Honors Pre-Calculus Review Packet Summer 2016

June 4, 2016 To all prospective Honors Pre-Calculus students: Honors Pre-Calculus promises to be a challenging endeavor that will force you to think critically and analytically. It will be a rigorous course that involves a lot of independent discovery, formulation of hypotheses, and proof of theorems. To best start off the new school year in September, you are asked to complete the attached worksheet and be prepared to turn it in on the first full day of class. The questions in the packet focus on the skills you were taught in Algebra 2 and those which will be most beneficial to you in Pre-Calculus. Some of the more important topics include factoring all types of polynomials, simplifying radicals, and solving equations. Some problems may be a bit involved, so it is not a good idea to wait until the last minute. Work needs to accompany each problem and all answers should be in simplified form. This packet is due at the beginning of class on August 31, 2016 for 9th and 10th grades or September 1, 2016 for 11th and 12th grades and will be counted as a grade. Any assignment turned in late will lose 5 points each day it is not turned in. If you have any questions regarding the assignment feel free to e-mail me during the summer at twaltrich@gmahs.org. This is not my primary e-mail address, so a response may take a little time. Also, please do not wait until the last week of summer vacation to e-mail me. I cannot guarantee that I will be able to respond in a timely fashion. Enjoy your summer vacation and your math packet. I look forward to a great school year starting in September. Mr. Waltrich Your Name _______________________________________

Classify each numbers as (a) natural number, (b) integer, (c) rational number, (d) irrational

number. Give all that apply.

1. 14 ___________________________________

2. 5

2 ___________________________________

3. 6 ___________________________________

4. 0 ___________________________________

Simplify the following statements, leaving only positive exponents when necessary. Give exact

answers only, no decimals.

5. 255 ___________________________________

6. 72

2 ___________________________________

7.

32

2

3

5

___________________________________

8. 4 56 ( 3) ___________________________________

9. 2

32(27) ___________________________________

10.

1

225

16

___________________________________

11. log 3 – log 8 ___________________________________

12. log6

3 ___________________________________

13. 3 3log u 5log v ___________________________________

Write in simplest radical form. Give exact answers only, no decimals.

14. 525x ___________________________________

15. 3

32

27

x ___________________________________

16. 50 18 ___________________________________

17. 3 8 5 2 __________________________________

18. 2

3 2 4 6 ___________________________________

19. 1

2 3 __________________________________

20. 5

6 2 ___________________________________

Perform the required operations and simplify your answer.

21. 2 3( 2 1)( 1)x x x ___________________________________

22. 3x7x2

1x

1x

1x22

2

___________________________________

23. 2

2 2

4 6 2 3

( 1) 2 3

x x x

x x x

___________________________________

24. 2 3 4

1 1x x x

___________________________________

25.

1 1

2 3 2 31 1

2 2 3

x x

x x

___________________________________

26. 75 ___________________________________

Perform the required operations and simplify your answer.

27. 3 2 6 13i i ___________________________________

28. 1 6 5 2i i ___________________________________

29. 4

3i ___________________________________

30. 3 2

5

i

i

__________________________________

Factor completely.

31. 23 14 8x x ___________________________________

32. 3 1x ___________________________________

33. 227 12y ___________________________________

34. 4 29 32 16x x ___________________________________

35. 3 2 2 2x x x ___________________________________

Solve each equation. Give exact answers only, no decimals.

36. 3 2( 5) 10x x ___________________________________

37. 1

3 2 1 52

x x ___________________________________

38. 1

32x

___________________________________

39. 26 3x x ___________________________________

40. 23 1 0x ___________________________________

41. 26 5 4x x ___________________________________

42. 2 6 3 0x x ___________________________________

Solve each equation. Give exact answers only, no decimals.

43. 3 212 84 120 0x x x ___________________________________

44. 4 4

13x x

___________________________________

45. 2 8 0x ___________________________________

46. 2 3 2x x ___________________________________

47. 32x = 24 ___________________________________

48. 5e3x+1 = 100 ___________________________________

49. 2 2log (2x 5) log 3x 2 ___________________________________

50. ln(3x+1) = 5 ___________________________________

Solve each inequality.

51. 2 4 0x ___________________________________

52. 2 2 3x x ___________________________________

53. 5

03

x

x

___________________________________

54. 2 3

1 1x x

___________________________________

55. 3 3

2 2x ___________________________________

56. 2 1x ___________________________________

Write an equation for the line described.

57. passes through ( 5, -1) and (-5, 5) ___________________________________

58. passes through ( -6, 4) and is perpendicular to

the line 3 4 7x y ___________________________________

Answer the following questions about functions.

59. Find the domain of 6

( )2 1

xf x

x

___________________________________

60. Find the domain of ( ) 3 6f x x ___________________________________

61. Find f g when 2( ) 3f x x x and ( ) 2g x x ___________________________________

62. Find the equation of the inverse of ( ) 6 5f x x ___________________________________