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StuwesantHigh School January 0084j. S. Teitel, Principal p1s.M. Ferrar4 Coordinator

MC1X Final ErarnCalculatorsare NOT permitted

Part I: Select hebest aruwer for al1questions-Record all alswer-son theNCS foro provided.Part is wortl 60points.

dvl. F:,nd fo r =4sin'(3r).

(A) 8si{3x) (B) 2asin(3x) (C) Ssin(lx)cos(3x) (D) 1:sin(3x)cos(3x) (E) :asin(3x)cos(3r)

2. A parliciemoves^alonghe x a.ds so hat at any ime r: 0 its position s givetrby

x( l ) - l - - Jt qr - L Forehar vatues f r i5dr epdrrrc le L esr?(A) no values (B) I only (C),r only (D) 5 only G) 1 and 3

- : . \ ' ! a t ; s l h e x c o c r d i r u t e o l t h e p o i n t o f i n l e c t i o n o f t h e g i a p h o f r = x r - 3 x 2 - 4 5 x + 8 1 t

(.{) --e (I}) -s (c) _1 (D) I (E)3

o . ( - r pF . se , r r \ : f y ' - 3 t i r cd l

a rhepo in , m - r r :

. ^ m 2 n ^ n - 2 m . ^ m 2 n _ h - 2 n _ . n + 2 m

2 m - n 2 n m 2 m - n 2 n - m-

2 n " m

,s. The valueof c ia theopen niEwal (0,4) ha!sahsfiesheMeanVajue Theo.em o. /(r) = .,[a -1-1 ;r.

(A)o (B ) : ( c ) : @)2 (E)35 J

;. The ride of a cubes expatrding l a coDstani:1teof 2 centimetaspersecond.Wlat is the rstantaneoEsate of cbrngeof th€sr.ufacereaof rhe cube,n cn7 persecond,when ts volume s 2? cubic ceDtimerers?

(A) 6 (B) 24 (c) 16 (D)54 (E) 72

7. fp(x) is a continuous]l]ctioll oB heclosedtrte.val1,3],wiihp(1) i K Sp(3)andc is n rhe losedntewal 1.3]. henwhichofthe tbllowing siat€mellsn]usrbc tsuc?

. p ( l ) p ( l ) , ( l ) - r ( l )r A ) p ( c l - r B l p { ) = : r - r . ' - f i F - . r , r " , c . ^ . - l a t u e c . s u c h U a l p ( c ) , K2 ' )

@) Thcr€ s onlyonc ,alue , suchlarp(c)= K (E)c= 2

I A particlemoves ra staight inc wi1h clcciv v(t) = 4 f fee!persecond.wlar js the otat islancehepanictedvets

be rween im e / , 0 nd r=3 econds r-^ j | f t 1u ) i r ( c )6 f t O l f r O f r .

9 lf /(i) =-2rr +6-r, then heabsolure arimum alue f ,t-r)on j, j]is:

(A)-.1

(B)-1

(C)16 tD) -:16 (E)The.e s no roa\imumvaiuer;-

. . J . r - l+ | | . t i l] C . l r m - e q u r t . r . \ i - . r , b r .

r . r - O r" '

f , o, - - j - 2 - r 2 : i

ti. lae lositicn of a.robj€ct:novmg along a srraight ine forI> 0 is gjven bV s1(r) = 1l aI, *U*eposjtionof a secondobj€ci

moving along he same irc is givea by s:(r) = i2 ffUor!ot"crs

begrn a! != 0. atwhat tmle $ rhedistance et.reen he objectsa

5 0ninimum? {A) 2 l?l 1

2:,c )

T(D)0 G) none of tirese

l: For r; 0, rhe slopeofthe Lange:tro I = rcosrequals zero wheneveri

l( , { )L r l i r = - . ! ( B ) t a n r - : ( C ) t a n r = ; @ ) s i n r c = , r ( ! ) c o s , i = j r

r . . f rcos(2r)-dr=q)+sin(4rr l -C et lcos' ( : r)-c (c) ls in(4/ . )+c, I J 2 " 8

rDt s:in(2r): + C (E)nonc rdese4

-1 t I . f . :r l r r - l ; a r - ( \ / - ' ( r I , : - a 1 g 1q r l ) : 1 t r - l ) ) + C

- 1 L J i

^ l r , 1 l, c ) : ( - r 1 ) r + ( r - 1 ) : +C (D)

; ( . r - 1 ) : . . C( I ) r 2 ( x 1 - : *6

. r . De t em met heva lueo f kso | l a t f( r ) i s conb rL rousont heen r i r e rea l t i ne * t .o t ( r )=J ' - 3 ' ' < -1" '

l 2 x k . x > - 1

i.\) -1 (B) -t (c) 0 (D) r G) 4

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