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Advanced Algebra: S1 Final Exam Review

Evaluate. 1) 2c ac 4b

b c

if a 1, b 2, and c 3

2) 2a b c

2c

if a 3, b 2, and c 5

Solve the following equations. 3) 2x 5 3 4) 2 3x 2 3 7 5) 2 x 5 14

6) 2 1 3x

3 2 4

7) 6 2x 1 2 3 x 4 8) 1 2x 3

4 5

9) 3 5 2x 3 2 4 2x 3 10)

15x 1 2x 6

2

11)

2x 2 9x 12

3

Solve each inequality. Write the solution in interval notation. 12) 3x 2 5 13) 2x 4 8 14) 2x 3 1

15) 3y 2 10 16) 3 2x 3 4x 4x 1

17) Given 2

g x 3x 1 5, find g 2 .

18) Given 2f x x 3x 2, find f 4 .

19) State the domain and range of the following relation. Is the relation a function?

1,3 , 5, 2 , 1,6 , 7,4

Domain___________________ Range_____________________ YES or NO

Write an equation of a line in slope intercept form that has the following conditions. 20) Passes through the points 5,8 and 1, 2

21) Passes through the points 6, 2 and 4, 2

22) Passes through the point 1, 5 and is parallel to the line 2x 3y 1

23) Passes through the point 5, 2 and is perpendicular to the line 2x y 5

Find the x-intercept of the equation. 24) 6x 3y 12 25) 3x 2y 9

Write an equation of the line shown in the graph. 26)

27)

State whether or not the graph represents a function. 28)

29)

Graph the equation. 30) Graph using the x- & y- intercepts: 4x 3y 12

x-intercept: y-intercept:

31) Graph y 3 x 1 2

32) Graph ( ) √

33) Graph ( ) √

34) Graph using slope-intercept form: 4x 6y 12

Solve by graphing. 35)

Solve by graphing: 3x 2y 8

x y 6

36)

Solve by graphing:

y 3x 4

y 5

x 1

37)

Solve by graphing:

y x 1

x y 4

x 5

Solve the system of equations using substitution method. 38) y 4x

2x y 2

39) x 3y 7

2x 7y 12

Solve the system of equations using elimination method. 40) 2x 5y 14

3x 2y 17

41) 4x 3y 2

3x 5y 7

Write and solve a system of equations. 42) A caterer bought several pounds of chicken salad

and several pounds of tuna salad. The chicken salad costs $9 per pound, and the tuna salad costs $6 per pound. He bought a total of 14 pounds of salad and paid a total of $111. How many pounds of chicken salad did he buy?

43) On opening night of the basketball season, a school made $1,413. They sold a total of 204 tickets. The school charged $9.50 for each adult ticket, and $6.00 for each student ticket. Determine how many student tickets were sold?

Solve the system of equations. 44) 2x y 3z 7

x 2z 3

3x 2y 2z 5

45) x y z 5

3x y 2z 1

4x 2y 3z 10

Write the equation (in vertex form) that represents the graphed function. 46) ( )

47) ( )

State the domain and range of the function. 48)

49)

50)

51)

Simplify. 52) 3 2

7 5 3

12x y z

8x y z

53) 3

2 3 23x y 2x y 54)

32 3

22 0

2x y

4x y

55) 2 26x 3x 5 4x 7x 3 56) 24 4 27 3 48 57) 2

5

58) 7

4 3

59) 49 3 60) 2 3 4i i

61) 4 11 63 40x y z 62) 7 12 94 16x y z 63) 2 14 4 21

64) 3481

65) 5 2

4

i

i

Factor completely. 66) 22x x 15 67) 3x 8 68) 249x 25

69) 364x 27 70) 210x 29x 21 71) 216x 81

Multiply. 72)

22y 4 73)

23 2i 74) 2x 3 x 5x 2

Use synthetic division to divide. 75) 4 3 24x 3x 8x 3 x 2 76) ( ) ( )

Use the discriminant to describe the roots of the equation. 77) 22x x 4 0

Solve. 78) 5x 1 2x 21 79) 3 2x 1 6 3 80) 3x 1 2 3

81) 3 x 2 82) 23x 36 0 83) 2x 7x 18 0

84) 22x 4x 3 85) 224x 15 2x

Solve the inequality. 86) 2x 6x 16 0 87) 26x 13x 5 0

Answer the questions about the parabolic trajectory. 88) The height in feet of a ball seconds after being tossed upward is given by the formula…

216 96h t t t

a. After how many seconds will the ball reach its maximum height?

b. What is the maximum height?

89) The height in feet of a cliff diver seconds after jumping off a cliff (from a trampoline) is given by the formula…

216 32 160h t t t

a. After how many seconds will the diver reach his maximum height?

b. What is the maximum height (above the water)?

Graph the following quadratic functions. Use completing the square when necessary. 90) 2y 3x 6x 1

91) 2y x 1

Graph the following quadratic inequalities. Use completing the square when

necessary. 92)

2y 2 x 4 3

93) 2y 4x 16x 11

Answers 1)

2)

3) x = 4, 1

4) 4

x , 03

5) No solution

6) 15

x8

7) 8

x15

8) 52

x5

9) x 14

10) 1

x3

11) x = 2

12) (

)

13) ( ] [ )

14) ( )

15) (

]

16) ( )

17) 20

18) 6

19) Domain: 5, 1, 7 , Range: 3, 2, 6, 4 , no

20) 5 1

y x3 3

21) y 2

22) 2 17

y x3 3

23) 1 1

y x2 2

24) ( )

25) ( )

26)

27)

28)

29)

30) 3, 0 0, 4

31)

32)

33)

34) 2

y x 23

35) 4, 2

36)

37)

38) 1, 4

39) 13, 2

40) 3, 4

41) 1, 2

42)

43)

44) 1, 3, 2

45) 2, 3, 4

46) ( )

47)

48) [ ) [ )

49) ( ] [ )

50) ( ) [ )

51) ( ) ( ]

52) 3

4 2

3y

2x z

53) 8 1054x y

54) 10 9x y

2

55) 22x 10x 8

56) 2 6

57) 2 5

5

58) 28 7 3

13

59) 7 3

60) 11 10i

61) 3 2 232xy z 5xy

62) 43 2 32xy z x z

63) 56 6

64) 27

65) 18 13

17

i

66) 2x 5 x 3

67) 2x 2 x 2x 4

68) 7x 5 7x 5

69) 24x 3 16x 12x 9

70) 5x 3 2x 7

71) 4x 9 4x 9

72) 24y 16y 16

73) 5 12i

74) 3 2x 8x 17x 6

75) 3 2 54x 5x 2x 4

x 2

76)

77) 2 real roots

78) 22

x3

79) x 14

80) 26

x3

81) no solution

82) 2 3i

83) x 9, 2

84) 2 10

x2

85) 5 3

x ,6 4

86) 2,8

87) 5 1

, ,2 3

88) Part…

a.

b.

89) Part…

a.

b.

90)

91)

92)

93)