Advanced Algebra: S1 Final Exam Review - D155ww2.d155.org/cls/tdirectory/KGreenfield/Shared...
Transcript of Advanced Algebra: S1 Final Exam Review - D155ww2.d155.org/cls/tdirectory/KGreenfield/Shared...
![Page 1: Advanced Algebra: S1 Final Exam Review - D155ww2.d155.org/cls/tdirectory/KGreenfield/Shared Documents/Algebra 2... · x 3 2 4 7) 6 2x 1 2 3 x 4 8) 12 x3 45 9) 3 5 2x 3 2 4 2x 3 10)](https://reader030.fdocuments.in/reader030/viewer/2022020411/5abcc4177f8b9a441d8e7255/html5/thumbnails/1.jpg)
Name:
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
![Page 2: Advanced Algebra: S1 Final Exam Review - D155ww2.d155.org/cls/tdirectory/KGreenfield/Shared Documents/Algebra 2... · x 3 2 4 7) 6 2x 1 2 3 x 4 8) 12 x3 45 9) 3 5 2x 3 2 4 2x 3 10)](https://reader030.fdocuments.in/reader030/viewer/2022020411/5abcc4177f8b9a441d8e7255/html5/thumbnails/2.jpg)
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
![Page 3: Advanced Algebra: S1 Final Exam Review - D155ww2.d155.org/cls/tdirectory/KGreenfield/Shared Documents/Algebra 2... · x 3 2 4 7) 6 2x 1 2 3 x 4 8) 12 x3 45 9) 3 5 2x 3 2 4 2x 3 10)](https://reader030.fdocuments.in/reader030/viewer/2022020411/5abcc4177f8b9a441d8e7255/html5/thumbnails/3.jpg)
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)
![Page 4: Advanced Algebra: S1 Final Exam Review - D155ww2.d155.org/cls/tdirectory/KGreenfield/Shared Documents/Algebra 2... · x 3 2 4 7) 6 2x 1 2 3 x 4 8) 12 x3 45 9) 3 5 2x 3 2 4 2x 3 10)](https://reader030.fdocuments.in/reader030/viewer/2022020411/5abcc4177f8b9a441d8e7255/html5/thumbnails/4.jpg)
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 ( ) √
![Page 5: Advanced Algebra: S1 Final Exam Review - D155ww2.d155.org/cls/tdirectory/KGreenfield/Shared Documents/Algebra 2... · x 3 2 4 7) 6 2x 1 2 3 x 4 8) 12 x3 45 9) 3 5 2x 3 2 4 2x 3 10)](https://reader030.fdocuments.in/reader030/viewer/2022020411/5abcc4177f8b9a441d8e7255/html5/thumbnails/5.jpg)
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
![Page 6: Advanced Algebra: S1 Final Exam Review - D155ww2.d155.org/cls/tdirectory/KGreenfield/Shared Documents/Algebra 2... · x 3 2 4 7) 6 2x 1 2 3 x 4 8) 12 x3 45 9) 3 5 2x 3 2 4 2x 3 10)](https://reader030.fdocuments.in/reader030/viewer/2022020411/5abcc4177f8b9a441d8e7255/html5/thumbnails/6.jpg)
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
![Page 7: Advanced Algebra: S1 Final Exam Review - D155ww2.d155.org/cls/tdirectory/KGreenfield/Shared Documents/Algebra 2... · x 3 2 4 7) 6 2x 1 2 3 x 4 8) 12 x3 45 9) 3 5 2x 3 2 4 2x 3 10)](https://reader030.fdocuments.in/reader030/viewer/2022020411/5abcc4177f8b9a441d8e7255/html5/thumbnails/7.jpg)
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
![Page 8: Advanced Algebra: S1 Final Exam Review - D155ww2.d155.org/cls/tdirectory/KGreenfield/Shared Documents/Algebra 2... · x 3 2 4 7) 6 2x 1 2 3 x 4 8) 12 x3 45 9) 3 5 2x 3 2 4 2x 3 10)](https://reader030.fdocuments.in/reader030/viewer/2022020411/5abcc4177f8b9a441d8e7255/html5/thumbnails/8.jpg)
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
![Page 9: Advanced Algebra: S1 Final Exam Review - D155ww2.d155.org/cls/tdirectory/KGreenfield/Shared Documents/Algebra 2... · x 3 2 4 7) 6 2x 1 2 3 x 4 8) 12 x3 45 9) 3 5 2x 3 2 4 2x 3 10)](https://reader030.fdocuments.in/reader030/viewer/2022020411/5abcc4177f8b9a441d8e7255/html5/thumbnails/9.jpg)
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
![Page 10: Advanced Algebra: S1 Final Exam Review - D155ww2.d155.org/cls/tdirectory/KGreenfield/Shared Documents/Algebra 2... · x 3 2 4 7) 6 2x 1 2 3 x 4 8) 12 x3 45 9) 3 5 2x 3 2 4 2x 3 10)](https://reader030.fdocuments.in/reader030/viewer/2022020411/5abcc4177f8b9a441d8e7255/html5/thumbnails/10.jpg)
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)?
![Page 11: Advanced Algebra: S1 Final Exam Review - D155ww2.d155.org/cls/tdirectory/KGreenfield/Shared Documents/Algebra 2... · x 3 2 4 7) 6 2x 1 2 3 x 4 8) 12 x3 45 9) 3 5 2x 3 2 4 2x 3 10)](https://reader030.fdocuments.in/reader030/viewer/2022020411/5abcc4177f8b9a441d8e7255/html5/thumbnails/11.jpg)
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
![Page 12: Advanced Algebra: S1 Final Exam Review - D155ww2.d155.org/cls/tdirectory/KGreenfield/Shared Documents/Algebra 2... · x 3 2 4 7) 6 2x 1 2 3 x 4 8) 12 x3 45 9) 3 5 2x 3 2 4 2x 3 10)](https://reader030.fdocuments.in/reader030/viewer/2022020411/5abcc4177f8b9a441d8e7255/html5/thumbnails/12.jpg)
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
![Page 13: Advanced Algebra: S1 Final Exam Review - D155ww2.d155.org/cls/tdirectory/KGreenfield/Shared Documents/Algebra 2... · x 3 2 4 7) 6 2x 1 2 3 x 4 8) 12 x3 45 9) 3 5 2x 3 2 4 2x 3 10)](https://reader030.fdocuments.in/reader030/viewer/2022020411/5abcc4177f8b9a441d8e7255/html5/thumbnails/13.jpg)
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
![Page 14: Advanced Algebra: S1 Final Exam Review - D155ww2.d155.org/cls/tdirectory/KGreenfield/Shared Documents/Algebra 2... · x 3 2 4 7) 6 2x 1 2 3 x 4 8) 12 x3 45 9) 3 5 2x 3 2 4 2x 3 10)](https://reader030.fdocuments.in/reader030/viewer/2022020411/5abcc4177f8b9a441d8e7255/html5/thumbnails/14.jpg)
88) Part…
a.
b.
89) Part…
a.
b.
90)
91)
92)
93)