Intermediate Algebra
Exam Answer Key
Course Introduction
Intermediate Algebra builds upon foundational algebraic concepts, focusing on the development and application of skills necessary for solving more complex equations and problems. Topics typically include linear and quadratic equations, inequalities, systems of equations, rational expressions, exponents and radicals, polynomials, and functions. The course emphasizes critical thinking and problem-solving abilities, preparing students for college-level mathematics courses and practical applications in science, technology, and business. Collaborative exercises and real-world examples are used to reinforce understanding and mastery of algebraic principles.
Recommended Textbook
Elementary and Intermediate Algebra 4th Edition by Mark Dugopolski Emeritus
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32 Chapters
840 Verified Questions
840 Flashcards
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Chapter 1: Section 1: Real Numbers and Their Properties
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Sample Questions
Q1) Translate the given sentence into an equation: "The product of n - 8 and n - 12 is 5."
A) (n - 8)(n - 12) = 5
B) (n - 8)(n - 12)(5)
C) n - 8n - 12 = 5
D) (n - 8) + (n - 12) = 5
Answer: A
Q2) Evaluate: (-13)(-9)
A) -117
B) 104
C) 117
D) 108
Answer: C
Q3) Write as a product without exponents: 8<sup>4</sup>
A) 8 + 8 + 8 + 8
B) 4·8
C) 8·8·8·8
D) None of these.
Answer: C
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3
Chapter 1: Section 2: Real Numbers and Their Properties
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Sample Questions
Q1) Translate the given sentence into an equation: "The product of n + 14 and n + 7 is 1."
Answer: (n + 14)(n + 7) = 1
Q2) Evaluate: (5)(10)
Answer: 50
Q3) Perform the indicated operation: 4 - (-12)
Answer: 16
Q4) Evaluate the expression for b = -10 and c = -11: c<sup>2</sup> - 3b - 1
Answer: 150
Q5) 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 yd<sup>3</sup>
Q6) Evaluate: (6 - 2)(5 - 12)
Answer: -28
Q7) Use the appropriate properties to evaluate 182<sup>2</sup>(4·10 - 40).
Answer: 0
Page 4
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Chapter 2: Section 1: Linear Equations and Inequalities in
One Variable
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Sample Questions
Q1) 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
Q2) Find y given that x = 6 and y = 3x - 1.
A) 17
B) 7
C) 5
D) 19
Answer: A
Q3) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. s + 6s = 7s
A) Ø, inconsistent
B) All real numbers, identity
C) {0}, conditional
Answer: B
Page 5
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Chapter 2: Section 2: Linear Equations and Inequalities in
One Variable
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Sample Questions
Q1) Lori built a dog lot for her dog, Chollie, by fencing in a rectangular area of her yard. If Chollie's lot required 60 feet of fence and the length is 10 feet longer than the width, then what are the length and width of Chollie's dog lot?
Q2) 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?
Q3) Find three consecutive integers whose sum is 216.
Q4) Graph the inequality: -2 < x < 3
Q5) Write the appropriate inequality symbol in the blank so that the two inequalities are equivalent.
-55 \(\ge\) 5y
-11 _____ y
Q6) Find y given that x = -7 and y = -4x + 5.
Q7) Carol drove for 3 hours on a two-lane state road. She then increased her speed by 20 miles per hour on the freeway and drove for 5 more hours. If the total trip was 420 miles, then what was her speed on the freeway?
Q8) James paid $234 for a DVD player that was priced originally at $260. What was the discount rate?
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Chapter 3: Section 1: Linear Equations and Inequalities in
Two Variables
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Sample Questions
Q1) A playground equipment manufacturer plans to spend $300,000 on a new facility plus $160 for each swing set made.The formula C = 160n + 300,000 gives the cost in dollars to manufacture n swing sets. What is the marginal cost of the nth swing set? [Hint - the marginal cost of the nth swing set is the difference in cost of producing n + 1 swing sets and n swing sets).
A) $170
B) $160
C) $300,000
D) $320
Q2) 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)
Q3) 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
Page 7
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Chapter 3: Section 2: Linear Equations and Inequalities in
Two Variables
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Sample Questions
Q1) Write a formula that expresses the relationship described below. Use k as a constant of variation.
P varies directly with T
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 slope of the line that contains the points (-11,2) and (8,-12).
Q4) Complete the ordered pair so that it satisfies the given equation. y = -4x + 3: (-10, ___)
Q5) Does the point (-4, -1) satisfy the inequality y \(\le\) 6x - 5?
A)True
B)False
Q6) Line l goes through (1, 3) and is parallel to the line through (4, 3) and (-3, 1). Find the slope of l.
Q7) Find the slope and the y-intercept of the line represented by 12x + 7y = 5.
Page 8
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
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Page 9
Chapter 4: Section 1: Exponents and Polynomials
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Sample Questions
Q1) What is the coefficient of x<sup>3</sup> in the polynomial -5x<sup>3</sup> + 10x<sup>2</sup>?
A) 3
B) 5
C) 10
D) -5
Q2) Find the quotient and the remainder. (x<sup>4</sup> - 5x<sup>3</sup> + 10) \(\div\) (x<sup>2</sup> + 2)
A) x<sup>2</sup> - 5x - 2, 10x - 6
B) x<sup>2</sup> - 2, -5x + 14
C) x<sup>2</sup> - 5x + 2, -10x + 14
D) x<sup>2</sup> - 5x - 2, 10x + 14
Q3) Find the product. -5y<sup>7</sup>·2y<sup>2</sup>
A) -10y<sup>9</sup>
B) -10y<sup>14</sup>
C) -5y<sup>7</sup>.2y<sup>2</sup>
D) -3y<sup>9</sup>
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Chapter 4: Section 2: Exponents and Polynomials
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Sample Questions
Q1) Find the quotient and the remainder. (x<sup>4</sup> - x<sup>3</sup> + 5) \(\div\) (x<sup>2</sup> + 2)
Q2) Simplify. -(11)<sup>0</sup>
Q3) Find the product. (n + 2)(n - 3)(n + 4)
Q4) Expand the binomial. (n - 2)<sup>3</sup>
Q5) Simplify. (xy<sup>3</sup>)<sup>3</sup>
Q6) The edges of a triangular homesite have lengths of 3x + 4, x, and x - 1. Write an expression for the perimeter of the property.
Q7) Perform the indicated operation. (-4m - 7) + (m<sup>2</sup> + 7m + 6)
Q8) Multiply. (6 + 5x)(6 - 5x)
Q9) Write in scientific notation. 957 \(\times\)10<sup>3</sup>
Q10) Multiply. (5x - 6)<sup>2</sup>
Page 11
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Chapter 5: Section 1: Factoring
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Sample Questions
Q1) Factor the given polynomial completely. c<sup>4 </sup>+ d<sup>4</sup>
A) c<sup>2</sup>d<sup>2</sup>(c<sup>2 </sup>- d<sup>2</sup>)
B) (c - d)<sup>2</sup>(c + d)<sup>2</sup>
C) The polynomial is prime.
D) (c - d)(c + d)(c<sup>2 </sup>+ d<sup>2</sup>)
Q2) Factor out the greatest common factor. (m - 4)8 + (m - 4)m
A) The polynomial is prime.
B) m<sup>2</sup> + 4m - 32
C) (m - 4)8 + m
D) (m - 4)(8 + m)
Q3) Solve the given equation. v<sup>3</sup> - 3v<sup>2</sup> - 13v + 15 = 0
A) -3, 1, 5
B) 3, -1
C) 1, 5
D) 3, 1, -5
Q4) Factor. 16r<sup>2</sup> - 25
A) The expression is prime.
B) (4r - 5)<sup>2</sup>
C) (4r - 5)(4r + 5)
D) (16r - 5)(16r + 5)
Page 13
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Chapter 5: Section 2: Factoring
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Sample Questions
Q1) Factor.
8x<sup>3</sup> - 27
Q2) Find the prime factorization.
115
Q3) Factor the given polynomial completely. If the polynomial is prime, say so. n<sup>2</sup> - 2n
Q4) Factor the given polynomial completely. z<sup>6</sup> + 2z<sup>3</sup> - 3
Q5) Factor.
uvw + 9u + 5vw + 45
Q6) Find the greatest common factor for the given numbers. 36, 80, 120
Q7) Factor out the greatest common factor. -63q<sup>2</sup>r<sup>2</sup> - 45q<sup>2</sup>r + 54qr<sup>2</sup>
Q8) Factor the given polynomial completely. x<sup>4 </sup>+ y<sup>4</sup>
Q9) Factor completely. 8u<sup>3</sup>v - 392uv
Q10) Solve the given equation. x<sup>3</sup> + 5x<sup>2</sup> - 2x - 24 = 0 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) Find the least common multiple of the given terms. r<sup>2</sup> - 8r - 9, r<sup>2</sup> - 18r + 81
A) (r - 9)
B) (r + 1)(r - 9)
C) (r + 1)(r - 9)<sup>2</sup>
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) 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. q<sup>2</sup> + 7q - 30, q<sup>2</sup> + 20q + 100
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) 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?
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Chapter 7: Section 1: Systems of Linear Equations
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Sample Questions
Q1) When three linear equations (each in three variables) are graphed, two of the equations are seen to be parallel planes. The system is
A) normal.
B) incomplete.
C) inconsistent.
D) dependent.
Q2) Suzanne invested $18,100 in two mutual fund accounts: the Abernathy Fund and the Brice Fund. During the subsequent year, The Abernathy Fund earned 11% and the Brice account earned 6%. At the end of the year, the total interest earned was $1,391. How much did Suzanne invest in each fund?
A) $6,600 in the Abernathy Fund, $11,500 in the Brice Fund
B) $5,100 in the Abernathy Fund, $13,000 in the Brice Fund
C) $6,100 in the Abernathy Fund, $12,000 in the Brice Fund
D) $6,600 in the Abernathy Fund, $11,700 in the Brice Fund
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Chapter 7: Section 2: Systems of Linear Equations
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Sample Questions
Q1) 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?
Q2) 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?
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 equations.
3x - 2y + 4z = 12
-5x - y - z = -10
-3x - 5y - 3z = -4
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Page 19
Chapter 8: Section 1: More on Inequalities
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Q1) Determine if the compound inequality is true: 4 \(\le\) 4 and 4 > 0
A)True
B)False
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) Trisha needs to adjust her cholesterol level to a target value of 150. She recalls that her cholesterol level differed from her target value by 16 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.
A) 118 or 134
B) 129 or 161
C) 134 or 166
D) 144 or 176
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Chapter 8: Section 2: More on Inequalities
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Q1) 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?
Q2) Write as a single interval if possible: (-9, \(\infty\))\(\cup\) [13, \(\infty\))
Q3) 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?
Q4) Solve the inequality and write the solution set in interval notation. 5 < |x| - 10
Q5) Write as a single interval if possible: [-1, \(\infty\))\(\cup\)(4, \(\infty\))
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Chapter 9: Section 1: Radicals and Rational Exponents
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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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Q1) The diagonal of a square measures 8 inches. What is the length of the sides?
Q2) Find all real solutions. (u - 2)<sup>-1/3</sup> = 1
Q3) Evaluate.
(27)<sup>-4/3</sup>
Q4) Find the difference. (-5 - 10i) - (-7 - 3i)
Q5) Simplify.
49<sup>2/3</sup> \(\div\) 49<sup>1/6</sup>
Q6) Find all real solutions. -10(x - 3)<sup>3</sup> = 0
Q7) Find all real solutions. (s + 3)<sup>2</sup> - 5 = 0
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Chapter 10: Section 1: Quadratic Equations and Inequalities
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Q1) Find the imaginary solutions: x<sup>2</sup> - 18x + 117 = 0
A) {9 + 6i, 9 - 6i}
B) {9 + 6i}
C) {-9 - 6i, 9 + 6i}
D) {9 + 6i, -9 + 6i}
Q2) Write a quadratic equation that has the solutions -10 and 3.
A) x<sup>2</sup> + 7x - 30 = 0
B) x<sup>2</sup> + 30 = 0
C) x<sup>2</sup> - 60x - 30 = 0
D) x<sup>2</sup> + 60x - 30 = 0
Q3) Find b<sup>2</sup> - 4ac and the number of real solutions for the given equation. x<sup>2</sup> + 3x + 4 = 0
A) -7, 2
B) 25, 0
C) -7, 0
D) 25, 2
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Page 24
Chapter 10: Section 2: Quadratic Equations and Inequalities
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Q1) Solve the given inequality and express the solution in interval notation. x<sup>2</sup> - 4x \(\ge\) 0
Q2) Find b<sup>2</sup> - 4ac and the number of real solutions for the given equation. x<sup>2</sup> - 2x + 1 = 0
Q3) Solve the inequality. Graph the solution set. x<sup>2</sup> - 8x + 12 < 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) = 0.02x<sup>2</sup> - 3x + 217.5. What number of batteries per hour minimizes the cost?
Q5) Find all real solutions of the given equation. x<sup>2/3</sup> - 3x<sup>1/3</sup> - 10 = 0
Q6) Find all real solutions of the given equation. (x<sup>2</sup> + 1)<sup>2</sup> - 11(x<sup>2</sup> + 1) = -10
Q7) Find the imaginary solutions: x<sup>2</sup> - 6x + 90 = 0
Q8) Solve: (q - 6)<sup>2</sup> = 36
Q9) Find the vertex for the graph of the parabola. f(x) = x<sup>2</sup> - 5
Page 25
Q10) 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) 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<sup>2</sup> and g(x) = x<sup>2</sup> + 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.
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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Q1) Determine whether f(x) = 2x and g(x) = 0.5x are inverses of each other.
A)True
B)False
Q2) Determine whether the given function is invertible. If it is invertible, then find its inverse.
{(-5,4),(-1,1),(-13,5)}
Q3) For the given polynomial, find the x-intercepts and determine the behavior of the graph of the polynomial at each x-intercept.
f(x) = x<sup>2</sup> + 2x - 3
Q4) How are the graphs of f(x) = x<sup>2</sup> and g(x) = x<sup>2</sup> + 7 related?
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) Let f(x) = -2x - 4 and g(x) = x<sup>2</sup> + 10x. Find (f ·g)(4).
Q7) Give the correct domain and range of the relation . {(-5, 4), (5, 4)}
Q8) How are the graphs of f(x) = (x + 4)<sup>2</sup> and g(x) = -(x + 4)<sup>2</sup> related?
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Chapter 12: Section 1: Exponential and Logarithmic Functions
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Q1) Solve log<sub>3</sub>(x<sup>2</sup> - 1) = 2 + log<sub>3</sub>(x<sup>2</sup> + 2).
A) {-2, 1}
B) Ø
C) {19}
D) {4, 7}
Q2) Write log<sub>8</sub>64 = 2 as an exponential equation.
A) 8<sup>2</sup> = 64
B) 8<sup>2</sup> = 8
C) 64<sup>2</sup> = 8
D) 64<sup>2</sup> = 64
Q3) Evaluate log<sub>1/3</sub>(3.6). Round to four decimal places.
A) -0.5064
B) -1.1660
C) 1.2809
D) -0.858
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Chapter 12: Section 2: Exponential and Logarithmic Functions
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Q1) Solve e<sup>x</sup><sup> + 2</sup> = 5.
Q2) Write log<sub>6</sub>216 = 3 as an exponential equation.
Q3) Solve log(x) = -4.
Q4) Solve -7<sup>-5-</sup><sup>x</sup> = -49.
Q5) If $10,000 is deposited in an account paying 7% compounded quarterly, then what amount will be in the account after 8 years?
Q6) Simplify ln(e<sup>9</sup>).
Q7) Rewrite log(75) in terms of log(3) and log(5).
Q8) Write ln(s<sup>5</sup>) + ln(s<sup>6</sup>) + ln(s) as a single logarithm. Assume s represents numbers for which the logarithms are defined.
Q9) Evaluate log<sub>1/5</sub>(6). Round to four decimal places.
Q10) Write log<sub>7</sub>(36) - log<sub>7</sub>(6) as a single logarithm.
Q11) Write log(64) in terms of log(4).
Q13) Write 3<sup>6</sup> = 729 as a logarithmic equation. Page 29
Q12) Solve log<sub>2</sub>(x<sup>2</sup> - 2) = 2 + log<sub>2</sub>(x<sup>2</sup> + 8).
Q14) Solve log<sub>12</sub>(x - 35) + log<sub>12</sub>(x + 35) = 2.
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Chapter 13: Section 1: Nonlinear Systems and the Conic Sections
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Q1) Solve the given system of equations. x<sup>2</sup> + y<sup>2</sup> = 625
Y = x<sup>2</sup> - 25
A) {(0, -25)}
B) {(-7, 24), (7, 24)}
C) {(0,-25), (-7, 26), (7, 26)}
D) {(0, -25), (-7, 24), (7, 24)}
Q2) Rewrite the given equation in the standard form for the equation of a circle and identify its center and radius. x<sup>2</sup> - 2x + y<sup>2</sup> + 2y - 98 = 0
A) (x + 1)<sup>2</sup> + (y - 1)<sup>2</sup> = 10; (-1, 1); 10
B) (x - 1)<sup>2</sup> + (y + 1)<sup>2</sup> = 10; (1, -1); 10
C) (x - 1)<sup>2</sup> + (y + 1)<sup>2</sup> = 100; (1, -1); 10
D) (x + 1)<sup>2</sup> + (y - 1)<sup>2</sup> = 100; (-1, 1); 10
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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Q1) Find the distance between (-10, 1) and (-12, 2).
Q2) 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?
Q3) Write the standard equation for the circle with the given radius and center. Center (8, -5), radius 12
Q4) Find two complex numbers that have a sum of -14 and a product of 58.
Q5) Solve the given system of equations. xy = 3
y = x
Q6) Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola.
(x + 9)<sup>2</sup> - y<sup>2</sup> = 1
Q7) Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola.
(x + 9)<sup>2</sup> + 3y<sup>2</sup> = 1
Page 32
Q8) Find the midpoint and length of the line segment with the endpoints (5,9) and (8,14).
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Chapter 14: Section 1: Sequences and Series Available
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Q1) Write the first four terms of the geometric sequence whose nth term is given. a<sub>n</sub> = (-6)<sup>n</sup><sup>-1</sup>
A) 1, -6, 36, -216
B) 0, -6, 36, -216
C) 1, 6, 36, 216
D) -6, 36, -216, 1296
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 15<sup>th</sup> year?
A) $16,501.70
B) $18,486.85
C) $13,009.59
D) $16,001.70
Q3) 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
Page 33
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Chapter 14: Section 2: Sequences and Series Available
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Sample Questions
Q1) Write the first five terms of the arithmetic sequence whose nth term is given. a<sub>n</sub> = -1 + (n + 1)(2)
Q2) Write a formula for the nth term of the given arithmetic sequence. 1, 7, 13, 19, 25, . . .
Q3) Find r for the geometric sequence that has a<sub>1</sub> = 3 and a<sub>4</sub> = 192.
Q4) List the first four terms of the given sequence and match your result to the correct answer below. c<sub>n</sub> = (-1)<sup>n</sup>(-4n + 3)<sup>2</sup>
Q5) 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, ...
Q6) Write the first four terms of the geometric sequence whose nth term is given. a<sub>n</sub> = (-3)<sup>n</sup><sup>-1</sup>
Q7) Write a formula for the nth term of the given geometric sequence. 3, -9, 27, ...
Q8) List all terms of the finite sequence a<sub>n</sub> = 3n + 2 for 1 n 5.
Q9) Use the binomial theorem to write out the first four terms of the given binomial. (x<sup>2</sup> + 1)<sup>22</sup> Page 34
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Chapter 15: Mathematical Problem Set
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Sample Questions
Q1) Solve the system of equations.
-0.75x + 3.5y = 3.125
0.6x + 1.5y = 1.8
Q2) Solve the given equation.
y<sup>2</sup> + 6y + 8 = 0
Q3) Simplify: u - 0.03(u - 300)
Q4) Factor.
125x<sup>3</sup> + 27
Q5) Solve and write your answer in interval notation. y + 6 < 7y - 36
Q6) Factor the given polynomial completely. If the polynomial is prime, say so. y<sup>3 </sup>- 6y<sup>2</sup> - 9y + 54
Q7) Factor completely. If the polynomial is prime, say so. 9q<sup>2</sup> + 8q + 2
Q8) 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?
Q9) Perform the indicated operation. (s<sup>2</sup> - 5s + 5) - (s<sup>2</sup> - 4s - 6)
Q10) Does the point (5, -12) satisfy the inequality y \(\ge\) 15x + 12? Page 36
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Chapter 16: Algebraic Equations and Problem Solving
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Q1) The temperature T of a gas sample varies jointly as the pressure P and the volume V. If the temperature is 297 kelvin when the volume is 4.6 liters and the pressure is 1.2 atmospheres, then what is its temperature if the gas is compressed to 1.5 liters at 2.9 atmospheres? Round your answer to the nearest tenth of a kelvin. [The unit "kelvin" is simply a temperature unit related to the Celsius degree. The exact relationship between the two plays no part in the solution of this problem.]
A) 230.8 kelvin
B) 234.0 kelvin
C) 198.9 kelvin
D) 242.9 kelvin
Q2) Simplify: r - 0.1(r + 400)
A) 0.9r - 40
B) 1.1r + 40
C) 1.1r - 40
D) 0.9r + 40
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) Solve 3<sup>10</sup><sup>x</sup><sup> - 8</sup> = 9<sup>4</sup><sup>x</sup><sup> - 1</sup>.
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) Find the imaginary solutions: 49x<sup>2</sup> + 70x + 125 = 0
Q4) Solve the given system of equations.
y = x<sup>2</sup>
y = 5
Q5) 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.
Q6) Find the product. (3a + 4)(2a + 1)
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Chapter 18: Algebraic Equation Practice
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Q1) If $700 is deposited in an account paying 9% compounded continuously, then what amount will be in the account after 5 years?
A) $1,097.82
B) $960.06
C) $2,157.15
D) $1,262.74
Q2) Factor. 64y<sup>3</sup> - 125z<sup>3</sup>
A) (4y + 5z)(16y<sup>2</sup> - 20yz + 25z<sup>2</sup>)
B) (4y - 5z)(16y<sup>2</sup> + 20yz + 25z<sup>2</sup>)
C) (4y - 5z)(4y<sup>2</sup> + 20yz + 5z<sup>2</sup>)
D) (4y - 5z)(16y<sup>2</sup> - 20yz + 25z<sup>2</sup>)
Q3) Find all real solutions of the given equation. (x<sup>2</sup> - x)<sup>2</sup>39(x<sup>2</sup> - x) - 126 = 0
A) {-7, 6}
B) {-7, 3, 6}
C) {-6, -3, 7}
D) {-6, 7}
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Page 40