Dear AP Calculus AB student, The packet of review material is a combination of materials I found on-line from other teachers of AP Calculus AB and from basic algebraic concepts I have seen my former Calculus students struggle with. What makes Calculus so much different from every other math class you have taken is that there are very few times where your homework consists of you doing a bunch of similar problems the same way. Calculus is an application of all of the mathematical skills you have learned & practiced to this point. There are very rarely a set of steps for you to follow when solving problems using Calculus. All of your Algebra skills will be needed for any given problem. Often you will need to try multiple Algebraic methods to get you to a point where you can use Calculus to solve a rather comple looking problem. I ask that you attempt to complete this packet on your own over the course of the summer and without use of a calculator, old notes/tetbooks, or the internet. Many problems you should find easy. When working on the harder ones, take time to think about, maybe even a day or two. IF you just cannot remember how to do a problem (and have stepped away from that problem at least twice), then please research how to solve that type of problem on-line or from a friend. Learning to use the internet as a resource will become critical not only for your learning this year, but for your entire academic career and even your life. Everything in this packet IS something you were taught at one time. Everything in this packet is something I will NOT be spending class time to re-teach. The packet is due the FIRST full day of class and will be your first test grade of the quarter. This is NOT meant to scare you. Calculus is an amazing tool! If you are thinking of going into a career in engineering, astronomy, physics, architecture, the biological sciences (nursing, medicine, biology of any kind), the actuarial sciences (eg: statistics), pharmaceutical studies, computer programming, or even as a graphic artist, you will need to know, understand, and use Calculus. Calculus was invented to solve problems that could not be solved (or could not be solved easily) using Algebra. It is a relatively new science (developed by Sir Isaac Newton around 1666 and separately by Gottfried Leibniz around 1674). It continues to evolve and develop as humans learn more about the world and universe we live in. Finally, please request to join Mrs. D s AP Calculus AB Class Facebook (https://www.facebook.com/groups/181760191677/) page. I will use this page ALL year to communicate with you outside of school. I post notes, helpful websites, answer keys, etc on this site. It is also a place for you to post a question to the entire class about homework or a concept we are learning, and it gives you an opportunity to chat with me directly when we need a little etra help. My former Calc students also chime in from time to time to encourage you and to let you know how much more rigorous college is.
Pre-Calculus Review Packet AP Calculus AB Name Due First FULL day of class 1 Directions: 10 Algebraic concepts to know cold. No calculators, notes, or internet. Just use that big beautiful brain you have been given 1. Find the domain of the function: f. Find the domain of the function: f. For what value of is the function f undefined? 5 4. What is the y-intercept of the graph of 5 the function f? 7 5. True or False? 9 9 6. Find the value of 16 7. True or False? 1 5 5 8. Find the domain of the function: 1 f
9. Find the domain of the function: 7 y 10. Find the range of the function: y 11. Find the domain of the function: 1 y 5? 1. For what values of is the function f 1 undefined? 1. At what point, besides the origin, do the graphs of y = and y = intersect? 14. True or False? If is any Real number, then 5 is also a Real number. 15. Find f 5 if f 8 15 16. Find f 5 if f 5
17. True or False? If = -, then 7 1 18. Find the domain of the function: 7 f 5 19. Find the domain of the function: f 5 0. True or False? If is a Real number, then 5 is a Real number 1. For what value of is the function 4 f undefined?. 7 sin 6. True or False? If, then sin1 1? 4. True or False? y sinis a reflection of the sine graph about the -ais.
5. For what value of is f undefined on the interval 6 sin,? 6. Find the domain of the function: 9 f 7. Find the -intercept of the function: 7 f 68 8. Find the slope of the line whose equation is: 6y 11 9. tan 4 0. Find the value of 1 8 1. Multiple Choice: what is the value of A. - B. DNE C. D. 1 1 4. True or False? Given that if > 100, then y < 0.01 1 y,
. Multiple Choice: how does the graph of? f 7 compare to the graph of A. slide 7 units up B. slide 7 units right C. slide 7 units down D. slide 7 units left f 4. csc 5. sin 6. Is the function function? f 6 a one-to-one 7. Find the y-intercept of the graph of y e 5 8. Find the inverse of the function f 5, where 0 9. True or False? If f and g are nonzero functions, then f g g f 40. At how many points do the graph of y 1and y 6intersect?
41. For what value of between & is 5 y cos 1 undefined? 4. Write the equation of the line with slope 7 that passes through the point (6, -) 4. If f 1 find f 44. If f 1, find f 1 function, or neither? 45. Is f an even function, odd 46. sec 47. Find the vertical asymptote of the graph of the function: f 1 48. Is the function y 7 5 an even function, odd function or neither?
7 5 49. Is the function y one-to-one? 50. If the graph of f is shifted two units to the right to form g(), what would be the equation of g()? 51. Write the equation of the line through the point (-9, ) that is parallel to the line 5y = 16. 5. Simplify: y y y 5. cos 4 54. tan 4 55. csc 56. Simplify: 10
57. Solve for, when 0 : cos 0 58. Solve for, when 0 : 1 sin 59. Solve for, when 0 : sec 60. Solve for, when 0 : tan 1 61. Find the domain of: y 5 6. cos csc 64. Solve for, when 0 : 6. sin
65. Solve for, when 0 : cos 66. Solve for, when 0 : csc 1 67. What is the domain of y tan? 68. Write the equation of the line through (9, -4) and (1, 5) 69. Calculate: 1 1 log a ab log ab b 70. Solve the equation: log 5
71. Solve the equation: log 1000 7. Solve the equation: log 4 5 7. Simplify: ln ln e e 74. The streptococci bacteria population N at time t (in months) is given by N N e where N 0 is the initial population. How long does it take for the bacteria population to triple its size? 0 t 75. Simplify: 5 76. Simplify: 1 15 64 y 77. Simplify: 64 y 1 15 78. Simplify: 64 y 1 15
79. Calculate: 80. Calculate: 4 81. Simplify: 6a 6a 8. Factor Completely: 5 8. Factor Completely: 4 6 9 84. Find the LCM of: 1 and 1 5 85. Is 5 5 divisible by 1 7 5 86. Find the range of the function y
f 5 4 87. Find the asymptotes of: 88. Find the remainder by long division: 5 4 5 1 divided by 4
Directions: Match the graph to the equation. Do not use a calculator or the internet! A. y m b B. F. K. y r G. y sin L. y a C. 1 y H. y cos M. y a y ln y tan D. I. N. y y e y 5 E. J. y y e 89. 90. 91. 9. 9. 94. 95. 96. 97. 98. 99. 100. 101. 10.