CP Algebra II Midterm Review Packet 2017-2018 CP Algebra II Midterm Review Packet 2017-2018 1.3 Solving

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  • CP Algebra II Midterm Review Packet 2017-2018

    1.3 Solving Equations Solve each equation.

    1. 2 3

    3 5 x  2. 3 4( 5) 6 22x x x    3. 8 3 5(2 1)x x  

    4. 3( 2) 4k k   5. 4

    3 6

    x x 

    1.5 Solving Inequalities

    Solve each inequality. Graph the solution set.

    6. 2 5 7z   7. 3 6x  8.  2 3 4 28f  

  • 10. Which of the following is a solution to the inequality 2 5 9x   ?

    a. 5 b. 6 c. 7 d. 8

    11. Which of the following is NOT a solution to the inequality 2 12 3 5x x   ?

    a. 16 b. 17 c. 18 d. 19

    2.1 Relations and Functions

    Determine if the relation is a function. State the domain and range.

    12. 13.

    Function? ___________ Function? ___________

    Domain: ____________ Domain: ____________

    Range: _____________ Range: _____________

    1

    3

    -5

    8

    2

    -3

    4

    5

  • 14. (7, 2), (4, 5), (6, 8), (9, -2), (7, 5) 15.

    Function? ___________ Function? ___________

    Domain: ____________ Domain: ____________

    Range: _____________ Range: _____________

    2.2 Linear Equations

    Write each equation in Standard Form and find the x-intercept and y-intercept . Remember, Standard Form is Ax By C  , where A, B, and C are whole numbers.

    16. 1

    3 4 2

    y x   x-intercept_______ y – intercept________

    17. 3

    2 4 4

    y x  x-intercept_______ y – intercept________

    18. 5 10 25y x  x-intercept_______ y – intercept________

    3 -4 5 6

    -2 8

    9 -4

    0 1

  • Name the x and y-intercepts.

    19. 2 5 10x y  20. 3 4 12 0x y  

    2.3 Slope

    Find the slope of the line that passes through each pair of points.

    21.  6, 5 ,(4,1)  22.  4,1.5 ,(4,6.5)

    23.  6,8 ,( 4,8) 24.  3, 10 ,( 2, 4)   

    25. Find the slope of the line parallel to the given line.

    a. 1

    27 3

    y x   b. 6 3 18x y 

  • 26. Find the slope of the line perpendicular to the given line.

    a. 2 18y x  b. 4 16x y 

    2.4 Writing Linear Equations

    State the slope and y-intercept of the graph of each equation.

    27. 3 5 20x y  28. 2 4 10x y  29. 12y  30. 1x  

    Write the equation in slope-intercept form for the line that satisfies each set of conditions.

    31. slope is 3, passes through (0,-6). 32. slope 3

    4 , passes through (-5,1).

    33. passes through (-2,5) and (3,1). 34. passes through (7,1) and (6,2).

  • 35. Determine if the lines are parallel, perpendicular or neither.

    a. b. c.

    2 9

    5

    5 11

    2

    y x

    y x

     

     

    2 7

    3

    2 3 36

    y x

    x y

     

     

    168

    492

    x

    y

     

    3.1 Solving Systems of Equations by Graphing

    Solve the system by graphing:

    36. 2 0

    6

    x y

    x y

     

      37.

    2

    4

    y x

    x y

      

      

  • 3.2 Solving Systems of Equations Algebraically

    Solve the system of equations by substitution or elimination:

    38. 3 2 8

    2 12 5

    x y

    y x

     

      39.

    3 5 6

    4 2 5

    x y

    x y

     

      

    40. Three lift tickets and two ski rentals cost Al Gebra’s family $335. The next week they went skiing

    again and brought some friends. Seven lift tickets and three ski rentals cost $690. What is the cost of

    one lift ticket? One rental?

    41. There are 42 more boys than girls in the sophomore class. The total number of students in the

    sophomore class is 506. How many girls are in the sophomore class?

  • 5.1 Monomials

    Simplify completely. Assume that no variable equals zero. DO NOT LEAVE ANY NEGATIVE EXPONENTS IN YOUR ANSWER.

    42. 25 nn  43. 4 2 3x x x  

    44. 34 )2( y 45. 2 5 4 3 1(4 )( 5 )d t v dt v  

    46. 2

    8

    m

    m 47.

    4

    65

    3

    12

    xy

    yx

    48.

    2

    32

    32  

      

    ba

    ab 49. 3)2(8 zu

    50.

    2

    52

    232 

      

       

    yx

    yx 51. 6523464 )()( pnmnm

    5.2 Polynomials

    Simplify completely.

    52. )272()33( 22  xxxx 53. )53()264(

    22  yyyy

  • 54. )43(2 4aaba  55. )432(3 3242  cddcdc

    56. )4)(7(  gg 57. )23)(23( yy 

    58. 2(3 1)x  59. 2( 1)(2 3 1)x x x  

    60. 22 (3 5) 3(3 5)x x x ax bx c     

    In the equation above, a, b and c are constants. If the equation is true for all values of x, what is the

    value of b?

    61. 2 22( 3 5) (4 4 10)x x x x    

    If the expression above is rewritten in the form 2ax bx c  , where a, b, and c are constants, what is

    the value of a?

    61a. 3 2

    3 2

    3 7 5

    2 8 13

    x x

    x x

     

      

    Find the sum of the two polynomials shown above?

  • 5.4 Factoring Polynomials

    Factor the following by using GCF.

    62. 3 57 3y y 63. 3 4 2 3 29 6 15x y x p y p 

    Factor the following by using Grouping.

    64. 2 5 5y y xy x   65. 21 7 3y x xy  

    Factor.

    66. 2 10 24y y  67. 2 6 16z z 

    68. 28 10 3y y  69. 29 18 8x x 

    Factor the following Difference of Squares.

    70. 29 25x  71. 2 216a c Factor the following Sum/Difference of Cubes.

    72. 38 27x  73. 3 364x y

  • Factor. Look for GCF first.

    74. 22 22 60y y  75. 33 12x x

    76. 2 2 1n n  77. 3 2 4 5 33 5x y x y x y 

    78. 22 13 7x x  79. 25 30 40x x 

    1.4 Solving Absolute Value Equations

    Solve each equation.

    80. 2 1 7x   81. 4 2x  

  • 82. 2 3 2 18x  83. 5 3 1 20x  

    2.6 Special Functions

    Graph each of the following. State the domain, range and any transformations.

    84. ( ) 3f x x  85. ( ) 2 2 1f x x   

    Domain: ___________________ Domain: _____________________

    Range: ____________________ Range: ______________________

    Transformations: ____________ Transformations: ______________

    __________________________ _____________________________

  • 7.7 Operations on Functions

    Use the following functions for #86-#96 2( ) 6 ( ) 2 9 18f x x g x x x      ( ) 4 2 3h x x k x x   

    86.   f g x 87.   g h x 88.  ( )h k x

    89. ( ) g

    x f

         

    90. ( )( )f k x 91.  ( )h k x

    92. ( )( )f h x 93. ( ) h

    x f

         

    94. ( ( ))f h x

    95.   3h k 96.   2h g

  • 7.8 Inverse Functions and Relations

    For #97-98, use the following functions.

            

            

    2,5 , 1, 4 , 3, 2 , 5,0

    4,2 , 3,5 , 6,0 , 1,3

    f

    g

       

      

    97. Find the inverse of f 98. Find the inverse of g For #99-#103, find the inverse of each function.

    99. 3 2

    ( ) 4

    x h x

      100. ( ) 5h x x  

    101.   1

    3 2

    f x x  102.   2 5f x x 

    103. 1y x 

  • 7. 9 Square Root Functions:

    Graph the following. Find the domain and range.

    104. 2 1y x   105. ( ) 4 6f x x  

    Doma

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