Keys to Success. 1. MC Calculator Usually only 5 out of 17 questions actually require calculators.


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1 Keys to Success Aout the Test:. MC Clcultor Usully only 5 out of 7 questions ctully require clcultors.. FreeResponse Tips. You get ooklets write ll work in the nswer ooklet (it is white on the insie) the colore pper with the question WILL NOT e seen y the grers. Eplin everything clerly c. If you re using justifiction/reson/eplntion from Prt A or B, use n rrow.. UNITS re importnt e. Cross out work tht you o not wnt to e re. Do not erse f. A justifiction is mthemticl eplntion AND/OR written eplntion. g. Do NOT use roune nswers in lter prts of prolem. Store these nswers in your clcultor. h. If you on t know something MAKE IT UP i. Even if you use your clcultor, you must show your work. Do NOT use clcultor jrgon in your work j. Be sure you hve nswere ll prts of the question. ** MC check nswers ckwrs (plug in the nswer choices) ** FR they re NOT in orer from esy to hr; however MC tens to e 3. Mke sure your clcultor is in RADIAN moe. 4. Alwys roun to 3 eciml plces, unless otherwise specifie.
2 (Mostly) Everything you shoul know for AP Clculus. Limit Definition of the Derivtive: f ( ) = lim f + h h h 0. Limit Definition of the Derivtive (Alterntive Form): f 3. Averge Rte of chnge of f ( ) on, 4. Averge Vlue of f ( ) on,]: f ]: f ( ) f f ( ) = 5. Intermeite Vlue Theorem:  Conitions: f() is continuous on the close intervl,, ]  Conclusion: There is vlue c such tht f c. lim f f f ( c) f or f f ( c) f n 6. Rolle s Theorem:  Conitions: f() is continuous on the close intervl,, ], n ifferentile on the open intervl (, ) n f()=f()  Conclusion: f ' c = 0 n <c< 7. Men Vlue Theorem:  Conitions: f() is continuous on the close intervl,, ], n ifferentile on the open intervl (, )  Conclusion: f ' c = f ( ) f n <c< 8. Etreme Vlue Theorem:  Conitions: f() is continuous on the close intervl,, ]  Conclusion: f() hs n solute mimum n solute minimum t criticl numer or n enpoint on, ] 9. Doule Angle Ientities:  sin = sin cos  cos = cos sin 0. Power Reucing Ientities:  sin cos =  cos + cos =. Criticl Numer: f hs criticl numer when f = 0 or is unefine. Incresing/Decresing:  f is incresing when  f is ecresing when f > 0 f < 0 3. Concvity:  f is concve up when  f is concve own when f is incresing f > 0 f is ecresing n f < 0 n 4. Reltive Etrem ( st Derivtive Test):  f hs reltive mimum when f chnges from positive to negtive.  f hs reltive minimum when f chnges from negtive to positive.
3 5. Reltive Etrem ( n Derivtive Test):  f hs reltive mimum when  f hs reltive minimum when 6. Point of Inflection  f hs point of inflection when 7. Funmentl theorem of clculus: f ( ) f () is the re uner the curve of f() f = 0 or is unefine n f < 0. f = 0 or is unefine n f > 0. f hs reltive etrem n = F F f () is negtive if the re is elow the is g( ) 8. Are Accumultion Functions: f (t)t To fin the erivtive: c $ $ 9. Volume y iscs (horizontl is): π r 0. Volume y iscs (verticl is): π r y g c % f (t)t' &' = f ( g ( ))g'. Volume y wshers (horizontl is): π ( R r ). Volume y wshers (verticl is): π ( R r )y 3. Volume y cross sections perpeniculr to the is: A( ) 4. Volume y cross sections perpeniculr to the yis: A( y)y ( ND FTC) f chnges signs. 5. Position/ Velocity/Accelertion (AB):  Spee is incresing when: ccelertion n velocity hve the sme signs  Spee is ecresing when: ccelertion n velocity hve opposite signs 6. Given grph of f n g() = f (t)t : The grph f is the grph of g f (t)t is the AREA uner the curve. 0 0 To evlute g(), evlute the integrl y using geometric shpes. 7. Derivtive Approimtions To pproimte f (c) f () f () f() e f g
4 8. Tngent Line Approimtions. Write the tngent line t the given point: (, f ()) y f () = f ()( ). Then plug in the point = y = f ()( ) + f () 9. Asolute etrem Compre the yvlues of the reltive etrem AND the enpoints. If there is only criticl numer then the criticl numer is oth reltive n solute etrem. 30. Prticle Motion  Position/ Velocity/ Accelertion PVAJ: o Position: (t) o Velocity: SPEED (t) = v(t) o Accelertion: (t) = v (t) = (t) o Spee: v t o INCREASING velocity n ccelertion hve the sme signs o DECREASING velocity n ccelertion hve opposite signs Initilly: t=0 At Rest: v(t)=0 Prticle Moving Right: v(t)>0 Prticle Moving Left: v(t)<0 Totl Distnce on, ]: v t Averge velocity on, ]: t () () Instntneous velocity t t=: v or = ' v( t)t 3. Derivtive Formuls c ] = 0 ] = f ()g() ] = f g' + f ' g f (g()) cos g' ] = f ' g( ) ] = sin csc ] = csc cot ln ] = tn ] = sec rcsin ] = c ] = c f () $ & = g g() % e f '( ) f g( ) c g' $ = cc $ = e sin cot ] = csc ] = cos sec ] = sec tn rctn ] = + 3. Integrtion Formuls = + c n = n+ n + + c = ln + c e = e + c sin = cos + c cos = sin + c tn = ln cos + c csc = ln csc + cot + c sec = ln sec + tn + c cot = ln sin + c sec = tn csc = cot + c u sec tn = sec + c csc cot = csc + c = rcsin u + c u = + u rctn u + c u u u u = rcsec u + c
5 BC TOPICS 33. lim + & % ( $ ' = e 34. Integrtion y prts: uv = uv vu 35. Arc Length of f on, ]: + f ' 36. Vectors  Position: ( t),y( t)  Velocity: ' ( t), y' ( t) ( ) (, y'' ( t) )  Accelertion: '' t  Spee (or mgnitue of the velocity vector): ' ( t)  Distnce trvele on, ]: ' t y = y t t ( ) + y' ( t) y = + ( y' ( t) ) t y $ & % t 37. Polr = r cosθ y = rsinθ  Slope of polr curve: y = y θ θ  Are enclose y polr curve on,]:  Are etween two polr curves on,]:  Polr Arc Length: r + r $ & θ θ % 38. Bsic 5 Mclurin Series n n+ r θ ( R r ) θ e n = sin = cos = n ( n +) = ( ) n n+ n rctn = n + ( ) n n ( n) 39. Lgrnge Error Boun: f n+ ( z) c ( n +) n+ 40. Alternting Series Error Boun: st neglecte term
Instantaneous Rate of Change of at a :
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