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Calculus
Summer Packet 2011
(Review of Precalc/Trig concepts)
The purpose of this summer packet is to review Trigonometry/Pre-Calculus
concepts that are essential for Calculus. All students entering Calculus are
required to complete the packet. Continued enrollment in the course is
determined by Mr. Hopkins based upon the completion of the packet and
performance on the Review exam. Please follow the instructions below.
1. The packet is due
- NO EXCEPTIONS!
An exam will be given on this material on ___________
2. The packet is worth 50 points. Points are awarded for accuracy. WORK MUST
BE SHOWN! NO WORK, NO POINTS! Show all work on the question
packet in the given space for each question. Transfer answers to the answer
sheet.
3. Web links have been posted on the district site that will help you with each of the
topics. Follow the instructions below to view the links.
a.
b.
c.
d.
e.
Open the School Website: http://www.cdschools.org
Select a school: Central Dauphin East High School
Click on ‘Staff’
Click on Mr. Hopkins
Click on ‘Summer Packet’
4. Extra Copies of the packet can be found on Mr. Hopkins’ website.
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1. Classify these numbers as rational or irrational.
a) 7329
b)
c) 0.95832758941…
2. Complete the identity
3. Factor this polynomial.
4. State the quadrant in which the terminal side of each angle lies.
a) -509
c) -340
5. Solve by substitution.
6. Express the given in the standard form of
7. Solve for x. Use the logarithmic properties.
8. Graph this piecewise function.
b)
d)
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9. Verify the following identity.
10. Solve the following logarithm.
11. Simplify
12. Factor this polynomial.
13. Simplify
14. Simplify using the logarithm properties
15. Convert to radian/Degrees
16. Simplify the following
17. Factor
18. Solve the following logarithm.
19. Simplify
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20. Solve
21. Graph the following
22. Solve for x.
23. Write the conjugate of
24. Solve using quadratic formula.
25. Simplify
26. Solve this using the calculator.
27. Solve using quadratic formula.
28. Solve the following logarithm
29. Find the Common Denominator
30. Simplify
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31. Simplify the following
32. Simplify the following
33. Factor
34. Evaluate the following for
A. f(7)
B. f(4)
Use the double-angle identity to find the exact value of each expression
35.
36.
37. What Comes Next…..
…., 1, 2, 4, ____, 16, …
38. Write the recursive formula for each sequence
15, 215, 415, 615, 815 …
39. Graph the following logarithm.
40. Graph the following:
Find the inverse of each function
41.
C. f(-3)
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42.
Simplify the following expressions:
43. -2(-6x-9)-4(4+9)
44. 7(1+9v)-8(-5v-6)
45. Which of the following identities is/ are true?
A.
C.
B.
D.
46. Use the Law of sins and cosines to solve.
A triangle has sides equal to 5 cm, 10 cm, and 7 cm. Find its angles (round answers to 1
decimal place) Hint: a = 10 cm, b = 7 cm, and c = 5. Find A, B, and C.
47. Solve the following equation:
48. Use the following formula to solve this problem.
The population of a town increases from 15,000 to 25,000 in 10 years. Assuming that the
population is growing exponentially, how long does it take the population to increase by 40%?
Find the polar coordinates:
49.
50. Multiply the following:
51. Factor the equation:
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52. Factor
53. A person’s blood pressure changes in rhythmic fashion, with a periodicity set by the beating of
the heart. Suppose a person’s blood pressure P in mm of mercury at time t (seconds) is given by
the formula.
a) Find the period of the function T (one cycle = one heartbeat)
b) Find the number of heartbeat (cycles) per minute.
c) Find the maximum and minimum blood pressure.
54. A radioactive isotope has a half-life of 450 years. Find how long it will take a sample of the
isotope to decrease from 6 mg to 2 mg. HINT:
55. The population of a town increases from 15,000 to 25,000 in 10 years. Assuming that the
population is growing exponentially, how long does it take the population to increase by 40% ?
56. Suppose Rex has learned a list of 500 vocabulary words, and that the number of words he
remembers after weeks decreases exponentially. If he remembers 450 words after 3 weeks, how
long does it take for the number of words he remembers to decrease by 40%?
57.
58.
59. Use the properties of logarithms to rewrite
60. Use trig identities to change
61. Use trig tidentities to change
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62. Simplify the expression
63. Simplify the expression
64. Find an equation of the circle which has the line segment from
65. Calculate the distance from the point
as a diameter.
to the line 3x-4y=21
66. Prove that
67. Given the equation

Find the following:
o Amplitude
o Period
o Horizontal Shift
o Vertical Shift
o Domain
o Range
o The four points that have a y-coordinate of 11
68. A man, standing on the top of a building that is 1,000 feet high, looks down, with an angle of
depression of 42 degrees, to the base of the building across the street. How far apart are the
buildings?
69. A total of $10,000 is invested for 10 years at 12% per year compounded quarterly. How much
interest will be earned during the 10 years?
70. Simplify the following
71. Find the rational zeros of
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72. Solve the following system of equations for x, y, and z:
73. Solve for x algebraically:
74. The radioactive element carbon-14 has a half-life of about 5,750 years. The percentage of
carbon-14 present in the remains of animal bones can be used to determine age. How old is an
animal bone that has lost 40% of its carbon-14?
75. Simplify the following:
76. Simplify the following: