TO: Next Year s AP Calculus Students

Transcription

1 TO: Net Yer s AP Clculus Students As you probbly know, the students who tke AP Clculus AB nd pss the Advnced Plcement Test will plce out of one semester of college Clculus; those who tke AP Clculus BC nd pss the Advnced Plcement Test will plce out of two semesters of college Clculus. In order to hve enough time to lern the mteril of college-level courses, we will strt lerning Clculus s soon s possible when school begins nd will not be ble to spend time reviewing the mteril you lerned in Algebr, Geometry, nd Preclculus. Attched is summer preprtion for clculus. The mteril in the pcket should be mteril you lerned in Algebr II nd Preclculus. The purpose of this ssignment is to hve you prctice the mthemticl skills from Algebr nd Preclculus. Ech question ws crefully selected nd every one of the questions in this review is etremely importnt. You my use reference mterils to ssist you (old notes, tetbooks, websites, etc.). There is brief list of websites below but you my use others. The first prt of the review is no clcultor nd the lst prt will be clcultor llowed, which will review ll clcultor skills tht re necessry. There is lso formul sheet, which consists of formuls tht you need to know without reference. If you need clcultor, plese see emultor directions below. Websites for reference: Clcultor emultor: Downlod wbbitemu Run wbbitemu.ee Select crete ROM imge using open source softwre Select clcultor type (recommended TI-84 C) Sve ROM file A window should pper From Clcultor menu, select enble skin. Pin to desktop by right clicking

2 Converting Degrees to Rdins ngle in degrees ngle in rdins 80 AP Clculus Preprtion Formuls Converting Rdins to Degrees ngle in rdins 80 ngle in degrees Right Tringle Rtios opposite leg y hypotenuse r sin csc hypotenuse r opposite leg y djcent leg hypotenuse r cos sec hypotenuse r djcent leg opposite leg y djcent leg tn cot djcent leg opposite leg y Unit Circle Reciprocl Identities sin = csc = csc sin cos = sec = sec cos tn = cot = cot tn Quotient Identities sin tn = cos cos cot = sin Pythgoren Identity sin cos Logrithms nd eponents b b ln( mn) ln m ln n m n ( y) y ln ln m ln n b ln m p pln m b y n y n Point Slope form y y m( ) ln e m m n n

3 AP Clculus Nme: Mth Preprtion for Clculus All work necessry to rrive t n nswer must be shown. I. Grphing functions Grph prent functions, including qudrtic, squre root, cubic, rtionl, nd trig Grph piecewise functions Find the - nd y-intercepts nd the domin nd rnge, nd sketch the grph. No Clcultor llowed.. y. y. y 4. y e 5. y ln 6. y 7. y 8., if. y, if 7, if 9.. if, 0 y, if 0 0. y sin,. y cos,. y tn,

4 II. Trigonometry Evlute trigonometric functions using either the unit circle or specil right tringles (no clcultor) Evlute inverse trigonometric functions using either the unit circle or specil right tringles (no clcultor) Solve trigonometric equtions Evlute ech of the following.. tn 4. cos 5. sin 4 6. cos 6 7. sec 5 8. cot 6 7 cos 0. csc sin 5. tn 4 4. sec 4. cot 4 Evlute the given function for the given -vlue on the intervl 5. y = cos - (), = 0 6. y = sin (), = y = rctn (), = 8. y = sec - (), = 9. y = rctn (), =0 0. y = rcsec (), = undefined 0. cos. sin( ) 0 4. cos( ) 0 Solve the following equtions for.

5 III. Algebric epressions nd functions Write equtions of lines, given informtion Fctor polynomils Evlute functions Find the inverse of function ( f ( ) ) Mke connections between function nd its inverse function Evlute compositions of functions Apply properties of rtionl eponents, including evluting rtionl eponentil epressions Apply properties of logrithms, including epnding nd condensing logs Solve polynomil, logrithmic, nd eponentil equtions Find ll verticl symptotes, point discontinuities (holes), nd horizontl symptotes of rtionl function Simplify rtionl functions using ddition, subtrction or lest common denomintor Solve rtionl equtions Find n eqution of the line with the given informtion. 5. Pssing through the point 6. Pssing through (, 8) nd (0, 5) with slope of. prllel to 5 y Find n eqution of the line perpendiculr to y 9 pssing through (4, 7). Solve ech eqution by fctoring completely If the grph of f () hs the point (, 7) then wht point will be on the grph of the inverse ( ) f? 45. Eplin how the grph of f () nd compre ( ) f. 46. Find the inverse of the function f ( ).

6 Let ( ) 47. () f nd g ( ). f 48. g ( ) 49. f (t ) 50. (g( )) f 5. g ( f ( k)) 5. g ( f ( m )) Let f ( ) sin( ) f 55. f 56. f Simplify or evlute ech epression ) ( Use properties of logrithms to simplify ech epression. 6. 9ln e 6. ln8 e 6. ln 64. ln e log ln log 4 ln log 68. ln e Epnd ech logrithm. 69. ln y ln 7. ln 4 y w y w Solve ech logrithmic or eponentil eqution. 7. ln( ) 5 7. ln 5k, (k is constnt) 74. e 7

7 Find ll verticl symptotes nd point discontinuities (holes), if ny eist. 75. f( ) ( ) 78. ( ) f f ( ) 4 Find ll horizontl symptotes: 80. ( ) f 8. f( ) ( 5) f( ) 8. ) f 84. ( f( ) * Remember Solve or simplify ech rtionl function: ( h) 5 h ( )( 7) 0 or undef

8 Clcultor llowed: Grphing Skill #: You should be ble to grph function in viewing window tht shows the importnt fetures. You should be fmilir with the built-in zoom options for setting the window such s zoom-deciml nd zoom-stndrd. You should lso be ble to set the window conditions to vlues you choose.. Grph y using the built in zoom-deciml nd zoom-stndrd options in your clcultor. Drw ech.. Find the pproprite viewing window to see the intercepts nd the verte defined by window editor to enter the nd y vlues. y 0. Use the. Find the pproprite viewing windows for the following functions:

9 Grphing Skill #: You should be ble to grph function in viewing window tht shows the -intercepts (lso clled roots nd zeros). You should be ble to ccurtely estimte the -intercepts to deciml plces. Use the built-in root or zero commnd. 4. Find the -intercepts of y. Window [-4.7,4.7] [-.,.] 5. Find the -intercepts of y. -intercepts: Grphing Skill #: You should be ble to grph two functions in viewing window tht shows the intersection points. Sometimes it is impossible to see ll points of intersection in the sme viewing window. You should be ble to ccurtely estimte the coordintes of the intersection points to deciml plces. Use the built-in intersection commnd. 6. Find the coordintes of the intersection points for the functions: 7. Find the coordintes of the intersection points of: f ( ) 4 nd ( ) g. Intersection points: Grphing Skill #4: You should be ble to grph function nd estimte the locl nd mimum or minimum vlues to deciml plces. Use the built-in m/min commnd. 8. Find the mimum nd minimum vlues of the function y Find the mimum nd minimum vlues of the function y Find the -intercepts, reltive mimum, nd reltive minimum of y.. Find the coordintes of the intersection points for the functions f ( ) 9 nd g( ) 4