To: AP Calculus Students 2006-2007

To: AP Calculus Students 2015 – 2016 From: Mr. Hanley and Mr. Buxbaum Subject: Summer Prep Work Congratulations! You have registered to take AP Calculus next year at Loch Raven High School! In preparation for the fall, you have to complete the attached review packet. The assignment should be completed on your own paper with all work shown. Your work should be neat and organized with the problems copied and in the order they are presented in the packet. You have approximately 12 weeks to complete this assignment. It should be ready to hand in by Tuesday, September 1stt. You may need to look back through your notes from pre-calculus to assist you with completing this packet. The topics covered in this packet are pre-requisites for a successful year in calculus. Therefore, this assignment should be taken seriously. Any assignment that is handed in with problems out of order or overly sloppy will be returned with the word REDO on the top. In addition to submitting this packet, you will be given a brief evaluation during the first week of school where you will be tested on material covered in the packet. Of particular importance is your MEMORIZATION of the unit circle in radians (say goodbye to degrees). You should be able to tell me all six trig functions evaluated from -2π to 2π for our known angles. On another note, you must have a working TI-83+ or TI-84 graphing calculator for this course (similar models with suffice). I do not recommend the TI-Inspire at this point. If you plan to use a calculator other than the TI-83/84, then you will be on your own in terms of finding the needed menus and syntax to solve the application problems. All tests will be taken with a TI-84 or one of its cousins, not an Inspire. A word to the wise; the primary reason you are begin given this assignment is to ensure that you know the required prerequisite material. It is my expectation that you will be able to do all the math you have been taught in the past. Your only other assignment this summer is to join our Facebook group for AP calculus. We have found this to be a valuable tool for students as it allows you to communicate with other students regarding homework etc. Mr. Hanley will also check the group daily during the year to answer questions you may have. The group is called “Loch Raven AP Calculus” so you can search for the group and request to join. This should be done before the school year is over! us at [email protected] or [email protected] at any time and we will get back to you as quickly as we can. We are looking forward to another great year of AP calculus, as well as a nice long summer vacation. Enjoy!

Mr. Hanley and Mr. Buxbaum Simplify the following expressions (need work here):

1) 2) = 3) =

4) = 5) = 6) =

7) 8) =

Solve each triangle: 9) 10)

Rationalize the denominator and simplify in each case (need work here)

11) = 12) = 13) =

Complete the polynomial division giving a simplified answer with a remainder when necessary (must use long division and show work)

14) (2x2 + 5x – 1) ÷ (x + 3) 15) (x4 + 4x2) ÷ (x2 – 2)

Expand the following using distribution etc… (show work)

16) (4x – 7y)2 17) (x + 3)3 18) (y + 2)5

Factor the following completely (show work)

19) 8x3 – 6x2 + 12x – 9 20 x3 + 2x2 – 5x – 6

Find all solutions to the following equations (show work here too)

21) 4x2 + 12x + 3 = 0 22) 2x + 1 = 23) 24) 2sin2 (x) = sin(x) + 1 25) 26)

27) 28)

Answer each question below (make sure you show work… getting tired of me saying that yet?)

29) Suppose g(x) =; determine the equation for g-1(x).

30) Find all the points where the graphs of y = x – 1 and y2 = 2x + 6 intersect.

31) Consider the ellipse defined by the equation: 2x2 – 8x + y2 – 10y = 60. Place this equation into standard form for an ellipse by completing the square.

32) Find the area of the right trapezoid shown below.

33) Determine the value of x in the right triangle show above.

34) Find the volume of a hollowed out cylinder if the outer radius is 18 feet, the inner radius is 15 feet and the height is 3 feet.

35) Given a sphere with a radius of 4 determine both the volume and the surface area.

For each function determine the equation for ALL asymptotes; vertical, horizontal, and slant. Justify your answers with math.

36) y = 37) 38)

Determine the equation of: (ok just show work from here on… )

39) A line that contains the points (-1, 3) and (2, -4). 40) A line that goes through the point (-1, 2) and is perpendicular to the line 2x – 3y + 5 = 0.

41) A line that goes through (2, 3) and the midpoint of the line segment from (-1, 4) to (3, 2).

42) A parabola with a vertex at (1, 1) through the point (3, -8).

43) A circle with a center at (2, 3) containing the point (-2,5)

44) A polynomial with roots 2, 4i and -4i.

Trig stuff: You will be expected to know the unit circle in radians the day you walk into class. You will need to be able to answer questions like the following without a calculator. Unless otherwise stated your domain is [-2π, 2π] and your answers should be exact. (no work here!)

45) 46) 47)

Find all values for x that satisfy the equation. 48) cot(x) = -1 49) sin(x) = 50) sec (2x) = 2