AP Calculus AB Summer Packet

Transcription

1 AP Clculus AB Summer Pcket Nme: Welcome to AP Clculus AB! Congrtultions! You hve mde it to one of the most dvnced mth course in high school! It s quite n ccomplishment nd you should e proud of yourself for getting this fr Not ll students do As prt of successful yer, you will need to complete this summer ssignment over mthemticl concepts needed for this course Complete this pcket over the summer nd hve it redy to turn in Fridy, Septemer st, 07 If you complete the pcket y Fridy, August 5, 07, you will receive 0 onus points If you misplce your pcket, copy will e ville on the school s wesite t wwwdickinsonisdorg Study groups re encourged, ut mke sure YOU understnd the mteril I cnnot stress enough how importnt it is to mke sure you understnd ech concept covered on this summer ssignment Tke your time to relern lgeric, eponentil, logrithmic nd trigonometric topics you my hve forgotten If you do not feel confident with your ilities or you need ny guidnce, plese study your notes from prior mth clsses, or find some tutorils on the internet Plese don t fke your wy through these prolems If you do not fully understnd the pcket, it will mke your Clculus eperience much more difficult We do not wnt you to do poorly in this clss ecuse of lck of prior knowledge You will hve test during the first week of school coving the topics ddressed in this pcket Heed our wrning nd BE PREPARED! Plese do not wit until the lst minute to complete the summer ssignment There re lot of prolems to solve nd we wnt to mke sure you tke your time understnding ech of them At the sme time, plese do not finish the whole pcket in the eginning of the summer The point of this ssignment is to refresh your memory of skills tht re needed in the course nd if you do ll the work erly, you my forget gin efore school strts All prolems re intended for you to complete WITHOUT clcultor though you my choose to use one to check your work We hope tht you re s ecited s we re for this new yer of Clculus we will e pursing together! Clculus is unlike ny other rnch of mthemtics nd we cnnot wit to shre its glory with you AP Clculus will not e n esy A ut with the right mount of work we should e in for very rewrding yer together! Plese feel free to contct either of us if you hve ny questions over the summer: dsmith@dickinsonisdorg erogers@dickinsonisdorg See you in August! Mrs Smith nd Mr Rogers

2 Stte if the following lger properties re true or flse: ) ( F c c E D h k h k C q p q p B y y A Evlute without clcultor Rewrite the following epressions using negtive eponents: 5 Solve the qudrtic eqution You my fctor or use the qudrtic formul 8 = 0 + = 0 c = 0 5 Fctor completely: (there should e no frctionl or negtive eponents) + 7

3 Find the point(s) of intersection of the grphs for the given equtions 6 y8 y7 7 y6 y 8 y y Comple Frctions When simplifying comple frctions, multiply y frction equl to which hs numertor nd denomintor composed of the common denomintor of ll the denomintors in the comple frction Emple: ( ) 5( )( ) ( ) ( ) ( ) ( ) 8 8 Simplify ech of the following

4 Functions To evlute function for given vlue, simply plug the vlue into the function for Recll: f g( ) f ( g( )) OR f [ g( )] red f of g of Mens to plug the inside function (in this cse g() ) in for in the outside function (in this cse, f()) Emple: Given f ( ) nd g( ) find f(g()) f ( g( )) f ( ) ( ) ( 8 6) 6 f g ( ( )) 6 Let ( ) f ( ) nd g( ) Find ech ft f g( ) c g f ( m) _ d [f()] g()= _ Let f ( ), g( ) 5, nd h( ) Find ech h f( ) g h ( ) Find f ( h) f ( ) h for the given function f 5 f ( ) 9 6 f ( ) 5

5 Eqution of line: 7 Use point-slope form to find the eqution of the line pssing through the point (0, 5) with slope of / 8 Find the eqution of line pssing through the 5 point (, 8) nd prllel to the line y 6 9 Find the eqution of line perpendiculr to the y- is pssing through the point (, 7) 0 Find the eqution of line pssing through the points (-, 6) nd (, ) Find the eqution of line with n -intercept (, 0) nd y-intercept (0, )

6 Unit Circle: You must KNOW the unit circle vlues for sine nd cosine for rdin vlues etween zero nd π In clculus we lwys use rdins! Never degrees You should lso hve the following trig identities memorized: Reciprocl Identities: csc sin sec cos Quotient Identities: sin tn cos cos cot sin Pythgoren Identities: sin cos tn sec cot csc Evlute without clcultor No Decimls! cos 0 sin 0 c tn π d cos π e sin π f sin π g sec π 6 h sin i tn j cos If cosθ = 5 nd θ is in qudrnt II, Find ll the remining trig functions Which of the following epressions re identicl? (circle ll tht pply) 5 Which of the following epressions re identicl? (circle ll tht pply) 6 Solve ech of the equtions for 0, sin cos c cos 0 d cos cos 0

7 Properties of Logrithms: KNOW THESE IDENTITIES WITHOUT A CALCULATOR: ln(e ) = e ln = ln = 0 e 0 = 7 Evlute A log 7 7 B log C log 9 D ln e Epnd or condense: log log log log 5 Solve: log log log 0 log log 9 ln() = e 0 = ln(e f() ) = 5 e ln +) =

8 Essentil Grphs 6 For ech grph, show two key points (lel coordintes) nd sic shpe of the grph f f c f sin π -π π π - - f d e f f f cos π -π π π g f() = e h f() = ln()