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AAT Semester 1 Final Exam Review Name: ______________________________ Period: __________
1. Explain how to find the vertex of a parabola if it is in vertex form. ( ) 2. Explain how to find the x-intercepts of a parabola if it is in factored form. ( )( ) 3. Explain how to find the y-intercept of a parabola if it is in standard form.
a. Can you apply the same method to any equation to find the y-intercept? 4. Match the equation to the graph.
a. ( )
b. ( )
c. ( )
d. ( )
5. Match the equation to the graph. a. ( )( )
b. ( )( )
c. ( )( )
d. ( )( )
6. Match the equation to the graph. a. b. c. d.
7. Match the equation to the graph. a. ( )
b. ( )
c. ( )
d. ( )
8. Without using your graphing calculator determine the vertex.
( )
9. Without using your graphing calculator determine the x-intercepts.
10. Without using your graphing calculator determine the y-intercept.
11. Without using your graphing calculator determine the x-intercepts.
( )( )
For questions 12-17, identify the key features of each equation. 12.
Vertex: ________________ Y-intercept: __________ X-intercept(s): __________
13.
Vertex: ________________ Y-intercept: __________ X-intercept(s): __________
14. ( )
Vertex: ________________ Y-intercept: __________ X-intercept(s): __________
15. ( )
Vertex: ________________ Y-intercept: __________ X-intercept(s): __________
16. ( )( ) Vertex: ________________ Y-intercept: __________ X-intercept(s): __________
17. ( )( ) Vertex: ________________ Y-intercept: __________ X-intercept(s): __________
18. Determine the number and type of solutions. (Number of real and number of imaginary) Show work to prove your answer.
a.
b.
c.
19. To show his love for his wife on Valentine’s Day, Mr. Sacco climbed to the top of an 84 foot cliff and launched a
set of fireworks at a velocity of 160 feet per second.
(round all answers to the hundredths place)
The equation below represents the situation:
a. How high did the fireworks get in the sky?
b. How long did it take the fireworks to reach that height
c. How long were the fireworks in the air?
d. Use the equation to find out how high the fireworks were after 8 seconds.
e. When else would it be at that exact height?
20. Ms. Boehl has taken her math textbook to the roof of her house and looks down at the ravine which is 52 feet
below. Ms. Boehl launches her book up into the air with an initial velocity of 96 feet per second. (round all
answers to the hundredths place)
a. How long is the textbook in the air?
b. What is the maximum height the textbook will reach?
c. How long will it take for the textbook to reach the maximum height?
d. What is the height of textbook after 4 seconds?
e. At what time(s) will the textbook be 150 feet in the air?
Use the following expressions for questions 21-26 to perform the indicated operations.
( ) ( ) ( ) 21.
22.
23.
24.
25.
26.
For questions 27-30, simplify. 27.
28.
29.
30.
Use the following expressions for questions 31-36 to perform the indicated operations.
( ) ( ) ( ) ( )
31.
32.
33.
34.
35.
36.
37. List the criteria that make an equation not a polynomial in one variable. (3) 38. Is a polynomial in one variable?
a. If so, what kind of polymonial is it? Monomial Binomial Trinomial Polynomial
39. Is
a polynomial in one variable? a. If so, what kind of polymonial is it? Monomial Binomial Trinomial Polynomial
Use the following equation to answer questions #40-41. 40. What is the degree of the equation and what does it tell you about the graph?
41. What two pieces of information do you need to determine the end behaviors of the graph?
Determine the End Behavior L: ____________ R: _____________
42. Sketch a polynomial function with the following features:
a. Degree 6
b. 3 real roots
c. Leading coefficient is positive
d. Negative y-intercept
43. Sketch a polynomial function with the following features:
a. Degree 3
b. 3 real roots (including a double root)
c. Leading coefficient is negative
d. Negative y-intercept
For questions 44-47, divide.
44.
45.
46. ( )( )
47. ( ) ( )
48. Consider the polynomial function ( ) .
a. How many total roots does have? Explain.
b. How many real roots does have? Explain.
c. How many imaginary roots does have? Explain.
d. State the following:
Leading coefficient: positive or negative
Number of Relative Maximum(s): ______________________
Number of Relative Minimum(s): ______________________
End Behavior: Left _______ Right _______
49. Consider the polynomial function .
a. Use the graph to find the real zero(es).
b. Use the remainder theorem to prove your answer(s)
from part “a” are correct.
c. Use synthetic division and the quadratic formula to find
the imaginary solutions.
d. Use the real zero(es) to express the polynomial as the product of a linear factor and a quadratic factor.
50. Find all roots, both real and imaginary, of the polynomial.
51. Find all roots, both real and imaginary, of the polynomial.
52. You have a box. You would like to increase each side of the box by the same amount so that
the new volume is 12 less than 3 times the original.
a. Write an equation to represent the situation.
b. How many inches will you have to add to each side of the box?
c. What are the new dimensions of the box?
53. You have a box. You would like to decrease each side of the box by the same amount so that
the new volume is 703 more than one-fourth the original.
a. Write an equation to represent the situation.
b. How many inches will you have to take from each side of the box?
c. What are the new dimensions of the box?
For #’s 54-57, write a polynomial function in standard form that has the given zeroes. 54. Assume “a”
55. Assume “a”
56. passing through ( )
57. passing through ( )
For questions 58-65, perform the indicated operation and write an equivalent rational expression in reduced form (simplify). Don’t forget to state restrictions.
58.
59.
60.
61.
62.
63.
64.
65.
For questions 66-69, solve. Check your solutions.
66.
67.
68.
69.
For questions 70-73, solve. Check your solutions.
70. √ √
71. √
72. √
73. √ √
74. Prove that √ has one solution.
List the key features then graph the rational equation.
75.
a. x-intercept(s): ______________
b. y-intercept: ______________
c. horizontal asymptote: ______________
d. vertical asymptote(s):_______________
e. hole(s): _______________
76.
a. x-intercept(s): ______________
b. y-intercept: ______________
c. horizontal asymptote: ______________
d. vertical asymptote(s):_______________
e. hole(s): _______________
77.
a. x-intercept(s): ______________
b. y-intercept: ______________
c. horizontal asymptote: ______________
d. vertical asymptote(s):_______________
e. hole(s): _______________
78.
a. x-intercept(s): ______________
b. y-intercept: ______________
c. horizontal asymptote: ______________
d. vertical asymptote(s):_______________
e. hole(s): _______________
79.
a. x-intercept(s): ______________
b. y-intercept: ______________
c. horizontal asymptote: ______________
d. vertical asymptote(s):_______________
e. hole(s): _______________
80.
a. x-intercept(s): ______________
b. y-intercept: ______________
c. horizontal asymptote: ______________
d. vertical asymptote(s):_______________
e. hole(s): _______________
List the key features and graph.
81. √
a. x-intercept: ______________
b. y-intercept: ______________
c. starting point: _______________
82. √
a. x-intercept: ______________
b. y-intercept: ______________
c. starting point: _______________
83.
√
a. x-intercept: ______________
b. y-intercept: ______________
c. starting point: _______________
84. √
a. x-intercept: ______________
b. y-intercept: ______________
c. starting point: ______________
85. It takes Emma 12 hours to decide what to watch on Netflix. It takes Camden 14 hours to decide. How long would it take them to find something to watch if they searched together?
86. Artemi Panarin has made 39 of his last 92 shots on goal. How many shots would he have to make in a row in
order to get his percentage up to a 60%? 87. I have 5 quarts of a 40% solution. I am going to add some of a 15% solution in order to make a mixture that is a
25% solution. Which equation fits this scenario?
a. ( ) ( )
b. ( ) ( )
c. ( ) ( )
d. ( ) ( )
88. I have 12 pints of 65% pure OJ that is too sweet. How much pure OJ can I add in order to get it up to an 80%
pure drink?
89. The number of people, y, involved in recycling in a community is modeled by the function √ where is the number of months the recycling plant has been open.
a. Find the number of people involved in recycling after the plant had been open for 3 months.
b. After how many months will there be 940 people involved?
90. The average amount of apples consumed by Americans (in pounds per person) can be modeled by the equation
√ where is the number of years since 2000. a. In what year were about 20 pints of apples consumed per person?
