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Introductory Algebra Final Exam

Course Introduction

Introductory Algebra is a foundational mathematics course designed to develop students understanding of basic algebraic principles and techniques. The course covers topics such as variables, algebraic expressions, linear equations and inequalities, polynomials, factoring, and problem solving. Emphasis is placed on applying algebraic concepts to real-world situations, building mathematical reasoning skills, and preparing students for higher-level mathematics courses. Throughout the course, students will practice equation manipulation, graphing, and interpreting mathematical relationships, fostering both computational proficiency and critical thinking abilities.

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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29 Verified Questions

29 Flashcards

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Sample Questions

Q1) Combine like terms if possible: 8m - (-5m)

A) 8m - (-5m)

B) 13m

C) 3m

D) -3m

Answer: B

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

Q3) Evaluate: 0 $\div$ 5

A) 0

B) 1

C) Undefined

D) 5

Answer: A

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Chapter 1: Section 2: Real Numbers and Their Properties

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29 Verified Questions

29 Flashcards

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Sample Questions

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

Answer: 19z

Q2) Translate the verbal expression into an algebraic expression: The difference of p and the square of a Answer: p - a2

Q3) Perform the indicated operation: 4 - (-12) Answer: 16

Q4) Evaluate: 7 - 3 · |3 - (52 - 2)|

Answer: -53

Q5) Evaluate: 11 - 14 + 10 - 15

Answer: -8

Q6) Write the interval of real numbers in interval notation. The set of real numbers less than -7 Answer: (- , -7)

Q7) Convert to a percent and a fraction: 0.7

Answer: 70%, 11ea9079_e301_cd10_aec7_0df6f8cf357c_TB3543_11

Q8) Translate the given sentence into an equation: "The product of n + 14 and n + 7 is 1."

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

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Chapter 2: Section 1: Linear Equations and Inequalities in

One Variable

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26 Verified Questions

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Sample Questions

Q1) Mark and Brenda wish to get $128,800 for their home. The real estate agent's commission is 8% of the selling price. What should the selling price be?

A) $141,200

B) $142,500

C) $128,800

D) $140,000

Answer: D

Q2) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. 64 - 4(s + 5) = 0

A) Ø, inconsistent

B) All real numbers, identity

C) {11}, conditional

Answer: C

Q3) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. 8u + 11u = 9u

A) Ø, inconsistent

B) All real numbers, identity

C) {0}, conditional

Answer: C

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Chapter 2: Section 2: Linear Equations and Inequalities in

One Variable

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Sample Questions

Q1) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. u + 5u = 6u

Q2) Liam invested some money in the Abernathy Fund and $2,498 more than that amount in the Carlson Fund. For the year he was in these funds, the Abernathy fund paid 6% simple interest and the Carlson Fund paid 14% simple interest. If the income from the two funds totalled $2,250.12, then how much was invested in each fund?

Q3) 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?

Q4) Ferdinand sold his algebra textbook using an internet auction site that charges a commission of 13% of the selling price. After the commission was paid, Ferdinand received $22.64. If x represents the selling price, then x satisfies x - 0.13x = 22.64. Solve this equation to find the selling price.

Q5) Find y given that x = -7 and y = -4x + 5.

Q6) 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?

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Chapter 3: Section 1: Linear Equations and Inequalities in

Two Variables

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Sample Questions

Q1) Gotham City's budget deficit was $6.2 million in 1993 and $2.4 million in 1998. Find the slope of the line through (1993, 6.2) and (1998, 2.4) and interpret your result.

A) -0.760 slope; the slope of the deficit is decreasing by $0.760 million per year

B) -0.760 slope; the deficit is increasing by $0.760 million per year

C) -0.760 slope; the deficit is decreasing by $0.760 million per year

D) -0.760 slope; the deficit decreased by $0.760 million during the period between 1993 and 1998.

Q2) The 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

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

Q2) 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).

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

Q4) Complete the ordered pair so that it satisfies the given equation. y = -4x + 3: (-10, ___)

Q5) Find the slope of the line that contains the points (-11,2) and (8,-12).

Q6) Does the point (-4, -1) satisfy the inequality y $\le$ 6x - 5?

A)True B)False

Q7) The budget deficit for Central City can be modeled by the equation D = 0.5n + 6.5 where n is the number of years since 1990 and D is the deficit in millions of dollars. Graph the equation for n ranging from 0 to 20.

Q8) Graph the line through (-1, 3) with slope -2. Page 8

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Page 9

Chapter 4: Section 1: Exponents and Polynomials

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28 Verified Questions

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Sample Questions

Q1) Find the product. (q2 + 3q - 7)(-5q - 7)

A) -5q3 - 22q2 + 14q + 49

B) -5q3 - 22q2 + 14q - 49

C) -5q3 + 22q2 + 14q + 49

D) -5q3 - 22q2 - 14q + 49

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) Simplify. (st5)6

A) st11

B) st30

C) s6t11

D) s6t30

Q4) Multiply. (-4r - 9)2

A) 16r2 + 72r + 81

B) -4r2 + 72r + 81

C) 16r2 + 81

D) 16r2 + 36r + 81

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Chapter 4: Section 2: Exponents and Polynomials

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Sample Questions

Q1) Find the product. (x2 + 5x - 2)(-x - 8)

Q2) Simplify.

5y4·(y4)5

Q3) Find the product. (5w2 - 4)(5w2 - 1)

Q4) What is the coefficient of x3 in the polynomial -11x3 + 13x2?

Q5) Simplify. (xy3)3

Q6) Find the product. -10t5·2t7

Q7) Multiply. (5x - 6)2

Q8) Expand the binomial. (n - 2)3

Q9) Perform the indicated operation. (t - 5) - (5t - 8)

Q10) Simplify. -(11)0

Page 11

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Chapter 5: Section 1: Factoring

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Sample Questions

Q1) Factor. 36u2 - 12u + 1

A) The expression is prime.

B) (6u - 1)2

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

D) (6u + 1)2

Q2) 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)

Q3) 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)

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Chapter 5: Section 2: Factoring

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Sample Questions

Q1) Factor.

8x3 - 27

Q2) Factor the given polynomial completely. If the polynomial is prime, say so. 7w2 - 24w - 16

Q3) Solve the given equation. y2 = 9y

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

Q5) Factor.

uvw + 9u + 5vw + 45

Q6) Factor the given polynomial completely. If the polynomial is prime, say so. n2 - 2n

Q7) Find the prime factorization. 115

Q8) Factor completely. 8u3v - 392uv

Q9) Factor completely. b3p3 - 6b2p2 + 9bp

Page 14

Q10) Find the greatest common factor for the given numbers. 36, 80, 120

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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) 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)

Q3) Among 100 college students, 45 said they study 11 or more hours per week while the rest said they did not. What is the ratio of those students who study at least 11 hours per week to those that do not?

A) 9 to 11

B) 20 to 11

C) 9 to 20

D) 11 to 9

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Chapter 6: Section 2: Rational Expressions

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Sample Questions

Q1) 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?

Q2) Find the least common multiple of the given terms. q2 + 7q - 30, q2 + 20q + 100

Q3) 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.

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) 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?

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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Page 17

Chapter 7: Section 1: Systems of Linear Equations

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Sample Questions

Q1) Solve the system of equations.

2x - 3y + z = 4

8x - 12y + 4z = 16

-4x + 6y - 2z = -8

A) {(-3, 6, 7)}

B) {(-4, -2, -1)}

C) {$\varnothing$}

D) {(x, y, z) | 2x - 3y + z = 4}

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 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.

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Chapter 7: Section 2: Systems of Linear Equations

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Sample Questions

Q1) 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

Q2) 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?

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.

-3.5x + 3y = -5.375

-0.875x - 0.5y = 0.53125

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

A) {-19, -3}

B) {-17, -5}

C) {-16, -2}

D) {-16, -4}

Q3) 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, $\infty$)

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Chapter 8: Section 2: More on Inequalities

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Sample Questions

Q1) Write as a single interval if possible: [-1, $\infty$)$\cup$(4, $\infty$)

Q2) 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.

Q3) Determine whether the absolute value inequality is equivalent to the inequality following it:

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

A)True

B)False

Q4) 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

Q5) 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

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) Simplify.

492/3 $\div$ 491/6

Q2) Find the difference. (-5 - 10i) - (-7 - 3i)

Q3) Find all real solutions. -10(x - 3)3 = 0

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

Q5) Evaluate. (27)-4/3

Q6) Find all real solutions. (s + 3)2 - 5 = 0

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

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Chapter 10: Section 1: Quadratic Equations and Inequalities

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Sample Questions

Q1) 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

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) Solve by factoring: x2 - x - 42 = 0

A) {-7, -6}

B) {-7, 6}

C) {-6, 7}

D) {6, 7}

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Chapter 10: Section 2: Quadratic Equations and Inequalities

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Sample Questions

Q1) Terrence paddles his canoe upstream a distance of 6 miles. He completes the return trip in 30 minutes less that the upstream journey. If the current flows at 4 miles per hour, what is Terrence's speed in still water?

Q2) Find all real solutions of the given equation. (x2 + 1)2 - 11(x2 + 1) = -10

Q3) Solve the inequality. Graph the solution set. x2 - 8x + 12 < 0

Q4) Use the discriminant to determine whether the given quadratic polynomial can be factored, then factor it if it is not prime. 7x2 + 7x + 9

Q5) Find the vertex for the graph of the parabola. f(x) = x2 - 5

Q6) Find all real and imaginary solutions to the equation. x-2 - 3x-1 + 5 = 0

Q7) Write a quadratic equation that has the solutions 8 and 1.

Q8) Find all real solutions of the given equation. x2/3 - 3x1/3 - 10 = 0

Q9) 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) 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 f(x) = 5x and g(x) = 0.2x are inverses of each other.

A)True

B)False

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Chapter 11: Section 2: Functions

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Sample Questions

Q1) How are the graphs of f(x) = (x + 4)2 and g(x) = -(x + 4)2 related?

Q2) Give the correct domain and range of the relation . {(-5, 4), (5, 4)}

Q3) Determine whether the relation |2x| = |-8y| is a function.

A)True

B)False

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

Q6) How are the graphs of f(x) = x2 and g(x) = x2 + 7 related?

Q7) Determine whether f(x) = 2x and g(x) = 0.5x are inverses of each other. A)True B)False

Q8) 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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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) Write log864 = 2 as an exponential equation.

A) 82 = 64

B) 82 = 8

C) 642 = 8

D) 642 = 64

Q3) Solve ex + 4 = 7.

A) {ln(7) - 4}

B) {ln(3)}

C) {4 ln(7)}

D) {ln(7) + 4}

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Page 28

Chapter 12: Section 2: Exponential and Logarithmic Functions

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Sample Questions

Q1) Simplify ln(e9).

Q2) Write log6216 = 3 as an exponential equation.

Q3) Evaluate log1/5(6). Round to four decimal places.

Q4) Solve ex + 2 = 5.

Q5) Solve log12(x - 35) + log12(x + 35) = 2.

Q6) Solve log2(x2 - 2) = 2 + log2(x2 + 8).

Q7) Write ln(s5) + ln(s6) + ln(s) as a single logarithm. Assume s represents numbers for which the logarithms are defined.

Q8) Write 36 = 729 as a logarithmic equation.

Q9) Solve log(x) = -4.

Q10) Solve -7-5-x = -49.

Q11) Write log(64) in terms of log(4).

Q13) Rewrite log(75) in terms of log(3) and log(5). Page 29

Q12) If $10,000 is deposited in an account paying 7% compounded quarterly, then what amount will be in the account after 8 years?

Q14) Write log7(36) - log7(6) as a single logarithm.

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Page 30

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

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Sample Questions

Q1) 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)}

Q2) Write the standard equation for the circle with the given radius and center. Center (-10, -2), radius 5

A) (x - 10)2 + (y - 2)2 = 25

B) (x - 10)2 + (y - 2)2 = 5

C) (x + 10)2 + (y + 2)2 = 5

D) (x + 10)2 + (y + 2)2 = 25

Q3) 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

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Chapter 13: Section 2: 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 + 5)2 + y2 = 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) Find the midpoint and length of the line segment with the endpoints (5,9) and (8,14).

Q5) Find two complex numbers that have a sum of -14 and a product of 58.

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

(x + 9)2 + 3y2 = 1

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

(x + 9)2 - y2 = 1

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) Find the common difference of an arithmetic sequence if the first term is -9 and the seventh term is -39.

A) -4

B) 3

C) -6

D) -5

Q2) 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

Q3) Write a formula for the nth term of the given geometric sequence. 3, -6, 12, ...

A) an = -3(2)n-1

B) an = 3(-2)n+1

C) an = 3(-2)n-1

D) an = 3(-2)n

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Chapter 14: Section 2: Sequences and Series Available

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Sample Questions

Q1) List the first four terms of the given sequence and match your result to the correct answer below.

cn = (-1)n(-4n + 3)2

Q2) Use the binomial theorem to write out the first four terms of the given binomial. (x2 + 1)22

Q3) Write the first four terms of the geometric sequence whose nth term is given. an = (-3)n-1

Q4) Find r for the geometric sequence that has a1 = 3 and a4 = 192.

Q5) 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 45th year?

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

Page 34

Q8) Write a formula for the nth term of the given arithmetic sequence. 1, 7, 13, 19, 25, . . .

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Chapter 15: Mathematical Problem Set

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Q1) Solve the given equation. y2 + 6y + 8 = 0

Q2) Factor completely. If the polynomial is prime, say so. 9q2 + 8q + 2

Q3) Perform the indicated operation. (s2 - 5s + 5) - (s2 - 4s - 6)

Q4) 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?

Q5) 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.]

Q6) Determine whether 14 is a solution of 11x + 5 = 149. A)True B)False

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Chapter 16: Algebraic Equations and Problem Solving

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Q1) 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

Q2) 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

Q3) Does the point (-15, 15) satisfy the inequality y $\ge$ -12x + 8?

A)True

B)False

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Chapter 17: Algebra and Math Problems

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Q1) 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

Q2) Raphael can load a large shipping truck in 15 hours. Working together, Raphael and Jana can load the same truck in 6 hours. How long would it take Jana to load the truck by herself?

Q3) Solve the given system of equations. y = x2 y = 5

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) Solve 310x - 8 = 94x - 1.

Q6) Find the inverse of the given function and include any domain restrictions. f (x) = (x - 4)2

Q7) Write a formula for the nth term of the given arithmetic sequence. 6, 10, 14, 18, 22, . . .

Page 37

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Chapter 18: Algebraic Equation Practice

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Q1) Write a formula for the nth term of the given arithmetic sequence. 9, 14, 19, 24, 29, . . .

A) an = 5n + 4

B) an = 4n - 5

C) an = 5n - 4

D) an = 6n - 5

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

A) y3 + y2 + y + 1

B) y3 + 1

C) y3 + 3y2 + 3y + 1

D) 3y3 + 3y2 + 3y + 3

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 12 seconds?

A) 240 ft

B) 192 ft

C) 1936 ft

D) 2304 ft

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