Download Alg 1 Sem 2 Review Answers 12-13

Algebra I Semester II Final Review
1. Solve the linear system by graphing:
y=
2
x+2
3
y = -x – 3
a. ( 3, 4)
b. ( 2, 5)
c. (3, 0)
d. (-3, 0)
2. Solve the linear system by graphing:
x–y=1
x+y=3
a. no solution
b. ( 1, 2)
c. ( 2, 1)
d. (-2, 1)
3. Solve the system by substitution: y = 2x + 6
y = 3x
a. ( -6, -18)
b. (6, 18)
c. All Real Numbers
d. (3, 12)
4. Solve the system by substitution: 3x + 2y = -6
y = -x – 2
a. ( -2, 0)
b. (10, -12)
c. ( 2, -4)
d. ( 3, 0)
5. Solve the system by linear combinations: 2x – 3y = 16
3x + 3y = 9
a. ( 7,
2
)
3
b. ( 8, 0)
c. (0, 3)
d. (5, -2)
6. Solve the system by linear combinations: 3x – 4y = 21
4x + 2y = 6
a. No Solution
b. (2, -1)
c. (3, -3)
7. Solve the system using linear combinations:
a. ( 1, -
4
)
5
8. Simplify:
b. (-5, 6)
d. (7, 0)
4x + 3y = -2
3x + 2y = -3
c. ( 5, -9)
d. None of these
(2x 3 y 6 )(5x 4 y)
10x7y7
3
9. Simplify: (5qr)
125q3r3
3 2
2 3
10. Simplify: (8x ) (2x )
512x12
-4
11. Simplify: a.) 3
12. Simplify:
13. Simplify:
4ab-3c -3
1
-2
9x y
-1
1/81
4a/b3c3
x2y/9
38
14. Write an equivalent expression: 4
3
-30x 5 y
15. Simplify:
-6x 4 y 3
b.) x
5x/y2
34 = 81
0
1
16. Simplify: (7x + 7x + 5) + (-5x - 5 + 9x)
4
4
2x4+16x
17. Simplify: (3x + 6x + 3) - (7x - 4 x + 4 x - 3)
3
2
3
2
-4x3+10x2-4x+6
18. Simplify:
a.) (- x 5 + 7x) - (2x + 5 + 3x 5 )
b.) (-9y 2 - 8x) + (-2xy - 2x 2 + y 2 ) + (- y 2 + 4 xy)
-4x5+5x-5
-2x2-9y2-8x+2xy
2
2
2
19. Simplify: -3x y(2x y - 5xy - 3y)
3
2
20. Simplify: -z (3 - z - 2z )
2z5+z4-3z3
21. Simplify: (x + 9)(x – 4)
x2+5x-36
22. Simplify: (p + 9)(p – 9)
p2-81
23. Simplify: (6x – 8)(4x + 2)
24x2-20x-16
24. Simplify: (x – 10)(3x – 5)
3x2-35x+50
-6x4y2+15x3y3+9x2y2
25. Simplify:
(2x - 3) 2
4x2-12x+9
26. Solve: (x – 6)(x – 5) = 0
x = 6, 5
27. Solve for x: (x + 2)(2x – 5) = 0
x = -2, 5/2
Write each of the following in scientific notation:
a.) 33 ¥ 10 -3
b.) 0.00214
3.3 x 10-2
2.14 x 10-3
11
4
10
28. Find the greatest common factor of the terms: 2e ,14e ,12e
2e4
29. Factor out the greatest common factor: 18u 4 v 5 + 30u 5v 4
6u4v4(3v+5u)
30. Factor out the greatest common factor: 24u 3 + 40u 2
8u2(3u+5)
Factor:
31. 16x 2 - 25
32. x 2 -14 x + 45
33. c 2 + 7c + 10
(4x+5)(4x-5)
(x-9)(x-5)
(c+5)(c+2)
Solve:
34. x 2 + x - 30 = 0
35. x 2 + 4 x -12 = 0
x = -6, 5
x = -6, 2
Factor:
36. 5x 2 - 33x -14
37. 3x 2 -13x -10
(5x+2)(x-7)
(3x+2)(x-5)
38. 7x 2 + 30x + 8
(7x+2)(x+4)
Simplify:
39.
12
40. 4 50
2√3
20√2
41. -10 200
42.
-100√2
6√10
43. 6 3 ∑ 4 8
44. -3 7 ∑ 7
48√6
-21
6 ∑ 60
450
30
45.
46.
√15
5
56
7
47.
48.
2√2
5
3
(5√3)/3
4
5
49.
50. 7 2 + 3 2 - 4 2
(2√5)/5
6√2
80 + 20
51.
6√5
53.
50
2
52. -2 6 - 2 25 + 2 24
2√6-10
3
24 x
8
54. 243
2
5
3
2
2x2 3x
9
Solve:
55. x 2 = 121
56. 64 x 2 - 49 = 0
x = ± 11
x = ± 7/8
Solve by using Quadratic Formula:
57. 2x 2 + 2x -1 = 0
58. x 2 - x - 5 = 0
x = (-1±√3)/2
x = (1±√21)/2
Use the Pythagorean Theorem to find the missing length
59. a = 5, b = 12, c = ?
60. a = ?, b = 8, c = 15
c = 13
a = √161
61. a = 7 2 b= 7 2 c = ?
62. a = 5 b =? c = 10
c = 14
b = 5√3
Solve.
63.
x - 20 = 0
x = 400
65. x = x + 12
x =4
64.
x=3
5x + 1 + 8 = 12
66. Mike wants to mix pens costing 25 cents with pencils costing 20 cents each. The
mixture will cost $3.60. If the number of pencils is 9 more than the number of pens, how
many of each type should be in the package?
[ A ] 5 pencils, 14 pens
[ B ] 12 pencils, 3 pens
[ F ] 4 pencils, 13 pens
[ C ] 13 pencils, 4 pens
[ E ] None of these
67. Which system of inequalities is graphed below?
[A]
[C]
x ≥2
y ≥ -2x + 4
x £2
y £ -2x + 4
68. Give the vertex of y = x 2 - 6x + 2
[ A ] (6, -2)
[ B ] (3, -7)
[ C ] (-7, 3)
[ D ] (2, -6)
69. Given the graph, which is the appropriate equation of the quadratic?
[A]
y = - x 2 + 2x + 5
[B]
y = x 2 + 2x + 5
[C]
y = -x2 - x + 5
[D]
y = x2 - x + 5
[B]
y ≥2
[D]
y £2
y ≥ -2x + 4
y £ -2x + 4
70. Which coordinates names a member of the solution set of the system shown?
x <y-2
y>x+5
[ A ] (-4,1)
[ B ] (4,-3)
[ C ] (3,-3)
[ D ] (5,1)
[E] (-7,-1)
71. The endpoints of a segment are (2, 5) and (-8, 8). Find the midpoint.
(-3, 13/2)
72. A segment has a midpoint of (4, -5) and an endpoint of (8, -4). What is the other
endpoint?
(0, -6)
73. Find the distance between (4, 1) and (7, 6).
≈5.83
74. A segment has endpoints at (-3, -7) and ( 3, 3), what is the length of the segment.
≈11.66
75. Graph y = 3 x - 2 +1