PreCal1 Review test3 2017 1. Find the point where the function f( x)=–x 2 –8x – 16 is at a maximum. 2. Find the point where the function f( x)= x 2 +2x + 1 is at a minimum. 3. Which of the following parabolas has an absolute minimum at x = 2? A) I only B) II only C) I and II only D) II and III only I. x 2 –4 x +1 II. –x 2 +4 x –1 III. –2x 2 +9 x +3 4. How many relative minimums and maximums does the periodic function y = sin(x)? A) 0 B) 1 C) 2 D) an infinite number 5. The height of a ball is determined by the function f(t )=–t 2 +4 t + 3. At what time does the ball reach its maximum height? A) t = 1 B) t = 2 C) t = 3 D) t = 4 6. At what value of x does a relative minimum exist for f( x )= x 2 A) x =0 B) x = –1 C) x =1 D) x =2 A) 17 feet B) 16 feet C) 14 feet D) 15 feet 7. At the circus the human cannon ball is shot into the air. His path is represented by the equation y = –14 x 2 + 29 x. He reaches a maximum height and then begins his descend. At what height does he begin to descend? A) 214 meters B) 215 meters C) 216 meters D) 217 meters 8. A baseball is hit high into the air. Its height, h meters above the ground, is a function of time t seconds after it was hit and is given the equation h = – 5.2 t 2 + 67 t. What would be the maximum height, to the nearest meter, attained by this model? A) 0 B) 5 C) 10 D) 50 9. When a current, I, flows through a given electrical circuit, the power, W , of the circuit can be determined by the formula W = 20 I – 2 I 2 . What amount of current, I, supplies the maximum power, W ? 10. The equation W = 250 I – 25 I 2 represents the power ( W ), in watts, of a 250–volt circuit having a resistance of 25 ohms when a current ( I ) is flowing through the circuit. What is the maximum power, in watts, that can be delievered in this circuit? 11. A ball is thrown into the air so that its height is given be the function h ( t ) = –5t 2 + 15 t , where h is the height in meters and t is the time in seconds. What is the maximum height of the ball? 12. Base your answer to the following question on Based on the the leading coefficient test, which function could have produced the graph shown below? A) B) C) D)
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PreCal1 Review test3 2017
1. Find the point where the function f(x) = –x2 – 8x – 16 is at a maximum.
2. Find the point where the function f(x) = x2 + 2x + 1 is at a minimum.
3. Which of the following parabolas has anabsolute minimum at x = 2?
A) I only B) II onlyC) I and II only D) II and III only
I. x2 – 4x + 1II. –x2 + 4x – 1III. –2x2 + 9x +3
4. How many relative minimums and maximumsdoes the periodic function y = sin(x)?
A) 0B) 1C) 2D) an infinite number
5. The height of a ball is determined by thefunction f(t) = –t2 + 4t + 3. At what time does the ballreach its maximum height?
A) t = 1 B) t = 2 C) t = 3 D) t = 4
6. At what value of x does a relative minimumexist for f(x) = x2
A) x = 0 B) x = –1C) x = 1 D) x = 2
A) 17 feet B) 16 feetC) 14 feet D) 15 feet
7. At the circus the human cannon ball is shot intothe air. His path is represented by the equation y = –14x2 + 29x. He reaches a maximum heightand then begins his descend. At what heightdoes he begin to descend?
A) 214 meters B) 215 metersC) 216 meters D) 217 meters
8. A baseball is hit high into the air. Its height, h meters above the ground, is a function of time t seconds after it was hit and is given theequation h = – 5.2t2 + 67t. What would be themaximum height, to the nearest meter, attainedby this model?
A) 0 B) 5 C) 10 D) 50
9. When a current, I, flows through a givenelectrical circuit, the power, W, of the circuitcan be determined by the formula W = 20I – 2I2. What amount of current, I, supplies themaximum power, W?
10. The equation W = 250I – 25I2 represents thepower (W), in watts, of a 250–volt circuithaving a resistance of 25 ohms when a current(I) is flowing through the circuit. What is themaximum power, in watts, that can bedelievered in this circuit?
11. A ball is thrown into the air so that its height isgiven be the function h(t) = –5t 2 + 15t, whereh is the height in meters and t is the time inseconds. What is the maximum height of theball?
12. Base your answer to the following question onBased on the the leading coefficient test,which function could have produced the graphshown below?
A)B)C)D)
13. 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
14. Which statement correctly describes the endbehavior of the function f(x) = –x98?
A) The function falls to both the right and leftB) The function rises to both the right and leftC) The function falls to the left and rises to the
rightD) The function rises to the left and falls to the left
15. Which statement correctly describes the endbehavior of the function f(x) = x99?
A) The function falls to both the right and leftB) The function rises to both the right and leftC) The function rises to the right and falls to the
leftD) The function rises to the left and galls to the
right
16. Which function falls to both the left and right?
A)B)C)D)
17. A cubic equation will rise to the left and fall tothe right if the leading coefficient is
18. 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
19. Divide.
20. Divide
A)B)C)D)
21.
22. Divide completely using long division. Showyour work.
23. Divide using long division. Show your work.
24. Divide using long division. Show your work.
25. The following function has which set ofpossible rational roots?
A) B)C) D)
26. Using the synthetic division table shownbelow, evaluate f(x) = x4 + 2x3 + 2x2 + x + 2at x = 3.
A) 51 B) 52 C) 156 D) 158
27. Divide.
28. When 3x3 + 4x2 + 5x + 6 is syntheticallydivided by x + 2 the result is
29. When 5x2 + 3x – 2 is synthetically divided by2x + 2 the result is
30. 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 +
31. 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 +
32. What are the numbers that should be written inthe second row of the synthetic division tableshown below?
33. 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
34.Evaluate without plugging in. Show yourwork.
A) B)C) D)
35.Evaluate without plugging in. Show yourwork
36.Evaluate without plugging in.
A) B) C) D)
37. f(x) = 2x4 + 3x3 + 4x2 + 5x + 6.Evaluate f(4) using the Remainder Theorem.
A) 683 B) 704 C) 794 D) 816
38. 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)
39. 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)
40. 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)
41. "Use Descartes' Rule of Sign to determinewhich is a possible function for the graphshown below.
"
A)B)C)D)
42. "Use Descartes' Rule of Sign to determinewhich is a possible function for the graphshown below.
"
A)B)C)D)
43. "Use Descartes' Rule of Sign to determinewhich is a possible function for the graphshown below.
"
A)B)C)D)
44. 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
45. What is the sum of the number of positive andnegative roots of the function
46. The function has
____ positive real roots.
A) B)C) D)
47. The function has ____ negative real roots.
A) B)C) D)
48.
A) three or one B) three or twoC) two or zero D) two or one
How many positive real zeros does this functionhave?
49. How many positive real zeros does thefunction have?
A) one B) three or oneC) two or zero D) none
50. According the to rational root test, which ofthe following is a real root possibility for thefunction:
A) B) C) D)
51. According the to rational root test, which ofthe following is a real root possibility for thefunction:
A) B) C) D)
52. According to the rational roots test, whichfunction has possible rational roots thatinclude and ?
A)B)C)D)
53. According to the rational roots test, whichfunction has possible rational roots thatinclude and ?
A)B)C)D)
54. The possible rational roots of 2x3 + x2 + x + 2 are
55. The possible rational roots of a function are . What is one possibility for
this function?
A)B)C)D)
56. Base your answer to the following question onThe possible rational roots of a a function are
. What could this functionbe?
A)B)C)D)
57.What are the possible rational roots of
58.What are the possible rational roots of
59. 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
60. 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
61. 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)
62. Find the quadratic which has the root 2 + i.
63. Write the polynomial function f(x) = x5 + x3 + 2x2 – 12x + 8 as the product oflinear factors.
64. Write out the correct factorization of x4 – 1.
65. The sum of the roots of the quadratic x2 + 16 is?
A) 0 B) 4 C) 8 D) 16
66. What are the two roots of the quadratic ?
A) B)C) D)
67. What are the two roots of the quadratic ?
A) B)C) D)
68. Calculate the product of 2 + 3i and itsconjugate.
A) 4 + 6i B) 4C) 9 D) 13
69. 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
70. Over the set of integers, factor the expression4x3 - x2 + 16x - 4 completely
A) x - 2 B) x + 2C) x - 4 D) x + 4
71. Which binomial is a factor of x4 - 4x2 - 4x + 8
A)B)C)D)
72. When factored completely, isequivalent to
A)B)C)D)
73. When factored completely, isequivalent to
A)B)C)D)
74. The completely factored form of is
A)B)C)D)
75. Which factorization is incorrect?
A)B)C)D)
76. Factored completely, the expression is equivalent to
77. Factor completely.
78. Factor completely:
A)B)C)D)
79. When factored completely, the expression is equivalent to
A)B)C)D)
80. When factored completely, equals
81. Factor the expression
82. Factor:
A)B)C)D)
83. Factored completely, the expression is equivalent to
A)B)C)D)
84. According to the rational roots test, whichfunction has possible rational roots thatinclude and ?
85. The possible rational roots of are
A) B) 2C) D)
86. Which is not a factor of ?
A)B)C)D)
87. Completely factored, isequivalent to
A)B)C)D)
88. Which expression is the complete factorizationof ?
89. Factor completely:
90. Find the exact roots of by completing the square.
A)B)C)D)
91. Which step can be used when solving by completing the square?
A) B)C) D)
92. Max solves a quadratic equation bycompleting the square. He shows a correctstep:
What are the solutions to his equation?
A) B) C) D) 49
93. Brian correctly used a method of completingthe square to solve the equation
. Brian's first step was torewrite the equation as . He thenadded a number to both sides of the equation.Which number did he add?
A) B)C) D)
94. If is solved by completing thesquare, an intermediate step would be
95. Solve the equation using thecompleting the square method only.
96. Solve using the completing the square methodonly.
97. Solve the equation using thecompleting the square method only.
98. Solve the equation by using thecompleting the square method only.
A) B)C) D)
99. Solve by the completing the square methodonly.
100. A rocket is shot vertically into the air. Its height, h, at any time, t, in seconds, can be modeledby the equation h = –16t2 + 184t. Determine algebraically, the number of seconds it will takethe rocket to reach a height of 529 feet.
A) 1.45 B) 1.84C) 2.10 D) 2.72
101. A cliff diver on a Caribbean island jumpsfrom a height of 105 feet, with an initialupward velocity of 5 feet per second. Anequation that models the height, h(t), abovethe water, in feet, of the diver in timeelapsed, t, in seconds, is
. How many seconds,to the nearest hundredth, does it take thediver to fall 45 feet below his starting point?
102. Barb pulled the plug in her bathtub and it started to drain. The amount of water in the bathtubas it drains is represented by the equation , where L represents the numberof liters of water in the bathtub and t represents the amount of time, in minutes, since the plugwas pulled.
How many liters of water were in the bathtub when Barb pulled the plug? Show yourreasoning.
Determine, to the nearest tenth of a minute, the amount of time it takes for all the water in thebathtub to drain.
103. The height of a projectile is modeled by the equation , where x is time, inseconds, and y is height, in feet. During what interval of time, to the nearest tenth of a second,is the projectile at least 125 feet above ground?
104. The height of a projectile is modeled by the equation , where x is time, inseconds, and y is height, in feet. During what interval of time, to the nearest tenth of a second,is the projectile at least 125 feet above ground?
105. a The side of a square is represented by x + 2. Express the area of the square in terms of x.b The dimensions of a rectangle are represented by 2x +1 and 2x – 4. Express the area of therectangle in terms of x.c If the area of the square in part a equals the area of the rectangle in part b, find x.
Answer KeyPreCal1 Review Test3 2017
1. (–4, 0)2. (–1, 0)3. A4. D5. B6. A7. D8. C9. B10. 625 watts11. 11.25 m12. C13. B14. A15. C16. C17. negative18. C19.20. C21.22.23.24.25. B26. D27.28. 3x2 – 2x + 9 – 29.30. B31. A32. 4, 22, 36, 1833. A34. A35.36. B
37. C38. B39. C40. A41. C42. B43. A44. D45.46. A47. D48. C49. A50. D51. C52. A53. A54. 1, 2, 0.555. B56. C57.
58.59. D60. C61. A62. x2 – 4x + 563. (x – 1)(x – 1)(x + 2)(
x – 2i)(x + 2i)64. (x – 1)(x + 1)(x + i)(
x – i)65. A66. D67. A68. D69. C70. (x2 + 4)(4x - 1)
71. A72. D73. D74. C75. C76. C77.78.79. C80. B81. ,
or 82.83. D84. A85. , , 86. A87. B88. D89.90.91. A92. B93. B94. B95.96.97.98.99. A100. 5.75, and correct
algebraic work isshown.
101. B102. 120 and 4.2103. 3.8 x 15.2
104.105. a.
b. c. 4
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