Post on 27-Mar-2018
Name _________________________________________ Date ________________ Period ____
West Essex Regional School District
Calculus Honors β 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 teachersβ 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 β x2)
22. x1/3(x2 + x β 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 Β½
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 Β½)
55. cos-1(cos7π
6)
56. Evaluate π(π₯+β)βπ(π₯)
β and simplify if π(π₯) = 3π₯2 β 4π₯
57. Expand (x + y)3
Find the intersection(s) of the equations.
58. x2 + y2 = 25 and 4x β 3y = 0
59. y = x2 + 3x β 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 β 5z β 4x = 0
Solve.
65. 04
4
2
x
x
66. 2x2 + 5x = 9
67. (x + 2)(x β 2) > 0
68. x2 β 5x β 14 β€ 0
West Essex High School Calculus Honors Summer Assignment
69. (x + 1)2(x β 2) + (x + 1)(x β 2)2 = 0
70. sin 2x = sin x, 0 β€ x β€ 2Ο
71. 12x2 = 4x
72. sin(2x) = 1/2 , 0 β€ x β€ 2Ο
73. x2 + 3x β 4 = 14
74. |x β 3| < 7
75. 2x2 + 5x = 3
76. 8823 x
77. (x β 5)2 = 9
78. 12x2 = 3
79. log x + log(x β 3) = 1
West Essex High School Calculus Honors Summer Assignment
80. (x + 3) (x β 3) > 0
81. 272x = 9x β 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 β 3y = 7 and through (5, 1)
87. Perpendicular to line -3y + 6x = 2 through point (4, 3)
Solve:
88. Let π be linear function where π(2) = β5 and π(β3) = 1. State the function π(π₯).
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 β 4
Domain _______________________
Range ________________________
West Essex High School Calculus Honors Summer Assignment
94. y = |x + 3| β 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. π¦ = {π₯2, π₯ < 0π₯ + 2, 0 β€ π₯ β€ 34, π₯ > 3
Domain _______________________
Range ________________________
103. π¦ = {π₯2 β 5, π₯ < β10, π₯ = β13 β 2π₯ π₯ > β1
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. β(π(π₯)
107. π(β(β2))
108. π(π(3)
109. ββ1(π₯)