According to the College Board,
“Before studying Calculus, all students should complete four years of secondary mathematics designed for college-bound students: courses in which they study algebra, geometry, trigonometry, analytic geometry, and elementary functions. These functions include those that are linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric and piecewise defined. In particular, before studying calculus, students must be familiar with the properties of functions, the algebra of functions, and the graphs of functions. Students must also understand the language of functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, and so on) and know the values of the trigonometric functions of the numbers and their multiples.”
ARE YOU READY?
The following items are needed for AP Calculus AB:
1)A package of 100 index cards. They will be used to make “flash cards” so choose the size and color that will work best for you.
2)A 1-inch, 3-ring binder with 8 dividers that will be kept in the classroom. It will hold sample AP questions from various prep books and the College Board.
3)A notebook (your preference) for class notes and homework.
4)Pens/pencils (your preference) for notes and homework.
5)Highlighter to emphasize important concepts in notes.
6)Pencils and erasers for tests and quizzes.
7)Hopefully, you already have a TI-83 Plus, TI-84, TI-89 or other graphing calculator.
8)If your parents/guardians are agreeable, download WinPlot (Google it) and spend some time playing with it. Figure out how to create a graph, copy it into a Word document, and change its size. This is free graphing software. (I used WinPlot to create the graphs in this assignment.)
For each of the problems in this assignment, read and carefully follow the directions. All work should be shown neatly and completely in the space provided.
#1-18) Cut the graphs apart and attach (glue/tape/staple) to index cards. On the reverse side of each index card, attach the equation for the graph. (They are mixed up — you have to match them.) You should be able to complete this part of the assignment without using your graphing calculator. If you need to use it, practice with the flash cards you just created until you no longer need the calculator.
Use the following equations for #1-18.
1) 2)
3) 4)
5) 6)
7) 8)
9) 10)
11) 12)
13) 14)
15) 16)
17) 18)
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19) Graph20) Graph
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Find all that exist or state that there are none:
a) vertical asymptotes (VA)
b) horizontal asymptotes (HA)
c) slant(oblique) asymptotes (SA)
d) x-values of removable discontinuities(holes) (RD)
21) 22) 23)
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24) The graph of contains a removable discontinuity (hole) at . What value of would make this function continuous?
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25) Write an equation of the line with a slope of , that passes through the point .
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26) A line with slope 6 is tangent to the curve when . Write an equation of the line.
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27) A “normal” line is perpendicular to a tangent line. Given the information in #26, write an equation of the normal line.
28) Odd functions are symmetric to ______.
29) Even functions are symmetric to ______.
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Find the x and y intercepts (if they exist). Tell whether the function is even, odd, or neither (e/o/n).
30)31)32)
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Simplify
33) 34) 35) 36)
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Solve for y in terms of x
37) 38)
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Solve for y. (Do NOT round. Give answer in exact form.)
39) 40)
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True or False?
41) 42)
43) 44)
45) 46)
47) 48)
49) 50)
51) 52)
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Find
53) 54) 55)
56) 57)
58) Given:
Find:
a) b) c) d)
59) Given:
Find:
60) Given: and
Find:
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Find:
61) 62) 63)
64) 65) 66)
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67) Show
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68) Find 69) Find
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70) Fill in the chart on the answer sheet that deals with set notation and interval notation.
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Factor completely
71) 72)
73) 74)
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Rewrite by completing the square
75) 76)
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Find a common denominator and simplify
77)
Long Division
78)
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Solve. Do NOT use a calculator. Give answers in exact form. Do NOT approximate! (Radians are used in calculus!)
79) 80)
81) 82)
83) 84)
85) 86)
87) 88)
89) 90)
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Solve. Use your graphing calculator to find the point(s) of intersection. (AP standard is to give a minimum of 3 decimal places in accuracy.)
91) 92) 93)
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Multiply by the conjugate. Simplify
94) 95)
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Solve. Show all work algebraically. Do NOT use your graphing calculator.
96) 97)
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98) Find the height of an equilateral triangle with side=7.
99) Find the area of a trapezoid with bases 6 and 4, with height .002.
100) Find the side of a square with diagonal 12.
101) Find the volume of a sphere with radius 3x.
102) Draw and label the coordinates of all parallelograms that pass through the points A(2,7), B(10,10), and C(2,12)
103) Given: . Show that
104) An equation that models vertical motion is . In this equation, is time, is initial velocity (when ), is the distance an object is above ground level at , and is the distance an object is above the ground at any time . (Up is considered positive, down is considered negative.)
A ball is thrown vertically down from the top of a 100 ft tall building at a speed of 25 feet per second. (This means that the velocity is -25) To the nearest second, how long does it take for the ball to reach the ground?
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105) If you force air into a spherical balloon at a constant rate of 10 cubic inches per second, when is the radius of the balloon increasing faster, when r = 3 inches or when r = 8 inches?
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106) Suppose you have a cone filled with water and an empty cylinder. Both have a radius of 10 inches. The cone is 12 inches deep and the cylinder is 8 inches deep. You let the water drip from the tip of the cone into the cylinder.
a) Will all the water in the cone fit in the cylinder? If so, how much space (in cubic inches) remains in the cylinder? If not, how much water (in cubic inches) overflows?
b) When the level of the water in the cone is 6 inches, what is the level of the water in the cylinder?