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Class:
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2015-2016 Midterm Review
Algebra 2 Honors Midterm Topics
1-1 Expressions and Formulas
1-2 Properties of Real Numbers
1-3 Solving Equations (including literal)
1-4 Solving Absolute Value Equations
1-5 Solving Inequalities
1-6 Solving Compound Inequalities
Interval Notation
2-1 Relations and Functions
2-2 Linear Relations and Functions
2-3 Rate of Change and Slope
2-4 Writing Equations of Lines
2-5 Scatter Plots and Lines of Regression
2-6 Special Functions
2-7 Parent Functions and Transformations
2-8 Graphing Linear and Absolute Value Inequalities
3-1 Solving Systems of Equations
3-2 Solving Systems of Inequalities by Graphing
3-3 Optimization with Linear Programming
3-4 Systems of Equations in Three Variables
4-1 Graphing Quadratic Functions
4-2 Solving Quadratic Equations by Graphing
4-3 Solving Quadratic Equations by Factoring
4-4 Complex Numbers
4-5 Completing the Square
4-6 The Quadratic Formula and the Discriminant
4-7 Transformations of Quadratic Graphs
4-8 Quadratic Inequalities
5-1 Operations with Polynomials
5-2 Dividing Polynomials
5-3 Polynomial Functions
5-4 Analyzing Graphs of Polynomial Functions
5-5 Solving Polynomial Equations
5-6 The Remainder and Factor Theorems
5-7 Roots and Zeros
5-8 Rational Zero Theorem
6-1 Operations on Functions
6-2 Inverse Functions and Relations
6-3 Square Root Functions and Inequalities
6-4 Nth Roots
6-5 Operations on Radicals
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NOTE: DO NOT STUDY FROM ONLY THIS PACKET.
TESTS/QUIZZES/HOMEWORKS SHOULD ALSO BE REVIEWED
TO PREPARE FOR THE EXAM.
Indicate the answer choice that best completes the statement or answers the question.
1. The flow rate of IV fluids is calculated using the formula
, where V is the volume of the solution in
milliliters, d is the drip factor in drips per minute, and t is the time in minutes. Determine the flow rate of 1500 milliliter
IV fluid for a patient for 24 hours if the drip factor is 1 milliliter per minute.
a. 1.04
b. 25
c. 10.4
d. 6.25
2. The formula to calculate the volume of a cylinder is
cylinder.
a.
b.
c.
. Write an expression to represent the volume of the
d.
Solve the given equation. Check your solution.
3. 5 |2s + 5| = 50
a. {2.5, 7.5}
b. {22.5, –7.5}
c. {–2.5, –7.5}
d. {2.5, –7.5}
Solve the given inequality. Describe the solution set using the set-builder or interval notation. Then, graph the solution set
on a number line.
4.
a.
The solution set is
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.
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b.
c.
d.
The solution set is
.
The solution set is
.
The solution set is
.
Mrs. Robinson, an insurance agent, earns a salary of $4800 per year plus a 3% commission on her sales. The average
price of a policy she sells is $6100.
5. How many policies must Mrs. Robinson sell to get an annual income of at least $10,000.
a. Mrs. Robinson must sell 29 policies to get the desired income.
b. Mrs. Robinson must sell at the most 28 policies to get the desired income.
c. Mrs. Robinson must sell at least 28 policies to get the desired income.
d. Mrs. Robinson must sell at least 23 policies to get the desired income.
Solve the given inequality. Graph the solution set on a number line.
6.
a. The solution set is {p | p > –5 or p < 5}.
b. The solution set is {p | p > 7 or p < –5}.
c. The solution set is {p | p > 6 or p < 1}.
d. The solution set is {p | –5 < p < 7}.
7. The sum of the circumference of circle A and the perimeter of square B is equal to 130 inches. The side of square B is
three times the side of square C. If the side of square C is 7 inches, what is the area of circle A? Round to the nearest
hundredth.
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8. A bulb manufacturing company claims that the average life of a bulb it produces is 1250 hours. On the basis of its
claim, a customer survey was conducted. The survey found that the actual life of the bulb is 25 hours more or less than the
claim made by the company. Write and solve an equation describing the maximum and minimum life of the bulb in hours.
Indicate the answer choice that best completes the statement or answers the question.
9. Find the value of f(–8) and g(8) if f(x) = –7x + 4 and g(x) = 6x + 22x–4.
a. f(–8) = 60
b. f(–8) = –56
g(8) = 48.01
g(8) = –47.99
c. f(–8) = –3
d. f(–8) = 52
g(8) = 70
g(8) = 47.99
10. Write the equation 2y = 15x + 0.1 in standard form. Identify A, B, and C.
a. 20x – 150y = 1 where A = 20, B = –150, and C = –1
b. 20x – 1y = 1 where A = 20, B = –150, and C = 1
c. 150x + 20y = –1 where A = 150, B = 20, and C = 1
d. 150x – 20y = –1 where A = 150, B = –20, and C = –1
11. Find the x-intercept and the y-intercept of the graph of the equation
a.
x + 8y = 14. Then graph the equation.
b.
The x-intercept is
The y-intercept is 2.
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.
The x-intercept is
.
The y-intercept is
.
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c.
d.
The x-intercept is
.
The y-intercept is
.
The x-intercept is
.
The y-intercept is 14.
12. The graph shows the value of a stock (to the nearest dollar) over an 8-hour period. Find the average rate of change in
the stock from hour 5 to hour 7. Round to the nearest cent if necessary.
a. $1.50/hr
c. $2.00/hr
b. –$1.00/hr
d. –$1.50/hr
13. Find the slope of the line that passes through the pair of points (
a.
b.
c.
d.
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,
) and (
,
).
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14. Write an equation in slope-intercept form for the line that satisfies the following condition.
passes through (11, –3), parallel to the graph of y =
a.
c.
y = 3x –
y=
x–
b.
d.
x+4
y = 16x +
y=
x+
15. Write an equation in slope-intercept form for the line that satisfies the following condition.
passes through (8, 9), perpendicular to the graph of 6x + 12y = 23
a. y = x +
b. y = x –
c. y = 8x +
d. y = 8x + 12
16. The ideal weight (in stones) of people of varying heights is given in the table below. Draw a scatter plot for the data.
Height (meters)
Weight (stones)
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1.52
9.1
1.55
9.5
1.57
9.8
1.60
10
1.63
10.4
1.65
10.8
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a. Graph I
c. Graph III
b. Graph II
d. Graph IV
17. The table below shows the median selling price of houses in the early 1990s. Use the second and seventh ordered pairs
shown below to write a prediction equation. Use the prediction equation to predict the missing value.
Year
Price ($ thousands)
1990
130
1991
135
1992
122
a.
; 161.01
b.
c.
; 36.19
d.
1993
145
1994
151
1995
139
1996
161
1997
?
; 166.2
; 210
Identify the domain and range of each function.
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18.
a. domain: all integers
range: all real numbers
c. domain: all real numbers
range: all integers
b. domain: all real numbers
range: all real numbers
d. domain: all integers
range: all integers
19.
a. domain:
range: all real numbers
c. domain:
range:
b. domain: all real numbers
range: all real numbers
d. domain: all real numbers
range:
Write the function shown in the graph.
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20.
a.
c.
b.
d.
21.
a.
b.
c.
d.
Describe the transformation in each function.
22. y = (x + 1)2
a. translation of the graph of y = x2 right 1 units
c. translation of the graph of y = x2 up 1 units
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b. translation of the graph of y = x2 down 1 units
d. translation of the graph of y = x2 left 1 units
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23. y = |x|
a. vertical compression of the graph of y = |x| by a
b.
translation of the graph of y = |x| up unit
factor of
c.
d. vertical expansion of the graph of y = |x| by a
factor of
translation of the graph of y = |x| left unit
24. Graph the given inequality.
y≤1–|x|
a.
c.
b.
d.
25. Graph the given inequality.
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a.
b.
c.
d.
26. Graph the given inequality.
a.
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b.
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c.
d.
27. Daniel pays $389 in advance on his account at the athletic club. Each time he uses the club, $7 is deducted from the
account. Write a linear function to calculate the value remaining in his account after x visits to the club. Use the linear
function to find the value remaining in the account after 11 visits.
28. A pyramid-shaped tower is 35 meters high and 25 meters wide. Find the slope of the tower.
29. The table below shows the cost of a Black Forest cake at two bakeries.
Find the distance for which the two bakeries charge the same price for the Black Forest cake.
Graph each function. Identify the domain and range.
30.
31.
32.
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33.
34. John got $6 from his father to buy pens and pencils for his final exam. If each pencil costs $0.20 and each pen costs
$0.30, write and graph an inequality that can be used to find out the number of pens and pencils he can buy.
Indicate the answer choice that best completes the statement or answers the question.
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many
solutions. If the system has one solution, name it.
35.
a. one solution; (–2, 7)
b. infinitely many
c. no solution
d. one solution; (7, –2)
Use substitution to solve each system of equations.
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36. x – 5y = –3
–7x + 8y = –33
a. (2, 7)
b. (–5, 1)
c. (7, 2)
d. (1, –5)
Solve the system of inequalities by graphing.
37. x > 1
y > 10
a.
c.
b.
d.
38. y > x – 5
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a.
b.
c.
d.
Find the coordinates of the vertices of the figure formed by each system of inequalities.
39. y + x ≥ –4
y≥x–6
3y + x ≤ 10
a. (1, –5), (–14, 8), (–11, 7)
b. (1, 5), (7, 1), (11, 7)
c. (1, 7), (–11, 1), (7, –5)
d. (1, –5), (7, 1), (–11, 7)
Given below are some inequalities. Plot the feasible region graphically.
40.
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a.
b.
vertices: (3, –3), (3, 0), (0, –3)
max: f(3, 0) = 3
min: f(0, –3) = –3
c.
vertices: (3, –3), (3, 0), (0, –3)
max: f(3, 0) = 3
min: f(0, –3) = –3
d.
vertices: (3, –3)
max: f(3, –3) = 0
min: f(3, –3) = 0
vertices: (3, –3), (3, 0), (0, –3)
max: f(3, 0) = 3
min: f(0, –3) = –3
Efficient Homemakers Ltd. makes canvas wallets and leather wallets as part of a money-making project. For the canvas
wallets, they need two yards of canvas and two yards of leather. For the leather wallets, they need four yards of leather
and three yards of canvas. Their production unit has purchased 44 yards of leather and 40 yards of canvas. Let x be the
number of leather wallets and y be the number of canvas wallets.
41. Draw the graph showing the feasible region to represent the number of the leather and canvas wallets that can be
produced.
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a.
b.
c.
d.
42. If the profit on a canvas wallet is $25 and the profit on a leather wallet is $40, write a function for the total profit for
both wallets.
a. f(x, y) = 40x + 25y
b. f(x, y) = 40x + y
c. f(x, y) = 25x + 40y
d. f(x, y) = x + 25y
43. What is the maximum profit?
a. $510
b. $250
c. $440
d. $550
Solve the given system of equations.
44. –2a = –8
6a + 2c = 10
2b + 5c = –41
a. a = –7, b = 4, c = –3
c. a = 4, b = –7, c = –3
b. a = 4, b = –3, c = –7
d. a = –4, b = –3, c = –7
Chocos is a dish made from wheat, sugar, and cocoa. Bertha is making a large pot of chocos for a party. Wheat (w) costs
$5 per pound, sugar (s) costs $3 per pound, and cocoa (c) costs $4 per pound. She spends $48 on 12 pounds of food. She
buys twice as much cocoa as sugar.
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45. Write a system of three equations that represents how much food Bertha purchased.
a. 5w + 3s + 4c = 48
w + s + c = 12
c = 2s
b. 5w + 3s + 2c = 48
w + s + c = 12
c = 2s
c. 5w + 3s + 4c = 12
w + s + c = 48
c = 2s
d. 5w + 3s + 4c = 48
w + s + c = 12
s = 2c
46. How much wheat, sugar, and cocoa will she use (in pounds) in her dish?
a. wheat: 6 lb, sugar: 3 lb, cocoa: 3 lb
b. wheat: 3 lb, sugar: 3 lb, cocoa: 6 lb
c. wheat: 3 lb, sugar: 6 lb, cocoa: 3 lb
d. wheat: 6 lb, sugar: 2 lb, cocoa: 4 lb
Solve the system of equations.
47. 5x – 5y + 7z = 94
–7x + 2y – 7z = –107
–6x + 6y + 4z = –26
a. (7, –1, 8)
b. (8, –1, 7)
c. (8, 1, 7)
d. (–8, –1, –7)
48. A customer at a movie theater purchased 4 adult tickets and 4 child tickets for $68.00. Another customer purchased 2
adult tickets and 5 child tickets for $56.50. What is the cost of an adult ticket and a child ticket to the movie theater? Set
up and solve a matrix equation.
a. adult: $9.00
child: $7.00
b. adult: $8.50
child: $6.50
c. adult: $9.50
child: $7.00
d. adult: $9.50
child: $7.50
49. Graph the system of equations and describe them as consistent and independent, consistent and dependent, or
inconsistent.
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50. A bag contains 19 red, green, and white balls. The number of red balls is five more than the number of white balls and
the number of green balls is 3 less than the number of red balls. Write and solve a system of equations that represents the
number of red balls, green balls, and white balls.
Indicate the answer choice that best completes the statement or answers the question.
51. Graph the quadratic function
a.
c.
.
b.
d.
Determine whether the given function has a maximum or a minimum value. Then, find the maximum or minimum value of
the function.
52. f(x) = x2 – 6x + 6
a. The function has a maximum value. The maximum value of the function is –3.
b. The function has a maximum value. The maximum value of the function is 33.
c. The function has a minimum value. The minimum value of the function is –3.
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d. The function has a minimum value. The minimum value of the function is 33.
Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are
located.
53.
a.
b.
The solution set is
.
The solution set is
c.
d.
The solution set is
.
The solution set is
Write a quadratic equation with the given roots. Write the equation in the form
integers.
54.
.
.
, where a, b, and c are
and –5
a. 4x2 + 17x – 15 = 0
b. 4x2 – 17x + 15 = 0
c. x2 + 17x – 15 = 0
d. x2 + 17x + 15 = 0
Solve the equation by factoring.
55. 4x2 + 7x + 2.5 = 0
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a.
{2,
b.
}
c. {2, 5}
d.
{
,
}
{
, 5}
Simplify.
56.
a. 14i
b. –7i
c. 7i
d. –7
57. (3i)(–4i)(5i)
a. –60
b. –60i
c. 60i
d. 60
58. (6 – 20i) – (23 – 10i)
a. –43 + 16i
b. –17 – 30i
c. –17 – 10i
d. 33i – 14i
59. (4 + 8i)(10 – 5i)
a. 40 + 60i – 40i2
b. 40 + 60i + 40
c. 44 + 80i
d. 80 + 60i
60.
a.
c.
+
i
+
i
b.
d.
–
i
–
i
61.
a. –i
c. i
b. –1
d. 1
62.
a.
c.
+
i
–
i
b.
d.
+
i
–
i
Solve the equation by completing the square.
63. x2 – 3x – 10 = 0
a. {–2, 5}
b. {–4, 10}
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c. {–4, 5}
d. {–5, 2}
Find the exact solution of the following quadratic equation by using the Quadratic Formula.
64. –x2 + 11x + 5 = 0
a. {(11
)/–2}
c. {(–11
)/–2}
b. {(–11
)/–2}
d. {(–11
)/–2}
Find the value of the discriminant. Then describe the number and type of roots for the equation.
65. –x2 – 20x + 3 = 0
a. The discriminant is 400. Because the discriminant is greater than 0 and is a perfect square, the two roots are
real and rational.
b. The discriminant is –412. Because the discriminant is less than 0, the two roots are complex.
c. The discriminant is 412. Because the discriminant is greater than 0 and is not a perfect square, the two roots
are real and irrational.
d. The discriminant is –388. Because the discriminant is less than 0, the two roots are complex.
Write the following quadratic function in vertex form. Then, identify the axis of symmetry.
66. y = x2 + 6x – 2
a. The vertex form of the function is y = (x + 3)2 – 11.
The equation of the axis of symmetry is x = –3.
b. The vertex form of the function is y = (x – 3)2 – 11.
The equation of the axis of symmetry is x = –3.
c. The vertex form of the function is y = (x + 3)2 – 11.
The equation of the axis of symmetry is x = –11.
d. The vertex form of the function is y = (x + 3)2 + 11.
The equation of the axis of symmetry is x = –11.
67. Write an equation for the parabola whose vertex is at (2, 8) and which passes through (4, –3).
a. y = (x + 2)2 – 8
b. y = 2.75(x – 2)2 + 8
c. y = –2.75(x – 2)2 + 8
d. y = –2.75(x + 2)2 – 8
68. Graph the quadratic function
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.
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a.
b.
c.
d.
Graph the quadratic inequality.
69.
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a.
b.
c.
d.
Solve the inequality.
70. x2 + 7x > 8
a. {x | x < 8
c. {x | x < 8
x > –1}
b. {x | x < –8
x > 1}
x > 1}
d. {x | x < –8
x > –1 }
71. At a state fair, each ride costs $1.50. On average, 50 people per hour take rides. For each 25-cent increase in the cost
of rides, the number of people taking rides drops by 5 per hour. Find the cost of each ride at the fair to obtain maximum
income from the rides.
72. The path of the water from a sprinkler is modeled by a quadratic function
where h(d) is the
height of water, in feet, at a distance of d feet from the jet. Find how far from the sprinkler the water hits the ground.
73. The sales revenue of a company is described by
number of units sold if the company’s revenue is $32,500.
, where is the number of units sold. Find the
74. A ladder 20 feet long is leaning against a wall and reaches the top of the wall. If the height of the wall is 4 feet more
than the distance between the foot of the ladder and the base of the wall, find the height of wall.
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75. Ryan is working on a science project. He has a roll of paper with an area of 5040 square inches. He has to cut the
paper into four equal pieces. He will need exactly 576 inches of crepe paper to make borders around the four equal pieces.
Find the dimensions of the four equal pieces.
Indicate the answer choice that best completes the statement or answers the question.
Simplify the given expression. Assume that no variable equals 0.
76. 13x(5xy13)(–12x–5y9)
a. –780x22y–60
b. 6y22
x3
c. –780x–3y22
d. –780y22
x3
Simplify the given expression.
77. (–10x2 – 2x + 20) – (17x2 + 19x – 6)
a. –27x2 – 21x + 14
b. –27x2 – 21x + 26
c. –27x2 – 17x + 26
d. –27x2 – 19x + 14
78. –2xy(6xy3 – 9xy + 7y2)
a. –12x2y4 – 9x2y2 + 7x2y3
c. –12x2y4 + 18x2y2 – 14xy3
b. –12x2y4 + 18xy + 14y2
d. –12x2y4 – 9xy + 7y2
Simplify the expression using long division.
79. (8x2 – 17x + 2) ÷ (x – 2)
a. quotient 8x – 17 and remainder 2
c. quotient 8x – 1 and remainder –4
b. quotient 8x – 1 and remainder 0
d. quotient 8x + 1 and remainder 4
Simplify the expression using synthetic division.
80. (4x3 – 71x2 + 306x – 360) ÷ (x – 12)
a. quotient 4x2 – 119x – 1122 and remainder 13,104
b. quotient 52x2 + 553x – 6,942 and remainder 82,944
c. quotient 4x2 – 23x + 30 and remainder 0
d. quotient 48x2 + 505x + 6,366 and remainder 76,032
81. Find p(–3) and p(5) for the function p(x) = 7x5 – 7x4 – 6x2 + 11x – 12.
a. –2,323; 17,349
b. –99; –107
c. –2,355; 17,405
d. –2,367; 17,393
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For the given graph,
a. describe the end behavior,
b. determine whether it represents an odd-degree or even-degree polynomial function, and
c. state the number of real zeros.
82.
a. The end behavior of the graph is
It is an odd-degree polynomial function.
The function has five real zeros.
b. The end behavior of the graph is
It is an odd-degree polynomial function.
The function has five real zeros.
c. The end behavior of the graph is
It is an odd-degree polynomial function.
The function has four real zeros.
d. The end behavior of the graph is
It is an even-degree polynomial function.
The function has five real zeros.
as
and
as
.
as
and
as
.
as
and
as
.
as
and
as
.
Factor the polynomial completely.
83. 3x4y – 6x2y2
a. 3x2y(x2 – 2y)
b. 3x2(x2y – 2y2)
c. x2y(3x2 – 6y)
d. 3(x4y – 2x2y2)
84. 18x3 – 30x2 + 60x – 100
a. 6x2(3x – 5) – 20(3x – 5)
c. 6x2(3x – 5) – 60x + 100
b. (6x2 + 20)(3x – 5)
d. (18x3 – 30x2) + (60x – 100)
85. 216x3 + 125y3
a. (6x – 5y)(36x2 – 30xy + 25y2)
c. (6x – 5y)(36x2 + 30xy + 25y2)
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b. (6x + 5y)(36x2 – 30xy + 25y2)
d. (6x + 5y)(36x2 + 25y2)
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2015-2016 Midterm Review
86. x4 – 45x2 + 324 = 0
a. 3, –3, 6, –6
c. 6, –6
b. 3, –3, 7, –7
d. 7, –7, 9, –9
87. Use synthetic substitution to find g(3) and g(–8) for the function g(x) = x5 – 8x3 – 3x + 2.
a. 20, –28,646
b. 38, –28,694
c. 452, 28,650
d. –142, 8,218
Given a polynomial and one of its factors, find the remaining factors of the polynomial. Some of the factors may not be
binomials.
88. 100x3 – 1000x2 – 121x + 1210; x – 10
a. (10x – 11)(10x + 11)
b. (100x2 – 121)
c. (10x – 11)
d. (10x – 11)(10x – 11)
89. Describe the possible real zeros of f(x) = –7x3 + 8x2 + 4x – 3.
a. 4, 2, or 0 2 or 0 positive zeros and 1 negative zero
b. 4, 2, or 0 positive zeros and 0 negative zeros
c. 4, 2, or 0 2 or 0 positive zeros and 1 negative zero
d. 4, 2, or 0 2 or 0 positive zeros and 0 negative zeros
90. Find all of the zeros of the function f(x) = x3 – 11x2 + 36x – 26.
a. 1, 5 – i, 5 + i
b. 5 – i, 5 + i
c. 1, 5 – i
d. –1, 5 – i, 5 + i
91. Find all of the zeros of the function f(x) = 5x3 – 79x2 + 354x – 432.
a.
b.
– , –2, 9
,9
c.
–
, 2, 9
d.
, 2, 9
92. Write a polynomial function of least degree with integral coefficients that has the given zeros.
–2, –8,–7 – 6i
a. x2 + 10 x + 16
b. x4 + 241x2 + 1074x + 1360
c. x4 + 24x3 + 241x2 + 1074x + 1360
d. x4 + 24x3 + 1074x + 1360
93. List all of the possible rational zeros of the following function.
f(x) = x6 – 4x5 – 17x4 + 90x3 + 28x2 – 22x + 100
a.
, , ,
,
,
,
,
b. –1, –2, –4, –5, –10, –20, –25, –50, –100
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c.
, , , ,
,
,
d. 1, 2, 4, 5, 10, 20, 25, 50
,
94. Find all the rational zeros of the function f(x) = 36x4 + 66x3 – 18x2 – 12x.
a.
b.
, 0,
,
, 0,
,
c.
d.
,
,0
95. The initial price of a stock was x dollars. The first week of trading, the price gained
dollars and the second
week it lost
dollars. Write an expression that represents the price of the stock at the end of the second week.
96. The perimeter of a triangle is
the third side of the triangle.
The length of two sides of the triangle are
and
Find the measure of
97. A door is made from a pane of glass 5 feet long and 2 feet wide in a wooden frame b feet wide on all sides. The entire
door has an area of 28 square feet. How wide is the frame?
98. A box in the shape of a rectangular prism has a volume of 210 cubic feet. The dimensions of the box are x feet high by
feet long by
feet high. How long is the box?
Indicate the answer choice that best completes the statement or answers the question.
99. Find
for the following functions.
f(x) = 2x2 + 3x + 2
g(x) = 8x + 2
a. 10x2 + 5x + 2
b. 2x2 + 11x + 2
c. 10x3 + 5x + 2
d. 2x2 + 11x + 4
100. Find
for the following functions.
2
f(x) = 4x – 11x – 12
g(x) = 13x – 3
a. 52x3 – 155x2 + 33x – 192
b. 52x3 + 12x2 – 266x + 36
c. 52x3 – 155x2 – 123x – 36
d. 52x3 – 155x2 – 123x + 36
101. Find
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for the following functions.
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a.
b.
,
,
c.
d.
,
102. Find
and
,
.
g(x) = 6x
h(x) = –9x3 + 11x2 – 7x + 3
a.
= –54x4 + 66x3 – 42x2 + 18x
= –1944x4 + 396x3 – 42x2 + 3x
b.
= –54x3 + 66x2 – 42x + 18
= –1944x3 + 396x2 – 42x + 18
c.
= 54x3 + 66x2 – 42x + 18
= –1944x3 + 396x2 – 42x + 3
d.
= –54x3 + 66x2 – 42x + 18
= –1944x3 + 396x2 – 42x + 3
Find the inverse of the given relation.
103. {(10, –1), (7, –4), (12, –3), (10, –8)}
a. {(–1, 10), (4, –7), (–3, 12), (–8, 10)}
b. {(–1, 10), (–4, 7), (–3, –12), (–8, 10)}
c. {(–1, 10), (–4, 7), (–3, 12), (–8, 10)}
d. {(–1, 10), (–4, 7), (–3, 12), (–8, –10)}
Find the inverse of the given function.
104. f(x) =
a. –1
f (x) =
b. –1
f (x) =
c. –1
f (x) =
d. –1
f (x) =
105. Determine whether each pair of functions are inverse functions.
1) f(x) =
, g(x) =
2) f(x) = x – 5, g(x) = x + 5
a. Both 1 and 2 are inverse functions.
b. Only 2 is an inverse function.
c. Neither 1 nor 2 is an inverse function.
d. Only 1 is an inverse function.
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106. Graph f(x) =
.
a.
b.
c.
d.
107. Graph the given function. State the domain and range.
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a.
b.
The domain is x ≤ and the range is y
The domain is x ≤ and the range is y ≤ 4.
4.
c.
d.
The domain is x
108. Graph the inequality
a.
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and the range is y
The domain is x ≤ and the range is y
4.
4.
.
b.
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c.
d.
Simplify.
109.
a.
b.
c.
d.
110.
a.
b.
c.
d.
111. Simplify
.
a.
b.
c.
d.
112. What is
a. 16
divided by
b. 256
c. 3
?
d. 32
Simplify.
113.
a. 5
c. 11
+
+ 11
+5
–
+
b. 5
– 11
d. 11
–5
114. (3 +
)(5 +
)
a. 15 + 3
+5
+
c. 15 + 3
+5
–
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b. 15 – 3
+5
+
d. 15 – 3
+5
–
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115.
a.
b.
c.
d.
116. (
–
a. 15 – 2
)2
c. 11 – 2
b. 15 + 2
d. 11 + 2
117.
a.
b.
c.
d.
A wireless optical mouse costs $29. John has a discount coupon for $20 and a coupon for 14% off. The composition of the
functions is given below.
d(x) = x – 20.00
p(x) = 0.86x
118. Find
and explain what this value represents.
119. Find the inverse of the function. Then graph the function and its inverse.
120. Find the perimeter of a regular hexagon whose sides measure
feet.
121. Which expression must represent a negative number when x is negative?
a) x2
c) x3
b) 4 + x
122. The numbers -9 and a) real numbers
e) none of these
1
are not
9
b) additive inverses
d) multiplicative inverses
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d) -x
c) reciprocals
e) rational numbers
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1
123. If x  1 
a)
1
1
3
3
b) 
2
3
2
124. If
, then x 
c)
1
2
d) 
1
2
e)
2
3
x
 x 2 , then the value of x can be which of the following:
3
1
1
I. 
II. 0
III.
3
3
a) I only
b) II only
c) III only
d) II and III only
e) I, II, and III
125. If you rent a van for one day and drive it 100 miles, the cost is $72. If you drive it 150 miles, the cost is $96. If the
function is linear, how much will it cost to rent the van for one day and drive it 200 miles?
a) $120
b) $ 96
c) $ 168
d) $ 144
126. If f ( x)  mx  b then simplify the expression
a) m
b)  m
c) m  k
d) m  1
e) none of these
f ( x  k )  f ( x)
k
e) NOT
127. If f ( x ) = 2 x 2 – 6 x and g ( x ) = x – 3 , find the values for which f ( x ) = g ( x )
a) -2, -1
b) 1/2, 3
c) 1, 2
d) 1, 3
e) none of these
1
f ( t )  4 , what is the value of t?
2
3
7
9
49
81
a)
b)
c)
d)
e)
2
2
4
4
2
x5
?
129. What is the domain of the function f ( x) 
x6
a) (,6)  (6, ) b) (,5)  (5, ) c) (−∞, −6) ∪ (−6, ∞) d) (−∞, −6) ∪ (6, ∞)
128. Let the function f be defined f ( x)  2 x  1 . If
130. Find the domain of the function f ( x ) =√36 − 𝑥 2
a) ( - , 6
b) ( - , -6 )
c)  - 6, 6 ]
d) ( -6, 6 )
f ( x  3)  f ( 3)
x
18  x
c) x – 6
d)
x
e) none of these
131. If f ( x ) = x 2 , x  0 , find
a)
9
x
b) x 2 + 6 x + 9
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e) none of these
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132. What is the domain of the function f ( x)  3x ?
a) the set of all nonnegative real numbers
c) the set of all real numbers
b) the set of all real numbers except 0
d) the set of all real numbers except -3
e) none of these
133.
a)
b)
c)
d)
134. Which of the following inequalities would have the same graph?
I x>4
II - 3 x < -12
a) I and II only
III x + 1 >3
b) II and III only
c) I, II, and III only
d) II, III, and IV only
135. Solve the system:
A) ( 1, -1, 3 )
B) ( 2, -5, -2 )
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IV 12 < 2 x + 4
e) NOT
x - y + z = 5
3 x + 2 y - z = -2
2 x + y + 3 z = 10
C) (-1, 7, 13 )
D) ( 3, -9, -7 )
E) none of these
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136. Graph:
137. The figure shows the graph of a quadratic function h whose
is h(2).
maximum value
y
If h(a)  0 , which of the following could be the value of a?
a) -1
b) 0
c) 2
d) 3
e) 4
1
x
1
138. The quadratic equation 𝑥 2 – 8x = –20 is to be solved by completing the square. Which equation would be a step in
that solution?
A (𝑥 − 4)2 = 4
C 𝑥 2 – 8x + 20 = 0
B x – 4 = ±2i
D 𝑥 2 – 8x + 16 = –20
139. Write an equation for the parabola whose vertex is at (–8, 4) and passes
through (–6, –2).
3
1
A y = – 2 (𝑥 + 8)2 + 4
B y = – 4 (𝑥 + 8)2 + 4
3
2
3
2
C y = − (𝑥 + 6)2 – 2
D y = – (𝑥 − 8)2 + 4
140. Which quadratic inequality is graphed at the right?
A y ≥ (x – 2)(x + 3)
C y > (x + 2)(x – 3)
B y > (x – 2)(x + 3)
D y < (x + 2)(x – 3)
141. What are the solutions of 2x3 + 10x2 +12x = 0
a) 2, 10, 12
b) 0, 3
c) 0, -2, -3
d) 0, 2, 3
e) -1, 0, 6
142. If the equation x2 – 4x + k = 1 has exactly one solution for the value of x, then k =
a) 5
b) 4
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c) 2
d) -1
e) none of these
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143. A ball is thrown vertically upward with an initial velocity of 80 ft/sec. Its height after t seconds is given by the
function h(t) = 80t – 16t2. The maximum height of the ball is:
a) 200 ft
b) 100 ft
144. When
a) 2
c) 2.5 ft
d) 5 ft
e) none of these
1  3i
is expressed in a  bi form, then a 
1 i
b) 1
c)
1
2
d) -1
e) -2
145. Determine the solution for the inequaltiy: (x – 3)(x – 4)(x – 5) > 0
146. Which of the following is the square of a binomial?
b) x2 – 13x + 36
a) x2 + 20x + 36
c) x2 – 12x + 36
d) x2 – 12z -36
e) none of these
147. If b  0 , which of the exponents or powers property is not written correctly?
1
b n
b)

(9b n )
9
a) b  1
0
c) b m  b n  b mn
d)
an
a
 ( )n
n
b
b
e) none of these
148. Which of the following is NOT a factor of x12  1?
a) x – 1
c) x 2 + 1
b) x + 1
d) x 4 + x 2 – 1
e) x 2 – x + 1
149. If x – 1 is a factor of x 2  ax  4 , then a has the value
a) 4
b) 3
c) 2
d) 1
e) none of these
150. Simplify x 2 n 1  x1 2 n
a) x
b) 1
c) 0
d) x 4 n
2
 4 n 1
e) none of these
151. Which of the following are true?
a) x2x3 = x6
b) ( -y )2 = - y2
c) ( -x )3 = - x3
d) x2 – y2 = ( x – y )2
e) none of these
152. If (x – 2) is a factor of x3 – x2 – x – 2, then f(2) =
a) -2
b) 0
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c) 1
d) 2
e) none of these
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Answer Key
1. a
2. b
3. d
4. b
5. a
6. d
7.
8.
, where is the life of the bulb in hours;
9. a
10. d
11. b
12. d
13. b
14. c
15. b
16. a
17. b
18. c
19. d
20. d
21. a
22. d
23. a
24. b
25. b
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26. b
27.
; $312
28. 2.8
29. 100 miles
30.
31.
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32.
33.
34.
, where denotes the number of pencils and denotes the number of pens.
35. a
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36. c
37. b
38. a
39. d
40. b
41. a
42. a
43. a
44. b
45. a
46. b
47. b
48. d
49.
The graphs of the lines intersect at one point, so there is one solution. The system is consistent and independent.
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50.
51. a
52. c
53. b
54. a
55. b
56. c
57. c
58. c
59. d
60. b
61. a
62. b
63. a
64. d
65. c
66. a
67. c
68. c
69. a
70. b
71. $2.00
72. 3.6 ft
73. 50 units
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74. 16 ft
75. 42 in. by 30 in.
76. d
77. b
78. c
79. b
80. c
81. d
82. b
83. a
84. b
85. b
86. a
87. a
88. a
89. c
90. a
91. d
92. c
93. a
94. a
95.
dollars
96.
97. 1 ft
98. 10 ft
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99. d
100. d
101. d
102. d
103. c
104. b
105. b
106. c
107. b
108. d
109. a
110. d
111. d
112. a
113. a
114. a
115. a
116. a
117. b
118. $4.94; 14% is taken off first and then the discount coupon is applied.
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119.
120.
feet
121. C
122. B
123. D
124. D
125. A
126. A
127. B
128. E
129. A
130. C
131. C
132. A
133. B
134. E
135. A
136. C
137. A
138. B
139. A
140. C
141. C
142. A
143. B
144. A
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145. A
146. C
147. C
148. D
149. B
150. B
151. C
152. B
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