Name: ________________________ Date: ____________
Algebra CD Chapter 6 - 11 Final Review Use your notes if you need help on any of these problems. Solve each inequality (6.2, 6.3) 1. 4 > -2 + m 2. 7 + n < 3
ANSWERS: 1. ______________ 2. ______________
3.
x > 12 6
4. -2y + 4 > -6
3. _______________ 4. _______________
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Solve each compound inequality and then graph the solution set. (6.4) 5. 3w < 6 and -5 < w 6. -4 < n or 3n + 1 < -2
5. _______________ 6. _______________
Solve each open sentence, then graph (6.5) (Be sure to write “and” or “or” in your answer!)
7. |2d – 1| < 9
8. |3 – 2x| > 7
7. _______________
8. _______________ Graph the inequality. (6.6) 9. x + 2y < 4 9. __ see problem __
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Graph the system of equations (7.1) 10. 2x + y = 3 x–y=3
ANSWERS: 10. __ see problem __
Substitution or Elimination Use substitution or elimination to solve each system of equations. If the system does NOT have exactly one solution, state whether it has no solution or infinitely many. (7.2, 7.3. 7.4) 11. y = 6x 2x +3y = -20
12. 3x + 2y = -9 5x – 3y = 4
11. ______________ 12. ______________
13. 7x + 4y = 2 7x + 2y = 8
13. ______________ 14. __ see problem __
Graph the system of inequalities by graphing. (7.5) 14 . y>x+2 y < -2x – 1
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Take Home Final Algebra CD
Simplify. Assume that no denominator is equal to zero. (8.1, 8.2) 15. (9c3 d5 )(-2cd2 ) 16. (2w5 y4 ) 3
ANSWERS: 15. ______________
17. 16r3 s-5 4r-1 s2
18.
(-8x2 y2 ) 2 (4x3 y) 3
16. ______________ 17. ______________ 18. ______________
Simplify. (8.5, 8.6) 19. (11m2 – 2mp + 8p2) + (8m2 + 4mp – 2p2 )
20. (x + 9) – (x + 6)
21. 3xy(2x2 + 5xy – 7y2 )
19. ______________
20. ______________ 21. ______________
22. 4c2 (c + 6) – 3c(2c2 – 3c + 1)
22. ______________
Solve. (8.6) 23. m(m – 5) + 8m = m(m + 2) – 4
23. ______________
Find each product. (8.7, 8.8) 24. (2x – y)(3x + 4y)
24. ______________
25. (2m + 2)(m2 – 2m + 3)
25. ______________ 26. (5c – 4)2
27. (3a – 4b)(3a + 4b)
26. ______________ 27. _____________
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Find the prime factorization of each integer. (9.1) 28. 531
ANSWERS: 28. ______________
29. Factor completely: 168pq2r _____________________
29. __ see problem __
Factor each polynomial. (9.2) 30. 8rs2 + 16rs
30. ______________
31. 3x2 + 21x + 27
31. ______________ 2
32. 12a – 15ab – 16a + 20b
(look closely with this one!)
Factor each polynomial, if possible. If the polynomial cannot be factored using integers, write prime. (9.3, 9.4) 33. x2 – 25 34. n2 – 7n – 18
32. ______________
33. ______________ 34. ______________
2
35. 5t + 17t – 12 35. ______________
36. 6m2 + 7m – 3
37. x2 + 12x + 5
36. ______________ 37. ______________
Solve each equation. (9.4) 38. (x – 5) (2x – 1) = 0
39. y2 + 4y = 45
38. ______________ 39. _____________
40. n3 – 3n2 – 10n = 0
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40. _____________
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41. The area of a rectangular room is 90 square feet. The length of the room is 1 foot longer than the width. Find the dimensions of the room.
ANSWERS: 41. ______________
Find the following information for each parabola. (10.1, 10.2) 42. y = x2 + 6x + 5 43. same equation
l.o.s. ________ vertex: _____ x-int: ______ y-int: ______
42. __ see problem__ 43. __ see problem __
Solve each equation by graphing. 44. x2 + 6x + 8 = 0
44. __ see problem __
45. Find the value of c that will make x2 + 3x + c a perfect square trinomial.
45. ______________
Solve … either factor or use the quadratic formula. (10.4) 46. x2 – 4x + 5 = 0 47. x2 + 4x – 6 = 0
46. ______________ 47. ______________ 48. _____________
Simplify. (11.1, 11.2) 48.
49. 3 84
12
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49. ______________
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50. _____________ G. Kelly 2011
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51.
32 75
52.
8 3+ 3
ANSWERS: 51. ______________
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52. ______________
Solve. (11.3) 53.
54.
5 p = 10
6p − 8 = p
53. ______________ €
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54. ______________
Find the length of each missing side. (11.4) 55.
a = ______
56. a = 16, b = 12, c = ?
15
57. a = 5, c = 74 , b = ? 39
55. ______________ 56. ______________ 57. _____________
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Find the distance between the two points. (11.5) 58. (12, 3), (-8, 3) 59. (-3, 8), (5, 4)
58. ______________ 59. ______________
Find the possible values of a if the points with the given coordinates are the indicated distance apart. (11.5) 60. (6, 1), (5, a); d = 10
60. ______________
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Yeah – You’re done!!! Page 6 of 6
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