pre cal1 review test3 name: pd - cardozo high
TRANSCRIPT
Pre cal1 review test3 Name: PD:
1. The function has
A) a horizontal asymptote on the -axis andvertical asymptotes at
B) one vertical asymptote at C) a vertical asymptote on the -axisD) two vertical asymptotes at but no
horizontal asymptoteE) no asymptote
2. The function has a verticalasymptote at
A)
B)C)D)E) y = 6
3. Imaginary roots always
A) are negativeB) are irrationalC) are conjugate pairsD) contain a real component
4. Find the roots of the following quadraticequation:
5. Find the roots of the following quadraticequation: x2 + 2x + 2
6. The sum of the roots of which quadratic is 0.5 ?
A) x2 + 3x + 3 B) 6x2 + 12x + 3C) 4x2 + 2x + 3 D) 4x2 – 2x + 3
7. The sum of the roots of the quadratic 3x2 + 387x + 9 is
A) 3 B) –3 C) 129 D) –129
8. The product of the roots of the polynomial x3 + 3x2 + x is
A) 2 B) –2 C) 3 D) 0
9. The sum of the roots of the polynomial x3 + 3x2 + x is
A) 2 B) –2 C) 3 D) –3
10. Consider the polynomial x2 + bx + c. Thesum of this quadratic's roots is 5 and theirproduct is 6. What is the sum of b and c ?
A) –1 B) 0 C) 1 D) 2
11. One imaginary root is a + bi. If this root isadded to its conjugate, the sum is always
A) 2(a+bi) B) 2biC) a D) 2a
12. Find the fourth degree polynomial whose rootsinclude i and 5i.
A) x4 + 26x2 + 5 B) x4 + 26x2 – 25C) x4 – 26x2 + 25 D) x4 + 26x2 + 25
13. Find the fourth degree polynomial whose rootsinclude 3i and 4i.
A) 2x4 + 25x2 + 144 B) x4 – 25x2 + 144C) x4 + 25x2 + 144 D) x4 + 25x2 – 144
14. Write out the correct factorization of x2 + 4.
A) (x + 2i)(x – 2i) B) (x + 2i)(x + 2i)C) (x – 2i)(x – 2i) D) (x + 2)(x – 2)
15. What are the roots of the function, f(x) = x4 – 2x3 + 6x2 – 8x + 8?
A) I only B) II onlyC) I and II only D) I and III onlyE) I, II, and III
I. 1 + iII. 1 – iIII 2i
16. Find the quadratic which has the root 2 + i.
17. Find a fifth degree polynomial whose rootsinclude , , and .
18. Find a fourth degree polynomial whose rootsinclude , , and .
Name:
19. Write the polynomial function f(x) = x5 + x3 + 2x2 – 12x + 8 as the product oflinear factors.
20. Write out the correct factorization of x4 – 1.
21. What are the two roots of the quadratic ?
A) B)C) D)
22. What are the two roots of the quadratic ?
A) B)C) D)
23. The sum of the roots of the quadratic x2 + 16 is?
A) 0 B) 4 C) 8 D) 16
24. What are the two roots of the quadratic ?
A) B) C) D)
25. Calculate the product of 2 + 3i and itsconjugate.
A) 4 + 6i B) 4C) 9 D) 13
26. Divide
A)B)C)D)
27. Divide using long division. Show your work.
28. Divide using long division. Show your work.
29. Divide using long division. Show your work.
30. The following function has which set ofpossible rational roots?
A) B)C) D)
31. Using the synthetic division table shownbelow, evaluate f(x) = x4 + 2x3 + 2x2 + x + 2at x = 3.
A) 51 B) 52 C) 156 D) 158
32. When 5x3 – 6x2 + 8 is synthetically divided by (x – 4) the result is
A) 5x2 + 14x + 56B) 5x2 + 14x + 56 + C) 5x2 + 26x + 49 + D) 5x2 + 14x + 56 +
33. What are the numbers that should be written inthe second row of the synthetic division tableshown below?
34. When 3x3 – 17x2 + 15x – 25 is syntheticallydivided by (x – 5) the result is
A) 3x2 – 2x + 5B) 3x2 + 2x + 5C) 3x2 + 2x – 5D) 3x2 + 2x + 25 +
35. What are the numbers that should be written inthe second row of the synthetic division tableshown below?
A) –3, 9, 3, –3 B) 3, 3, –3, 9C) 3, –9, –3, 3 D) 3, 9, 3, 3
36. Divide.
Name:
37. Use synthetic division to find the remainderwhen dividing by
38.Evaluate without plugging in. Show yourwork.
A) B)C) D)
39. f(x) = 2x4 + 3x3 + 4x2 + 5x + 6.Evaluate f(4) using the Remainder Theorem.
A) 683 B) 704 C) 794 D) 816
40.Evaluate without plugging in. Show yourwork
41. Base your answer to the following question onUse Descartes' Rule of Sign to determinewhich is a possible function for the graphshown below.
A)B)C)D)
42. Base your answer to the following question onUse Descartes' Rule of Sign to determinewhich is a possible function for the graphshown below.
A)B)C)D)
43. How many positive and negative zeros doesthe function have?
A) positive zero, negative zeros
B) positive zero, negative zero
C) positive zero, negative zero
D) positive zero, negative zero
44. What is the sum of the number of positive andnegative roots of the function
45. The function has
____ positive real roots.
A) B)C) D)
46. The function has ____ negative real roots.
A) B)C) D)
47. How many positive real zeros does thefunction have?
A) one B) three or oneC) two or zero D) none
Name:
48. According the to rational root test, which ofthe following is a real root possibility for thefunction:
A) B) C) D)
49. According to the rational roots test, whichfunction has possible rational roots thatinclude and ?
A)B)C)D)
50. According to the rational roots test, whichfunction has possible rational roots thatinclude and ?
A)B)C)D)
51. The possible rational roots of 2x3 + x2 + x + 2 are
52. The possible rational roots of a function are . What is one possibility for
this function?
A)B)C)D)
53. Base your answer to the following question onThe possible rational roots of a a function are
. What could this functionbe?
A)B)C)D)
54.What are the possible rational roots of
55.What are the possible rational roots of
56. The function f(x) = x3 + 3x2 + x – 1 rises
A) to the left onlyB) to the right onlyC) to both the left and rightD) to neither direction
57. Which function falls to both the left and right?
A)B)C)D)
58. A cubic equation will rise to the left and fall tothe right if the leading coefficient is
59. Which statements correctly describe the endbehavior of the function y = –x2
A) I only B) I and II onlyC) I and III only D) II and III only
I. falls to the rightII. rises to the leftIII. falls to the left
60. What is the end behavior of the followingfunction?
A) As increases, the function approaches one.B) As increases, the function approaches two.C) As increases, the function approaches two-
thirds.D) As increases, the function approaches
infinity.
61. What is the end behavior of the followingfunction?
A) As , B) As , C) As , D) As ,
Name:
A) 2(16 – 9y 2)B) 2(4 – 3y)2C) 2(3y + 4)(3y – 4)D) 2(4 – 3y)(4 + 3y)
62. Which expression is the complete factorizationof 32 – 18y2?
63. Factor completely: 3t3 + 5t2 – 12t
64. Factor completely: 3x 3y – 12xy
A) 2.25 B) 6C) 4.5 D) 9.2
65. A ball is thrown straight up at an initialvelocity of 54 feet per second. The height ofthe ball t seconds after it is thrown is given bythe formula h(t) = 54t – 12t2. How manyseconds after the ball is thrown will it return tothe ground?
66. The equation W = 150I – 15I 2 represents thepower (W), in watts, of a 150–volt circuithaving a resistance of 15 ohms when a current(I), in amperes, is flowing through the circuit.What is the current of the circuit when thepower is 185 watts, to the nearest tenth? Thecurrent cannot exceed 5 amperes.
67. A baseball player throws a ball from theoutfield toward home plate. The ball’s heightabove the ground is modeled by the equation y= –16x 2 + 48x + 6, where y represents height,in feet, and x represents time, in seconds. Theball is initially thrown from a height of 6 feet.
How many seconds after the ball is thrownwill it again be 6 feet above the ground?
What is the maximum height, in feet, that theball reaches?
68. Solve for the positive value of :
69. Solve for and check.
70. Solve for :
71. Factor completely: 3x 3 – 192x
72. Factor completely: 9x3 – x
73. Factor completely: x 4 – 16
74. Factor completely: 5x2y3 – 180y
75. Factor completely: 2x3 – 98x
76. Factor completely: 3x 3y 2 – 147x
A) 4x + 3 B) 2x + 3C) 3 D) –1
77. The expression (2x + 1)2 – 2(2x2 – 1) isequivalent to
A) x2 + 6x + 10 = 0B) x2 + 6x + 8 = 0C) x2 – 6x + 8 = 0D) x2 – 6x + 10 = 0
78. Which quadratic equation has roots of 3 – i and 3 + i?
A) = x – 4 B) = 4 – xC) = D) =
79. Which equation has both 3 and 6 as roots?
80. Write a quadratic equation whose roots are 5 + i and 5 – i .
Name:
81. Use synthetic division to find the remainder when dividing by .
A) 5 B) 10 C) 13 D) 26
82. If the perimeter of a square is 28 and the areaof the square is , what is thepositive value of x?
83. Over the set of integers, factor the expression4x3 - x2 + 16x - 4 completely
A) x - 2 B) x + 2C) x - 4 D) x + 4
84. Which binomial is a factor of x4 - 4x2 - 4x + 8
A)B)C)D)
85. When factored completely, the expression is equivalent to
A)B)C)D)
86. When factored completely, equals
A) 0 B) 2 C) 3 D) –3
87. If is a factor what is thevalue of ?
A)B)C)D)
88. Which expression can be rewritten as
A)B)C)D)
89. When factored completely, isequivalent to
A)B)C)D)
90. The expression isequivalent to
A)B)C)D)
91. The completely factored form of is
A)B)C)D)
92. Factored completely, the expression is equivalent to
Name:
93. Factor completely.
A) B)C) D)
94. The zeros for are
95. Factor completely:
A)B)C)D)
96. When factored completely, the expression is equivalent to
Answer KeyPrecal1 Review Test3 2018
1. A2. C3. C4.
5. –1 i6. D7. D8. D9. D10. C11. D12. D13. C14. A15. E16. x2 – 4x + 517.18.19. (x – 1)(x – 1)(x + 2)(
x – 2i)(x + 2i)20. (x – 1)(x + 1)(x + i)(
x – i)21. D22. A23. A24. B25. D26. C27.28.29.30. B31. D32. B33. 4, 22, 36, 1834. A
35. A36.37.38. A39. C40.41. B42. C43. D44.45. A46. D47. A48. D49. A50. A51. 1, 2, 0.552. B53. C54.
55.56. B57. C58. negative59. C60. D61. A62. D63. t(3t – 4)(t + 3)64. 3xy(x – 2)(x + 2)65. C66. 1.4 amperes67. 3 s and 42 ft68.69.
70.71. 3x(x – 8)(x + 8)72. x(3x
1)(3x – 1)73. (x 2 + 4)(x + 2)(x –
2)74. 5y(xy + 6)(xy – 6)75. 2x(x + 7)(x – 7)76. 3x(xy + 7)(xy – 7)77. A78. D79. D80. x2 – 10x + 27 = 081.82. A83. (x2 + 4)(4x - 1)84. A85. C86. B87. C88. A89. D90. D91. C92. C93.94. A95.96. B