Pre-Calculus FjnglElgm by www.DumbLittleDoctor.com

$ Thts .'s a difH.af,,t exant, TLe unw* t{

(c) For 2u +3v, magnitude :

ctord a $o

l. (l points) arcsintsint*l) ' + has t, h G* ' *)'3-t2

(1 points) Change the degree measure to radian measure: o': L__7to-

To get full credits, show all riffiSary work. No calculators, closeif6xam.

(1 points) Solve for: lo9(0.00000001):

2. (3 points) Given u :<7,3 ),v :12,-1), perform the calculations for :

(a) 2u'3v= 1?,b)'16.-17 ? iz -tt -*L(b) 2u+3v: <2.6>f < 6,', > 2 <8,3 >

ffi",{W*{;t.

)(o"v+ 7=

zf,-

12.*t

)6o"

3. (4 points) Solve the equation: 1og, (x + 5) *logr(x- 5) -logz1O24

+ I-g^ # = &{, )'o Answer: x=A'5 J'

9 $ =',zt-\=/ tDrlX= Ef 5.to:f

.,- 5'toe5t\' ,or3

4. (5 points) Find the summation of the sequence: 8, 16,32, ..., 65536 (step by step).

J:t^/rbpottaa. 8,, &,2, &"t.1, ,-

? J+'s q jeorl.rLhtc Y*,drYlt tcrtt* 4r' 8, Y = z.

,\^rl^, lr^or,3 *vtru^, {L= t+ .

g !u"nt =Jrr ; al (.t:r:)PY

8, 8.2 , &"2', -

0. il- 2'v )

-d

l-Z

lrs-,///-^^

,6. 2' = 65i )6, t.8f?:

" r. frl

t@

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5. (3 points) Find the equivalent expressions for

cns' (arccntx) +sin2 (arccot x) : I

&ecoil, c,6t0* s,6'o=l

0

(3points) Find the equivalent expressions fo. t*lrirll' ,):---Y (step by step)

,Ar*ae, []rax= 0 (r) .rfup= X n<ed b f;"d a,* 5*tzr0.

t>.,r7r

8. (5 points) Solve the rational inequalities and leave the solution set in interval notation.:x -2012

(r-2009Xr-2010) > 0

=), I (X')o1z) { x-}osf ) c{'?'alo) ?r oII rY-)-oof ) LF-2Alo) +o Ldr.rcaittw\sr)

fiS fu r,Xh* fvta{e, ta*g = x

J.x1 x

7.

Jo 3J= *' JT:xt

(4 points) First the exact value of tanA. given sina = *! ^"a

afrfb tt" }..etf aSle -f.e,a^,"l^. (6

tu*, -l'"0,l+ t/<S^

?.o <2n . € Ov+r&*+ fl2

f .*.^ e t4an$<o

- -*,. @7,

a,)

4*rl >A

+

t+*

=) pxif,ilro- W, Lzalu?,zolo) lJ (eoiz,t&)/@

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9. (5 points) Solve the inequality and leave the solution set in interval notation:

Sol,rption: hrotice

fo X=-t i"l

(*$, -l) DL-t, +)

2x3 + x' -4x -3 < o.

d^ y.n".vf od&trr*W. Zf('tl.)='Z s. rnv.n 4 "n€ {3'l'r$' l-)>-2.

cDto w,*. a) zxl+x'-1-x-, ,cx+t) c>X'*x'l),.1 azX -,

=(X+r)(zX-r)LXa) r X+t /iXrixl+x-r4 | +nx'

-- -x'-*x-x"- x

-rx*),10. (5 points)Find and simplif, the difference quotient, [r+I9, of f (x) = x, + x -3 .

f uMmt,'

= :"yhth'+klt

= zyak+|.

tVtat

1 1. (5 points) Solve J*, - G = 2

=)' JE= zr'IiSlun* , )X-z : (z{,ti)'* ttl7a' tt'6

9 2X-( , 4,lX

=) Y-) =>&

4 Lx4)', t*X.

9 x'-bYi+f-+N?o

9 1x-t ) LX'to) *1 X*l rt \=lo.

bais +r- d,-"il" d*rk / ;t 7filart "t "rfu }'=i'

Y=l twr. foltrJ"'eJ t

$1,r* ryaitt

= '.|t+l) l{25-3,; < o.

+ drf,-]) so & (Y+l)'+".

4 x"3 kx=q,

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12. (3points)Findtheinverse f-t forthefunction: -f (x)=!.6rs':1. Answer: -f'(r)=sq r, g= *: ,5x-) 2

, . sg_)x: * 6

- ,y-)) zX= 6

+ la; zx= 5t4 ,

3 + \ozX----_5

13. (5 points) Write the equation of the hyperbola that has asynptotes ! : 2x - 5 &, y :and y-intercepts (2, 9) & (2, -11). t ^_L^. r \ e {ltf(c li+

+ j (g'.J.. JEl, .o 1 Le,r\tefll C 1;l )

I c --b,- -t + !gJlI-- (g, =tIa-"loo>5"( z-= 1'

a,*lo, b*5

14. (5 points) Solve step by step

n exokngx &9,

.lE, y.{ri^e -5," g ,

0 x2:

o- e,

b-2t 7J52

L{r,*iot.

3

[:

-t-)

=,

w

4

q.

0

0

(

23

?

LZ.

Pk tJfl) Le ih,k

@

@

2J.

I3-4

tl :- t5.

I

, 2 t *r,ralr

/;: o({x=rt $Gy'-F

5gg )+46zxe Y'ry-2x +3,

dSrrea(* t

twl

fot^r*rvlul.

l&1 o

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15. (3 points) Write a slope-intercept equation of the line passes through the point [t, - ]l *U\ L)

is perpendicular to 8x + 10y = J .

), Rocall:1turo ?evpcrJiS6, tiner ,\4!a sty rnr, ltlz, de^ mt= -k*.? Af,.M{4 tt"a- od^o,ri line ; loX-gJ = C. (swiiak w$*+et*1 & X k g ).

p6rs tf,-*). z) /o (5)-,.(-+/ :( = 5p t.rf, v/8 .

=),tex-3g,Ze + S"+\*f16. (3 points) Sketch the graph of the solution *"t to {*'

+ y' < 4 ttW

lY<x-z

17. (4 points) Find all real numbers that satis$r the equation cot 3x = 1.

9 r,rb tx= |

, )x= kr+x. ff+

x2 +x*37

krrZ.

Ee7

18. (5 points) Find the partial fraction decomposition forqbci-r ' xr)' ()frr)L

= 4(xtlt:+ bcx-zlcr+t/ tc f .t-L/

(X-:. ) (x+))r

(4.7-tZ

(x + 3)'z (x -2)

r,e. l>fX-)t

let X. z.t

l*, X*') i

let X= o.

ro ) a=-lq= $

t &LxtilL+, bcx-r-) tx+, )f < c Y,-z)

4*z-)l 2 $.L$to

Q-3-1, =-5c +-)l = ?o -bb -zC

= ? t-t) - 6b-xax-f I -r :

( I +l)'( x--) x-z xr-)

2.5 + b=Z

L5(It)) t

srb,

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t9.

Pre-Calculus Final Exam by www.DumbLittleDoctor.com

(5 points) For the function y = -tt cos(-?.* !) - 2 ,determine:

(a) (1 points) Domain : L-*, i a )

(b) (1 points):Amplitude : lC

(c) (l points) Phase shift:

(d) (1 points)period : )*l = I(e) (1 points) Range : {- f -^ _ - -^).

20. (4points)Prove the identity step by step: cscx - 1' z cot x .' cotx /'cscx+l

Needv tLu,\ (cscx-l )ccxa)lr*'x(=) cttx^, : c,^rftx

A0*,r.{ tru,e t, trmw

21. (5 points) Eliminate the parameter, and identify the graph of the pair of parametric equations:

(P *)'., i *1. (tr,s lurye puarwyeaf)

t,x,tf ) |.

x

Extra credit(2 points): 'rdrat's most memorable or fuony thing during the lecture or during thediscussion? (which you might still remember even when you are over 80 years old)

,:-5.[-sinr, !:5cosz/, -oo<l<@+ , X'- 4C t-ttnt]

e stw=t-S /Jr)*ce : t*'t I o*,+ =t

I

fk< insimxtat n\etuhVr-e4 ilwk , "' t{z;ilt*e|ra.8 is 4s4 p,76e | "

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