Summer Review Packet. for students entering. AP Calculus BC

Transcription

1 Summer Review Packet for students entering AP Calculus BC The problems in this packet are designed to help you review topics that are important to your success in AP Calculus. Please attempt the problems on your own without any notes and show all work! In addition, do not use your calculator for these problems. When you come across topics that require a little review, feel free to look at your old notes, search a website or ask a friend for help. If you want to check your work with a calculator, that is fine also. You are epected to get each problem correct. It is recommended that you work with one or more people, but each person must submit his/her own work. Before you leave school, write down the names, phone numbers, and/or addresses for at least two people who are also taking AP Calculus in the fall. Name _ Phone _ _ Name _ Phone _ _ Bring the finished packet with you to your AP Calculus class on the first day of school. After you have an opportunity to ask questions, you will be assessed on these skills during the first week of school as part of your 1st quarter grade. Enjoy your summer! I am looking forward to seeing you in August. If you have any questions, please contact Mrs. Atamas: Faina_Atamas@mcpsmd.org.

2 I. Simplify. Show the work that leads to your answer II. Complete the following identities. 1. sin + cos =. 1 + tan =. cot + 1 = 4. cos = 5. sin = III. Simplify each epression h AP Calculus BC Summer Review Packet Page of 11

3 IV. Solve for z: yz = 0. y + yz 8z 4 = 0 V. If f() = {(,5), (,4), (1,7)} g() = h() = {(,), (4,), (1,6)} k() = + 5 determine each of the following: 1. (f + h)(1) =. (k g)(5) =. (f h)() = 4. (g k)(7) = 5. f -1 () = 6. k -1 () = 7. 1 f( ) = 8. (kg)() = VI. Miscellaneous: Follow the directions for each problem. 1. Evaluate f ( h) f ( ) h and simplify if f() =.. Epand ( + y). Simplify: = ( 5 + )= 4. Simplify: + = 5. Eliminate the parameter and write a rectangular equation for = t + y = t AP Calculus BC Summer Review Packet Page of 11

4 VII. Epand and simplify 1. 4 n =. n0 1 n1 n =. 1 k k=0 = 4. 1 = n! k=0 VIII. Simplify 1.. ln e. (1 ln ) e 4. ln 1 5. ln e log 7. log 1/ ln 9. ln e 10. 4y 1 1 y / 1. (5a / )(4a / ) 1. (4a 5/ ) / 14. ( n 1)! 5 n! AP Calculus BC Summer Review Packet Page 4 of 11

5 IX. Using the point-slope form y y 1 = m( 1 ), write an equation for the line 1. with slope, containing the point (, 4) 1.. containing the points (1, ) and ( 5, ).. with slope 0, containing the point (4, ). 4. perpendicular to the line in problem #1, containing the point (, 4) 4. X. Given the vectors v = -i + 5j and w = i + 4j, determine 1. 1 v. w v. length of w 4. the unit vector for v XI. Without a calculator, determine the eact value of each epression. 1. sin 0. sin. sin 4 4. cos 5. cos cos 7. tan tan 6 9. tan 10. cos(sin -1 1 ) 11. Sin-1 (sin 7 ) 6 AP Calculus BC Summer Review Packet Page 5 of 11

6 XII. For each function, determine its domain and range. Function Domain Range 1. y 4. y 4. y 4 4. y 4 XIII. Determine all points of intersection. 1. parabola y = + 4 and line y = y = cos and y = sin in the first quadrant XIV. Solve for, where is a real number. Show the work that leads to your solution = ( 5) = = 8 AP Calculus BC Summer Review Packet Page 6 of 11

7 Solve for, where is a real number. Show the work that leads to your solution. 5. ( + )( ) > = 8. sin = sin, 0 9. < ( + 1) ( ) + ( + 1)( ) = = 9 1. log + log( ) = 1 AP Calculus BC Summer Review Packet Page 7 of 11

8 XV. Graph each function. Give its domain and range. 1. y = sin. y = e Domain Range Domain Range. y = 4. y = Domain Range Domain Range AP Calculus BC Summer Review Packet Page 8 of 11

9 Graph each function. Give its domain and range. 5. y = ln 6. y = + Domain Range Domain Range 7. 1 y 8. if 0 y if 0 4 if Domain Range Domain Range AP Calculus BC Summer Review Packet Page 9 of 11

10 XVI. Identify, by name, each polar graph. Give at least one characteristic of each graph (e.g. radius, location, length of petal, point (other than the pole) on the graph, etc.) Then sketch a graph of each. 1. r =. r = sec θ. r = 1 + sin θ 4. r = cos θ XVII. Compute each of the following limits: 1. cos lim. lim sin. 1 lim lim lim 5 6. lim AP Calculus BC Summer Review Packet Page 10 of 11

11 XVIII. 1. Let 1, if 4 f, if, if Compute the following limits: a) lim f b) lim f c) lim f d) lim f e) lim f f) lim f XIV. Write each sum using summation notation, assuming the suggested pattern continues = = = = = = XV. Remember that you are not using a calculator. 1. In a triangle ABC, angles A and C measure 45 and 0 degrees respectively. Side BC is 14 centimeters long. Sketch a diagram and find. Find the area of the shaded region. a) AB b) Area of the triangle ABC AP Calculus BC Summer Review Packet Page 11 of 11