2008 Exam - Georgia Southwestern State University

STATEUNIVERSITY
GEOBGIASOUTHWESTERN
TOURNAMENT
MATHEMATICS
TESTBOOKLET
2008
There
examination.
40-problem,
multiple-choice
Thisis a 90-minute,
INSTRUCTIONS:
qne
question
problem.
the
possible
You
are
to
select
(5)
or
responses
to each
arefive
(l ) "best"answerto each.Youmaymarkonthetestbooklet,
andthe backof each
you
pagemaybe usedfor additionalwork
aresureof youranswer,circle
space.when
theletterof thechoiceyouhavemadeonthetestbooklet.Afteryouhaveworkedall
problems
youcanwork,transferyouranswers
to thescoresheetwhichhasyour
theblankbelowtheletterof your
studentnumberencoded.Darkencompletely
witha No.2pencil.lf youmust
boldly
Markyouranswers
response
to eachquestion.
eraseyourfirstchoiceandthenrecordthenewanswer.
changeananswer,completely
willbescoredas an incorrect
multiple
marksfor anyquestion
Incomplete
erasures
and
bytheformula40 +
response.Donotmarkbelowrow40. Yourscorewillbecomputed
I
represents
the
(4C- l),whereC represents
thenumberof correctanswersand
ruleoutat leastonechoiceit willbe
numberoI incorrect
answers.lf youcandetinitely
guessfromtheremaining
choices.Thereis no penaltytor
in yourfavorto randomly
problems
onthistest.
Youmavnotusea calculator
leftunanswered.
numberha!
Reviewandcheckyourscoresheetcaretully.Yourstudentidentification
beenencodedonyourredandwhitescoresheetandhasbeencheckedby our
atthetop;if
is inthe"l.D.Number"
section
marked-sense
cardreader.Thisnumber
youalterthisnumberin anywayyoumaydisqualifyyourselfand your teamfrom
lor any awards.
consideratlon
yourtest,bringyouranswersheetto theTestMonitor.Youmay
Whenyoucomplete
keepyourpencilandtestbooklet.Youmayleavetheroomafteryouhavehandedin
youranswersheet.
PLEASEDO NOTOPEN
TO DOSO
UNTILINSTRUCTED
compostbiD. He is consideng one
1 . FarmerCliett is plqnningto build a cubical-shoped
that is 4 feet o! earhedgeandonethat is 5 feet on eacbedge,The volumeof the tfoot
cubicalbin is about how muchla.rgerthao that ofthe,l-foot cubicalbir? (Choosetbe
b€st aosw€I.)
A. About 20%Ia.rger
B. About 4070larger
C. About 60%Ia,rger
D. About 8070la,rger
E. About 100%la.rger
Iu how manywayscao you ms.ke25 cetrtsusingsta,rdardUg coitr8?
A. 4 wayg
B. 9 weys
C. 12 ways
D. 13ways
E. 25 way8
;,
r- t.:
c atr(l;:
{r loelrp+q |E
A. 1
R
-20 -g-
c.;3
D.+
Era
A latber's age tod8y is three tioe8 that of his son. Twelve years ftom now, the father
will be twice as old 8s hir son. Wtrat is tbe sum of the ageoof the father aod sol today?
-
A. 60y€s.rs
B. 48yea.re
C. 36 yeErg
D. ,14yesrg
E, 75 y€ars
At the GSW CaoeeDeli, two sBLds ard a 'leggie lov€r' ss,Ddwichcost $5.25. Five
"veggie lovey'' saadwichesald tbee salsds cost $15.75, Wh&t is the coat for oDe58.lad
ead one saodwicl?
A. q2.25
B. $3.75
c. s4.25
D. 54.75
E. $5.00
Three tenuisballs are euuglypackedinto a ca,nthat is i! the ebapeof a ght circula.r
cyliader. Wlat ftaction of the volumeol the can ie occupiedby the tea.uisbals?
A]
...
?
8. 3
(1. 2
nl
n!
7. BK a.ndJC start from the sa,melocationat th€ sametine a,trdride their bicycleein
oppooitedirections.After 6 hours,they are 132milesapo.rt. If JC rides 2 mph faster
ths,EBK, s'hat is JC's speed?
A. E mph
B. 10mph
C. 12roph
D. 15mpb
E. 18mph
of the equstiol tl+t2+rz+T1
8. Wlat is the luEb€r of integta.lEolutioDs
q>L, rz>-2, tr > 3, a,!dt1 > 4?
A. 60
B. 56
c. 52
D, 48
E. 42
Page2
= 15for which
9. Which of the followiagis the leastpositiveintegern for wlLichnm > 13m?
A .6
8.4
D .9
E .8
10.If r4 ie the Eetof r".luesat whichJ(r) = 0 aod B is the set of vgluesat wbichg(t) = 0,
whichof the fotlowingddnes the set C of valuesat which /(t)9(") : 0?
A .C =A nB
B . C E A etdQgB
Q . C =A uB
D .C :A -B
E . C =B -A
ll. Ilow DEDyidegels from I to 1000are divisibleby 26 but oot by 20?
.
A. 12
B. 35
c.38
D .47
E. 50
L2. Wlicb of the followirg iE equatto sec(r)cot(d)siD'z(d)?
A. cot(d)
B. coe(d)
C. csc(0)
D. sir(O)
E. ta,n(d)
The solutions€t for the inequa.lity-1 2 ln(r) ie whic.hof the following?
A . e 3e
B ' o(!
C .0<c < j
D .0<rS e
E. Nooeof the ebove
Ps€e3
true? ? = lk-5)
14. For howma.nyvaluesof c is tbiestatement
A. l ra,lue
-ft
B. 2 va.luee
C. 3 va,lues
D. 4 va.luee
E. It is tr€vertrue.
15. How msoy times doeethe grapbof 3t= 04- 2xx+ a - 2 intersectthe t-axis?
4.0
c.2
D.3
E.4
16. m.ich oueof the followingis greeterthao1?
a
.!!
-€
n. ;t
a Ell9l
-
h(ro)
D .:
E.#
surmoudedby a semicircle)hasa pelimeterof 200itrc.hes.
17. A Norma,uwindow(recta,ogle
the
Tbe vertical sideof the rectalrgleDessu€sh irchee' Fitd a formulsthat represents
width,rr, of the adndowin termsof ft
A. ru= .io
B. q,= rP+-;/i
I
c. r= *i^
D '/-+#r
n . u =%L
Page4
18.SupposeC1 is a pexabola!,'hoseaJ<isof symmetry it paxallel to eithe! ihe ,-axis or the
g-a).is,atrdsupposethat C2is the paxabolay-- a2. Il C1and C2 are difierentpaxabolas,
what is the maximum number of points of int€lsection of the two curves?
4 .2
B ,3
c.4
D.6
E.8
1( |
Order the followi.ngfrom least likely to most likely.
,4: Rolling two fair six-sidedd.iceand gettilg I tota,l of 6.
B: Tossing3 fair coi.:rsaDd getting three consecutiveheads.
C: Tossing4 faL coins and getiirg exa.ctly2 heads.
A . A , B ,C
B . A ,C , B
c . B ,A , C
D , B , C ,A
E. C,A,B
20. ffiich one of ihe following is largest?
A. Ein(46')
B. tan(46')
C. cos(46')
D. csc(46')
E. sec(46')
2I, The figrue show! consists of a square adjoini4 two isosceleslight triangles. If the
diagooal of the squareiB 2\,/t, what is the combineda,reaof the tbI€e geometric figures?
A .6
8.4
c. 2./3
D. 3yE
E. v40
Page5
may be factoredas 25.34 53. I{ow manyperfectsquaresdivide
22. The number324,000
evedyinto 324,000?
A .5
B. r0
Q. 12
D. 15
E. 18
23. According to NCAA data, 52% of a,ll student-athletes$aduate: 55% of fema.legtudentathletes graduate aJxd48% of nole student-athletes $aduate. Wlat is the l&tio of the
uumber of male studeot-aihletes to the Dumberof female student-athl€tes?
"^34
R9
n2
-3
n!
/ !!l\
u(i, - ''L-.3
roro: ltr(i) - m(rl = ''"
24. Sorve
'
A . a =20
B . x :14
E . r:15
25. What is the pe meter of the heptagon ABCDEFG? Each triangle thown is a
trianEle.
A. 10
8.7 +\/1
c. 7+2 4
D. y'$-
8.2,/fr
Page6
ght
26. ln an isosceles ght triargle, one of the argles that is Dot a rlght angle measures9.
,-,.-^
^! E(r)'
6'uc u,
v ;44,
A. 1
B,A
D.,/5
E. Not euough information is giYetr
27. ll a 1y : 5 a.!d c3 + 93 : 100,what i8 4rcg?
A .5
R
29
-3
10
/r
v .T
D. 10
F,q
-'t
tdaogle basa perimeteroI48 c!0. The altitude io its baseis 12 cm. What
28. An isosceles
is the a,reaof the triangle?
A. 132cm2
B. 108cm':
C. 96 co2
D. 66 cm2
E. 54 cur2
29. The cardboa,rd6gures shown here a,refolded to make aumber cubeeof "dice." All four
"dice" a.retossedsimultareously. What is the probability that the sum of the numbels
showilg otr the tops of tbe "dice" ig 6?
.' '
lt
tt. ;
v , 6hl
Page 7
30. Wtich oDeofthe followilg trigooometricirnctioDsi8 a,! eveDfunctio!?
A . Y :s i n(o* '| )
B . g:s i !(c -i )
C .9=ta'E (t+tr)
D. y: cos(r+ i)
p. y =c oe(o-i )
.." ti---i
Jr. Jrmpulyla+fu,.
lllrl
ql
B . lE
60
c. llg60
D . rTFl
30
E. Eld
60
of c ia radiansif ve how that si!(o)+co6(o):f,a,nd0<o<$.
32. Fiadthe exactva.lue
^.ft
B .E
c .f,
NE
-3
33. Find the equatiotrof the Betof points, (o,g) in the plaoewhosedistsocetom the line
r: -8. is tqriceits dists,me&omtbe poirt (-2,0).
e. $+ $: t
5.fi -i l :,
c. $-,u d=l
u
id+r2L:
l
E.t-g=1
ord 9999consistof four distirct diSits?
34. How nany odd nunbe!8betw€€! 1OOO
A. 1110
B. 1720
c. 2220
D. 2240
E. 2280
PageE
35. Fild the €rect value of sin(arc"rin(|) - arcsia(|)).
r. &46
p .4
c' 'fi{6
n
!'/t-2.6
6
E.i
36. Iu how maoy poink does the byperbola (r + 3)r - (g - 3)'l = 9 iaters€ct the o a.ndgt
axes?
A. In a total of 4 pointe
B. ID & total of 3 poiqts
C. In a tota,l of 2 poiDtg
D. Iu a tot8l of l poilt
E. ID rc poiDts
37. Which of the followiug is the certer of the circle ihat pass€stbrough the points (0, -1),
('73,0),
aaa(-y'3,0)r
A. (o,o)
B. (0,r/2)
c. @,\f3/2)
D. (0,r)
E. (0,/5)
38. Trio circlesof radius r - I areshom. The cent€Eof eachcircle lies on the other circle.
Whet is the areaof the (shaded)regioathat lier insideboih cAcba?
A. r- li
B. (2r - ^/i)/4
a. @r-4^,fqq
D. (+r -3.'fql6
E. (61t- 4\fs)le
P"ge 9
the foci of the ellipseGS a rvlil' : 1
39. w!&t is the distancebetweeD
B. 10
c.,6 4
D.2,/il
8.8
40. Squa.reABCD hasa sidelelgth of 2y'5. ABF a.ndCDE a,reequila.teraltria.ngl€s'm8t
is the total areacov€redby thesetwo overlappiugtriaagles?
A .9
B. 10
C. 6\/5
D. 6+2\/i
E. L2- 2\/g
Page10