Advanced Placement Calculus AB Summer Assignment

Transcription

1 Advanced Placement Calculus AB Summer Assignment Greetings! I hope you are having a great summer. Well, school is right around the corner. Before you return, I need you to begin thinking about some mathematical concepts as well as review past material so that you are ready for the first day of class. The following steps will help guide you. First, read through section of this packet. It contains the material that you need to know and understand. It should look familiar and will be a valuable resource for you as you do your work in section 4 and throughout the upcoming year. Second, go online (the Internet), and search for math sites that you think might be helpful for you this year. See if you can come up with 5-0 websites. I ll give you one: will help you with basic math skills (like what you will do in section 4 of this packet.) Third, I d like you to perform the simple eperiment in section 3. You might need a buddy to help you with this. Finally, complete the algebra practice in section 4. Like most students, you may find that you are rusty with some of the problems that I have given you. If so, refer to the helpful resources on the internet that you have found. You may also work with other students in your class, but BE CAREFUL. Do not split the assignment up to make it less work. You need to be sure that you complete each problem yourself and that you fully understand how to solve each one. Otherwise, you will be shooting yourself in the foot and will likely not be ready for Calculus. I will give you fair warning. Students who get A s in Calculus do every single problem assigned and there will be a lot of them. I will collect sections 3&4 on the first day of school. It will be worth a test grade and will be graded on completeness, correctness and neatness. You must show the steps you took to solve each problem. Just an answer will earn no credit. There will be a 0% reduction for each day that it is late. This brings me to where I need your help. Not all students have signed up to Remind.com, which means that not everyone knows about the summer assignment. Please check with your friends who you think have also signed up for Calculus. Please give them the information you have and feel free to complete the packet with your friends. As long as you are focused on learning, then this packet will serve its purpose. I look forward to working with you this year. I think that you will find my classes lighthearted and fun, yet difficult and challenging. P.S. If you get stuck, send me an (kevin.winter@sno.wednet.edu). If this seems overwhelming, don t panic and certainly don t quit on Calculus. Just get in touch with me and I ll gladly help you out. This goes for the entire year. Best regards, Mr. Winter

2 Section (pg.) - Review

3 Section (pg.) - Review Stuff You Must Know Cold from Geometry

4 Section (pg.3) - Review Stuff You Must Know Cold from Trigonometry

5 Section (pg.4) - Review Other Stuff You Must Know Cold from Geometry

6 Section (pg.5) - Review

7 Section (pg.6) - Review

8 Section (pg.7) - Review

9 Section (pg.8) - Review

10 Section Helpful Websites

11 Section 3 Eperiment For this eperiment, you will need a ball (a tennis ball will work great, a bowling ball not so much), and a timer. You may get help from a friend or parent if you d like. Use these definitions to help you answer the following questions. I) Position includes the distance (length) and direction (this sign +/-) of an object from a starting reference point. (Your hand will be the starting reference point and will have a position of 0 ft.) When the ball is above your hand, its direction is positive. When the ball is below your hand, its direction is negative. II) Velocity is the change in position over the change in time VV = pppppppppppppppp. Velocity includes the speed (ft/s) III) Eperiment tttttttt and direction of an object. If the ball is moving upward, its velocity if positive. If the ball is moving downward its velocity is negative. Notice that speed and velocity are not the same. Speed is always positive, where velocity can be positive or negative. Acceleration is the change in velocity over the change in time aa = vvvvvvvvvvvvvvvv. The sign of acceleration is a tttttttt bit tricky because we usually think of it as speeding up or slowing down. Here is some helpful guidelines to use. If the speed is increasing in a positive direction, then acceleration is positive. If the speed is decreasing in a positive direction, then acceleration is negative. If the speed is increasing in a negative direction, then acceleration is negative. If the speed is decreasing in a negative direction, then acceleration is positive. (You may need to read that a few times slowly to get it.). Throw the ball as high as you can and catch it at the same point where you released it. Record approimately how long the ball is in the air. Don t forget to include units. Time (t) =. At what time(s) is the position of the ball 0 ft? 3. At what time(s) is the position of the ball greatest? 4. When is the ball traveling fastest? 5. When is the velocity of the ball 0 ft/s? 6. When is the velocity of the ball positive? 7. When is the velocity of the ball negative? 8. Does the ball have a positive or negative acceleration as it is going up? 9. Does the ball have a positive or negative acceleration as it is going down?

12 Section 4 Algebra Practice There is not enough room to show your work on this worksheet. Please do your work on another sheet of paper. When doing homework this year, include your name, the name of the assignment (typically you will use the section and problem numbers from the book), and the date you started the assignment. Be sure that there are no frayed edges from tearing the sheets out of a spiral binder. For each problem, make sure that you write the problem down first and then show each step below the previous one. This will help you avoid the evil run-on equation. Simplify by multiplying by the conjugate pair. secθ + tanθ. + sin 3. sin Write the epression in its simplest form ( + ) ( + ) 4 ( + )( + ) Rewrite trig functions in simplest form csc( ) tan( ) 7. cos( ) 8. sec( )sin( ) csc( )cot( ) 9. cos θ + sin θ sin θ Use the unit circle to solve for θθ (show your work by drawing the unit circle and using special right triangles to figure it out.) 0. θ = sin. θ = tan. θ = cos 3 3. secθ = 4. cotθ = 3 5. cscθ = 3 Solve for in terms of y 6. y + 4= 3 y 7. y ( + ) = + y 8. y y = + Simplify the comple fractions (fractions are comple when either the numerator and/or the denominator contain fractions ( + ) ( )

13 Simplify the epressions so that there are no negative eponents. 3 5 ( y ) ( + ) ( + ) 4 ( + ) ( + ) y 3 4 Rewrite epressions so that all terms are in the numerator (Your answers may have negative eponents) y y ( + ) ( + ) ( + ) ( y) Divide using long division or synthetic division n 3 n n + + n + Write each epression in terms of ln and ln3 in their simplest form 30. ln 6 3. log ln log 44 If = uu +, make substitutions to rewrite the epressions in terms of u. (Be sure to simplify) 34. ( ) Find solutions to the equations using the ZERO function ( nd CALC ZERO ) on your calculator. (You do not need to show your work.) = = (EXTRA CREDIT) Use the helpful websites that you found to show each step to the solution of the derivative and the integral below. These are two concepts that we will learn this year. I don t epect you to understand the solution. I just want to see if you have found a good resource online. d d (3 0 ) d