Requirements for AP Calculus

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1 AP CALCULUS KLEINKE STYLE YOU ARE ABOUT TO EMBARK ON A GREAT JOURNEY THROUGH THE STUDY OF LIMITS, DERIVATIVES, AND INTEGRALS!! WE WILL HIT A FEW SMALL ICEBERGS BUT NOTHING THAT WILL CAUSE USE TO SINK LIKE THE TITANIC!! ENJOY YOUR SUMMER (WITH A LITTLE HELP FROM YOUR MATH SUMMER HOMEWORK)!! What is AP Calculus All About? We will cover all topics in the AP Calculus AB topic outline as they appear in the AP Calculus Course Description. The major textbook is Calculus Graphical, Numerical, Algebraic by Finney et. Al. Of course my main objective for us is do well on the AP exam but I also want you to become better problem solvers using mathematics and be able to explain solutions to each other. I also want you to adapt to using a graphing calculator. My goal for you is to learn to appreciate the power of calculus and to give you the tools necessary to be successful in future math classes. You will work harder than you ever have before but I am here to help you and we will work together to succeed in calculus. Requirements for AP Calculus Graphing Calculator (with you daily) Binder with Tabs not optional 1 in, plastic cover on front and back is helpful! Pencil Summer homework turned in no LATER than the first day of school. Summer Homework Timing: Please start sometime in late July/early August If you complete it before school is on you will not score very well on the first test of the year. If you rush to do it the week before school, you will miss the chance to earn extra credit and possibly receive extra help, The entire summer homework should take a few hours. Details on Summer Homework: 1) All problems are given in worksheet form. Extra copies of this homework can be found on my calculus page of my weebly site (kleinkeland.weebly.com). On this website you will find a SUMMER tab. ) Signing up for Remind101 is an assignment also. to Sign-up by June 17 earn the full points! Sign-up by August 1 earn of the points. Between August The First Day of school only worth 1 point. ) All summer homework should be completed in pencil and final answers should be highlighted in yellow. 4) All answers should be rounded to decimals or written as improper fractions. 5) All intervals should be given in INTERVAL notation. Extra Help on Summer Homework Extra Help Session will be on August??, 018 from 9:0 11:0am in room N108 at ABHS o This your time to ask questions this homework assignment before you turn it in. o This is also the time to turn it in for EXTRA CREDIT! If you turn your summer homework in on this date (during this time only) you will earn +5 extra credit points. Any papers turned in after 11:0am will not earn the extra credit! Summer homework is graded for completeness and accuracy.

2 AP calculus Summer Homework Name Directions: Please complete all work IN THE SPACE PROVIDED!!! Write answers on the given lines or IF no line is given then highlight your answer!! 1. Graphs we learned about in Precalculus include: *Match each of the equations below with the graphs given without using your calculator!! y = x y = x y = x y = x 1/ y = x 1/ y = 1/x y = x y = ln x y = e x y = 1/x y = [x] y = sinx y = cosx y = tanx y = cotx y = secx y = cscx a. b. c. d. e. f. g. h. i. j. k. l. a. b. c. d. e. f. g. h. i. j. k. l.. Reduce each of the following as much as possible, then highlight your final answer in YELLOW!! 1 1 x 9x a. b. x 5 9 x c. x 7x x x 5 d. a b e. a b 1 b a 1 f. 9ab

3 . Solve for x (no calculator allowed). Please highlight your final answer in yellow!! a. 5 x+1 = 5 b. log x = c. log x = log 4 4log 5 4. Solve the following for the indicated variable: x y z a. 1, for a b. x yd = y + xd, for d a b c a = d = 5. Factor Completely, then highlight your final answer: a. x 6 16x 4 b. 4x 8x 5x + 50 c. 8x Solve for x in the interval [0, π), then highlight your final answer: a. sin x = cos x b. cos x sin x = sin x

4 7. Solve the equations for values of x. Give answers as reduced improper fractions or reduced radicals. No decimals on these questions please. 5 x 1 x a. 4x + 1x + = 0 b. x + 1 = c. 0 x x x 1 a. x = b. x = c. x = 8. Let f(x) = x, g(x) = x + 5, and h(x) = x -1. Find the value of each expression given below. Please highlight your final answer. a. h(f(-)) b. f(g(x 1)) c. g(h(x )) 9. Find each of the following limits, then write your answer on the lines given at the right. x 4 a. lim b. x 4 x x 4 4 x lim a. x5 x 5 b. x lim4 x lim x c. x d. 1 1 x 1 c. d.

5 x lim x e. x 6 x f. x 5 4x lim x 5x x e. f. x 5 g. lim x 5x x 7x 6 x h. lim x 14x x g. h. 10. Find the domain for each of the following functions below. Please provide the work that leads to this answer. 1 a. y = ln (x 1) b. f(x) = c. g(x) = x 5x 14 4x 1x 18 a. b. c. 11. Find the area of an equilateral triangle whose sides 6 cm each Find the area of a trapezoid with height 1inches and bases of 6 inches and 9 inches Solve for x without the usage of a calculator. Show the work that leads to your answer. a. ln e = x b. ln e x = 4 a. b. c. e ln 5 = x d. ln 1 ln e = x c. d.

6 e. ln 6 + ln x ln = f. ln (x + 5) = ln (x 1) ln (x + 1) e. f. 14. Write the point-slope equation for the line through the point (-4, 0) with a slope of Write the slope-intercept equation for the line with slope 1/ and y-intercept Write an equation for the line through point (-, ) that is (a) Parallel to x + y = 4 (b) perpendicular to x + y = 4. a. b. 17. Find the value of x for which the line through points (-8, -) and (x, ) has the slope of Write a formula that expresses the first variable as a function of the second. a. The area of a circle as a function of its diameter b. The height of an equilateral triangle as a function of its side length c. The surface area of a cube as a function of the length of the cube s edge d. The volume of a sphere as a function of the sphere s radius

7 1 19. Given the function y = x a. Find the domain (with work) b. Find the range (calculator) c. Determine symmetry (E, O, N) *show work* 0. Given the function y 1 x a. Find the domain (with work) b. Find the range (calculator) c. Determine symmetry (E, O, N) *show work* 1. Given the function y = x / a. Find the domain (with work) b. Find the range (calculator) c. Determine symmetry (E, O, N) *show work* 1, x 0. Given the function f ( x) x, x 0 a. Graph the function on the axes provided. b. Determine the domain using your graph. c. Determine the range using your graph.

8 x, x 0. Given the function g ( x) x,0 x 1 x 1, x 1 a. Graph the function on the axes provided b. Determine the domain using your graph c. Determine the range using your graph 4. Write a piece wise function for the graph given below. 5. Write a piece wise function for the graph given below.

9 6. Given the set of functions: f(x) = x + 1 and g(x) = x 1, find each of the following. Show the work that leads to your final answer. a. f(g(x)) b. g(f(x)) a. b. c. f(g(0)) d. g(f(0)) c. d. e. g(g(-)) f. f(f(x)) e. f. 7. Without the usage of a graphing calculator, match the function with its graph. I. y = x II. y = -x III. y = - -x IV. y = x V. y = -x VI. y = 1.5 x a. b. c. d. e. f. 8. Using your graphing calculator and the function y = e x +. Highlight your final answer please!! a. Find the domain b. Find the range c. Find the intercepts 9. Rewrite the following exponential expressions to have the indicated base. Highlight your final answer please!! a. 9 x, base b. 16 x, base c. (1/8) x, base

10 0. Solve without a calculator: -x = If John invests $00 in a savings account with a 6% interest rate compounded annually, how long will it take until John s account has a balance of $4150? 1.. Determine how much time is required for an investment to double in value if interest is earned at the rate of 6.5% compounded monthly... Determine how much time is required for an investment to triple in value if interest is earned at the rate of 5.75% compounded continuously.. 4. The number of bacteria in a petri dish culture after t hours is B = 100e 0.69t. a. What was the initial number of bacteria present? A. b. How many bacteria are present after 6 hours? B. c. Approximately when will the number of bacteria be 00? C. 5. Determine whether the functions below are one-to-one. Cirlce the correct answer. a. y = x + 1 b. y = 1/(x + 1) c. y = int x d. y = x Yes or No Yes or No Yes or No Yes or No

11 6. Find the inverse of the given functions below. a. y = x b. y = x 1 x a. b. 7. Solve the equation algebraically. a x = a. b. e x + e -x = b. c. e x 4e x + = 0 c. 8. Solve for y: ln (y 1) ln = x + ln x 8. y =

12 9. Given an angle that lies at the center of a circle is The arc length of this piece is 10. Find the radius of the circle. Highlight your final answer please!!! 40. Find the following information for the curve: y = cos x a. Period b. Amplitude Period: Amp: 41. Find the following information for the curve: y = 5 sin 0.5x a. Period b. Amplitude Period: Amp: 4. Solve the equation in the given interval! a. Cos x = -0.7 [π, 4π) b. Sec x = - [-π, π) a. b. 4. Evaluate the expression without a calculator! a. Sin(cos -1 (7/11)) b. Tan(sin -1 (9/1)) a. b. 44. Evaluate the trigonometric expressions without a calculator! Highlight your final answer! a. sin b. sin c. 4 sin d. sin 0 e. sin f. cos g. cos Evaluate the natural log expressions and exponential expressions without a calculator. Highlight your final answer! a. ln e b. ln 0 c. e ln x d. e o

13 46. Simplify without a calculator. Highlight your final answer! a. 5 8 b Factor Completely then Highlight your final answer! a. x x 1 b. x x 4xe x e c. x 4x 1 d. x 10x 8 e. x 6 f. x Solve without a calculator. a. x x 0 a. b. 4x 10x b. c. x x 4x c. 49. Water is poured into a conical container with a diameter of 0 cm and a height of 8 cm. If the volume of a cone is one-third the volume of a cylinder, write an equation for the volume of water as a function of the height of the water in the container. Highlight your final answer!

14 50. At 8am, the North Hallway copier was making 100 copies per minute. Its counter read At 4pm, the copier was only making 84 copies per minute (it gets tired) and the counter read Find the average number of copies made per minute from 8 am to 4pm. Highlight your final answer! 51. Solve algebraically: 4x 5 x Simplify: a. (csc x tan x)(sin x)(cos x) a. b. Sin x cos x b. c. cos x sin x c. d. sin x + cos x d. e. cos x sinx e. First impressions are lasting impressions.impress me!!

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