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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