Precalculus with Trigonometry Honors – Summer Packet

Welcome to Precalculus with Trigonometry Honors! We look forward to guiding you through an

informative and exciting year en route to Calculus! In order to be prepared for the rigor of this course,

you must complete the attached assignment.

Please complete this assignment on a separate sheet of paper and bring it with you the first day of school. It

will be collected on the first day of school. You must SHOW ALL WORK on all problems. If this is not done, you

will not receive credit. Calculators are NOT allowed on this assignment except to find trig values of non-special

right triangles.

THE MATERIAL INCLUDED IN THIS REVIEW ASSIGNMENT IS ESSENTIAL FOR UNDERSTANDING FUNDAMENTAL

CONCEPTS OF TRIGONOMETRY AND PRECALCULUS. Please understand that strategies presented in this review

will be utilized extensively throughout the curriculum.

Please note that calculators are not provided for student use in this class. It is recommended that each student

has a graphing calculator (TI-83, TI-83 plus, TI-84 or TI-84 plus) of his/her own.

Please use your notes from previous years, the internet, or work with other students.

We look forward to meeting you. Please contact us if you have any questions.

Mrs. Mishin (jmishin@fcps.edu) Mrs. Rigby (serigby@fcps.edu)

Use the appropriate procedures to simplify each of the following rational expressions.

1. 2 2

2

2 3 2

2 1

x x x x

x x

2.

3 5

1 1x x

3. 4 3 0 2( 2 ) (6 )x x x 4.

1

2

3

36

State whether the relation is a function. Write yes or no. State the domain and range of each function.

5. {( 1,2), (3,10), ( 2,20), (3,11)} 6. { (0,2), (13,6), (2,2), (3,1) }

Name all the values of x that are in the domain of the given function. Give the answer in interval

notation.

7. 2

( )4

xf x

x

8. 2( ) 25f x x

9. 2

2

3 10( )

25

x xf x

x

For problems 10-14, use 22( ) ( ) 2

4f x and g x x

x

to find each function.

10. ( 5)f 11. 1( )g x

12. ( )f g x 13. ( )fg x 14. ( )f

xg

For problems 15-16, find ( ) ( )f g x and g f x . Then decide whether the functions are inverses of

each other or not. Write yes or no.

15. 5

( ) , ( ) 3 53

xf x g x x

16. 2( ) 2 5 1, ( ) 2 3f x x x g x x

State the inverse of each function. Tell whether the inverse is a function. Write yes or no.

17. ( ) 3 7f x x 18. 5( )f x x 19. 2( ) 4f x x

Factoring and Solving Quadratic Equations

Factor completely:

20. 3 27 6x x x 21. 23 75x

22. 2 28 40 112x xy y 23. 3 3x y

24. 216 24 9x x 25. 3 38 27x y

26. 225 10x x 27. 2 7 8x x

28. 281 169x 29. 4 213 36x x

Expand the following expressions:

30. 31.

Solve by factoring:

32. 2 49 0x 33. 26 10 4x x

34. 25 37 14 0x x 35. 4 290 10x x

Solve using the quadratic formula: x =2 4

2

b b ac

a

(You will be required to memorize this formula.)

36. 23 1 0x x 37. 25 8 12x x

Solve by completing the square:

38. 2 2 5 0x x 39. 2 4 2 0x x

Simplify:

40. (5 3 )(2 4 )i i 41. (4 5 )

(9 )

i

i

42. 2 3

2 3 2

2log

x y

y x

43. 33

27log

243

x

x

2(2 3 )a b2

1 2

3 3x

Solve for x. Leave your answer in terms of .

44. 5

6x

45.

180 330

x

Solve each equation algebraically:

46. 1 2

53 7

x x 47. 15 2x x

48. 1 4 5t 49. 22( 3) 8x

50. 3log 4x 51. 2 12 8x x

52. log( 4 ) log3 log(2 )x x 53. 2 23log 2log (5 ) 2x x

Solve each inequality algebraically. Use interval notation for the solution. Graph the solution set on a

number line.

54. 1 4 5x 55. 2 3 4 0x x

Find an equation for the line with the given properties. Express your answer using slope-intercept form.

Graph. (Blank graphs are at the end of the packet.)

56. x-intercept: 2,0 y-intercept: 0, 1 57. 2 3 6x y

Graph the following functions and give the domain and range in interval notation. Show all important

information (vertex, asymptotes, holes, etc.) (Blank graphs are at the end of the packet.)

58. ( ) 4 5f x x 59.

2 13 5

( ) 15

2

x if x

f xx if x

60. 2 3

( )1

xf x

x

61. 1( ) 3 4xf x 62. ( ) 2 1f x x 63. 2( ) ( 2) 3f x x

64. 3( ) ( 3) 1f x x 65. 1

( )2

x

f x

66. ( ) xf x e 67. ( ) lnf x x

68. Find the Quotient using Long Division: 3 24 8 5 7

2 1

x x x

x

69. Find the Quotient using Synthetic Division: 3 24 2 6

3

x x x

x

Domain & Range Review

Domain: The possible x-values of a function Range: The possible y-values of a function

Give the domain and range of the following.

Example: 70. D: _____________ 71. D: _____________

Domain: All real numbers R: _____________ R: ____________

Range: All real numbers

72. D: _____________ 73. D: _____________ 74. D: ____________

R: _____________ R: _____________ R: ____________

75. D: _____________ 76. D: _____________ 77. D: _______________

R: _____________ R: _____________ R: _______________

5

( )1

f xx

Radical Review

Simplify. Rationalize where appropriate.

78. 45 79. 24 80. 1

2

81. 2 72 82. 4 27 3 12 83. 5 11 6 4

84. 2 500 5 20 85. 6 8 3 18 86. 2

101

87. 2

5 8 88. 7 3f g h 89. 9 654m n

90. 2

20 91.

4 2 3

5 2 92.

4

2 7

93. 5

3 2 94.

3 1

3 1

45 45 90 Triangles

45°

Hypotenuse

Leg

45° Leg

Find the missing sides of the triangles. Each triangle measures 45 45 90 . Leave answers as

simplified radicals.

95. 96. _____ 97. 8 2

____ ____ _____ 10 ____ ____

6

98. 99. 100.

5 2 _____

_____ 9 ____ _____ 14 2 _____

______

101. 102. ______ 103. ______

_____

_____ 6 3 8 6 _____

13

____

The ratio of leg-leg-hypotenuse is 1:1: 2

Hypotenuse = Leg 2

45

45

45

45

45

45

45

45

45

30 60 90 Triangles

30°

Long Hypotenuse

Leg

60° Short Leg

Find the missing sides of the triangles. Each triangle measures 30 60 90 . Leave answers in

simplified radical form.

____

104. 105. 106.

12

____ _____ ______ 10 3 _____

_______

60

8

107. 108. ______ 109.

______ 12 ______

7 3 9 _____ ______ _______

110. 111. 112.

_____ 5

8 2 ______ ______

12 6 _____

_____

The ratio of short leg-long leg-hypotenuse is 1: 3 : 2

Hypotenuse = Twice the Short Leg

Long Leg = Short Leg 3

30

30

60

______

30

60

60

60

60

Basic Trigonometry Review: SOH-CAH-TOA

Find the length of the two missing sides of the triangle. You MAY use a calculator for these problems.

Round to 3 decimal places.

113. 114.

115. 116.

Hypotenuse Opposite (hyp) (opp)

Adjacent (adj)

sin

cos

tan

oppA

hyp

adjA

hyp

oppA

adj

10

50

37

12

5.1

68

4.2

33

A