Dear AP Calculus BC Students, Welcome to the most exciting math class in high school! There are three major tasks you have to accomplish over the summer:. Prepare psychologically: Each day repeat I love AP Calculus! I m an excellent math student! I m a girl who can do math! Fact: I will get a FIVE! 2. Prepare intellectually: Look at the review topics and problems at the beginning of the summer and decide your weak areas. Make a plan of review it is much better to watch one video clip each day than to cram them all into few days. Spend 5 minutes on a regular basis reviewing for AP Calculus develop the virtue of consistency during the summer!!! 3. Create the AP Calculus community: You will have a much easier time studying Calculus if you do it together! Schedule some group review opportunities over the summer. Take the responsibility for the AP Calculus class it is YOUR class make it into a fun one. Pray for all AP Calculus students and teachers. This is not You vs Calculus, use your friends and I to help you. WORK TOGETHER Don t be like a bad prom date, communicate. Have a wonderful summer! Sr. Peter Verona, O.P.
Make yourself familiar with Khan Academy website: http://www.khanacademy.org it will be a great resource for review in lecture style during the summer and the coming year!!! Use the videos to review over the summer the topics you are not comfortable with. You should be able to solve the provided review problems with ease. If you cannot solve them easily, you must spend time reviewing with Khan Academy videos. Also, there are plenty of great instruction videos on youtube. The internet is a fantastic resource and for math, Wikipedia and Wolfram Alpha are great website. Explore Wolfram Alpha this summer. Become familiar with it. Essential Prerequisites: Make sure you are familiar with major Pre-Calculus terminology: function, domain, range, roots, max, min, inflection points, increasing, decreasing, concave up, concave down, even, odd, periodic, vertical asymptote, horizontal asymptote, slanted asymptote, inverse functions, removable discontinuity, jump discontinuity, piece-wise function. Suggestion: make a cheat-sheet for each of the following topics: I. Basic Geometry: area, volume, similar triangles. II. Factoring memorize special formulas and Pascal s triangle III. Simplifying Rational Functions and Expressions with Radicals can you graph a rational function without TI-84 by finding asymptotes, roots, and curve snaking? IV. Graphing using Transformations do you know all basic graphs including trig and inverse trig functions? V. Rules of exponents, logarithms, and trigonometric identities do you know all rules of exponents, rules of logarithms, and trigonometric identities for sine and cosine? VI. Solving Equations and Inequalities What are the methods for solving polynomial, rational, exponential, logarithmic, and trigonometric equations and inequalities? What are the common mistakes you need to avoid? VII. Factoring, Curve Snaking, and Inequalities. VIII. Parametric Curves. - Can you sketch parametric curve by making a table? - Can you eliminate t? IX. Polar Coordinates. X. Limits. - What are the four formulas used to translate between polar and Cartesian coordinates? Do you know the basic polar graphs?
Review Problems. All problems are to be solved correctly and turned in on the first day of class. Sloppy work won t be accepted so use blank paper (it is what you will have on the exam) with a proper heading, clean-cut edges, use only pencil, staple multiple pages, etc SHOW ALL YOUR WORK. Proper Heading: Your full name AP Calculus BC MDSA 207-8. Find the volume and surface area of a cone whose base has radius 3 and height is 5. 2. Factor the following polynomials: (a) x 2 + 0x + 25 (b) 3x 2 5x + 2 (c) x 3 27 (d) 2x 3 3x 2 + 4x 6 (e) 2x 4 49x 2 25 3. Simplify the following expressions: (a) 2 x+2 x 2 (b) 2 x+ + x x 2 2x+3 (c) 2 x + x 2 +x (d) 49(x 3) x 2 9 (e) ( x 3 + 3x3 2 x 3 + ) (x3 + ) 4. Find the equation of the line passing through (,3) and ( 3, 5). 5. Find the equation of the line parallel to 2x + 3y = 2 passing through (2,3). 6. Find the equation of the line perpendicular to 2x + 3y = 2 passing through (2,3).
7. Graph the following functions: (a) y = 2 x 3 (b) y = ln( x ) 2 (c) y = 2 sin(3x) (d) y = arctan(x) (e) y = { tan x for 3π < x < 2 4 x 2 for x < 4 x 3 for x 4 8. Simplify the following expressions: (a) log 3 9 3 (b) Expand the logarithm ln ( ex2 y 3 3 ) z (c) Compress the logarithm 5 ln(x + ) + 3 ln 2x 4 ln(x ) (d) Verify the identity: (e) Verify the identity: cos x sin x = +sin x cos x sin x sin x+cos x = tan x +tan x (f) Verify the identity: cos (x + π ) sin (x + π ) = sin x 6 3 9. Solve the following equations: (a) x 3 x 2 4x + 4 = 0 (b) log 2 (x 2 ) = 4 (c) ( 3 )x2 + = 27 (d) cos 2x = 3 2 (e) tan x =
0. Solve the following inequalities: (a) x 2 9 (x )(x+2) 0 (b) log 2 (x ) 3 (c) ( 2 )x2 6 (d) 2 sin 3x (e) tan x. Snake the following functions. For the more complicated functions: factor, find roots, and plug in points to figure out whether the function is positive or negative. (a) f(x) = x 4 6 (b) f(x) = (c) f(x) = x2 +x 2 (x 3)(x 2 +) ln x x 2 4 (d) f(x) = (ex )(x 2) x 2. Find the Cartesian equation (in terms x and y) for the parametric curve x = + 2t and y = 3 t and find its vertical and horizontal asymptotes. 3. Graph the following polar curve without the calculator r = 5 sin 3θ 4. Find the following limits: x+ (a) lim x x 2 x+2 (b) lim x 2 x 2 4 (c) lim x x 3 x 3 (d) lim 2x2 + x 2 3x 2 (e) lim x (2ex + x + 2) (f) lim 2x 2 x x+8 3