IB Mathematics HL /AP Calculus AB Summer Packet There are certain skills that have been taught to you over the previous years that are essential towards your success in IB HL /AP Calculus. If you do not have these skills, you will find that you will consistently get problems incorrect net year, even though you may understand the calculus concepts. It is frustrating for students when they are tripped up by the algebra or trigonometry and not the calculus. This summer packet is intended for you to retain/review/relearn these topics. This packet can be found and printed off at my WHS AP Calculus/HL website (Washburnmath.weebly.com). 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. As stated before, students that are weak in these skills often have a difficult time succeeding in calculus. Work needs to be shown, when possible, in a neat, legible, organized manner. Do not always rely on your calculator. Half of your AP eam net year is taken without the use of a calculator. I believe you will benefit the most from this packet by starting it towards the end of June. 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 it out. There is additional practice (with eamples) on my website if you need them. This summer assignment will not be graded when you return but, there is a good chance I will give a quiz on this material at the end of the first week. If you have any questions, please email me at jeanne.dobson@mpls.k.mn.us. I look forward to working with you net year. Ms. Dobson Helpful Websites http://www.mathematicshelpcentral.com/inde.html http://www.mathtv.com/ http://archives.math.utk.edu/visual.calculus/
Simplify using only positive eponents.. 5 4 9 / 9.. 4. 6 y / 4 5. / sin 6. 4 4 6 4 7. 5 / 8. 4 y y / Find the domain of the following functions. Make sure to use interval notation (e: [0, )). 9. y log 0. 4 y 4. y 56 8. y. y 4. y 9 9 5. y 8 4 5 6. y tan 7. y 5 4 8. y 4 9. y 6 0 0. y cos Factor completely... 5 80. 50 0 y y Solve the following inequalities by factoring and making sign charts. 4. 6 0 5. 66 0 6. 0 7. 5 8. 4 4 9. sin sin
Describe, in words, the transformations that would take place to f 0. f 4. f 4. f in each of the following.. 5f 4. f 5. f Determine if each function is even, odd, or neither. Show all work. 6. f 7 7. 8. f 4 4 4 9. f 4 f Solve each equation by factoring, graphing, or using the quadratic formula. 40. 4. 7 0 4 5 4. 6 4 0 4. 44. 0 45. 6 46. 9 8 0 47. 0 9 0 48. 6 4 Find the equations of all vertical ( =?) and horizontal (y =?) asymptotes (if they eist). 49. 4 y 50. y 4 5. y 5. y 9 8 5. y 54. y 0 Simplify the following. 55. 56. 4 57.
58. y y y y If f g h 59.,, and, find the following. 60. 6. f g 6. g f 6. f h 64. g f h Solve each equation. 65. 5 66. 6 6 5 67. 68. 6 5 5 5 69. 60 60 5 70. 5 5 Solve each equation on the interval 0,. Give eact values e: if possible. 7. sin 7. cos cos 7. cos 0 74. 4sin 75. sin sin 76. cos cos 77. sin cos sin 0 78. 8cos cos 79. sin cos 0
Answer the following questions over a variety of topics. 80. Let f be a linear function where f 5 and f. Find f. 8. Find an equation for the line, in point-slope form, that contains 5, and is perpendicular to 6y. 8. Use the table to calculate the average rate of change from t = to t = 4. t 0 4 t 8 7 5 8. Order the points A, B, and C, from least to greatest, by their rates of change. 84. Find the distance between the points 8, and 4, 6. 85. If g, find g (the inverse of g). 86. Find the points of intersection in the graphs of y and y 6. ln ln 6ln as a single logarithmic epression. 87. Rewrite 88. Evaluate the following. 7 a) sin 6 b) csc60 c) cos0 d) sec e) tan f) cot 5
89. Sketch a graph of the piecewise function 5, f 0,. 6 4, f. 90. Describe the left and right end-behavior of the function 9. Find the domain and range of each function (without a calculator if possible). a) f b) f 4 c) f f 4 d) f 5sin e) tan f) f e 9. The circle below has a radius of 6 ft. Find the area and circumference of the circle, then find s. 9. Find the area of the trapezoid. 94. Find the missing sides and angles of the triangle. Then find its area. 95. Find the volume of a washer with outer radius of 8 ft., inner radius of 5 ft., and height of ft. 96. Rewrite log 5 into an equivalent epression using only natural logarithms.
97. 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. 75e 98. The number of elk after t years in a state park is modeled by the function Pt 0.0t 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? 99. Simplify csc tan sin cos. 00.Use long division, or synthetic division, to rewrite the epression 7 4 8. 4 0.Rewrite 4 in verte form y k h by completing the square. 0.Sketch a graph of the piecewise function, f,. 5, 0.Use a graphing calculator to solve e. 04.Do the lines 5y and 7y 9 intersect? 05.The function f is graphed below. Find the following. a) f b) f 0 c) f 0 d) lim f e) lim f f) lim f 06.Find the following limits. a) lim 7 9 b) lim 4 8 c) limsin 4 5
d) lim4cos e) lim 6 f) lim 0 tan g) lim 0 9 h) lim h h where 4, 5,