HONORS MATH III: FINAL EXAM REVIEW Name: ______
1. Find cos300°
2. Solve 6x2-5x+3=0
3. What is the horizontal asymptote of y=x2+2x-8(x+6)2
4. Write a43 in its simplest radical form
5. Solve ex-3=455
6. A scientist recorded the growth (g) of pine trees and the amount of rainfall (r) the received in their first year
r (in) / 0 / 3 / 5 / 12 / 17 / 22 / 34 / 35 / 45g (in) / 1 / 4 / 6 / 9.5 / 10.8 / 10.9 / 6 / 5.3 / 1
Which equation best fits the data?
A. g=-0.017r+6.38
B. g=-0.019r2+0.797r+1.94
C. g=5.02(0.995)r
D. g=-0.092r2+1.62r+2.51
7. Of the 25 students who take a standardized test, the minimum score is 98 and the maximum score is 472. The mean score is 216, and the standard deviation is 52. What is the number of standard deviations that includes all the data values?
8. Simplify 5(6-2i)+3i(3-2i)
9. The equation height h(in feet) of a ball t seconds after it is thrown upward is y=-16t2+60t+5. What does the constant term 5 in the equation represent?
10. Find tan2π3
11. Determine the hole(s), if any, for the following:
y=x+3x+2x+3
12. Over the last ten years, the population of Jamestown, N.Y. grew from 45,600 to 64,800. Find the annual growth rate for this city?
13. Simplify 3x12y4x2y32
14. Given fx=x4-3x3+21x2-75x-100 find all real and complex roots.
15. Describe all transformations for y=4x-2-3 and state the domain.
16. Express log2x+4log2y as a single logarithm.
17. Find cot-5π4
18. Simplify: t2-1t-2∙t2-3t+2t2+4t+3
19. Mr. Greene has 8.5 by 11in cardboard sheet. He wants to make an open top box under the following conditions:
I) Each box must be made by cutting small squares from each corner of a cardboard sheet.
II) The box must have a volume of 48 in3.
III) The amount of cardboard waste must be minimized.
What is the approximate side length for the small squares that would be cut from the cardboard sheet?
20. What is the standard deviation for the normal distribution curve shown below?
21. Simplify 4x2-3x+63x-9
22. Which is the simplest form of the expression 418x4-372x4 ?
A. -6x22
B. -6x2
C. -6
D. None of the above
23. If x→∞, the degree is odd, and the leading coefficient is positive, what does f(x)→ (approach)?
24. Write a polynomial whose roots are x=4, -2, 3, 0
A. x4+5x3-2x2-24x
B. x3+5x2-2x-24
C. x3-5x2-2x+24
D. x4-5x3-2x2+24x
25. In a laboratory the rate of growth for a culture of bacteria is 45.4% per hour. Approximately how long would it take to grow from 30 to 195 bacteria?
26. Find csc5π4
27. Scores on an exam are distributed normally with a mean of 76 and a standard deviation of 10. Out of 230 tests, about how many students score above 96?
28. What is the vertical and horizontal asymptotes of gx=x+2(x-3)x(x-3)
29. Simplify 3-2i4-3i
30. Give the value of the discriminant, and describe the nature of the roots of the equation 5x2=4x+6
31. Max opens up a savings account with $450. The account has an interest rate of 4.3% compounded twice a year. How much money will Max have in his account after 4 years?
32. A ball is tossed from the top of a building. This table shows the height, h (in feet), of the ball above the ground t seconds after being tossed.
t / 1 / 2 / 3 / 4 / 5 / 6h / 299 / 311 / 291 / 239 / 155 / 39
According to a quadratic best-fit model of the data, how long after the ball was tossed was it 80 feet above the ground?
33. Find secπ6
34. For the rational function fx=x2+5x+6x-1, determine the location of the vertical asymptote, if any.
35. What is the quadratic function that has roots (5+2i) and (5-2i)?
A. x2+10x+21
B. x2-10x+29
C. x2+10x+29
D. x2-10x+21
36. Solve 7x2+196=0 for x
37. Express 1612=4 in logarithmic form
38. Find cotπ
39. Solve 52x+1=50
40. Which is a factor of 6x2+5x-4
A. 2x+2
B. 2x+1
C. 2x-1
D. 6x+1
41. Simplify 53x2+ 33x2
Use the graph below for questions 42-44
42. What are the solution(s) for the graph?
43. What is the interval increasing for the graph?
44. What is the range of the related quadratic equation?
45. The table below shows the total sales for a new product during the first five years of production.
Year / Sales(thousands of $)
1 / 2
2 / 6
3 / 11
4 / 29
5 / 68
According to the best-fit exponential model, what was the approximate annual rate of growth in sales during this period?
46. Find the area of the rectangle
47. Which of the following are two forms of the same angle measure?
I. 2400, 7π6 II. 1350, 3π4 III. 1500, 5π6
A. I and II only
B. I and III only
C. II and III only
D. I, II and III
48. A data set has a mean of 255 and a standard deviation of 12. All of the data values are within two standard deviations of the mean. Which of the following could be the maximum value of the data?
A. 232
B. 244
C. 268
D. 280
49. Where does the minimum value of the function fx=x-5-4 occur?
50. Solve 63x=30
51. Simplify 3-108x3y5312xy
52. What is the horizontal asymptote for a rational function whose top degree is less than the bottom degree?
53. A hardware store sells a mixed bag of nails. The number of nails of a given length is distributed normally with a mean length of 5 in. and a standard deviation of 0.03 in. About how many nails in a bag of 120 are between 4.97 in. and 5.03 in. long?
54. Jose tosses a rock upward from the top of a 192 ft building. The height of the rock above the ground, h, after t seconds is represented by the function
ht=-16t2+64t+192
After how many seconds does the rock hit the ground?
55. Which is the logarithmic form of the exponential equation 23 = 8?
A. log82 = 3
B. log83 = 2
C. log38 = 2
D. log28 = 3
56. The table below shows the cost of attending a private school for the years 1997-2001. Let x = 0 in 1997.
Year / Cost(dollars)
1997 / 17,500
1998 / 18,000
1999 / 19,000
2000 / 20,000
2001 / 22,000
Which equation below best represents the cost of the school?
A. y=1,100x+17,100
B. y=214x-70.3
C. y=214.3x2+242.9x+17,528.6
D. y=1.5x2-70.3x
57. Simplify 2-34+8
58. Simplify the following and find the restrictions:
2m-1m2-3m-10÷4m2-14m+8
59. Find a negative coterminal for 9π2?
Use the data below for numbers 60 and 61
Day / Deliveries1 / 14
2 / 15
3 / 19
4 / 15
5 / 15
6 / 16
7 / 19
8 / 20
60. What is the mean of the data set?
61. What is the interquartile range of the data?
62. What is the vertex of the graph y=2x+5?
63. What is the rate of growth in the equation y=125(1.364)6?
64. Solve x+9-x=1
65. Solve log84x+14=2
66. Simplify 30m2-25+3m+5
67. Which angle measure is equivalent to 4 3π?
A. 60o
B. 120o
C. 135o
D. 240o
68. Which equation describes the parabola that has a vertex (-2,9) and passes through the point (1,0)?
A. y=9(x+2)2+9
B. y=-(x+2)2+9
C. y=-9(x+2)2-9
D. y=(x+9)2-2
69. Solve the following system for x and y
x+4y=-58x-y=-7
70. Factor 8x3-27
For Questions 71 and 72, let fx=-2x2+4x-7
71. Does the graph of f(x) open upward or downward, and does it have a maximum or minimum value?
72. What is the vertex of the function?
73. Which of the following is NOT coterminal with the other 3?
A. 150o
B. -150o
C. -210o
D. 510o
74. Find the value of y in the given system
3x+8y=2z-82x+5z=13-4y-x-6y+3z=8
75. Solvex-1=2x-8
76. Find sinθ if tanθ=3
77. Jason opened a savings account at a bank in Raleigh. He deposited $1,000 at 4% interest compounded quarterly. To the nearest year, how long will it take Joffre’s money to double?
78. Factor 4y3-32 completely.
79. Express 15+155 in simplest form.
80. What is the sum of the roots of the equation x2-11x+10=0?
81. Expand logx3y2:
82. What type of function does the following graph represent?
A. Odd degree; positive leading coefficient
B. Even Degree; positive leading coefficient
C. Odd degree; negative leading coefficient
D. Even Degree; negative leading coefficient