Developmental Mathematics Exam Questions - 840 Verified Questions

Developmental Mathematics

Exam Questions

Course Introduction

Developmental Mathematics is designed to build fundamental mathematical skills and concepts necessary for success in college-level mathematics courses. The course covers topics such as whole numbers, fractions, decimals, ratios, proportions, percentages, basic algebraic expressions, and introductory problem-solving techniques. Emphasis is placed on understanding mathematical reasoning, improving computational fluency, and applying mathematical concepts to real-life situations. Through a supportive learning environment, students develop the confidence and competence required for further study in mathematics and related fields.

Recommended Textbook

Elementary and Intermediate Algebra 4th Edition by Mark Dugopolski Emeritus

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32 Chapters

840 Verified Questions

840 Flashcards

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Page 2

Chapter 1: Section 1: Real Numbers and Their Properties

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Sample Questions

Q1) 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) Use the appropriate properties to evaluate 227²(4·5 - 20).

A) 51,529

B) 12

C) 0

D) 2,061,160

Answer: C

Q3) Evaluate the expression for b = 14 and c = 7: c² + 6b + 6

A) -41

B) 139

C) 97

D) -29

Answer: B

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Page 3

Chapter 1: Section 2: Real Numbers and Their Properties

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Sample Questions

Q1) Use the appropriate properties to evaluate 182²(4·10 - 40).

Answer: 0

Q2) Determine the value of |-2|.

Answer: 2

Q3) Evaluate: 7 - 3 · |3 - (5² - 2)|

Answer: -53

Q4) Translate the given sentence into an equation: "The product of n + 14 and n + 7 is 1."

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

Q5) Evaluate: 0 \(\div\) 2

Answer: 0

Q6) 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

Q7) Translate the verbal expression into an algebraic expression: The difference of p and the square of a Answer: p - a²

Q8) Evaluate: 23 + (-24)

Answer: -1

Page 4

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Chapter 2: Section 1: Linear Equations and Inequalities in

One Variable

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Sample Questions

Q1) Carol drove for 2 hours on a two-lane state road. She then increased her speed by 20 miles per hour on the freeway and drove for 6 more hours. If the total trip was 480 miles, then what was her speed on the freeway?

A) 60 mph

B) 65 mph

C) 45 mph

D) 67 mph

Answer: B

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) 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

Page 5

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Chapter 2: Section 2: Linear Equations and Inequalities in

One Variable

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Sample Questions

Q1) The length of a rectangle must be 8 centimeters more than the width, and the perimeter must be at least 36 centimeters. What is the range of values for the width?

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) 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.

Q4) 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?

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

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) James paid $234 for a DVD player that was priced originally at $260. What was the discount rate?

Q8) Find three consecutive integers whose sum is 216.

Q9) Graph the inequality: -2 < x < 3

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Chapter 3: Section 1: Linear Equations and Inequalities in

Two Variables

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Sample Questions

Q1) 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

Q2) Does the point (2, 14) satisfy the inequality y \(\le\) 2x - 2?

A)True

B)False

Q3) 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.

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Chapter 3: Section 2: Linear Equations and Inequalities in

Two Variables

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Sample Questions

Q1) Find the slope of the line that contains the points (-11,2) and (8,-12).

Q2) Does the point (-4, -1) satisfy the inequality y \(\le\) 6x - 5?

A)True

B)False

Q3) 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.

Q4) Graph the equation y = -3x + 1.

Q5) Find the x- and y-intercepts of x + 3y + 2 = 0 and use these intercepts to graph the equation.

Q6) 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

Q7) Complete the ordered pair so that it satisfies the given equation. y = -4x + 3: (-10, ___)

Q8) 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).

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) Multiply. (-4r - 9)²

A) 16r² + 72r + 81

B) -4r² + 72r + 81

C) 16r² + 81

D) 16r² + 36r + 81

Q3) Write in scientific notation. 274 \(\times\)10³

A) 2.74 \(\times\)10⁵

B) 2.74 \(\times\)10⁶

C) 2.74 \(\times\)10¹

D) 274 \(\times\)10³

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

A) x³+ 15x² + 12x - 36

B) x³+ 5x² + 12x + 36

C) x³+ 11x² + 36x + 36

D) x³+ 5x² - 12x - 36

Page 10

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Chapter 4: Section 2: Exponents and Polynomials

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Sample Questions

Q1) Perform the indicated operation. (t - 5) - (5t - 8)

Q2) The edges of a triangular homesite have lengths of 3x + 4, x, and x - 1. Write an expression for the perimeter of the property.

Q3) Simplify. (xy³)³

Q4) Multiply. (6 + 5x)(6 - 5x)

Q5) Find the product. -10t⁵·2t⁷

Q6) State the degree of the polynomial and determine if it is a monomial, binomial, or trinomial. x⁴

Q7) Write in scientific notation. 957 \(\times\)10³

Q8) Find the quotient and the remainder. (x⁴ - x³ + 5) \(\div\) (x² + 2)

Q9) Simplify. -(11)⁰

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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. c⁴+ d⁴

A) c²d²(c²- d²)

B) (c - d)²(c + d)²

C) The polynomial is prime.

D) (c - d)(c + d)(c²+ d²)

Q3) Factor completely. 8w³x - 800wx

A) The expression is prime.

B) 8wx(w - 10)(w + 10)

C) 8wx(w - 10)²

D) 8wx(w² - 10²)

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Chapter 5: Section 2: Factoring

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Sample Questions

Q1) Solve the given equation.

x³ + 5x² - 2x - 24 = 0

Q2) Factor the polynomial below completely, given that the binomial following it is a factor of the polynomial.

u³ + 2u² - 11u - 12, u - 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) Factor.

q² + 6qr + 36r²

Q5) Factor the given polynomial completely. If the polynomial is prime, say so. n² - 2n

Q6) Find the prime factorization.

115

Q7) Factor the given polynomial completely. z⁶ + 2z³ - 3

Q8) Factor out the opposite of the greatest common factor. 10z³ - 2z²

Page 13

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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) 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) 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?

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

Q5) 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.

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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Page 15

Chapter 7: Section 1: Systems of Linear Equations

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Sample Questions

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

5x - 8y = 40

A) {(-2, -4)}

B) {(0, -5)}

C) No solution. The system is inconsistent.

D) {(2, -2)}

Q2) 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

Q3) Solve the system of equations. 0.5x + 2y = 1.25

-0)875x + 1.5y = 2.8125

A) {(-1, 1.5)}

B) {(0, 1)}

C) {(0, 3)}

D) {(-1.5, 1)}

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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) Solve the system of equations.

-x + 5y - 3z = 31

-4x - 5y + 4z = 6

3x - 15y + 9z = -91

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) Cashews sell for $5 per pound and peanuts sell for $2 per pound. How many pounds of each would you use to make 15 pounds of a mixture that sells for $3.20 per pound?

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Page 17

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) 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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Page 18

Chapter 8: Section 2: More on Inequalities

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Sample Questions

Q1) Write as a single interval if possible: (-9, \(\infty\))\(\cup\) [13, \(\infty\))

Q2) Write as a single interval if possible: [-1, \(\infty\))\(\cup\)(4, \(\infty\))

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) 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?

Q5) Solve: 12 - |-13 - x| = 2

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

A)True

B)False

Q7) Solve the inequality and write the solution set in interval notation.

5 < |x| - 10

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Chapter 9: Section 1: Radicals and Rational Exponents

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Sample Questions

Q1) Find the difference. (1 + 4i) - (-7 + 7i)

A) -6 - 3i

B) 8 + 11i

C) -6 + 11i

D) 8 - 3i

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20

Chapter 9: Section 2: Radicals and Rational Exponents

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Sample Questions

Q1) Evaluate.

(27)^-4/3

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

Q3) Find the difference. (-5 - 10i) - (-7 - 3i)

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

Q5) Find all real solutions. -10(x - 3)³ = 0

Q6) Simplify.

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

Q7) Find all real solutions. (u - 2)^-1/3 = 1

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21

Chapter 10: Section 1: Quadratic Equations and Inequalities

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Sample Questions

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

A) 224 batteries

B) 130 batteries

C) 80 batteries

D) 120 batteries

Q2) Solve: (x - 7)² = 100

A) {-3, 17}

B) {3, 17}

C) {-3, 3}

D) {17, 17}

Q3) Use the discriminant to determine whether the given quadratic polynomial can be factored, then factor it if it is not prime. 10x² + 10x + 6

A) The expression is prime.

B) (x + 10)(x + 6)

C) (10x + 6)(x + 10)

D) (10x + 10)(x + 6)

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Page 22

Chapter 10: Section 2: Quadratic Equations and Inequalities

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Sample Questions

Q1) Find all real and imaginary solutions to the equation. x^-2 - 3x^-1 + 5 = 0

Q2) Find all real and imaginary solutions to the equation. t⁴ - 6561 = 0

Q3) Solve by factoring: x² - 5x - 50 = 0

Q4) Write a quadratic equation that has the solutions 8 and 1.

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

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

Q7) Solve the inequality. Graph the solution set. x² - 8x + 12 < 0

Q8) 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?

Q9) Find all real solutions of the given equation. (x² + 1)² - 11(x² + 1) = -10

Page 23

Q10) Find the vertex for the graph of the parabola. f(x) = x² - 5

Q11) Solve: (q - 6)² = 36

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Page 24

Chapter 11: Section 1: Functions

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Sample Questions

Q1) Determine whether f(x) = 5x and g(x) = 0.2x are inverses of each other.

A)True B)False

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.

Q3) Determine whether the relation |6x| = |-7y| is a function.

A)True B)False

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Chapter 11: Section 2: Functions

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Sample Questions

Q1) Determine whether the relation |2x| = |-8y| is a function.

A)True

B)False

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

Q5) A gas station charges $1.67 per gallon for regular gasoline. Write an expression for the cost c(g) as a function of the number of gallons g and use this function to determine c(13).

Q6) Determine whether the given function is invertible. If it is invertible, then find its inverse.

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

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

Q8) Determine whether f(x) = 2x and g(x) = 0.5x are inverses of each other.

A)True

B)False

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Chapter 12: Section 1: Exponential and Logarithmic

Functions

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Sample Questions

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

A) -0.5064

B) -1.1660

C) 1.2809

D) -0.858

Q3) 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)

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Chapter 12: Section 2: Exponential and Logarithmic Functions

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Q1) Write 3⁶ = 729 as a logarithmic equation.

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

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

Q4) Evaluate log_1/5(6). Round to four decimal places.

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

Q6) Solve -7^-5-^x = -49.

Q7) Simplify ln(e⁹).

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

Q9) Rewrite log(75) in terms of log(3) and log(5).

Q10) Solve log₁₂(x - 35) + log₁₂(x + 35) = 2.

Q11) Write log₇(36) - log₇(6) as a single logarithm.

Q12) Write log₆216 = 3 as an exponential equation.

Q13) If $10,000 is deposited in an account paying 7% compounded quarterly, then what amount will be in the account after 8 years? Page 28

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

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Sample Questions

Q1) 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

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) 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

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

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Q1) Find the midpoint and length of the line segment with the endpoints (5,9) and (8,14).

Q2) Solve the given system of equations.

xy = 3

y = x

Q3) 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

Q4) Find two complex numbers that have a sum of -14 and a product of 58.

Q5) Write the standard equation for the circle with the given radius and center. Center (8, -5), radius 12

Q6) 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?

Q7) Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola.

(x + 5)² + y² = 1

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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 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

Q2) 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

Q3) List the first four terms of the given sequence and match your result to the correct answer below. c_n = (-1)ⁿ(-2n + 3)²

A) 1, -1, 9, -25

B) 1, -1, 1, -9

C) 1, -9, 25, -49

D) -1, 1, -9, 25

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Chapter 14: Section 2: Sequences and Series Available

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Q1) Find r for the geometric sequence that has a₁ = 3 and a₄ = 192.

Q2) List all terms of the finite sequence a_n = 3n + 2 for 1 n 5.

Q3) Write a formula for the nth term of the given arithmetic sequence. 1, 7, 13, 19, 25, . . .

Q4) 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?

Q5) Write the first four terms of the geometric sequence whose nth term is given. a_n = (-3)ⁿ^-1

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 general term of the given sequence and match your result to the correct answer below. -4, -3, -2, -1, 0, ...

Q8) 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

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Chapter 15: Mathematical Problem Set

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Sample Questions

Q1) Simplify: u - 0.03(u - 300)

Q2) Solve and write your answer in interval notation. y + 6 < 7y - 36

Q3) Find the product. (3a + 7)(a + 9)

Q4) Solve the given equation. y² + 6y + 8 = 0

Q5) Factor the given polynomial completely. If the polynomial is prime, say so. y³- 6y² - 9y + 54

Q6) 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.

Q7) Solve the system of equations.

-0.75x + 3.5y = 3.125

0.6x + 1.5y = 1.8

Q8) Perform the indicated operation. (s² - 5s + 5) - (s² - 4s - 6)

Q9) Determine whether 14 is a solution of 11x + 5 = 149. A)True B)False Page 34

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Chapter 16: Algebraic Equations and Problem Solving

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Sample Questions

Q1) 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)

Q2) Solve the given equation. x² + 10x + 24 = 0

A) 4, -6

B) -4, 6

C) -4, -6

D) 4, 6

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

A)True

B)False

Q4) Simplify: r - 0.1(r + 400)

A) 0.9r - 40

B) 1.1r + 40

C) 1.1r - 40

D) 0.9r + 40

Page 36

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Chapter 17: Algebra and Math Problems

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Q1) 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.

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

Q3) If $1,300 is deposited in an account paying 11% compounded continuously, then what amount will be in the account after 3 years?

Q4) 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?

Q5) Find the inverse of the given function and include any domain restrictions. f (x) = (x - 4)²

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Chapter 18: Algebraic Equation Practice

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Q1) Raphael can load a large shipping truck in 12 hours. Working together, Raphael and Jana can load the same truck in 3 hours. How long would it take Jana to load the truck by herself?

A) 3 hours

B) 5 hours

C) 6 hours

D) 4 hours

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) Solve 4^-6^x^{- 10} = 16^-4^x^{- 1}.

A) {5}

B) {-4}

C) {6}

D) {4}

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