Calculus Summer Packet There are certain skills that have been taught to you over the previous years that are essential towards your success in Calculus. This summer packet is intended for you to retain/review/relearn these topics. Below is a list of several websites that may help you when you come across a difficult problem. If you are unsure of how to attempt these problems, please look online for help, or send me an email. Feel free to use all resources available to you via internet and tetbooks. Please take these problems seriously, students who are weak in these skills have a difficult time succeeding in calculus without them. Work needs to be shown, when possible, in a neat, legible, organized manner. Do not always rely on your calculator. Yes, there are some skipped numbers. This is a course where assertive and disciplined students succeed the most. I STRONGLY SUGGEST SEARCHING ONLINE FOR AND PRACTICING FINDING LIMITS (ALGEBRAICALLY, NUMERICALLY AND GRAPHICALLY) AS WELL AS FINDING DERIVATIVES USING THE DIFFERENCE QUOTIENT. I believe you will benefit the most from this packet by starting it towards the end of June or the beginning of July. You should try to complete a few problems each day, as if it was a daily journal. Do not do all of it now, and do not wait and do it a week before we start school in August. You are more likely to retain the information if you spread out your work over the course of the entire summer break. This summer assignment is due no later than the end of the first week of class after you return. If you have any questions, please email me at chris.wode@jpthegreat.org Mr. Wode Helpful Websites www.coolmath.com
http://www.mathtv.com/ http://archives.math.utk.edu/visual.calculus/ The Calculus Summer Reading List: l Calculus Resources: http://www.calculus.org/ Info on AP Calculus, college prep, SAT, etc. http://www.collegeboard.com/student/testing/ap/calculus ab/calc.html Calculator: http://www.ticalc.org/ On line Help: http://www.askrose.org/
Simplify using only positive eponents.. 3. 3 5( )(4 9) ( 9 ) 3. ( )[ ] ( ) 4 4. (6 y) 3 5. ( )sin 6. 4 6 4 3 (( 4)) 7. (+5) 3 3 Find the domain of the following functions. Make sure to use interval notation (e. [0,3)). 8. y = log( ) 9. y = 4 0. y = 5 6 +4 3 8. y =. 3. y = 3 + 3 y = +9 9 4. y = + 8+ 5. y = tan 6. y = 5 4 4 +5 3 7. y = 4+ 8. y = cos Factor completely. 9. 5 + 3 80 0. ( 3) ( + ) 3 + ( 3) 3 ( + ) 3
. 50y 0y + Solve the following inequalities by factoring and making sign charts.. 6 > 0 3. + 6 6 > 0 4. 3 0 5. 3 + 4 4 6. sin sin Describe, in words, the transformations that would take place to f () in each of the following. 7. f() 4 8. f( 4) 9. f( + ) 30. 5 f() + 3 3. f () Determine if each function is even, odd, or neither. Show all work. 3. f () = 7 33. f () = 4 3 34. f () = 4 4 + 4 Solve each equation by factoring, graphing, or using the quadratic formula. 35. 7 3 = 0 36. 4( ) 5( ) = 37. + 6 + 4 = 0 38. 3 + 3 = 0 39. ( + )( 3 ) = 40. + = 6 3 4
4. 4 9 + 8 = 0 4. 0 + 9 = 0 43. = 6 Find the equations of all vertical ( =?) and horizontal (y =?) asymptotes (if they eist). 44. y = 45. y = +4 46. 3 y = +4 + 3 9 + 3 8 47. 48. y = 3 3 Simplify the following. + 4 49. 50. 5. + y y +y y 3 5. 53. 54. + + + + If f () =, g() =, and h() =, find the following. g 55. f (g()) 56. g (f()) 57. f(h( )) 58. (f(h( ))) Solve each equation. 59. 60. 3 5 6 = + 6 = 5 5
+5 + 5 = 6 5 6. 6. 60 60 63. 5 = 5 + 3 = 5 Solve each equation on the interval [0, π ). Give eact values (e. ) if possible. 64. s in = 65. cos = c os 66. sincos + s in = 0 π 3 67. 8cos cos = 68. sin cos = 0 Answer the following questions over a variety of topics. 69. Let f be a linear function where f () = 5 and f( 3 ) =. Find f (). 70. Find an equation for the line, in point slope form, that contains (5,) and is perpendicular to 6 3 y =. 7. Use the table to calculate the average rate of change from t = to t = 4. t 0 3 4 (t) 8 7 5 6
7. Order the points, A, B, and C, from least to greatest, by their rates of change. 73. Find the distance between the points (8, ) and ( 4, 6). 74. If g (), find = +3 g ()(the inverse of g). 75. Find the points of intersection in the graphs of y = and y = + 6. 7
76. Rewrite ln ( 3 ) + l n ( + ) 6ln as a single logarithmic epression. 77. Evaluate the following. a) in ( 7π ) b) c sc (60 ) c) c os (0 ) s 6 d) π sec ( 3 ) e) tan ( ) f) π cot ( 35 ) 78. Sketch a graph of the piecewise function f () = { 5, < 0, = 6 4, >. 79. Find the domain and range of each function (without a calculator if possible). a) f () = ( 3) + b) f () = 4 3 c) f () = 3 8
d) f () = 5sin e) π f () = tan ( 4 ) f) f () = e 80. The circle below has a radius of 6 ft. Find the area and circumference of the circle, then find s. 8. Find the area of the trapezoid. 8. Find the missing sides and angles of the triangle. Then find its area. 9
83. Find the volume of a washer with outer radius of 8 ft., inner radius of 5 ft., and a height of 3 ft. 84. Three sides of a fence and an eisting wall form a rectangular enclosure. The total length of fence used for the three sides is 40 ft. Find if the area enclosed is 5500 ft. 6 85. The number of elk after t years in a state park is modeled by the function P (t) = a) What was the initial population? b) When will the number of elk be 750? c) What is the maimum number of elk possible in the park? +75 e.03t 86. Simplify csc t ansincos. 0
7 + 4 8 4 87. Use long division, or synthetic division, to rewrite the epression. 3 88. Rewrite y = 3 4 + in verte form (( k) + h) by completing the square. 89. Sketch a graph of the piecewise function f () = {, <, = 3 + 5, < 3. 90. Do the lines + 5 y = and 7 y = 9 intersect?
9. The function f () is graphed below. Find the following. a) f () b) f (0) c) f () = 0 d) lim + f() e) lim f() f) f() lim