarithms cannot be combined.

C) ln(x⁶⁰)

D) ln(x¹⁶)

Q4) 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

Page 36

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