Algebra 2 Final Review

1. Which property is illustrated: 3+(x+5)=(3+x)+5 Associative of Addition

2. Which property is illustrated: 4∙5=5∙4 Commutative Property of Multiplication

3. Which property: 3(2a + 7) = ( 2a + 7)3 Commutative property of multiplication

4. Which property: 6v + 5v = (6 + 5)v distributive

5. What are the set of integers? {…-2, -1, 0, 1, 2 …}

6. Is pi a rational or irrational number?

7. Factor: x2 + 8x + 15 (x + 5)(x + 3)

8. Factor 8x3 -10x2-12x 2x(4x+3)(x-2) , don’t forget to pull what’s in common out first

9. Factor 5y²-17y-12 (5y+3)(y-4)

10. Solve: 2x2 + 5x = 3 -3 and 1/2

11. (4-6i)(3+8i) 60+14i

12. Multiply: (5x - 4) 2 25x2 - 40x + 16

13. Simplify √-48 4i√3

14. Using y=P(1+r/n)nt, assume $5000 is deposited in a savings account 14. Using y=P(1+r/n)nt, assume $5000 is deposited in a savings account. If the interest rate is 3% compounded monthly, approximately how much money is in the account after 8 years? $6354.34

15. 7 + 6² ÷ 9 - 20 -9

16. x²-x-6 • x²+7x+12 x²-2x-8 x²-9 X+4 x-4

17. What is the domain of y= 2x+2 3x+9 (-∞,-3)(-3,∞) All real numbers except -3

18. What is the domain of y= 2x+2 x²-16 (-∞,-4)(-4,4)(4,∞) All real numbers except -4 and 4

19. Find all asymptotes: y= x-5 x²-9 Vertical x=3,-3 Horizontal y=0

20. 10 log4x=30 64

21. Solve for n. 2 log3n + log 3 3 = 4 3 3

22. Which is the equivalent of 5³ = 125 a. log125 3 = 5. b 22. Which is the equivalent of 5³ = 125 a. log125 3 = 5 b. log3 5 = 125 c. log5 3 = 125 d. log5 125 = 3 d. log5 125 = 3

23. If y=x5 is the parent graph, describe the translation for y=-3(x-1)5+7 Flipped, steeper, right 1 and up 7

24. Simplify: x-2y-1(-2)x-1y-2 xy(-2)3 1___ 4x4y4

25. What are the odds of rolling a 3 on a die? What is the probability? Odds: 1 to 5 or 1:5 or 1/5 Probability: 1/6

26. Evaluate: 3+7[13-(6+2)] 38

27. 5(3x + 2y) - 4(6y - x) 19x - 14y

28. Solve: -(5-2x) = x+3 8

29. Solve: |y - 8| - 7 = 3 18 or -2

30. Solve: |5-6x|< 2 ½<x<7/6 (1/2, 7/6)

31. Solve 𝑥 2 −8𝑥−28 < -19 (-1,9) -1<x<9

32. Find the mean, median, and mode for: 72, 80, 79, 95, 64, 77, 82, 88, 79 mean is 79.6 Median is 79 Mode is 79

33. Use grouping symbols so that the given expression has a value of 3 15÷(3+2)-1+1

34. Sketch the graph of 3x + 2y = 3

35. Graph y > 3x - 1

36. Graph y = |x+2| - 3

37. Name the x and y intercept 2x-3y=18 X-intercept is 9 and the Y-intercept is -6

38. What is the slope of 3x + 4y = 7 -3/4

39. What is the slope of the line containing (1,4) and (3,8) 2

40. What is the equation that passes through (-1,-2) and has a slope of 3? y = 3x + 1

41. What is the equation of the line that passes through (1,4) and is perpendicular to: y = 2/3 x + 5? y = -3/2 x + 11/2

42. Write the equation of the line that passes through (-2,1) and (-6, -4). y = 5/4 x + 7/2

43. What type of equation is y = 5x + 4. a. Linear. b. Quadratic c 43. What type of equation is y = 5x + 4? a. Linear b. Quadratic c. Greatest integer d. Constant A. Linear

44. Find the slope intercept form for a graph that passes through (2,7) and is parallel to y=-2x+8

45. Determine if the lines y-5x=10 and 5y+x=3 are parallel, perpendicular, or neither.

46. What type of equation is y = 𝑥. a. Linear. b. Quadratic c 46. What type of equation is y = 𝑥 ? a. Linear b. Quadratic c. Greatest integer d. Constant C. Greatest integer

47. What does the solution to a system of 2 equations represent? Point of intersection

48. What is the x value of the solution for: 7x + 2y = -16 9y = 6x + 3

49. Solve : x2 + y2 = 53 x + y = 5 (-2, 7), (7,-2)

50. Solve the system: 2x + y = 1 4x + 2y = 2 Infinite solutions (they are the same line, coinciding)

51. Simplify: 18x3 y4 24x-3 y-6 3/4 x6 y10

52. Simplify: (3y4)(2y²)3 24y10

53. Simplify (3x-1/y-2 )0 1 , anything to the zero power is 1

54. What is the remainder: (2x4 - 32x2 – 40x - 300) ÷(x - 5) -50

55. Multiply : (5 + 2√3)(2 - 4√3) -14 - 16√3

56. Solve: ∛(y - 3) - 6 = -4 11

57. √x+5 = -10 No solution, an even root can never be negative

58. √x +4 = 2√3 X = 8

59. Divide using synthetic division: (2x4 - 3x3 - 6x2 - 8x - 3) / (x - 3)

60. Solve: 2x2 + 5x = -3 -3/2 and -1

61. What is the discriminant, and how many roots does 5n2 = 4n + 6 have? 136 , 2 real solutions

62. Graph 𝑥 2 9 + (𝑦+2) 2 25 =1

63. Find the vertex: y = x2 - 8x + 16, axis of symmetry, and tell which way would it open? Vertex is (4,0), axis of symmetry is x=4, and the parabola opens up

64. For the following function, determine the axis of symmetry, vertex, direction, x-intercept(s), y-intercept, and graph: y = x²-4x+3 Axis of symmetry is x=2, vertex is (2,-1), direction is up, x-intercepts are 1 and 3, y-intercept is 3

65. Graph y > x2 - x -12 (find vertex and zeros) Zeros 4 and -3

66. What picture does the graph of an absolute value equation make. a 66. What picture does the graph of an absolute value equation make? a. Line b. Parabola c. V d. steps C. V

67. Mr. Stewart has found that the cost of producing wooden benches is modeled by C(x)= 13x2-416x+3580, where C(x) is total cost and x is the number of benches. How many benches should he produce to minimize his cost? 16

68. What does the solution to a quadratic equation tell you about its graph? Zeros or x-intercepts

69. By using parent graph rules, graph y = -x2 - 5

70. What does it mean about the graph if there are imaginary solutions? The graph doesn’t cross the x axis

71. Find the zeros: y=5x3+10x²-15x 0,-3, and 1

72. Find the solutions to y-10= 4x2 - 5x No real solution OR 5 ± i√135 8

73. Describe the end behavior of the graph and the possible number of turns: y = x3-x2 - x + 1 The graph will start low, end high, turn 2 times

74. Describe the end behavior and number of turns of y = -5x5 +2x2 -1 The graph will start high, end low and have 4 possible turns

75. List all possible rational zeros for : y = 4x3 - 5x2 + 7x - 8 + 1, 2, 4, 8, 1/2, 1/4

76. Find g(f(x)) if f(x) = x2 - 1 and g(x) = x + 3 Y = x2 + 2

77. Find the slope and the y-intercept of the inverse of y = 4x + 3 y intercept is -3/4 and slope is 1/4 (up 1 , right 4)

78. Find the inverse of y=(2+x)1/3+5

79. Which of the following is used to solve for exponents. a. matrices 79. Which of the following is used to solve for exponents? a. matrices b. rref c. Logarithms d. Factorials C. Logarithms

80. Name the center and radius of the following: (x+3)²+(y-1)²=16 Center (-3,1) and radius is 4

81. Write an equation for the ellipse with endpoints of the major axis at (7,1) and (-7,1) and endpoints of the minor axis at (0,5) and (0,-3). x²/49 + (y-1)²/16 = 1

82. Four cards are randomly drawn from a standard deck of cards 82. Four cards are randomly drawn from a standard deck of cards. What is the probability that the cards drawn are a Heart, diamond, heart, diamond, in that order. Round to thousandth. .004

83. Two letters are chosen from the word “Algebra” 83. Two letters are chosen from the word “Algebra”. What is the probability they are both vowels? 1/7

84. Mrs. Hess is selecting one student to be the leader of her Algebra 2 classes. Her classes consist of the following: 8 sophomore boys, 7 sophomore girls, 5 junior boys, 8 junior girls, 1 senior boy, and 2 senior girls. What is the probability she will select a boy or a sophomore? 21/31

85. A license plate has two letters followed by two numbers 85. A license plate has two letters followed by two numbers. How many different plates are possible? 58500

86.Solve the matrix equation for x. −4 𝑥 6 𝑦 = 𝑧 8 6 0

87. What are the dimensions of the product of AB 87.What are the dimensions of the product of AB? A= 2 −1 4 3 0 2 𝐵= 2 1 3 0 5 1 2 x 2

88. Find the bottom row of 2 A + B A= 3 8 −1 7 𝐵= 0 −2 1 5 [-1 19]

89. Find the value of the determinant. −8 −1 2 6 -48 - -2 = -46

90. log2x+ log2(x-4)= log221 7

Other things to look over: Probability Combination (order doesn’t matter) Permutation (order matters) “or” add probabilities (don’t forget to subtract if inclusive) Matrix Adding, subtracting, and multiplying matrices Determinants, Area of a triangle using determinants Solve a system of 3 equations using a matrix Quadratics Vertex, axis of symmetry, x and y intercepts, graph Directrix and focus Logarithms When to use ln (natural log) Special properties of logarithms Parent graphs What each looks like and how they shift