2018 Summer Assignment AP Calculus BC. Due Dates: Part 1 is due no later than Aug. 1 Part 2 is due no later than Aug. 15

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1 08 Summer Assignment AP Calculus BC Due Dates: Part is due no later than Aug. Part is due no later than Aug. 5 The assignment must be postmarked or hand delivered to the school (preferably to me Part : The following problems will review essentials of Algebra, Geometry, Trig, Functions, and other requisite skills for success in AP Calculus Complete the attached review packet. Follow all directions completely. The assignment is mandatory and will be graded based on completion/effort/correctness. If you can t do a problem, try to put in words what you think you should do. Show your work, even if you are in doubt about the correctness of your result. The assignment is to be done by you alone, without assistance from anyone else. Try your best to solve every problem without the aid of outside references you gain very little by copying answers without full understanding of how and why. If you reach a dead end, use of tetbooks or web sites is permissible. But do so only to seek understanding. The assignment is to be completed in pencil, done neatly, and on separate paper. Copy each problem and show necessary work or indicate the steps you followed to reach the answer. Answers without work or justification will not receive full credit. Trial and error is an essential skill for mathematicians, scientists, and engineers. Be patient; don t give up easily; challenge yourself; if at first you don t succeed, try and try again 5 Use a calculator only when directed, and only when absolutely necessary. This assignment may take some time to complete. Don t wait until the last minute to start work. I suggest starting in mid to late July. This assignment will engage you to be a lifelong learner and take ownership for your education. In the past, students felt that by completing this assignment, they were prepared for Calculus. Part due Tuesday Aug 5 Tetbook is on Blackboard. CHAPTER : LIMITS READ the sections for understanding and review. Algebraic and Graphical Limits P. 55 # 9, 0, 6, 7, 9,, 6,,, 6. Properties of Limits P. 67 # 5, 7,, 7,, 9,, 7, 9, 5, 5, 6. Continuity P. 79 #, 7, 6, 70, 98.5 Infinite Limits P. 88 #, 5,, 7, 6, Summer assignments should be mailed or delivered to your CGS site by due dates. Colonial Forge High School Stafford High School Mr. Thompson mthompson@cgs.k.va.us Stafford Indians Lane 550 Courthouse Road Stafford, Virginia 05 Stafford, Virginia 55 Telephone: Telephone: North Stafford High School Mrs. Thompson kthompson@cgs.k.va.us 89 Garrisonville Road Stafford, Virginia 55 Telephone: Riverbend High School Mr. Conlee jconlee@cgs.k.va.us 0 Spotswood Furnace Road Fredericksburg, Virginia 07 Telephone: Spotsylvania High School Ms. Kronander ckronander@cgs.k.va.us 6975 Courthouse Road Spotsylvania, Virginia 55 Telephone:

2 Part I. Simplify the following Algebraic Epressions (hint: factor first II. Operations with rational epressions (simplify. + h III. Compositions and Inverses Let f ( +, g (, and h(. Evaluate the following and state domain and range for each: 7. f ( g ( 8. g ( h( 9. h ( IV. Slope. Use of point-slope form, y y m( is recommended. 0. Find the slope between the points (, and ( 5,. Write equation with slope of -, containing the point (,. Write equation of a parallel to y 7 and passes through ( 5,. Write equation of a perpendicular to #, containing the point (,. Write equation of a horizontal line through (, 5. Write equation of a vertical line through (,

3 V. Simplifying Epressions using properties of eponents, logs, and factorials! (5 a ( a 5 ( a e ln ( ln e ln. ln e 7.. ln e ln 5. ln ( e 6. ln 5 7. y ! 7! k k! n +! ( n! Simplify to single term. ln 6 ln. ln 5 + ln VI. Series. Epand the series and simplify each term.. n n 5. n 0 n VII. Trig. Simplify without using a calculator 6. sin 0 7. sin 8. sin 9. cos 0. cos. sin 6. tan 6. cot. cos ( 5. tan 6. sin (.5 VIII. Use graph paper to sketch the graph of each function by hand, then confirm with graphing calculator. List the Domain and Range for each. 7. y 8. g ( 9. f ( e 50. y 5. f ( + 5. h( e 5. y ln ( + 5. y arctan 55. y , 0 y, 0, 0 y, 0 Parametric Mode cost 58. over 0t y sin t 59. t y t over 0t

4 IX. Show your work to solve each equation or inequality. No Calculator ( log + log( log ln 7. e 5 7. sin, 0 7. e ( + e ( 0 X. Show your work to solve for the indicated variable ky solve for k L 75. T solve for L g 76. F m ( v f vi solve for v f 77. y y + y solve for XI. Yes Calculator. Perform the indicated task. Calculator in radian mode. 78. Evaluate sin ( 79. Solve tan over 0, 8. Find any point(s of intersection y sin and 80. Solve e 8. Solve ln y + XII. Using a Table or chart. Let f ( and ( g be continuous functions over the domain,. 8. Estimate the slope at 8. Find g( f ( 85. Find ln ( g ( 0 for f ( 86. Between which two values of, is the f the steepest? slope of ( 87. How many roots eist for f ( and ( g? Eplain how you came to this conclusion. f ( g(

5 XIII. Miscellaneous word and thinking problems. SHOW SETUP AND WORK 88. Two cars start moving from the same point. One travels south at 00 km/hour, the other west at 50 km/hour. How far apart are they two hours later? 89. A children s picture book is being designed so that each page contains 0 square cm of print and pictures surrounded completely by a white boarder as shown below. The margin on each page is to be cm at the top and cm on the other three sides. Let be the height of the printable area. Write an equation in terms of for the area of the total page (printable area plus margin area. 90. A right triangle has one side and a hypotenuse of 0 meters. Find the area of the triangle as a function of. 9. An isosceles triangle has one verte at the origin and its base parallel to the - ais with the remaining two vertices on the upper portion of the curve y 9. Write an equation in terms of for the area of the triangle. 9. A right circular cylinder has a radius r and a height equal to twice r. Find the volume of the cylinder as a function of r. V r h 9. Epress the distance d d + d, in the figure below, as a function of.

6 XIV. Limits. Evaluate the following limit problems. Show work. 9. lim ( lim 96. lim Given lim h ( and lim g ( 5, evaluate: a 97. lim ( g( h( a a 98. ( h( g lim a 99. A piecewise function f(, with domain, is shown below. Use the graph to answer the questions. A. lim f ( y B. C. D. E. F. G. lim f ( lim f ( + lim f ( lim f( lim f( + lim f( H. f ( 0 I. f ( J. f ( K. lim f( L. lim f ( M. True or False: the range is (,