Precalculus Exam Questions - 840 Verified Questions

Precalculus Exam Questions

Course Introduction

Precalculus is designed to bridge the gap between algebra, geometry, and calculus, providing students with a strong foundation in the mathematical concepts and skills necessary for advanced study in mathematics. The course covers key topics such as functions and their properties, polynomial and rational expressions, exponential and logarithmic relationships, trigonometry, and analytic geometry. Emphasis is placed on problem-solving, mathematical reasoning, and the use of technology to explore and analyze mathematical models. This course prepares students for the rigor of calculus by reinforcing essential precalculus concepts and fostering analytical thinking.

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Elementary and Intermediate Algebra 4th Edition by Mark Dugopolski Emeritus

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840 Verified Questions

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Chapter 1: Section 1: Real Numbers and Their Properties

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Sample Questions

Q1) Use the distributive property to factor the expression. 24p - 36

A) 6(3p - 6)

B) 24(p - 2)

C) 12(2p - 3)

D) 8(3p - 4)

Answer: C

Q2) Write as a product without exponents: 8⁴

A) 8 + 8 + 8 + 8

B) 4·8

C) 8·8·8·8

D) None of these.

Answer: C

Q3) 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

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Page 3

Chapter 1: Section 2: Real Numbers and Their Properties

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Sample Questions

Q1) Evaluate: 0 \(\div\) 2

Answer: 0

Q2) Evaluate: 7 - 3 · |3 - (5² - 2)|

Answer: -53

Q3) T.L. and Quina plan to add a 9-inch thick layer of gravel to their driveway. The driveway is 29 yards long and 3 yards wide. What volume of gravel in cubic yards is required? Assume that the driveway layer is in the shape of a rectangular slab.

Answer: 11ea9079_e301_cd11_aec7_8d887fb183cb_TB3543_11 yd³

Q4) Convert to a percent and a fraction: 0.7

Answer: 70%, 11ea9079_e301_cd10_aec7_0df6f8cf357c_TB3543_11

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

Answer: 5(-7p + 4)

Q6) Translate the verbal expression into an algebraic expression: The difference of p and the square of a Answer: p - a²

Q7) Write as a product without exponents: 12⁴

Answer: 12·12·12·12

Page 4

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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) 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) At a 10% discount rate, Jack's discount was more than $27 on the jacket he purchased. Write an inequality to describe this situation using p for the original price of the jacket.

A) 0.1p > 27

B) 0.9p > 27

C) 0.1p \(\ge\) 27

D) 1.1p > 27

Answer: A

Page 5

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Chapter 2: Section 2: Linear Equations and Inequalities in

One Variable

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Sample Questions

Q1) Mark and Brenda wish to get $135,240 for their home. The real estate agent's commission is 8% of the selling price. What should the selling price be?

Q2) At a 30% discount rate, Jack's discount was more than $12 on the jacket he purchased. Write an inequality to describe this situation using p for the original price of the jacket.

Q3) How many pints of a 9% cleaning solution must be mixed with 2 pints of a 13% cleaning solution to give a 11% solution?

Q4) Solve for x.

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

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

80 - 5(t + 4) = 0

Q6) 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?

Q7) 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.

Page 6

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) 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)

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

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

A)True

B)False

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Chapter 3: Section 2: Linear Equations and Inequalities in

Two Variables

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Sample Questions

Q1) Graph the equation y = -3x + 1.

Q2) Find the equation (in standard form) of the line through (2, 0) and (4, -1).

Q3) 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

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

Q6) Find the slope of the line that contains the points (-11,2) and (8,-12).

Q7) 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.

Q8) Graph the line through (-1, 3) with slope -2.

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

Q10) Does the point (-4, -1) satisfy the inequality y \(\le\) 6x - 5?

A)True B)False

Q11) Write a formula that expresses the relationship described below. Use k as a constant Page 8

P varies directly with T

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Page 9

Chapter 4: Section 1: Exponents and Polynomials

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Sample Questions

Q1) The edges of a triangular homesite have lengths of 3x - 2, x, and x + 1. Write an expression for the perimeter of the property.

A) 4x - 1

B) 5x - 1

C) 6x - 1

D) 5x - 3

Q2) Perform the computation. (2 \(\times\)10^-15)²

A) 4 \(\times\)10^-15

B) 4 \(\times\)10^-30

C) 2 \(\times\)10^-30

D) 4 \(\times\)10^-13

Q3) 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) Simplify. -(11)⁰

Q2) Simplify. 5y⁴·(y⁴)⁵

Q3) Simplify. (xy³)³

Q4) Multiply. (5x - 6)²

Q5) Multiply. (6 + 5x)(6 - 5x)

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

Q7) Perform the indicated operation. (-4m - 7) + (m² + 7m + 6)

Q8) What is the coefficient of x³ in the polynomial -11x³ + 13x²?

Q9) The edges of a triangular homesite have lengths of 3x + 4, x, and x - 1. Write an expression for the perimeter of the property.

Q10) Find the product. (n + 2)(n - 3)(n + 4)

Page 11

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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) 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 - 54t + 306. How many seconds elapse before the marble hits the ground?

A) 6 sec

B) 5 sec

C) 3 sec

D) 4 sec

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 the given polynomial completely. If the polynomial is prime, say so. 7w² - 24w - 16

Q2) Factor out the greatest common factor. -63q²r² - 45q²r + 54qr²

Q3) Factor the given polynomial completely. If the polynomial is prime, say so. c³+ cd + 3c² + 3d

Q4) Factor.

q² + 6qr + 36r²

Q5) Factor out the greatest common factor. (y - 6)4 + (y - 6)y

Q6) Solve the given equation. y² = 9y

Q7) Factor.

9z² - 6z + 1

Q8) Factor.

tu + 5u - 7t - 35

Q9) Factor completely.

8u³v - 392uv

Q10) Factor.

uvw + 9u + 5vw + 45

Page 14

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Page 15

Chapter 6: Section 1: Rational Expressions

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Sample Questions

Q1) 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

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

Q3) Find the least common multiple of the given terms. r² - 8r - 9, r² - 18r + 81

A) (r - 9)

B) (r + 1)(r - 9)

C) (r + 1)(r - 9)²

D) (r + 1)(r - 9)(r + 9)

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Chapter 6: Section 2: Rational Expressions

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Sample Questions

Q1) 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.

Q2) 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?

Q3) Find the least common multiple of the given terms. q² + 7q - 30, q² + 20q + 100

Q4) Among 100 college students, 40 said they study 11 or more hours per week while the rest said they did not. What is the ratio of those students who study at least 11 hours per week to those that do not?

Q5) 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.

Q6) 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?

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Chapter 7: Section 1: Systems of Linear Equations

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Sample Questions

Q1) Solve the system of equations.

-x + y - z = 8

4x - 2y + 5z = -28

2x - 2y + 2z = -14

A) {(0, 4, -4)}

B) {\(\varnothing\)}

C) {(x, y, z) | -x + y - z = 8}

D) {(x, y, z) | 4x - 2y + 5z = -28}

Q2) Cashews sell for $5 per pound and peanuts sell for $2 per pound. How many pounds of each would you use to make 20 pounds of a mixture that sells for $4.25 per pound?

A) 13 lb cashews, 7 lb peanuts

B) 16 lb cashews, 4 lb peanuts

C) 17 lb cashews, 3 lb peanuts

D) 15 lb cashews, 5 lb peanuts

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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) 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?

Q3) Solve the system of linear equations by the substitution method.

-5x = -2y + 9

5x + 5y = -30

Q4) For Monday morning's staff meeting, Jim bought 2 bags of bagels and 3 packages of cream cheese and paid $9.00 (excluding sales tax). For Friday's meeting, he bought 4 bags of bagels and 2 packages of cream cheese and paid $10.00 (again, excluding sales tax). How much do bags of bagels and packages of cream cheese cost?

Q5) Solve the system of equations.

3x - 2y + 4z = 12

-5x - y - z = -10

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

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Chapter 8: Section 1: More on Inequalities

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Sample Questions

Q1) 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, \(\infty\))

Q2) Carla wants to purchase insurance for her landscaping business. She determines that she needs at least $137,500 of property coverage and at least $159,500 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 $300 of liability coverage. Plan B provides $260 of property coverage and $290 of liability coverage for each dollar of premium paid. How much should she spend on each plan to minimize her insurance cost?

A) $290 for Plan A and $250 for Plan B

B) $550 for Plan A and $0 for Plan B

C) $250 for Plan A and $290 for Plan B

D) $320 for Plan A and $300 for Plan B

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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) Solve: |x - 5| = 3

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

Q2) Find all real solutions.

-10(x - 3)³ = 0

Q3) Simplify.

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

Q4) Find all real solutions. (u - 2)^-1/3 = 1

Q5) Find all real solutions. (s + 3)² - 5 = 0

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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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) Write a quadratic equation that has the solutions -10 and 3.

A) x² + 7x - 30 = 0

B) x² + 30 = 0

C) x² - 60x - 30 = 0

D) x² + 60x - 30 = 0

Q3) Solve the given inequality and express the solution in interval notation. x² + 9x \(\ge\) 0

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

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

C) [-9, 0]

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

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Chapter 10: Section 2: Quadratic Equations and Inequalities

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

Q3) Find the imaginary solutions: x² - 6x + 90 = 0

Q4) Find all real solutions of the given equation. (x² + 1)² - 11(x² + 1) = -10

Q5) Solve by completing the square. 2x² - 5x + 1 = 0

Q6) Find all real solutions of the given equation. x^2/3 - 3x^1/3 - 10 = 0

Q7) Find all real and imaginary solutions to the equation. x^-2 - 3x^-1 + 5 = 0

Q8) Solve the inequality. Graph the solution set. x² - 8x + 12 < 0

Q9) Solve by factoring: x² - 5x - 50 = 0

Page 25

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

Q11) Write a quadratic equation that has the solutions 8 and 1.

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Chapter 11: Section 1: Functions

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Q1) How are the graphs of f(x) = x² and g(x) = x² + 6 related?

A) The graph of g(x) is the same as that of f(x), but translated upward by 6 units.

B) The graph of g(x) is the same as that of f(x), but translated downward by 6 units.

C) The graph of g(x) is the same as that of f(x), but translated 6 units to the right.

D) The graph of g(x) is the same as that of f(x), but translated 6 units to the left.

Q2) Determine whether the relation |6x| = |-7y| is a function.

A)True

B)False

Q3) 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)}

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Chapter 11: Section 2: Functions

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Q1) 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).

Q2) Let f(x) = -2x - 4 and g(x) = x² + 10x. Find (f ·g)(4).

Q3) Determine whether the given function is invertible. If it is invertible, then find its inverse.

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

Q4) How are the graphs of f(x) = (x + 4)² and g(x) = -(x + 4)² related?

Q5) Determine whether f(x) = 2x and g(x) = 0.5x are inverses of each other.

A)True

B)False

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

A)True

B)False

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) = x² + 2x - 3

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Q8) How are the graphs of f(x) = x² and g(x) = x² + 7 related?

Chapter 12: Section 1: Exponential and Logarithmic Functions

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Q1) Write log₉(28) - log₉(7) as a single logarithm.

A) 9³⁵

B) The logarithms cannot be combined.

C) log₉(4)

D) log₉(35)

Q2) Solve log₇(x - 24) + log₇(x + 24) = 2.

A) {26}

B) {-25}

C) {25}

D) {27}

Q3) Evaluate log_1/3(3.6). Round to four decimal places.

A) -0.5064

B) -1.1660

C) 1.2809

D) -0.858

Q4) Write log₈64 = 2 as an exponential equation.

A) 8² = 64

B) 8² = 8

C) 64² = 8

D) 64² = 64

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Chapter 12: Section 2: Exponential and Logarithmic Functions

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Sample Questions

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

Q2) Simplify ln(e⁹).

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

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

Q5) Solve -7^-5-^x = -49.

Q6) Solve log(x) = -4.

Q7) Write log₆216 = 3 as an exponential equation.

Q8) Evaluate log_1/5(6). Round to four decimal places.

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

Q10) Write log(64) in terms of log(4).

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

Q13) Write 3⁶ = 729 as a logarithmic equation. Page 30

Q12) Solve log₁₂(x - 35) + log₁₂(x + 35) = 2.

Q14) Rewrite log(75) in terms of log(3) and log(5).

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Page 31

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

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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) 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)}

Q3) Solve the given system of equations. y = x² - 10

5x + y = 4

A) {(2, 14), (-7, 59)}

B) {(2, -6), (-7, 39)}

C) {(2, 4), (-7, 49)}

D) {(2, -6), (-7, 49)}

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

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

(x + 1)² - y = 1

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) Rewrite the given equation in the standard form for the equation of a circle and identify its center and radius.

x² - 18x + y² + 6y - 10 = 0

Q4) Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola.

(x + 5)² + y² = 1

Q5) Solve the given system of equations. xy = 3

y = x

Q6) Solve the given system of equations. x² + y² = 25

y = x² - 5

Q7) Find two complex numbers that have a sum of -14 and a product of 58.

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Chapter 14: Section 1: Sequences and Series Available

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Q1) Write a formula for the nth term of the given arithmetic sequence. 4, 10, 16, 22, 28, . . .

A) a_n = 6n - 2

B) a_n = 7n - 3

C) a_n = 6n + 2

D) a_n = 2n - 6

Q2) 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

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

Q2) Find r for the geometric sequence that has a₁ = 3 and a₄ = 192.

Q3) Write a formula for the nth term of the given geometric sequence. 3, -9, 27, ...

Q4) Write the first five terms of the arithmetic sequence whose nth term is given. a_n = -1 + (n + 1)(2)

Q5) Use the binomial theorem to expand the given binomial. (b + 2)⁴

Q6) Each time an aluminum beverage can is recycled, some amount of the material is lost due to a variety of reasons. If each recycling step is 80% efficient, what percent of the original material remains if a can is recycled 3 times? Round to the nearest tenth of a percent.

Q7) 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?

Q8) Write the first four terms of the geometric sequence whose nth term is given. a_n = (-3)ⁿ^-1 Page 35

Q9) List all terms of the finite sequence a_n = 3n + 2 for 1 n 5.

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Page 36

Chapter 15: Mathematical Problem Set

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Q1) Factor the given polynomial completely. If the polynomial is prime, say so. y³- 6y² - 9y + 54

Q2) Solve the given equation. y² + 6y + 8 = 0

Q3) 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?

Q4) Find the product. (3a + 7)(a + 9)

Q5) 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?

Q6) The temperature T of a gas sample varies jointly as the pressure P and the volume V. If the temperature is 274 kelvin when the volume is 4.6 liters and the pressure is 1.3 atmospheres, then what is its temperature if the gas is compressed to 1.7 liters at 4 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.]

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Chapter 16: Algebraic Equations and Problem Solving

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Q1) Find the product. (3b + 5)(b + 6)

A) b²+ 23b + 30

B) 3b²+ 23b + 30

C) 3b²+ 11b + 30

D) b²+ 9b + 18

Q2) Simplify: r - 0.1(r + 400)

A) 0.9r - 40

B) 1.1r + 40

C) 1.1r - 40

D) 0.9r + 40

Q3) Sarah has 12 coins (nickels, dimes, and quarters) in her piggy bank with a total value of $1.65. There are 2 more dimes than nickels. How many of each type of coin does Sarah have?

A) 2 nickels, 8 dimes, and 3 quarters

B) 3 nickels, 5 dimes, and 4 quarters

C) 0 nickels, 4 dimes, and 5 quarters

D) 4 nickels, 7 dimes, and 3 quarters

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Chapter 17: Algebra and Math Problems

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Sample Questions

Q1) Graph both equations of the system on the same coordinate axes. Use elimination to find all points of intersection. y = - x² 2x² - y² = 1

Q2) Justin is shopping for new tires for his 4-wheel-drive truck. In addition to the price of the tires, there is a 5% sales tax plus a state-mandated $36 fee for disposing of his old tires. If Justin has determined that he will spend less than $502.20 total, then what is the price range he can spend on the tire set?

Q3) Solve the inequality. Graph the solution set. x² + 6x + 5 0

Q4) 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?

Q5) Find the product. (3a + 4)(2a + 1)

Q6) Solve. (z - 8)^1/3 = -3

Q7) Simplify: t - (6t + 7)

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Chapter 18: Algebraic Equation Practice

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

A) (9, 15), 13

B) (8, 14), 13

C) (-2, -10), 26

D) (8, 14), 26

Q2) 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

A) Crosses at (10, 0) and at (-10, 0) but does not cross at (0, 0)

B) Crosses at (10, 0) but does not cross at (0, 0)

C) Crosses at (10, 0)

D) Crosses at (10, 0) and at (0, 0)

Q3) 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.

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