2015 2nd Semester Exam Review

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1 Algebra nd Semester Exam Review 1. Write a function whose graph is a translation of the graph of the function in two directions. Describe the translation. 2. What are the solutions to the equation? 3. Solve using factoring: a. b. 2, 4 c. d. Factor. 4. a. ( 4x 1)( x 36) c. 4( x 3)( x 3) b. ( 2x 6)(2x 6) d. ( 4x 1)( x 36) Write as the product of two factors: Solve. 7. a. 0, 2 b. -2, 2 c. -2, 1 d. 0, Solve =.

2 Factor completely Find the zeros of the function if is a function of. 11. = 12. Find a quadratic equation that has roots 3 and -6. Simplify the expression

3 Solve. 15. no real-number solution 16. Solve the equation. Find the maximum value of the quadratic equation. 17. a. max = -16 b. max = -38 c. max = -20 d. max = Solve 19. Solve a. b. c. d. 20. Use the discriminant to determine the number of real solutions of the equation.

4 Simplify the expression. 21. a. b. c. d Use synthetic substitution to evaluate when = A rectangle has a lenth of and a width of. Which equation below describes the perimeter, P, of the rectangle in terms of x? 25. Find the product. Factor each polynomial completely

5 Find the real-number solutions of the equation. 29. = 0 a. 0, 2 b. 2, 1 c. 2, 2 d. 0, a. 3 b. 2 c. 0 d a. 5 b. 4 c. 6 d Divide. 34. a. b. c. d. 35. a. b. c. d.

6 36. Given polynomial function f and a zero of f, find the other zeros. 37. Find all real zeros of the function. 38. Find all zeros of the polynomial function Identify the number of solutions of the equation or the number of zeros of the function. 42.

7 43. Determine the possible numbers of positive real zeros, negative real zeros, and imaginary zeros for. 44. Rewrite using radical notation. Simplify: Which is written in simplest form? 50. Simplify. Simplify the expression. Write your answer using only positive exponents. 51.

8 Simplify the expression Let. Find. a. 3 b. 81 c. 27 d. 27 For #58, let. Perform the indicated operation and state the domain Are the functions f and g below inverses of each other? 60. Given the function, what is the range of h(x)?

9 61. Which represents the graph of? 62. Find the domain and range of the function 63. Solve the equation. Check for extraneous solutions Solve. 67. Find the y-intercept of the equation. a. 4 b. 21 c. 3 d. 7

10 68. The amount of money, A, accrued at the end of n years when a certain amount, P, is invested at a compound annual rate, r, is given by If a person invests $250 in an account that pays 9% interest compounded annually, find the balance after 15 years. a. $911 b. $2500 c. $37,500 d. $ The projected worth (in millions of dollars) of a large company is modeled by the equation The variable x represents the number of years since What is the projected annual percent of growth, and what should the company be worth be in 2008? 70. If there are initially 4000 bacteria in a culture, and the number of bacteria double each hour, the number of bacteria after t hours can be found using the formula. How many bacteria will be present after 9 hours? a. 1,024,000 b. 4,096,000 c. 72,000 d. 2,048, Explain the difference between a linear function and an exponential function. Give an example of each function type. 72. A piece of equipment costs $95,000 new but depreciates 14% per year in each succeeding year. Find its value after 10 years. Use Simplify: 73. a. b. c. d The formula can be used to find the dollar value of an investment of $6000 after t years when the interest is compounded continuously at a rate of r percent. Find the value of the investment after 8 years if the interest rate is 8%. Find the value of the investment after 12 years if the interest rate is 4%. a. $10,017.99; $ c. $11,378.89; $11, b. $10,017.99; $11, d. $11,378.89; $

11 76. Evaluate without using a calculator. 77. Evaluate without using a calculator. 78. Solve for x. 79. Solve for x. 80. Find the inverse of the function Explain the difference between a common logarithm and a natural logarithm. 83. True or False: 84. Expand the expression. 85. Condense the expression. 86. Use the change-of-base formula to evaluate the expression. 87. Evaluate to three decimal places. 88. Solve: = a. b. c. d.

12 Solve the equation. Check for extraneous solutions Multiply the expressions. Simplify the result Perform the indicated operation(s) and simplify a. b. c. d Evaluate: 96. a. b. 18 c. 6 d.

13 97. Evaluate the expression. 98. Find the inverse of the function Convert 72 to radians. a. 5 2 c. 2 5 b. 4 5 d Convert to degrees. a. 648 b. 100 c. 50 d. 25 Evaluate the function without using a calculator a. 1 c Without using a calculator, find the exact value of. a. 1 3 c. b. 1 2 d Find one positive angle and one negative angle that are coterminal with the given angle Find the reference angle for 93.

14 107. Find the reference angle for. Solve the equation for Round your answer to three significant digits Find the measure of the angle Given triangle ABC with a = 8, A = 49, and B = 21, find c. Round your answer to the nearest hundredth.

15 Algebra nd Semester Exam Review Answer Section 1. Sample answer: ; The graph of is a translation of the graph of 3 units right and 2 units up. 2. A 3. C 4. C 5. C 6. C 7. D D 11. B D 14. C 15. C C 18. D 19. B D B 24. B C A 30. B 31. C A 34. C 35. D

16 A 40. B 41. 1, 1,, B D 58. domain: 59. No B y =

17 C 68. A 69. 7%; $ million 70. D 71. Sample answer: A linear function in one in which the growth is constant. Its graph is a straight line; example: y = 2x + 3. An exponential function in one in which the rate of growth is not constant. Its graph is a curve; example:. 72. $21, D D x = Sample answer: A common logarithm is base-10, and the notation "log" is used to indicate a common logarithm. A natural logarithm is base-e, and the notation "ln" is used. 83. False C x = -4 or B D C

18 100. C 101. C 102. B 103. D 104. Positive coterminal angle: 471 Negative coterminal angle: Positive coterminal angle: Negative coterminal angle:

Algebra II: Chapter 4 Semester Review Multiple Choice: Select the letter that best answers the question. D. Vertex: ( 1, 3.5) Max. Value: 1.

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