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

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. Simplify (5-4i)² 9-40i

12. (4-6i)(3+8i) 60+14i

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

14. Simplify √-48 4i√3

15. Using y=P(1+r/n)nt, assume $5000 is deposited in a savings account 15. 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

16. 7 + 6² ÷ 9 - 20 -9

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

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

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

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

21. 10 log4x=30 64

22. Solve for x: 7 log2(x+2)=35 30

23. If y=4x-1, then simplify 2x-y in terms of x. -2x+1 or 1-2x

24. On a right triangle, side a measures 4 cm and side b measuers √40 cm. Find the simplified hypotenuse. 2√14 cm

25. If the radius of a circle is quadrupled, what happens to its area? Area is multiplied by 16

26. If the height of a triangle is tripled, what happens to its area? It is tripled

27. If the sides of a square are doubled, what happens to its area? Area is multipled by 4

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

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

30. 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

31. If 2 die are rolled, what is the probability of rolling a sum of 4? 1/12

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

33. 5(3x + 2y) - 4(6y - x) 19x - 14y

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

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

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

37. Solve -2|3x – 3|+5 < -19 (-∞,-3)(5,∞) x<-3 or x>5

38. 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

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

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

41. Graph y > 3x - 1

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

43. Graph y=-4│x-1│

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

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

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

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

48. 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

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

50. What type of equation is y = 5x + 4? Linear

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

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

53. Is y-x5=x linear? No

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

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

56. Solve : 2x - 2y = -8 7x + 6y – 11 = 0 (-1, 3)

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

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

59. Simplify: (3y4)(2y)3 24y7

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

61.Simplify: (7x3 - 2x2+3) - (x2 - x - 5)

62. Simplify : (4x2 + 6) - (5x2 -x) -x2 + x + 6

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

64. Solve: ∛(y - 3) - 6 = -4 11

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

66. √x +4 = 2√3 X = 8

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

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

69. Solve: 5x2 = 25x + 120 8 and -3

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

71. Graph y = (x - 2)2 - 1

72. 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

73. 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

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

75. What type of equation is y = x2 - 5? quadratic

76. What picture does the graph of a quadratic equation make? parabola

77. 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

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

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

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

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

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

83. 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

84. 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

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

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

87. 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)

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

89. Find the inverse of y = x2 -1

90. Find the inverse of y = (5x -7) / 2

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

92. 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

93. Write an equation for the parabola with focus (4,0) and directrix y=2 Y=-1/4(x-4)²+1

Other things to look over: Probability (3 more questions) Combination (order doesn’t matter) Permutation (order matters) “or” add probabilities (don’t forget to subtract if inclusive) Matrix (4 questions) Adding, subtracting, and multiplying matrices Determinants Area of a triangle using determinants Solving for variables using matrices Solve a system of 3 equations using a matrix