1. Algebra 1-2 Semester 2 Final Review
Pick up your Final Review Form B Packet
2nd Semester Review

2. 1.) Solve & graph the inequality: 4x-3 < 2(x+2)
4x -2x - 3 < 2x -2x + 4
2x - 3 < 4
2x < 4+3
2x < 7
x < 7/2
(A) -4 -2 2 4
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3. 2.) Graph -4 < x < 3 -4 < x < 3 (C) Closed Dot Open Dot -22 4 6 8
Closed Dot
Open Dot
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4. 3.) Solve -6 < -2x + 6 < 8 -6 < -2x + 6 < 8
(B)
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5. Remember: < is and , > is or
4.) Solve |x+1| > 6
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x+1 < -6
x+1-1 < -6-1
x < -7
x+1 < -6 x+1 > 6
x+1 > 6
x+1-1 > 6-1
x > 5
x < -7 or x > 5
(A)
Remember: < is and , > is or

6. 0 < x < 4 5.) Graph |x - 2| < 2 x - 2 < 2 x - 2+2< 2+2
(B) -4 -2 2 4 6
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7. 4x -3y < -12 4x - 4x -3y < -4x -12 -3y < -4x -12
6.) Graph 4x - 3y < -12
4x -3y < -12
4x - 4x -3y < -4x -12
-3y < -4x -12
-3y/-3 < (-4x -12)/-3
y > 4/3x + 4
Graph it
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8. Now pick a point on one side of the dotted line -(0,0)
6.) Graph 4x - 3y < -12
Sketch y = 4/3x + 4 Y
Now pick a point on one side of the dotted line -(0,0) X
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9. Since it’s False, Shade the opposite side of (0,0).
Test a Point
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Take the point (0,0) and plug in the values in y > 4/3x + 4
y > 4/3x + 4
0 > 4/3(0) + 4
0 > 4
False
Since it’s False, Shade the opposite side of (0,0).

10. 6.) Graph 4x - 3y < -12
(C) Y X
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11. 7.) Solve by linear combination
4x-2y = 16 3x+2y = 5
4x-2y = 16 3x+2y = 5
7x = 21
7x/7 = 21/7
x = 3
3x+2y = 5
3(3)+2y = 5
9 + 2y = 5
9-9+2y=5-9
2y = -4
y = -4/2= -2
(B) (3,-2)
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12. 3x + y = 14 6x + 2y = 28 -2(3x + y = 14) -6x - 2y = -28 6x + 2y = 28
8.) Determine if the system has no solutions, one solutions, or many solutions.
3x + y = 14 6x + 2y = 28
-2(3x + y = 14)
-6x - 2y = x + 2y = 28
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13. (D) True Many Solutions
8.) Determine if the system has no solutions, one solutions, or many solutions.
-6x - 2y = x + 2y = 28
0 = 0
(D) True Many Solutions
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14. 9.) Determine the solution to the system of inequalities
y > x + 1 3x + y < 5
y > x + 1 3x + y < 5
3x -3x + y < -3x + 5
y < -3x + 5
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15. 9.) Determine the solution to the system of inequalities
y > x + 1 3x + y < 5
y > x y < -3x + 5
Graph
Pick a point
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16. Now pick a point on one side of both lines - (0,0)
y > x + 1 y < -3x + 5
(9) Y
Now pick a point on one side of both lines - (0,0) X
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17. Since it’s True, Shade the (0,0) side.
Test a Point
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Take the point (0,0) and plug in the values in y > x + 1
y > x + 1
0 < (0) + 1
0 < 1
True
Since it’s True, Shade the (0,0) side.

18. y > x + 1 y < -3x + 5
(9) Y X
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19. Since it’s True, Shade the (0,0) side.
Test a Point
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Take the point (0,0) and plug in the values in y < -3x + 5
y < -3x + 5
0 < -3(0) + 5
0 < 5
True
Since it’s True, Shade the (0,0) side.

20. y > x + 1 y < -3x + 5
(9) Y X
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21. 43 • 42 (4•4•4) • (4•4) (A) 45 10.) Simplify 43 • 42
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22. (32)9 (D) 318 11.) Simplify (32)9 (32)(32)(32)(32)(32)(32)(32)(32)(32)
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23. 12.) Simplify the product (2fg6)4(fg)5
(A) 16f9g29
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24. 13.) Simplify the product a7 • a-4
a7 • 1/a4 = a7/a4
a•a•a•a•a•a•a a•a•a•a
a3 (D)
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25. 14.) Rewrite using positive exponents 5-1
5-1 = 1/51 = 1/5 (A)
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26. 15.) Multiply 30 • 4 • 22
30 • 4 • 22 =
1 • 4 • 4
16 (C)
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27. 16.) Rewrite using positive exponents 6ab2c-3
6ab2/c3 (B)
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28. 17.) Which is equivalent to 515/55
515/55 = = 510
(A)
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29. (18x7y4) (-9x3y5) = -2x4/y (D) 18.) Simplify (18x7y4)/(-9x3y5)
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30. 19.) What’s the perimeter of the triangle.
a2 + b2 = c2
= c2
= c2
289 = c2
17 = c
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(A) 8
Perimeter = =40

31. 20.) Solve 36x = 0
36x =
36x2 = 49
36x2/36 = 49/36
x2 = 49/36
x = 49/36
x = ± 7/6 (A)
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32. 21.) Graph y = x2 - 2
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33. 22.) Solve by the Quadratic formula: x2 -x -3 = 0
x = -b b2 - 4ac a
x = (-1)2 - 4(1)(-3) (1)
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34. 22.) Solve by the Quadratic formula: x2 -x -2 = 0
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35. 23.) Simplify: (5e3 + 5) - (4e2 + 1)+ (2e3 + 5e2)
7e3 + e (B)
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36. (x-4)(x+2) foil x2 +2x - 4x - 8 x2 -2x - 8 24.) Multiply (x-4)(x+2)
(C)
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37. (4u+9)(4u-9) foil 16u2 -36u + 36u - 81 16u2 - 81
25.) Multiply (4u+9)(4u-9)
(4u+9)(4u-9) foil
16u2 -36u + 36u - 81
16u2 - 81
(A)
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38. (x + 1)(x2 - x - 2) x3 - 3x - 2 x3 -x2 -2x + x2 -x -2
26.) Multiply (x+1)(x2 - x - 2)
(x + 1)(x2 - x - 2)
x3 -x2 -2x + x2 -x -2
x3 -x2 + x2 -2x -x -2
x3 - 3x - 2
(C)
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39. 27.) Multiply using the Vertical format
2y2 + 7y y - 6
(C)
2y y2 + 2y
- 12y2 - 42y - 12
2y3 - 5y2 - 40y - 12
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40. 28.) Factor x2 - 16 x2 - 16 (x )(x ) (x - 4)(x + 4) (A)
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41. 29.) Factor x2 - 2x - 24 x2 - 2x - 24 (x )(x ) (x - 6)(x + 4) (B)
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42. x2 - 49 (x )(x ) 30.) Factor x2 - 49 (x - 7)(x + 7) (D)
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43. x2 + 3x - 10 = 0 (x - 2)(x + 5) = 0 x - 2 = 0 & x + 5 = 0
31.) Solve x2 + 3x - 10 = 0
x2 + 3x - 10 = 0
(x - 2)(x + 5) = 0
x - 2 = 0 & x + 5 = 0
x = 2 & x = (B)
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44. 32.) Solve c/3 = 5/45
c =
45c = 15
45c/45 = 15/45
c = 15/45 = 1/3 (A)
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45. 33.) Solve (x-1)/3 = (x+5)/(x-1)
x2-2x-3x+1 = 3x-3x+15
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46. 33.) Solve (x-1)/3 = (x+5)/(x-1)
x2-2x-3x+1 = 3x-3x+15
x2- 5x =
x2- 5x = 0
(x -7)(x + 2) = 0
x - 7 = 0 & x + 2 = 0
x = 7 & x = -2 (B)
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47. x = 5 2x-1 3 3x = 10x - 5 -7x = -5 x = -5/-7 = 5/7 (C)
34.) Solve x/(2x-1) = 5/3
x = 5 2x
3x = 10x - 5
-7x = -5
x = -5/-7 = 5/ (C)
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48. 35.) What % of 4 is 1? is % of ? 1 = • .01 • 4 1 = .04x
1 = • .01 • 4 x
1 = .04x
1/.04 = .04x/.04
25 = x (A)
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49. 36.) 90% of 40 is what #? is % of ? = 90 • .01 • 40 x = 36 (D) x
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50. 37. ) A van travels 48 miles on 4 gallons of gas
37.) A van travels 48 miles on 4 gallons of gas. How many gallons will it need to travel 120 miles?
48/4 = 120/ x
48x = 480
48x/48 = 480/48
x = 10 (C)
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51. 38. ) Ten balls numbered from 1 to 10 are placed in an urn
38.) Ten balls numbered from 1 to 10 are placed in an urn. If one ball is selected at random, find the probability that it is number 10.
1/10 ( D)
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52. 39.) Which of the following is a function?
B.) {(6, -4), (-4, 0), (6, 3)}
C.) {(6, -4), (-4, 6), (3, 3)}
D.) {(6, -4), (0, 3), (0,6), (3, 0)}
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53. 40.) Find f(-1) given f(x) = 4x - 2
f(-1) = (C)
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54. 41.) Decide whether the graph represents y as a function of x
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55. 42.) Find the slope of f(-3) = 2, f(5) = -2
(-3, 2) and (5, -2)
(x1, y1) and (x2, y2)
m = y2 - y1 = x2 - x
m = -4/8 = -1/2 (C)
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56. 43.) Find the equation of f(-3) = -9, f(3) = 3
(-3, -9) and (3, 3)
(x1, y1) and (x2, y2)
m = y2 - y1 = x2 - x
m = 12/6 = 2
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57. 43.) Find the equation of f(-3) = -9, f(3) = 3
m = 12/6 = 2 & y = mx + b
3 = 2(3) + b
3 = 6 + b
-3 = b
y = 2x (B)
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58. 44.) Draw a Box&Whisker Plot for: 29, 23, 6, 22, 33, 28, 13
6, 13, 22, 23, 28, 29, 33
Median 1st Quartile
Median 2nd Quartile
Median 3rd Quartile
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59. 44.) Draw a Box&Whisker Plot for: 29, 23, 6, 22, 33, 28, 13
6, 13, 22, 23, 28, 29, 33
(A) 6 13 23 29 33
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60. 45.) What is the mean of: 17, 20, 6, 24, 28, 25, 23, 1
17, 20, 6, 24, 28, 25, 23, 1
144
144/8 = 18 (C)
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61. 46.) What is the median of: 10, 10, 22, 22, 22, 9, 1, 4, 21, 11, 22
1, 4, 9, 10, 10, 11, 21, 22, 22, 22, 22
Median
(A)
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62. 47.) Name the mode or modes of: 9,8,11,27,17,25,10,27,7,16,17
7,8,9,10,11,16,17,17,25,27,27
(D)
Modes
Modes
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63. 120 = 2•2•2•3•5 = 2 30 = 48.) Simplify 60 • 2 60 • 2 = (B)
60 • 2 =
120 = 2•2•2•3•5 =
2 30 =
(B)
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64. 3•3•6 + 5•5•6 3 6 + 5 6 8 6 49.) Simplify 54 + 150 54 + 150 (B)
3•3• •5•6
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8 6
(B)

65. 50.) Simplify 3 (4 + 6) 4 3 + 18 = 4 3 + 2•3•3 = 4 3 + 3 2 (B)=
•3•3 =
(B)
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