Math Exam and Answer Key
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8/3/2019 Math Exam and Answer Key
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tafi 1010 bram #2 J$ame:EaIt 2011
Graphu the ineguality: 5y 5x
Solve the equation : 12- 5"1 = -12
3.) Let r(")
- lzr-4
r(*) :- e(*).
1.)
2.)
and g(")
- l+5"1 . Find all values of x for which
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6)
1.1 Sohrcfte lrrcquaffiry -5<4r+l<3 ild grryhfiesdutbn set-
5.) Solve ffle irqualtty' 1(3x-l)-5 26r-4(3-r) and urite the solution as an
interval.
Factor 45y3x2 -5y*o
Factor: 9yt -72
8") Sofue - 2x3 +2lx - -L7x2
7.)
9.) Sohrc fiZr-{<ll ard write the solution set as an interval.
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10-) Solre ffF ilrequalrtf 3r-3>12 or 4x+6>1 (Graph ffre solutiffi set ard
wrib the sohrtion usittg interval notation.)
11.) Letfl = {-2,-1 ,1 ,0,4,6,8,9}, B = {-3,1 ,2,6,8}, and C = {-2,-4,A,2,4,6}find(arrc)v B .
12.) Solve lZ*+31 -5 >6 and write the solution using interval notation.
13.} Factor yt + 5y' - 4y -2A
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14-) U\rtrat b the dornain d ,f(r)- f -5 ,12 +16
-
15.) A rectangular gard,gn is 25 m longer then it is wide. lf the garden is to containan area of 7500 m', what are the dimensions?
Bonus: Solve the systemfz
1l=x13 2'{
I 1x+ 3v -3lz r'
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M. ath 1010f a:- - 2i::
Exarm #2 key Narne:
nct
Solve the equation: l?-5rl = -12
No solution because absolute value is never negative.
3.) Let f {*) _ ltx-tl and e(*) _ l+ s*l . Find all values of x for which
r t")You are looking for where the two graphs intersect. Therefore, set them
equal andsolve.
lZx - 1 | = 14 - Sxl there are two cases!
divide by 7.
4+5x3 = 3x now d ivide by 3
2.)
iase 1 2x-1=S -5xSin-piirving gives 7x = 5 now
-;{-/J
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S3'i**''p, f€ n,g:elq.6,fiir[* -j < i--,, - I < j &nro g€p,h -inig so;.,iiilo,n sgt
isc,iate x lm ilne rr't#ddle S'lbtmd -l[frrc r ell
A -ji ^^.b LiiES"
-5<-[x-l<] +
each side by 4 +
-6<-[r<] nowdlvftde
-6 .{.r 7
14.1
Don't need to switch directions ofinequality!
-3 I<x
Take out GCF+ 451'3xt - sJo'
squares)
5-r.tt {9-t" - rt) =+ 5,r-*'(3.1'- rX3"},' + Jr)
7") Factor: 9],t -72
as an
- t') look for special forrns (difference of
5.) Solve the inequality -2(3x - l) - 5 > 6x -1(3 - r) and write the solution
interval.
-2(3r "1) - 5 > 6r - 4(3 -;) + distribution gives
-6x +2-5 > 6.u- 17+4.r * collect like terms * -6x-3> l0x -LZNow isolate x. Add 3 to both sides and subtract 10x frorn both sides.
-16:r > -9 now divide both sides by -16, and remember to switch directions ofinequality.
e { e \x 3 - now write as an interval, ,r € i -*-: I16 \ 'l6J
6. ) Factor 45 7,3 xt - 5J**
- 5,,x'{g-rr'
- 72 - g(]'' - s) look for special forms (difference of cubes)
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lll.A
-.\.t-rt
'n't;
-':
---s+---?\- r '-
a +A|ii4ra-: b/r.{ar '.\d.LJ 3 g"
t/{r"F +. i '-: i'
Ar,
F
F
ZgrO 3,n 'C"ine Sr-dgl ,\g','* Fam0fi ]-anqg O;i
h;is':,u*: fe'dcr surulirer 2* 21 = 42. What are fadors of 42 whlch cornbine to give 17?
!2 = ''l ,+ n 3 and 14 + 3 ='[ 7 thls is the pairof numbers thatworks. Now rewrite€xpr"e$sncn repilacing 17 by that pair of numbers.
lr: - l7r -?l =+ 2.rr +l4x*3r+?t pair up first two terms and factor out 2x. Pair upsecond two terms and factor out a 3.
2.r: -14r+3r +?l = 2x(x+7)+3{x+7) now factor out the x + 7.
2r(; *7)+3(x -7) = (x+7X2;+3)
Therefore,
Now set each factor to zero!
x = 0 or 2x + 3 = 0 orx + 7 - 0 and solve each.
X = 0 Or X = -312 Or X = -l
g.) Solve lZr-31 <11 and write the solution set as an interval.
Since this is "less than", the 2x - 3 must be trapped between -1 1 and 11.
lzt-31 < l1=-11< 2x-3<ll now solve by isolating x in the middle.
-1 I S 2:'-3 < I I= -8< 2x <14 add 3 to all sides.
-t lr 14
l?2
1 C" ) Solve the inequality: 3r - 3 > 1? ot" 4x + 6 > -? (Graph the solution set and
write the solution usins interval notation.Sofve each lnequaliU:
:-:^-:l' ii--, li--+r':i
-.&'-<-a/
t. _i
t'q,[o'*$hliTjD'n EEon "Cf' ils the union.
rn'*'he: ':S Sn,&CeC? FfOm -2 tC ilmf;nity.-*'_
2x3 +17 x2 +?lx = 0 =+ r(zxt + 17 x +21) = o =+ x(Zr+3Xx + 7) - 0
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1l-l lxtfi= l.L t"l ,O,4,6,qgl, $ = {-3,1.2"6,q}, rld Q = {-2,4,03'46}find{'lncl-fr-
ffiinsnagm: AnC-t-L0,4,61 uffi&Aard C have h mnrnpn? (lntersection)
ilorr ur*rn iliswi& B- lhbn='or'
i-2-o4-6!, .r{-3,1.,?"6"E} - {-3, a.0,1* 2-4,6,9}
12"1 Solve lZ= * 3l - 5 > 6 and write the solution using interval notation.
SimpFfy by adding 5 to both sides!
lz* * 3l > I Irhis is "greater than" which means "extreme ends" further away from the
origin.
l2x+31 > 11 means2x+3> 11 or2x+3<-11
Solve each of these:
2x +3 > 11 + 2x > I + divide bV2+ x > 4
or
2x+3<-1 1+ 2x<-14+divideby2*x <-7
Extreme ends:
r € (-'rc.-7)
u'{4^ oc,}
1.t
!
(r.J
4*t-r:l;{6e
:J.
13-) Facttr _1,-=+ 5-1-= - 47,_ZA
Fqn brrls m palr-wlse factor! Pair up first two terms take out t' and pair up secondhobnnsatd talre 0ut4r-t *5J'-4r, -Zg=+ rlb-+s)- 4$1,+S)
lftrtare;(r5) + J,'(J,+5)-4{},+5}=(-u= -4}{}'+5} bok for special forrn
{ffidsqurm}+(l'=_4}tl,+5}+(y+2N,},-2}(:,+5)stop.
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