Algebra II Double Period Final Exam Review. 3. Solve. 4. Solve.
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1 Algebra II Double Period Final Exam Review Name: Chapter 5 Quadratic Equations and Parabolas 1. Solve. 3. Solve. 2. Solve. 4. Solve. 5. Graph each function. Identify the vertex and zeros for each function. a. y = x b. y = (x 3) What is the discriminant of the equation? 7. Find the number of solutions of the equation.
2 Simplify the following Solve the equation Perform the indicated operation Solve the equations over the set of complex numbers Algebra II Final Exam Review Double Period (13-14) Page 2 of 12
3 26. Scottie tossed a stone up and into a pond. The function that describes the position of the stone at any time it is in the air is, where t is the time in seconds and h is the height in feet. The graph of this function is shown below. a) How many seconds will it take for the stone to reach maximum height. Explain. b) How many seconds will it take for the stone to hit the pond? Explain 27. What are the x- intercepts of graph also known as? Perform the following operations. Chapter 6 - Polynomials Solve for x by factoring Algebra II Final Exam Review Double Period (13-14) Page 3 of 12
4 Algebra II Final Exam Review Double Period (13-14) Page 4 of Use synthetic division to divide the following: 37. Use the Remainder Theorem to evaluate the function: 38. Is a factor of? How do you know? Chapter 7 Function Operations and Inverses Simplify. Assume all variables are positive: Simplify. Assume all variables are positive ( 3 4 5) ( ) ( 2 2 7) ( ) Algebra II Final Exam Review Double Period (13-14) Page 4 of 12
5 Algebra II Final Exam Review Double Period (13-14) Page 5 of 12 Solve: Find the following if:,, and a. b. c. d. e. 54. Find the inverse of 55. Find the domain of the following function: 56. What is the range of the function when the domain is? 57. Find the domain and range of the following functions: a. b. Algebra II Final Exam Review Double Period (13-14) Page 5 of 12
6 Algebra II Final Exam Review Double Period (13-14) Page 6 of 12 Chapter 8 Exponential & Logarithmic Functions 58. Determine whether the functions model exponential growth or exponential decay AND then find the rate of growth/decay (as a percent). a. y = ( ) x b. y = 1 ( ) x c. y = ( 2) x 59. How is the graph of y = 3( 1.4) x translated from the graph of y = 3( 1.4) x? 60. How is the graph of y = 1 ( 2 4 ) x 4 translated from the graph of y = 1 ( 2 4 ) x? 61. Graph the given functions. a. y = 1 x +3 2 b. y = 2( 2) x A motorcycle is purchased new for $12,500 and depreciates 8% each year. Write a function that represents the value of the motorcycle after x years. 63. In 1981, the Australian humpback whale population was 350 and increased at a rate of 14% each year since then. Write a function to model population growth. Use the model to predict what the population will be in Algebra II Final Exam Review Double Period (13-14) Page 6 of 12
7 Algebra II Final Exam Review Double Period (13-14) Page 7 of A student wants to save $8000 for college in five years. How much should be put into an account that earns 5.2% annual interest compounded continuously? A = Pe rt The battery power available to run a satellite is given by the formula P = 50e, where P is power in watts and t is time in days. a. How much power does the battery have originally? t b. What is the battery power after 50 days? c. How long can the satellite run if it requires 15 watts? Solve each of the following for x Write the given expressions as a single logarithm. 69. log log log8 2 log6 + log log 3 2 log 3 4 Solve for x. 72. log5 log2x =1 73. log4 + 2log x = x = x = e 3x = ln3x = e 2x 1 =16 Algebra II Final Exam Review Double Period (13-14) Page 7 of 12
8 Algebra II Final Exam Review Double Period (13-14) Page 8 of 12 Write the function that is obtained by translating the graph of y = log 4 x as given. 79. right 6 units and up 2 units 80. left 3 units and down 4 units 81. Graph the given functions. a. y = log 3 (x 1) + 2 b. y = log 4 (x + 2) The number of camera phones shipped globally can be modeled by y =1.28e 1.31x where x is the number of years since 1997 and y is the number of camera phones shipped (in millions). In what year will there be 900 million camera phones shipped? Chapter 9 Rational Functions 83. Suppose that x and y vary directly, and when. Write the function that models the direct variation. 84. Suppose that z varies jointly with w and x when. Write the function that models the relationship. 85. y varies inversely with x, find the value of k when and. Algebra II Final Exam Review Double Period (13-14) Page 8 of 12
9 Algebra II Final Exam Review Double Period (13-14) Page 9 of On a string instrument, the length of a string varies inversely as the frequency of its vibrations. An 11- inch string has a frequency of 400 cycles per second. What is the frequency of a 10- inch string? Find the points of discontinuity and horizontal asymptotes (if any) for the rational function 87. f ( x) = x2 + x 42 x 2 4x f ( x) = x2 + 9x + 20 x 2 + 4x Hole(s): Vertical Asymptote(s): Horizontal Asymptote: Hole(s): Vertical Asymptote(s): Horizontal Asymptote: Write the equation for the translation of y = 3 with the given shifts. x 89. right 6 units and up 2 units 90. left 3 units and down 4 units 91. Graph the given functions. a. y = b. y = x + 3 x State the restrictions for the given rational expression x 2 49 x 2 + 4x 21 Algebra II Final Exam Review Double Period (13-14) Page 9 of 12
10 Algebra II Final Exam Review Double Period (13-14) Page 10 of 12 Perform the operations and simplify Perform the operations and simplify x x x x Solve Algebra II Final Exam Review Double Period (13-14) Page 10 of 12
11 Algebra II Final Exam Review Double Period (13-14) Page 11 of 12 Chapter 11 Sequences and Series Identify the sequence as arithmetic or geometric. Then find the common difference or common ratio , 90, 180, 360, , 35, 40, 45, Find the first five terms for each sequence: 106. a n = 2a n 1 + 3, where a 1 = a n = 5n 108. a n = 3a n 1, where a 1 = a n = 2 3 n Chapter 4 Matrices Use matrices A, B, & C to perform the given operations in problems # A = 2 1 B = 0 2 C = A + B 111. C B B A - 3B 114. Det(A) 115. Det(C) Algebra II Final Exam Review Double Period (13-14) Page 11 of 12
12 Algebra II Final Exam Review Double Period (13-14) Page 12 of 12 Determine whether each product is defined or undefined. F = 2 3 G = H = 5 J = FG 117. FH 118. FJ [ ] Solve the equation: X 3 = X = Algebra II Final Exam Review Double Period (13-14) Page 12 of 12
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