Calculus Summer Packet
There are certain skills that have been taught to you over the previous years that are essential
towards your success in Calculus. This summer packet is intended for you to
retain/review/relearn these topics.
Below is a list of several websites that may help you when you come across a difficult
problem. If you are unsure of how to attempt these problems, please look online for help, or
send me an email. Feel free to use all resources available to you via internet and textbooks.
Please take these problems seriously, students who are weak in these skills have a difficult time
succeeding in calculus without them.
Work needs to be shown, when possible, in a neat, legible, organized manner. Do not always
rely on your calculator. Yes, there are some skipped numbers. This is a course where assertive
and disciplined students succeed the most. I STRONGLY SUGGEST SEARCHING ONLINE
FOR AND PRACTICING FINDING LIMITS (ALGEBRAICALLY, NUMERICALLY AND
GRAPHICALLY) AS WELL AS FINDING DERIVATIVES USING THE DIFFERENCE
QUOTIENT.
I believe you will benefit the most from this packet by starting it towards the end of June or
the beginning of July. You should try to complete a few problems each day, as if it was a
daily journal. Do not do all of it now, and do not wait and do it a week before we start school in
August. You are more likely to retain the information if you spread out your work over the
course of the entire summer break.
This summer assignment may be graded when you return (assume it will be). If you have
any questions, please email me at [email protected]
Mr. Wode
Helpful Websites
www.coolmath.com
http://www.mathematicshelpcentral.com/index.html
http://www.mathtv.com/
http://archives.math.utk.edu/visual.calculus/
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The Calculus Summer Reading List:
Calculus Readiness Assessment:
http://vvww.math.unb.ca/ready/exercise.h
tml
http://mdtp.ucsd.edu/crtest/intro4.asp
Calculus Syllabi:
BC Calculus
http://apcentral.collegeboard.com/apc/public/courses/teachers
corner/2118.html AB Calculus
http://apcentral.collegeboard.com/apc/public/courses/teachers corner/2178.html
Calculus Resources:
http://www.calculus.org/
http://www.chipola.edu/instruct/math/mathlab/calculus.htm
Calculator:
http://www.collegeboard.com/student/testing/ap/calculus ab/calc.html
http://www.ticalc.org/
http://www.calculator.com/
On-line Help:
http://mathforum.oredr.math/
http://www.askrose.org/
http://cs.gmu.edu/cne/modules/dau/
Success in Calculus:
http://www.math.ucdavis.edu/—kouba/CalculusTips.html
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Simplify using only positive exponents.
1.
4.
2.
3.
5.
6.
7.
Find the domain of the following functions. Make sure to use interval notation (ex. [0,3)).
8.
9.
10.
11.
12.
13.
14.
15.
16. y
17.
18.
Factor completely.
19.
20.
21.
3
Solve the following inequalities by factoring and making sign charts.
22.
23.
25.
26.
Describe, in words, the transformations that would take place to
27.
28.
30.
31.
24.
in each of the following.
29. –
Determine if each function is even, odd, or neither. Show all work.
32.
33.
34.
Solve each equation by factoring, graphing, or using the quadratic formula.
35.
36.
37.
38.
39.
40.
41.
42.
43.
Find the equations of all vertical (x = ?) and horizontal (y = ?) asymptotes (if they exist).
4
44.
45.
47.
48.
46.
Simplify the following.
49.
50.
52.
53.
51.
54.
If
55.
56.
57.
58.
Solve each equation.
59.
60.
61.
62.
Solve each equation on the interval [0, 2
. Give exact values (ex.
63.
if possible.
5
64.
65.
66.
67.
68.
Answer the following questions over a variety of topics.
69. Let
be a linear function where
and
Find
70. Find an equation for the line, in point-slope form, that contains (5,1) and is perpendicular to
.
71. Use the table to calculate the average rate of change from
t
0
8
1
7
2
5
3
1
to
4
2
72. Order the points, A, B, and C, from least to greatest, by their rates of change.
6
73. Find the distance between the points (8, -1) and (-4, -6).
74. If
find
75. Find the points of intersection in the graphs of
76. Rewrite
and
as a single logarithmic expression.
77. Evaluate the following.
a)
b)
c)
d)
e)
f)
7
78. Sketch a graph of the piecewise function
.
79. Find the domain and range of each function (without a calculator if possible).
a)
b)
c)
d)
e)
f)
80. The circle below has a radius of 6 ft. Find the area and circumference of the circle, then
find s.
81. Find the area of the trapezoid.
8
8
8
8
12
82. Find the missing sides and angles of the triangle. Then find its area.
83. Find the volume of a washer with outer radius of 18 ft., inner radius of 15 ft., and a height of
3 ft.
84. Three sides of a fence and an existing wall form a rectangular enclosure. The total length of
fence used for the three sides is 240 ft. Find x if the area enclosed is 5500
9
85. The number of elk after t years in a state park is modeled by the function
a) What was the initial population?
b) When will the number of elk be 750?
c) What is the maximum number of elk possible in the park?
86. Simplify
87. Use long division, or synthetic division, to rewrite the expression
88. Rewrite
in vertex form
89. Sketch a graph of the piecewise function
90. Do the lines –
and
.
by completing the square.
.
intersect?
10
91. The function
is graphed below. Find the following.
a)
b)
c)
d)
e)
f)
11