Name _________________________________________ Date ________________ Period ____

West Essex Regional School District

Calculus Honors – Summer Assignment

2015-2016

Calculus Honors introduces the student to calculus of a single

variable. The course is problem-driven in response to the

calculus reform movement and integrates applications to

management, life, and social science in exercises throughout

the course. Functions are presented graphically, numerically

and algebraically to give students the benefit of alternate

interpretations. Graphing calculators will also be used

extensively.

Course Goals

Students will be able to

Work with functions represented in a variety of ways: graphical, numerical, analytical, or

verbal, and understand the connections among these representations.

Understand the meaning of the derivative in terms of a rate of change and use derivatives to

solve a variety of problems.

Understand the meaning of the definite integral both as a limit of Riemann sums and as the

net accumulation of change, and use integrals to solve a variety of problems.

Understand the relationship between the derivative and the definite integral as expressed in

both parts of the Fundamental Theorem of Calculus

Model a written description of a physical situation with a function or an integral.

Understand the connections of calculus to other disciplines by solving application problems.

Use technology to help solve problems, experiment, interpret results, and verify conclusions.

Develop an appreciation of calculus as a coherent body of knowledge and as a human

accomplishment.

As stated above, the year must be devoted to topics in differential and integral calculus.

Therefore, the summer assignments listed below are designed to help you review topics from

algebra, geometry, and pre-calculus so that when you arrive in September, you are ready to

begin with the first main theme to be covered this year.

All assignments will be collected the first week of school and be counted as 5

homework grades.

Copies of the packet are also available on the teachers’ websites.

Please complete ALL work in pencil, and box in final answers where work is required

to find them.

Work should be completed during the weeks immediately preceding your return to

school in September.

West Essex High School Calculus Honors Summer Assignment

Simplify

1. 4

1242

2

x

xx

2. 3

273

x

x

3. 103

52

xx

x

4. 16

42

x

x

5. x

x 4

3

4

3

6. hhx

22

7. 4

8

2

x

x

8. (5a3)(4a2)

9. (4a5/3)3/2

10.

8

34

5

2

1

11. 272/3

West Essex High School Calculus Honors Summer Assignment

12. 32

8

1

1

96

222

xxxxx

x

13. !5

)!1(3

n

n

14. (6a4/3)(2a3/2)

15. (4a5/2)3/2

16. 1

23

18

12

xy

yx

17. x

x

5

15 2

18. yx

yx2

24

15

3

19. 82/3

20. x

x3 2

21. x2/3(x + x5/2 – x2)

22. x1/3(x2 + x – x5/2)

23. e2ln 5

West Essex High School Calculus Honors Summer Assignment

24. e(2 + ln x)

25. ln e7

26. log5(1/5)

27. log1/2 8

28. ln ½

29. e3ln x

30. log2 8

31. log100

1

32. ln e5x

33. ln 1

34. e0

35. sin2x + cos2x

36. 1 + tan2x

37. cot2x + 1

West Essex High School Calculus Honors Summer Assignment

Find the exact values without a calculator.

38. cos 0 39. sin3𝜋

4 40. sec

2𝜋

3 41. cos

3𝜋

4

42. cot7𝜋

4 43. csc

3𝜋

2 44. sin 𝜋 45. cot

2𝜋

3

46. tan11𝜋

6 47. sin

𝜋

2 48. cos 𝜋 49. cos

7𝜋

6

50. cos𝜋

3 51. tan

7𝜋

4 52. tan

2𝜋

3 53. tan

𝜋

2

54. sin(cos-1 ½)

55. cos-1(cos7𝜋

6)

56. Evaluate 𝑓(𝑥+ℎ)−𝑓(𝑥)

ℎ and simplify if 𝑓(𝑥) = 3𝑥2 – 4𝑥

57. Expand (x + y)3

Find the intersection(s) of the equations.

58. x2 + y2 = 25 and 4x – 3y = 0

59. y = x2 + 3x – 4 and y = 5x + 11

60. y = cos x and y = sin x in the first quadrant

West Essex High School Calculus Honors Summer Assignment

Expand and then simplify.

61.

4

0

2

2n

n

62.

3

03

1

n n

Solve for x.

63. 2x + 6yz = 0

64. 2y2 + 4yz – 5z – 4x = 0

Solve.

65. 04

4

2

x

x

66. 2x2 + 5x = 9

67. (x + 2)(x – 2) > 0

68. x2 – 5x – 14 ≤ 0

West Essex High School Calculus Honors Summer Assignment

69. (x + 1)2(x – 2) + (x + 1)(x – 2)2 = 0

70. sin 2x = sin x, 0 ≤ x ≤ 2π

71. 12x2 = 4x

72. sin(2x) = 1/2 , 0 ≤ x ≤ 2π

73. x2 + 3x – 4 = 14

74. |x – 3| < 7

75. 2x2 + 5x = 3

76. 8823 x

77. (x – 5)2 = 9

78. 12x2 = 3

79. log x + log(x – 3) = 1

West Essex High School Calculus Honors Summer Assignment

80. (x + 3) (x – 3) > 0

81. 272x = 9x – 3

82. 4e2x = 12

Write the equation of the line in slope-intercept form.

83. Slope -3, through point (2, 4)

84. Through points (0, -3) and (-5, 2)

85. Slope 0, through point (5, 1)

86. Parallel to line 2x – 3y = 7 and through (5, 1)

87. Perpendicular to line -3y + 6x = 2 through point (4, 3)

Solve:

88. Let 𝑓 be linear function where 𝑓(2) = −5 and 𝑓(−3) = 1. State the function 𝑓(𝑥).

89. Find the distance between the points (8, -1) and (-4, -6)

West Essex High School Calculus Honors Summer Assignment

Graph each function. Identify the domain and range.

90. y = sin x

Domain _______________________

Range ________________________

91. y = ex

Domain _______________________

Range ________________________

92. y = 2x

Domain _______________________

Range ________________________

93. y = x2 – 4

Domain _______________________

Range ________________________

West Essex High School Calculus Honors Summer Assignment

94. y = |x + 3| – 2

Domain _______________________

Range ________________________

95. y = 1/x

Domain _______________________

Range ________________________

96. y = x

Domain _______________________

Range ________________________

97. y = 3 x

Domain _______________________

Range ________________________

West Essex High School Calculus Honors Summer Assignment

98. y = ln x

Domain _______________________

Range ________________________

99. y = 24 x

Domain _______________________

Range ________________________

100. y = x2 + 4x + 3

Domain _______________________

Range ________________________

101. y = 2x

Domain _______________________

Range ________________________

West Essex High School Calculus Honors Summer Assignment

102. 𝑦 = {𝑥2, 𝑥 < 0𝑥 + 2, 0 ≤ 𝑥 ≤ 34, 𝑥 > 3

Domain _______________________

Range ________________________

103. 𝑦 = {𝑥2 − 5, 𝑥 < −10, 𝑥 = −13 − 2𝑥 𝑥 > −1

Domain _______________________

Range ________________________

104. Identify the vertical and horizontal asymptotes of 4

532

2

x

xy

105. Given 5)(,3)(,3

)( 2

xxhxxgx

xxf , find:

106. ℎ(𝑔(𝑥)

107. 𝑓(ℎ(−2))

108. 𝑓(𝑓(3)

109. ℎ−1(𝑥)