Algebra 2 Semester One Test Review     Name:__________________________PD:___

default_horizontal_line

 

1.  Solve:  10x + 1 = 51

 

            A.  52                          B.  50                          C.  3                            D.  5

 

2.  What is the solution?   6x + 5 + 2x + 4 = 33

 

            A.  24                          B.  3                            C.  1                            D.  34

 

3.  What is the solution?  4x 7 + 2x = 8x 2x + 10

 

            A  all real numbers      B.  no solution             C.  1.4                         D.  0.7

 

4.  Find the solution.  3(x + 5) 1 = 4(x + 7) x - 14

 

            A.  all real numbers     B.  no solution             C.  14                          D.  18

 

5.  Which equation has infinitely many solutions?

           

            A.                                                  B. 

           

C.                             D. 

 

6.  You are painting three stripes on your bedroom wall.  The stripes are 2 feet wide, and the wall is 15

     feet long.  You want an equal amount of space between the ends of the wall and the stripes, and  

     between each pair of stripes.  How far apart should the stripes be placed?

           

            A.  4.5 feet                  B.  2.25 feet                C.  3 feet                     D.  1.5 feet 

 

7.  You want to install 3 ceiling lights in a row to improve the visibility in your garage.  Each light is 3

     feet long and your garage is 27 feet long.  The distance between each light should be the same.  Also

     the distance between the group of lights and the walls should be half of the distance between any 2

     consecutive lights.  What is the distance between successive lights?

 

            A.  6 feet                     B.  5.25 feet                C.  7 feet                     D.  3 feet

 

8.  Solve:  12b 16 < 13b + 6

 

            A.  b > -22                   B.  b < 28                    C.  b > 22                    D.  b = 10

 

9.  Find the solution.  

           

A.    B.           C.             D. 

 

10.  Solve:  -x + 8 = 5x + 6

 

            A.                                      B.                        C.                          D.    

11.  What is the solution?    2(x 3) = 15 + 4x

 

            A.  5.5                       B.  9                          C.  3.5                         D.  10.5

 

12.  Solve:  -8x + 18 > - 6

 

            A.  x < 3                      B.  x > 3                      C.  x < 3                    D.  x > 1.5

 

13.  Find the solution.  x  Check for extraneous solutions

 

            A.  5, -13                     B.  , -2/5                  C.                            D.  2/5

 

14.  What is the solution?   

 

            A.  1, 4                                    B.  4                            C.  -1, 4                       D.  -4, 1

           

15.  Name the vertex and direction the absolute value function will open:  y = 3|x 3| + 9.

 

A.  (-3, 9); down         B.  (-3, 9); up               C. (3, 9); up                 D.  (3, 9); down

 

16.  Choose the graph that matches the function:  y = -|x + 2| + 5.              

 

[image][image][image][image]A.                                B.                                C.                                   D.    

 

 

 

 

 

 

 

[image]17.  What is the equation for the following graph: 

 

            A. 

 

            B. 

 

            C. 

 

            D. 

 

18.  Graph the linear equation by finding x- and y-intercepts.  4x 4y = -16

 

A.                                B.                                C.                                D.

 

 

 

19.  Graph the line y = -5x + 7

 

A.                                B.                                C.                                D.

 

 

 

 

 

 

 

20.  Mary works full-time for a company earning $8 per hour.  If she works more than 40 hours per

       week she receives overtime pay which is one and one-half times her regular pay.  Last week Mary

       worked for 55 hours.  What was her pay before any deductions?

 

A.  $180                      B.  $320                      C.  $440                      D.  $500

 

21.  You and your friend are planning on painting houses for a summer job.  If it takes you 3 hours to    

       paint a side of the house and it takes your friend 4 hours to paint the same side.  How many hours  

       would it take for you and your friend working together?

 

      A.  .14 hours               B.  1.71 hours              C.  3.50 hours              D.   7.00 hours

 

22.  Graph:  3x + 7y = 21

 

A.                                B.                             C.                              D.

 

 

 

 

 

 

 

23.  Graph:  3x y = 9

 

A.                                B.                             C.                              D.

 

 

 

 

 

 

 

24.  Write an equation of a line that has a slope of 7 and a y-intercept of 3.

 

A.  y = 7x + 3              B.  x = 7y + 3              C.  y = 0.14x 3         D.  y = 7x 3

 

25.  Write the equation of the line, in slope-intercept form, that passes through the point (-1, -5) and has

a slope of 4.

 

A.  y = 4x + 9              B.  y = -4x 9             C.  y = 4x 9              D.  y = -4x + 9

 

26.  The variables x and y vary directly.  If x = -3 and y = 9, write and equation that relates the variables.

 

A.  y = 0.3x                 B.  y = -3x                   C.  y = -0.3x                D.  y = 3x

 

27.  Write the slope-intercept form of the line that passes through point (3, -4) and has a slope of 4.

 

A.  y = -4x + 8                        B.  y = 4x + 8              C.  y = 4x 8              D.  y = -4x 8

 

28.  Write the equation of the line that passes through the point (-1, 2) and is parallel to 5x 5y = -4.

 

A.  y = - x + 1             B.  y = x + 3                C.  5x 5y = 2                        D.  2y = - x + 1

 

29.  Write the equation of the line that passes through the point (3, -5) and is parallel to y = 3x + 6.

 

A.  y = -3x + 14          B.  y = 3x + 18            C.  y = 3x 14                        D.  y = -0.3x 4

 

30.  Write an equation to model the following situation.  A music club membership costs $21 and then

        the member may purchase CDs at $6 each.

 

A.  y = 21x 6            B. y = 6x + 21             C.  y = 21x + 6            D.  y = -6x + 21

 

31.  In 1980 the average price of a home in Brainerd County was $97,000.  By 1985 the average price of

       a home was $122,000.  Which of the following is a linear model for the price of a home, P, in

       Brainerd County in terms of the year, t?  Let t = 0 correspond to 1980.

 

A.  P = 122,000 25,000t                              B.  P = 25,000t + 97,000

C.  P = 122,000 5000t                                  D.  P = 5000t + 97,000

 

32.  Write the equation of the line passing through (-2, 1) and (4, -5).

 

A.  y = -x 1               B.  y = x + 3                C.  y = -3x 5             D.  y = 3x + 7

33.  What is the equation for this line?

 

A.  x = 5                      B.  y = 5                     

 

C.  x = -5                     D.  y = -5

 

 

34.  What is the slope of the line whose equation is 2x 5y = 9

            A.                            B.                          C.                          D.  2

 

35.  Use the given table to write an equation relating x and y.  x and y vary directly.

 

x

20

40

60

80

100

y

$0.50

$1.00

$1.50

$2.00

$2.50

 

            A.  y = 40x                  B.  y = 0.025x             C.  y = 2.5x + 0           D.  y = -40x + 0

36.  This table shows the age and systolic blood pressure for a group of people who donated blood.  Find the line of best fit.  

 

x (age)

24

26

30

34

35

37

41

48

50

55

y (pressure)

108

104

132

119

128

121

132

140

135

146

 

A.  y = 83x + 1            B.  y = 0.44x + 48       C.  y = 1.13x + 83.5    D.  y = 2.25x

 

37.  Using the line of best fit from problem 36, find the blood pressure for a 54-year-old person.

 

A.  71.8                       B.  144.6                     C.  121.5                     D.  154

 

38.  Using the line of best fit from problem 36, what aged person has a blood pressure of 134.5?

 

A.  22                          B.  38                          C.  45                          D.  60

 

39.  The table below shows the average yearly incomes in dollars for women in the United States.  Create a scatter plot from this data and determine the line of best fit.  Then predict the average salary for women in the year 2000.

 

Years since 1950

10

20

30

35

40

Income ($)

3257

5323

11197

15624

19822

 

            A.  $28,447                 B.  $32,188                 C.  $23,879                 D.  $32,163

 

40. 

 

A.                                B.                                C.                                D.

 

 

 

 

 

 

 

 

41. Solve the system by graphing:  x + y = 8

         y = 3x 4

 

A.                                B.                                C.                                D.

 

           

 

 

 

 

 

(-6, 14)                                    (2, 6)                            (3, 5)                            (1, -1)

 

 

42.  Graph the linear system and estimate the solution:  x + y = 1

    2x y = -4

 

A.                                B.                                C.                                D.

 

 

 

 

 

 

 

 (3, 2)                           (1/3, 2/3)                      (-1, 2)                          (4/3, -4/3)

 

43.  Solve the system by graphing:  x + y = 1

        y = 2x 5

 

A.                              B.                              C.                                          D.

  

 

 

 

 

 

 

 

44.  To solve the system by substitution, which expression in equation II can be substituted into

       equation I?           I.   3x 4y = -2

                                    II. -2x - y = -1

 

A.     2x +                B. 2x - 1                       C. x +                 D.  -2x + 1

 

45.  Solve:  3x + 3y = -1

        y = -x

 

            A.  No solution           B.  (1, -3)                     C.  (-4, 4)                     D.  (1, 3)

 

46.   You want to eliminate x by addition in the system:       5x 2y = 5

                                                                                    3x 9y = 15

 

If you multiply both sides of the bottom equation by 5, by which number would you multiply both sides of the top equation?

 

A.  3                            B. 3                           C.  2                            D. -2

 

47. 

 

           

A.                                 B.                               C.                                D.

                                   

 

 

48.

 

 

A.                                B.                                C.                               D.

  

 

 

 

 

 

 

 

49. 

 

 

 

A.                             B.                               C.                                                D.

  

 

 

 

 

 

 

[image]

50.  Which ordered pair is a solution to the system of inequalities? 

 

 

                                    A.  (0, 4)

 

B.  (-6, 2)

 

C.  (-3, -7)

 

D.  (2, 1)

 

 

51. Which ordered triple is a solution of the system of equations?

 

4x 4y + 8z = 9

8x + 4y 4z = 4

12x 8y + 4z = 9

 

A. (0.75, -0.5, 4)         B. (0.75, 2, -1)             C. (-0.75, 0.5, 1)          D. (0.75, 0.5, 1)

 

52.  Solve the system:  3x 3y + 5z = 28

 x + y + z = 12

5x + 3y + 2z = 39

 

A.  z = 8                      B.  y = 3                      C.  x = 5                      D.  none of these

53.  Solve the system of equations:  x + y + z = 8

          -2x y + z = 1

           x 2y z = -8

 

A.  (-1, -2, -5)              B.  (5, 2, 1)                  C.  (-5, -2, -1)              D.  (1, 2, 5)

 

54.  What is the solution for x in the following linear system?   3x 4y = -14

    -3x + y = 8

 

A.  -2                           B.  2                            C.  5                            D.  No solution

 

55.  Solve the linear system:  2x + 2y = -5

y = -x + 1

 

A.  (-3, 3)                    B.  No solution            C.  (-5, 2)                     D.  (5, 2)

 

56.  Mr. Jones bought 10 tickets to a puppet show and spent $71.  He bought a combination of children tickets for $5 each and adult tickets for $12 each.  Which system of equations below will determine the number of adult tickets, a; and the number of children tickets, c?

 

A.  a = c 12               B.  5a + 5c =50           C.  a + c = 71              D.  12a + 5c = 71

         12a + 5c = 71                  a + c = 10                  a + c = 10                      a + c = 10

 

57.  Tickets to a local movie were sold at $4 for adults and $2.50 for students.  If 180 tickets were sold for a total of $645, how many student tickets were sold?

 

A.  145                                    B.  50                          C.  80                          D.  130

 

58.   What is the solution for y in the following linear system?  x + 4y = -13

                                                                 x + y = -7

 

            A.  -4                           B.  -2                           C.  -5                           D.  No solution

 

59. 

 

 

 

A.                              B.                                  C.                              D.                            

  

 

 

 

 

 

 

 

60. 

 

 

 

 

 

 

61. 

 

 

 

 

 

 

62.  Find the values of x and y in this matrix problem.

           

A.  x = 3, y = 1.6         B.  x = 6.5, y = 2         C.  x = 18, y = -0.6      D.  x = 3, y = 2

 

63.  Find the value of z in this matrix problem.

                A.  z = 7                    B.  z = - 2                                  C.  z = 5                    D.  z = - 1 

 

 

64.

 

 

 

 

 

 

 

 

65.  Student council and the Key Club at WHS are ordering supplies.  They supplies they need are listed below.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

66.  Find the inverse of the matrix

 

 

 

67.

 

 

 

 

 

 

 

 

 

68. Graph:  y = x2 + 1

 

A.                                B.                                C.                                D.

 

69. Determine the vertex of the following:    y = -3(x + 1)2 1

 

            A.  (1, -1)                    B.  (-1, 1)                     C.  (-1, -1)                   D.  (1, 1)

 

70.  Determine the vertex, axis of symmetry and opening of the following:   y = (x 3)2 4

 

A. vertex (-3, -4)         B. vertex (3, -4)           C. vertex (3, -4)           D. vertex (3, -4)

            axis x = -3                       axis x = 3                      axis x = -3                   axis x = 3

            opens up                          opens down                  opens up                      opens up

 

71.  What is the maximum or minimum of the parabola:       

            A.  (0, -2)                    B.             C.   (-1, -2)                  D.  (1, 2)

 

72.  What is the maximum or minimum of the parabola:  

 

A.  (5, 7)                      B.  ( -5, 7)                    C.  (-5, -7)                   D.  (5, - 7)

 

73. Find the x-intercepts of the graph of y = x2 2x 15

 

A.                                B.                                C.                                D.

3, -5                             2, -3                             -3, 5                             -2, 3

 

74. Find the zeros of the equation:  2x2 x = 3 + y

 

            A.                       B.                       C.                       D. 

75. Determine the equation of the parabola shown:

 

            A.  y = -3(x + 4)2 + 1              B.  y = 3(x 4)2 + 1

           

C.  y = -4(x 4)2 1               D.  y = -4(x + 4)2 1

76. A twirler tosses a baton.  The baton leaves her hands 6 feet above the ground with an initial velocity of 45 feet per second.  The twirler catches the baton when it falls back to 5 feet.  How long is the baton in the air?  Use h = -16t2 + vot + ho where t represents time, vo represents initial velocity, and ho represents initial height and h is the height.

 

A.  2.8 seconds           B.  5 seconds               C.  6 seconds               D.  45 seconds

 

77. The distance, d (in meters), traveled by a falling object is given by the equation

d = 4.9t2, where t is the time in seconds.  From what height was the object originally dropped if it took 6.48 seconds to hit the ground?  Round answers to the nearest whole number.

 

     A  206 meters              B.  1009 meters           C.  32 meters               D.  42 meters

 

78.  Factor:  x2 7x + 10

 

A. (x 7)(x 3)          B. (x 2)(x 5)          C. (x + 2)(x 5)          D. (x + 2)(x + 5)

 

79. Give one of the factors for:  x2 2x 24

 

A.  (x + 3)                  B.  (x 8)                    C. (x 4)                     D.  (x 6)

 

80. Find the zeros of y = x2 8x + 9 using a graphing calculator

 

A  no solution             B.  1.35, 6.65              C.  1, 7                                    D.  8, 9

 

81. Factor:  x2 25

 

A.  (x 5)(x + 5)         B.  (x + 5)(x + 5)         C.  (x 5)(x 5)         D.  (x + 1)(x 25)

 

82. Factor:  x2 + 10x + 25

 

A.  (x 5)2                  B.  (x + 10)2                C.  (x + 5)(x 5)         D.  (x + 5)2

 

83. Give one of the factors for:  8x2 + 18x + 9

 

A.  (2x - 3)                  B.  (x + 1)                    C.  (4x + 3)                  D.  (8x + 9)

 

84. Find the solution.  x2 + 9x = -20.

 

A.  4, 5                                    B.  20                       C.  5, -4                     D.  20, 1

 

85. Solve:  4x2 + 7 = 23

 

            A.                 B.                      C.                     D. 

 

86. Multiply:  (x 4)(x + 6)

 

A.  x2 24                                B.  x2 + 2x 24         C.  x2 2x 24         D.  x2 10

 

87. Simplify:  (2 + 3i) + (4 6i)

 

A.  8 3i                     B.  6 + 3i                     C.  6 3i                     D.  8 18i

 

88. Simplify:  (-3 + 4i)   (6 2i)

 

A.  3 + 2i                     B.  9 + 6i                   C.  9 + 2i                   D.  3 6i

 

89. Simplify:  (2 + 7i)(3 4i)

 

A.  34 + 13i                 B.  6 28i2                  C.  6 13i                   D.  6 28i

 

90.  Solve

                                   

A.   9, -9                      B.  9, -10                     C.  0, -9                       D.  0, 9

 

91. What are the solutions for the equation  ?   

           

          A.  x = -9, 5                 B.  x = 4, -8                 C.  x = -11, 7               D.  x = -10, 6

 

92. What are the solutions for the equation  ?

      

            A.  x = 6, -4                 B.  x = 1, -24               C.  x = 12, -2               D.  x = 8, -3

 

93. Find the x-intercepts of the graph of      

 

A.  1, 3                                                B.  -2, -6                                  C.  -1, -3                                  D.  2, 6

                     

94. Find the zeros of the equation             

 

       A.   x = -5 and x = 5/3     B.  x = 5 and x = -5/3      C.   x = 5 and x = -5/3       D.  x = - 5 and x = 3/5

 

95.  Solve over the set of complex numbers:      

 

    A.  1 + 8i, 1 - 8i       B.  1 + 4i, 1 - 4i           C.  -1 + 8i, -1 - 8i        D.  -1 + 4i, -1 - 4i

 

96. Solve: 

 

                    

 

 

97.   Solve: 

 

A.                       B.         

 

C.                              D.

 

98. Solve:             

           

A.                       B.    

 

C.                         D.

 

99.  Solve: 

 

           

 

100.  Solve over the set of complex numbers: 

 

                                       

 

                                      

 

 

101.  Find the discriminant and describe the solutions:  y = 3x2 2x + 7

 

A. -80; 2 real               B. -80; 2 imaginary     C.   -88; 2 imaginary   D. -88; 2 real

 

 

102.  Find the discriminant and describe the solutions:   y = -2x2 + 4x + 9

 

A.  56; 2 real               B. 56; 2 imaginary       C.  88; 2 real                D.  88 2 imaginary     

 

103.  In an experiment, a petri dish with a colony of bacteria is exposed to cold temperatures and then warmed again.  Find the quadratic equation that models the data shown.  What is the coefficient of the  term?

    

 

A.  0.39                       B.  0.23                       C.  0.29                       D.  0.37

104.  Bandar throws rocks into a quarry lake from the top of a 58 foot high wall. The chart gives the horizontal distance, x (in feet), the rock has traveled from Bandar and the height, y (in feet), of the rock above the lake.  Choose the equation that best fits the path of the rock from Bandar to the lake below?

           

 

           

 

105.  How many distinguishable permutations of the letters in BALLOON are there?

 

            A.  210                                    B.  340                                    C.  1260                      D.  2880         

 

106.  How many distinguishable permutations of the letters in BANANA are there?

 

            A.  60                          B.  120                                    C.  180                                    D.  360           

 

107.  You have an equally likely chance of choosing any number from 1 to 10.  What is the probability that you choose a number less than 4?

 

            A.                            B.                            C.                           D.   

 

108.  You have an equally likely chance of choosing any number from 1 to 15.  What is the probability that you choose a number greater than 10?

 

            A.                           B.                             C.                            D.   

           

109.  How many different license plates are possible if three digits are followed by two letters?  Assume letters and digits CAN BE repeated.

 

            A.  1560                      B.  676,000                 C.  1,320,000              D.  1,845,300 

 

110.   How many different license plates are possible if two digits are followed by three letters?  Assume letters and digits CANNOT repeat.

 

            A.  98                          B.  876,450                 C.  1,404,000              D.  1,757,600             

 

111.  If you are taking a trip and want to take along 3 CDs out of 15, how many different ways could you make your choices?

 

A.  5 ways                   B.  45 ways                 C.  455 ways               D.  2730 ways

 

112.  In how many ways can a 7 person committee be chosen from a group of 10 people?

 

            A.  120                                    B.  1260                      C.  12,600                   D.  60,480      

 

113.  In how many ways can 8 runners finish a race 1st, 2nd, or 3rd?

 

            A.  3                            B.  8                            C.  24                          D.  336           

 

 

114.  A dart thrown at the target shown is likely to hit anywhere inside the target.  What is the

         probability that the dart hits the circular region?

 

 

A.                                      B.                            C.                          D.

 

           

 

 

115.  A dart thrown at the target shown is likely to hit anywhere inside the target.  What is the

         probability of the dart hitting the shaded region?

 

 

 

 

 

A.  0.215                     B.  0.785                     C.  2.356                     D.  0.843