Math 2 - Precalculus Algebra a r ,n a rrrrlrrrra ,n^Dr E!il,re

Name K EYFINAL PRACTICE PROBLEMS I I/,/

Solve for w.aJ,

I ) m=-w'+twL2' -(

Nty)ft) wao _,,.f,f77

o = lru*+ \fw - )nn-J

^--)) b-4't C=-Irr4r _ e7

2) a) Find the equation of the linp connecting the points (:,-f ) d. 1-2,51.r .:- -*" -*-r\ PVt:ltle l"l{, r* {r tr n*1,

b) Find the equation of the line perpendicular to this line that goes through the point (tZ,-Z).frt lt

4t*w

-tttm;'tr= 2̂

J=-L-w +

S1r_

5

tt --l

:-l+

)Y-TL :J -)_Simplify the expression completely.

E(r-w)Vnr --\b

6;1",* [ ( - ]*ul

cs[ar-^r(3

4{u

+(t-r)?'

4) The height of a pole vaulter is approximated by the function

H(t1= -2t2 +32t -110 where n (t)>0 and r 2 0 is the time in seconds.

a) How many seconds did it take to reach the maximum height?

tt

Sketch the graph below.

H(0 / ,;\ Y -Va{-^^q Vertg(

Y srcb) What was the maximum height reached?

t( -r =

zeros. Then sketch the graph below.

Puss',6* "ants

'- H2, il, t Yrt 3, Wt b (

->l I 0 'q -'l la) -e 1 ro -ta

-

| -L-; (" o33

ltD-k

tl-L Ole

k(-) =-l[r)*+ a;{r) - rrb

= - fly 4 Lbb -lt}

c) How many seconds did it take for the pole vaulter to land on the ground after reaching the max height?

0 = -2ta+\tt-l/ttp= _+(tLtat+5r)5a\o = (-,, 1(t-f )

Write as a product of linear factors and frnd al| the

5) f (*)=-2xu +18xa + 8x3 -24x2n -x' {L

kt)= -rf(**-qf-,f* *.l})

1("\ '- -J.'(**t) t"-tYr-r)brust [t ],-)v,{,nt}, gj-*$*

6) Findtheinverse of f(x)=(x+:)'for x<-3. Verify f(ft(x))=.f'(-f(x))=x. Graph /(x) and

.f-' (*) together on the same graph.

i:.1

=-F(*.r\-)? x +3-9

g,!-,(r" i L^L = fu-)) I^ l-

ep"

/,

ft/li

l "JtL,Yr1 <)

= ---9- :

n-lrf

-z3 0,t+

I =Y t-/ /Sol-ve this equation for x. Write exact an3wer and as a decimal to 3 places.

&rl*'L*v.hl = 7,1^C -#**

l-,0^ (,'3/"^/Q

+yl^ , rZ/^C=-xlA-'.n*/L r(?ht,

4 =:bt"-l*t-2 J!^L f !4" 2-

39^G-\a^"2 lnstb -W!^7* ?x.

e*ockSolve this inequality and express solution in interval notation.

s) *.* Lc\ : :(*-rYr-i)-/t:--

(sa)t - +,8)\-or+_,- *-r)[x_4

3k-A -s{v->\ ( t

_ _+___

.&-,.#f 'o \I

t{-q-}r t{ /'--

-

<o JlcD

/ ' /l

a,

r)

,,-\-

4Ll5-

]2.11,r\ X =l-5 tK+ ) r6

o

{+

F)

x5 -,ffi'o{k-ike

e) Find the zeros of /, express f as aproduct of line4r factors, and sketch the graph below.

f (*)=x'+xo -6x3 -l4x'-llx-3 .- "f n

l-t 5 -3 0*( Ag ht{-t x= 7r, a *"{-f,'fl

-l-t-l

-0 A_

K +)-

I -L-3 o3

o

--(

3

Simplify any complex fractions.

Sketch the graph of f (x). Include V.A.'s, H.A. or O.A., H.A. or O.A. intercept, x-intercepts, and y-intercept.

,2+x-12 _ [rt(tr/r.-:\il) "f(*)=? -- L>ri-.-i +t Ktd \,r,t[fr5ug1 <"( /A

LaDtr r=i v ,:i-

(u,-o)

10)

-1 [.1** alvrsro."..J

tSaL-x-l)

@-

3= x--l

&{.-D=*1rr:-frrr=&l,t

- [>-(l

o

6'h i,,*

*1

[ry) ,-r =#(q)

("*{rr) : x1x{)_ 4

't^-,[At"'U {;+h

€u,{,(e,o)

, -4vtv*{

a=V-r r=ftr-t

K =*/*L{v-5

(**s\kr,)=-O

={)

L,.t

,ffiffi;fr,*,

Solve.

13) log(a-x)-tog(zx+13) = loe(x+8)

{-r ={srt{*r*t|){/Lf'=2,r'* J?rr /o{

-4rk +y -f

.?t)r

r6?

,{dtdtIt ) x*

ryffi'=Y+Y(ff C = J*r*% ?Jr P{uo

3f *' 4{" e+ tf r s= €a)

o *-fx +lofr"f)

{or^+{v - fi

X=X,-7

\ =-

(;r-3ri)<x**rX

Solve. z-;;;"" rorr-ffi+rog(3 -2x)=1

tll*n*t tu3[ur) =t

b4v = 1{:*C +(r

,&)rJ*{p'fi

r3A*

)sr%J o* 3) -

Solve. ^Wls) (zfe,.6+log, x'-tog, (z-x)=2

[,1, J\ + lryr*1t ry, {:*r) =a

['1,'t*,1'-o) =2

@#'T{q)

J+,\?r-l(=o

J*l = l* -?1tTv-tV *''h odr ,-q

fzX =L,

t'6ffi) --'e'-3{. + b)=6

\" -- 4?n d^= 4y1-

16) Find the focus, directrix, and focal diameter of the parabola, *l (.,.n its graph.

a) x = -4y'

) r="#

a) t_*t_=,'49

', b,fi) , (tho)

.x2v'a) -- -!-=7'25 9

rlar4tcqa : (J E.)

"s1*phts - \= t?f

LtQ

b) x2 =3yrl ^ ,1P, - v=7

verleK, (O,o)

'1=-+

c)

Y=-;

6',ifr1

b) t{ry'-,)=6)i,f -f,= |

Verrhcsd " (O,t-q ^ J l.'t

Fa

vrn l1y : (O,o\

$",a ,(-t,o)

*Ir**rix i x =h

&r.* . [0, t)J.irr*r1y

,V17) Find the vertices and foci of the ellipse, and its graph.

b) 4x2 + v2 =16, G i6Gt'.ff=l

venttcpz . (0,>1) ,@,o\$,zci : (o, frrI?)

I ' (o,eG)

E 6,-rre) 5:(o'+G)18) Find thb vertices, foci, and asymptotes of the hyperbola, and sketch its graph.

A*'+5-y'=3L7otu30rC*#=l

b5m4\6r

- t. ' \ve*tay; (Ltb,o) )

fu c' : (tt, o)

\\Et-r-o.

u,frvu' UtD,r)(,.. '(0,*)G)*Y\,; L; .("*,")j))-tr

rTr I . llE .-

ac'1h^pLt s :r.j = *$f t f0"?lr *rkt), 3=r; =iDlt

r\[*8,u)-el'F i

Solve the following systems of equations Algg@plly.

-,*z , ,,2 -1e ":&S"? u'-?t'{ +f =o: Ylfj

19) 2x2 +f = 13 '1\-*r> J

nbsr*,fi rxl:t--\ ( ' (" -4(u --t) = o

\i-ff ) u=t t,t= I

Jx{+f(p 4K I ' k-t. ,t\gf.&**

ftiro'ffi{=,,fl / #^fuI I I L,.-Ji i--% |

(x*A, *da)

[*t ,rq)\*/ ,/

rtz-&,tl- =('t / Jer{-[ yx*ttb >o

*{r 4 *qr\ r\'2*2 -'rr2 - 2120) * t>:

,u*k#'{ r*r7l;7*S =: )

(s, a)

Y^- ff*)'(/-**- 4f 4\

lq{:

x2 +2y2 =16

4x2 -y2 =24 -12r)

nAd&rn

7-tb - !97/1a'n

v'

-r'{ft)

-t- 2t lottvleJ)

x

fxtuL{ P

^_ 4!l'lr 1t'l *'= bj-Tq

'-f-{qE3K=!

Ic\t(+

€)

o)l

I

Graph the system of equations, and then solve the system algebraically to find the exact points of intersection.S..icii'&

,r)o;=-"q} -) f= q1o Teqy;- If* trc,1t[rrtr,

-4')X=-9 tr =d

23)

x --J**'J'

fr {-t)+r

{= y' -2y4

Y=7-1

(,x1o

O=Oa-

1=1-"0

K >C2

++t ,H+f

+/A.n t(r\ = y -{t]

)<+t =(q-t\*

1o):'x=4{

x*\ -- nLGx*4

' o , *u-**nloo =(r.-q[Y-])

Vn*,V'= x' -6x+9

laq)

a=F-, tf :tr ,;=-_i

(zr)Cr, l)

ctl(^e{o?s)

.fu,ne-

x2 + v2 =10,&x?/*"+)L'o

*L rt,{x +{ =t o' -[o -t0s-a*&+( v -Q 4

*(*& rr -r) 4(x * r\/t*,) =">

'{ ={

3=3

Word Problems

26) Find out how long it takes a $3200 investment to double if it is invested at 8o/o compounded monthly.\r,

r+l I

n)-

00t

Round

L* N=

T?= PT*F^ -t/- -\

27) The formul a A = 265e'o"' models the population of a particular city, in thousands, / years after I 998.When will the population of the city reach 457 thousand?

29) If Emery has $1500 to invest at 12Yo per year compounded monthly, how long will it be before he has

Jc{ 2-G;

o,^ +* = -b*o,tl tYTGS/

NWw5{a.071

L-ptavvr.) lrr )_

Pe(. E )*' ,

30) Cindy will require $19,000 in 4 years to return to college to get an MBA degree. How much moneyshould she ask her parents for now so that, if she invests it at 9o/o compounded continuously, she will haveenough for school? (Round your answer to the nearest dollar.) j- - p^ r \-- f y-^\ r to the nearest dollar.)

fu = P* .?

[1rd=?g(,rnrd

# /Z);r,yf,o -)W\ - €o'Tb11, ooo =-

c''6

31) The Feldmans bought their first house for $17,000. Over the years they moved three times into bigger and

bigger houses. Now, 41 years later, they are ready to retire and want a smaller house like the first one

they bought. If inflation in property values has averaged3.l% per year during that time, how much willt_

k = Pu"'

v.# bo 5?f,ctaA culture of bacteria obeys the law of uninhibited growth. If 140,000 bacteria are present initially and

there are 609,000 after 6 hours, how long will it take ion to reach one million?

tr d. tr- trJ =}.i,e ot -.hl =AL

o"?{;t

K.b I - ' 'Q Y- *--*r o_"qrtg--w< r tzh/,^,t\ ltJnruvrf/,6ut,6(p =t.to trto I ',/",*"{*b tL I 14 a, oatt

{^ffi =ry:: j_ L^# = /,;Lv,:^ 0 o"( rv\ 14

g, cd, hu(" tv -rt'\ - I L' - o'a45I

33) The amount ofi certain drug in the bloodstream is modeled by the function y = yoe-oo'', where yo is the

amount of the drug injected (in milligrams) and t is the elapsed time (in hours). Suppose that 10

milligrams are injected at 10:00 A.M. If a second injection is to be administered when there is 1

milligram of the drug present in the bloodstream, approximately when should the next dose be given?

34)

f = W *- ,+6 * 5$ l"'r =SArs'1fi*',Assume that the half-life of Carbon- 14 is 5700 years. Find the age (to the nearest year) of a wooden axe

in which the amount of Carbon- 14 is 30% of what it originally had. l=-** . ^^:;,-00u1

^ T1

,\ E;/ k/

N t+) =/Jo €LT

rsrS t/^^57oo

/-ek N = *Y, L& /V= -3N, b{")

= 1769, b3

yft ulil

N{= Ail "r(rw)tr" nl,

;*fu*ek

./^ rs.3

*oefl).L*Ld-

l0

lo 3 oo

b i(5ffr

;5M= $?'-*"'x/n.l = Wo'octoDx{

f"=