CP Pre-Calculus Chapter 1 Prerequisite Skills Review
CP Pre-Calculus Chapter 1 Prerequisite Skills Review
The following problems are aligned to concepts that you should have mastered in Algebra I and Algebra II. Please practice the sections that you need to review, because these skills are needed to be successful in Chapter 1 of Pre-calculus.
I. ORDER OF OPERATIONS--Use order of operations to simplify each expression
1.[pic] 2. [pic]
3. [pic] 4. [pic]
5. [pic] 6. [pic]
II. SIMPLIFYING EXPRESSIONS--Use distributive property to simplify.
7. [pic] 8. [pic]
9.[pic] 10. [pic]
11. [pic] 12. [pic]
13. [pic] 14. [pic]
III. ABSOLUTE VALUE EQUATIONS
15. [pic] 16. [pic]
17. [pic] 18. [pic]
IV. SOLVING INEQUALITIES--Graph to find the solution and write your answer in interval notation.
19. 2(x – 5) – 3(2x – 5) < 5x + 1 20. [pic]
21. [pic] 22. [pic]
23. [pic] 24. [pic]
25. [pic] 26. [pic]
27. [pic] 28. [pic]
29. [pic] 30. [pic]
31. [pic] 32. [pic]
33. [pic] 34. [pic]
35. [pic] 36. [pic]
V. SOLVING ABSOLUTE INEQUALITIES
37. [pic] 38. [pic]
39. [pic] 40. [pic]
VI. EQUATIONS OF LINES
Find the slope of each line.
41. (-3,6) and (4,-1) 42. [pic] and [pic]
43. 44.
Find the x-intercepts and y-intercepts of each line
45. [pic] 46. [pic]
Graph the following lines.
47. [pic] 48. [pic]
49. Graph a line through (3, 1.5) that is perpendicular to the graph of [pic].
50. Graph a line through (-4,-2) with an undefined slope.
51. Graph the line perpendicular to the graph of [pic] that intersects it at its x-intercept.
52. Graph the line that passes through (-3,-1) and has a slope of .75.
53. Write an equation of a line using point slope given the point [pic] and rewrite in standard form.
54. Write an equation of a line using point slope given the point (– 2, – 4), m = 0.4 and rewrite in standard
form.
55. Find an equation in standard form that passes through the points ( – 2, 3) and (– 2, 6).
56. Find an equation in standard form that passes through the origin and has slope 0.
57. Find an equation in standard form that has a y-intercept of 6 and is parallel to the x-axis.
58. Find an equation in standard form that has an x-intercept of – 4 and is perpendicular to the x-axis.
59. Find an equation in standard form that passes through (1,2) and perpendicular to y – 2x = 3.
VII. QUADRATIC EQUATIONS
Solve the following quadratic equations.
60. [pic] 61. [pic]
62. [pic] 63. [pic]
64. [pic] 65. [pic]
66. [pic] 66. [pic]
67. [pic] 68. [pic]
69. [pic] 70. [pic]
CP Pre-Calculus Chapter 1 Prerequisite Skills ANSWER KEY
1. 18 2. 1 27. [pic]
3. 9 4. -8 28. [pic] or [pic]
5. 45 6. -45 29. [pic]
7. [pic] 8. [pic] 30. [pic] or [pic]
9. [pic] 10. [pic] 31. [pic] or [pic]
11. [pic][pic] 12. [pic] 32. [pic]
13. [pic] 14. [pic] 33. [pic] or [pic]
15. [pic] 16. [pic] 34. [pic] or [pic]
17. [pic][pic] 18. [pic] 35. [pic] or [pic]
19. [pic] 20. [pic] 36. [pic] or
[pic] [pic] [pic]
21. [pic] 22. [pic] 37. [pic] or
[pic] [pic]
23. [pic] 24. [pic] 38. [pic] or
[pic] [pic] [pic]
25. [pic] 26. [pic] 39. [pic]or [pic]
[pic] [pic]
40. [pic] or 50.
[pic]
41. -1
42. [pic]
43. 0
44. [pic] 51.
45. x-int: [pic]
y-int: [pic]
46. x-int: [pic]
y-int: [pic]
47. 52.
48.
49.
53. [pic]
54. [pic]
55. [pic]
56. [pic]
57. [pic]
58. [pic]
59. [pic]
60. [pic]
61. [pic]
62. [pic]
63. [pic]
64. [pic]
65. [pic]
66. [pic]
66. [pic]
67. [pic]
68. [pic]
69. [pic]
70. [pic]
CHAPTER 2 (2.1-2.5) PRE-REQUISTIE SKILLS
Multiplying Polynomials:
1. a. [pic] b. [pic] c. [pic]
2. a. [pic] b. [pic] c. [pic]
3. a. [pic] b. [pic] c. [pic]
4. a. [pic] b. [pic] c. [pic]
5. a. [pic] b. [pic]
c. [pic] d. [pic]
Factoring:
6. [pic] 7. [pic] 8. [pic]
9. [pic] 10. [pic] 11. [pic]
12. [pic] 13. [pic] 14. [pic]
15. [pic] 16. [pic] 17. [pic]
18. [pic] 19. [pic] 20. [pic]
21. [pic] 22. [pic] 23. [pic]
24. [pic] 25. [pic] 26. [pic]
27. [pic] 28. [pic] 29. [pic]
Solve by factoring:
30. [pic] 31. [pic] 32. [pic]
33. [pic] 34. [pic] 35. [pic]
Solve by completing the square:
36. [pic] 37. [pic] 38. [pic]
39. [pic] 40. [pic] 41. [pic]
Solve by using the quadratic formula:
42. [pic] 43. [pic] 44. [pic]
45. [pic] 46. [pic] 47. [pic]
Divide:
48. [pic] 49. [pic] 50. [pic]
51. [pic] 52. [pic]
Answers:
1. a) [pic] b) [pic] c) [pic]
2. a) [pic] b) [pic] c) [pic]
3. a) [pic] b) [pic] c) [pic]
4. a) [pic] b) [pic] c) [pic]
5. a) [pic] b) [pic]
c) [pic] d) [pic]
6. [pic] 7. [pic] 8. [pic]
9. [pic] 10. [pic] 11. [pic]
12. [pic] 13. [pic] 14. [pic]
15. [pic] 16. [pic] 17. [pic]
18. [pic] 19. [pic] 20. [pic]
21. [pic] 22. [pic] 23. [pic]
24. [pic] 25. [pic] 26. [pic]
27. [pic] 28. [pic] 29. [pic]
30. [pic] 31. [pic] 32. [pic] 33. [pic]
34. [pic] 35. [pic] 36. [pic] 37. [pic]
38. [pic] 39. [pic] 40. [pic] 41. [pic]
42. [pic] 43. [pic] 44. [pic] 45. [pic]
46. [pic] 47. [pic] 48. [pic] 49. [pic]
50. [pic] 51. [pic] 52. [pic]
PreCalculus Chapter 3 Pre-requisite Skills Review
Simplify using exponent rules
1. [pic] 2. [pic] 3. [pic] 4. [pic] 5. [pic]
Simplify
6. [pic] 7. [pic] 8. [pic] 9. [pic] 10. [pic] 11. [pic] 12. [pic]
Solve the radical equations
13. [pic] 14. [pic] 15. [pic]
Solve each equation
16. [pic] 17. [pic] 18. [pic]
Factor
19. [pic] 20. [pic] 21. [pic]
22. [pic] 23. [pic] 24. [pic]
______________________________________________________________________________Answers
1. [pic] 2. [pic] 3. [pic] 4. [pic] 5. [pic] 6. [pic]
7. [pic] 8. [pic] 9. [pic] 10. [pic] 11. [pic] 12. [pic]
13. x = 5 and x = 8 14. x = 4 15. x = 2
16. n = 64 and n = -64 17. b = 27 18. n = 24
19. [pic] 20. [pic] 21. [pic]
22. [pic] 23. [pic] 24. [pic]
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