gs1m

CE GREAT MINDS PREBOARD PRACTICE MATHEMATICS, SURVEYING, AND TRANSPORTATION ENGINEERING

INSTRUCTION: Select the best answe !" each "! the !"ll"w#n$ %&est#"ns' Ma( "nl) "ne answe !" each #te* b) sha+#n$ sha+#n$ the b" c"es-"n+ c"es-"n+#n$ #n$ t" the lette "! )"& ch"#ce ch"#ce "n the answe sheet -".#+ -".#+e+' e+' STRICT/Y NO ERASURES A//O0ED' Use -enc#l n"' 1 "nl)' 2'

The bases bases "! a #$ht -# -#s* s* ae -enta$"n -enta$"ns s w#th each s#+e s#+e 3 c* l"n$' The bases bases ae 24 c* a-at' a-at' 0hat #s the ."l&*e "! the -#s* #n c&' c*5 a' 674 b' 891 c' 786 +' 837

1'

#n+ the the aea aea "! the e$#"n e$#"n b"&n+ b"&n+e+ e+ b) the c&.e c&.es s ) ; 21 < =1 >4? , the @a#s ,  ; 2, an+  ; 4' a' 4 ln 3 b' ln 14 c' 3 ln 26 +' 3 ln 4

'

A e.ese+ e.ese+ c&.e "! e%&al a+## a+## c"nnects c"nnects tw" -aallel -aallel tan$ent tan$ents s 21 *etes a-at' a-at' The len$th "! the ch"+s !"* PC t" PT #s 249 *' Dete*#ne the a+#&s "! the c&.e' a' 417'3 * b' 498' * c' 48'6 +' 487'4

4'

It #s the st&+) "! a ta!!#c beha.#"& beha.#"& nea nea a ceta#n ceta#n sect#"n sect#"n whee +e*an+ +e*an+ ecee+s ecee+s +e*an+ +e*an+ ca-ac#t)' a' &e&e#n$ b' Est#*at#n$ c' Chaacte##n$ +' D#st#b&t#n$

6'

A s-#al s-#al ease*en ease*ent t c&.e has has a len$th len$th "! 89 *' an+ the a+#&s a+#&s "! the centa cental l c&.e #s 199 *' Dete*#ne the *a#*&* .el"c#t) that a ca c"&l+ -ass th"&$h the s-#al ease*ent c&.e' a' 81'4 (-h b' 73' c' 82'3 +' 7'3

3'

P 199,999 was +e-"s#te+ +e-"s#te+ "n an 2, 288 at at the #nteest #nteest ate "! 14F c"*-"&n+e+ c"*-"&n+e+ se*#@ann&al se*#@ann&all)' l)' H"w *&ch w"&l+ the s&* be "n an 2, 25 a' P 312,729'99 b' P 321,297 c' P 312 279 +' P 317 229

7'

In h"w *an) *an) wa)s wa)s can 29 "bec "bects ts be es-ect#.el)' a' 116 b' 99

SITUATION 2: Acc"+#n$ Acc"+#n$ t" C"ns&*e D#$est, D#$est, !"ll"ws: A+< be+""* Ch#l+ be+""* O!!#ce " +en Othe be+""*s Othe ""*s 8'

'

s-l# s-l#t t

#nt" #nt" tw"

c' 179

$"& $"&-s -s c"nta c"nta#n #n#n #n$ $

4

an+ an+

3

"be "bect cts, s,

+' 129

the -"bable l"cat#"n l"cat#"n "! -es"nal c"*-&tes c"*-&tes #n the h"*e as

9'9 9'26 9'49 9'24 9'18

0hat #s the -"ba -"bab#l# b#l#t) t) that that a PC #s #n #n a be+""* be+""*5 5 a' 9'38 b' 9'1 c' 9'49

+' 9'41

0hat #s the -"ba -"bab#l# b#l#t) t) that that a PC #s n"t n"t #n the the be+""* be+""*5 5 a' 9'38 b' 9'1 c' 9'49

+' 9'41

29' H"w *an) l#tes "! -&e -&e alc"h"l *&st be a++ a++e+ e+ t" 9 l#tes "! 19F alc"h"l alc"h"l t" "bta#n a *#t&e wh#ch #s 49F alc"h"l s"l&t#"n5 a' 8 l#tes b' 3 c' 21 +' 29 22' R#.e R#.e #.e s-ee+ a' 16

A !l"ws at a ate "!  (-h an+ #.e B at 2 (-h' It ta(es the b"at b"at t" ta.el tw#ce tw#ce #n A !" a +#stance "! 28 (* than #t t""( the b"at t" ta.el 29 (* #n #.e B' C"*-&te the "! the b"at #n st#ll wate' (-h b' 12 c' 28 +' 21

21' The s#+es "! a s%&ae l"t ha.#n$ an aea "! 1'16 hectaes hectaes wee *eas&e+ *eas&e+ &s#n$ a 299 * ta-e that was 9'94 * t"" sh"t' C"*-&te the e" #n the aea #n s% * a' 23 s% * b' 28 c' 19 +' 11 2' "& *#l( *#l( cans ae b&n+le+ b&n+le+ t"$ethe t"$ethe &s#n$ a -#ece "! st#n$' I! )"& all"w 6 c* !" t)#n$ the (n"t, what #s the sh"test a*"&nt "! st#n$ that )"& nee+ #! each can has a a+#&s "! 4 c*5 a' 31'21 c* b' 72'1 c' 84'66 +' 9'21 24' A ectan$&la ectan$&la b#n , "-en at the t"- , #s e%&#e+ e%&#e+ t" c"nta#n 218 218 c& * ' I! the b"tt"* #s t" be a s%&ae at a c"st "! P 1'99 -e s%&ae *ete , what +#*ens#"ns w#ll *#n#*#e the c"st5 a' s ; 4 , h ; 4 b' s ; 8 , h ; 8 c' s ; 8 , h ; 4 +' s ; 4 , h ; 8

26' C"*-&te the ba(#n$ +#stance !" a ca *".#n$ at an #n#t#al .el"c#t) "! 39 (-h an+ a !#nal .el"c#t) "! 49 (-h' The sl"-e "! the "a+wa) #s >6F , C"e!!#c#ent "! !#ct#"n bet' "a+ -a.e*ent an+ t#es ; 9'26 , an+ Pece-t#"n@eact#"n t#*e #s 9'76 s' a' 7'66 * b' 2'26 c' ' +' 4'66 23' #n+ an e%&at#"n "! the l#ne th"&$h =2, @2? -e-en+#c&la t" the l#ne   4) ; 29' a' ) ; @4 >2 b' ) ; 4 @2 c' ) ; @4  2 +' ) ; 4 >2 SITUATION 1: " the ell#-se 4 1 > )1 > 8  1 ; 9, 27' #n+ the +#stance !"c&s !"* the cente' a' 1'76 b' 1'14

c' 1'63

+' 1'28

28' #n+ the *a" a#s , a' a'  b' 4

c' 6

+' 1

2' #n+ the eccent#c#t) "! the ell#-se' a' 2 b' 9'

c' 9'76

+' 9'6

19' The n&*be "! acc#+ents !" 3 )ea -e#"+ #n a h#$hwa) #s 641' I! the a.ea$e +a#l) ta!!#c #s 473, Calc&late the acc#+ent ate' a' 6491 b' 666 c' 621 +' 6122 12' A *a(s*an !#es at a ta$et 69 *etes awa) an+ heas the b&llet h#t the ta$et 1 sec"n+s a!te he -&lle+ the t#$$e' An "bse.e 499 *etes awa) !"* the *a(s*an an+ 419 *etes !"* the ta$et, neas the b&llet h#t the ta$et 2 sec"n+ a!te he heas the #!le e-ent' #n+ the s-ee+ "! the b&llet' a' 9 *
c' 24'39

+' 196'7

1' Calc&late the cental an$le "! the sec"n+ c&.e' a' 14 47J b' 18 3J c' 1 62J

+' 3 21J

14' 0hat #s the stat#"n#n$ "! PT #! PC #s at 19 > 641'19 5 a' 12 > 214'23 b' 13 > 314'22 c' 12 > 413'21

+' 11 > 223'42

16' A telec"*s c"*-an) has a !#e+ c"st "! P 269,999,999 -e *"nth an+ a .a#able c"st "! P 1999 -e *"nth -e s&bsc#be' The c"*-an) cha$es P 6 -e *"nth t" the# s&bsc#bes' #n+ the n&*be "! &ses t" *a(e bea( e.en' a' 269 97 b' 212 2 c' 296 69 +' 4 188 13' Y"& ae $#.en 8 n&*bes wh#ch a++ &- t" 238' One "! the n&*bes #s 18' #n+ the a.ea$e "! "the 7 n&*bes' a' 16 b' 19 c' 26 +' 29 17' #n+ the lat&s ect&* "! the c&.e 1 ; @21) a' 21 b' @21 c' @3

+' 3

18' In a #$ht s-he#cal t#an$le ABC , B ; 7 an+ b ; 2' #n+ the .al&e "! A' a' 3 c' 6 c' 6 +' 3 1' #n+ the n&*be "! te*s "! the se#es 6 , 8, 22 K "! wh#ch the s&* #s 2916' a' 19 b' 11 c' 14 +' 16 9' In a .ect" 1# >  > 3( , c"*-&te the an$le A wh#ch *a(es w#th @a#s' a' 34'31 b' 74'76 c' 7'4 +' 2 2' #n+ the *a$n#t&+e #n =9?' a' 3 b' 7

c' 8

+' 

1' A se#es "! n&*bes wh#ch ae -e!ect s%&aes #s calle+: a' "&#e Se#es c' E&leJs n&*be c' e*atJs n&*be +' #b"nacc# n&*bes ' I! a $"&- "! -"s#t#.e #nte$es has a s&* "! 8 ,what #s the $eatest -"+&ct the $"&- can ha.e5

a'

23

b' 7

4' C"n.et 1  4)  4 #nt" -"la !"*' a'  ; 1<=2@ s#nL? b'  ; 1=2@ s#nL?

c' 28

+' 8

c'  ; c"sL > s#nL

+'  ; 2 > s#nL

6' #n+ the a+#&s "! $)at#"n "! the aea #n the !#st %&a+ant b"&n+e+ b) the l#nes  ; 9 , ) ; 4 an+ the c&.e ) 1 ; 8 w#th es-ect t" @a#s' a' '36 b' '29 c' '61 +' '77 3' In h"w *an) wa)s can 6 +#!!eentl) c"l"e+ *ables be aan$e+ #n a "w5 a' 219 b' 48 c' 216 +' 14 7' The !#st c"st "! a *ach#ne #s P 2,899,999 w#th a sal.a$e .al&e "! P 99,999 at the en+ "! the #ts l#!e "! 6 )eas' Dete*#ne the b""( .al&e a!te  )eas &s#n$ sta#$ht l#ne *eth"+' a' 2,999,999 b' 99,999 c' 699,999 +' 469,999 8' #n+ the aea "! the %&a+#lateal ha.#n$ s#+es "! 29 , 6 , 24'24 , an+ 26 an+ the s&* "! the "--"s#te an$les #s 116 ' a' 226 b' 229 c' 296 +' 299 ' The s&* "! the nth te* "! a se%&ence #s $#.en b) S=n? ; n=n  ? ' Dete*#ne the nth te* "! the se%&ence' a' 1n@1 b' 1n@4 c' 1n>1 +' 1n>4 49' A tw" +#$#t n&*be #s ch"sen an+"*l)' 0hat #s the -"bab#l#t) that #t #s +#.#s#ble b) 75 a' 7<69 b' 2<9 c' 2<7 +' 7<46 42' #n+ the ."l&*e "! s"l#+ "! e."l&t#"n b"&n+e+ b) the c&.es )1 ;  , the @a#s an+  ; 4' a' 1 b' 34 c' 3 +' 218 41' A la++e #s -lace+ 69 * !"* a wall at an an$le L w#th the h"#"ntal' T"- "! the la++e #s  *etes ab".e the $"&n+' I! the b"tt"* "! the la++e #s -&she+ t"wa+ the wall, !#n+ the ate "! chan$e "!  w#th es-ect t" L when L ; 46 a' 1'6 *<+e$ B' 2'9 C' 2'76 +' 2'69 4' I! )"& ae #n.est#n$ the *"ne), wh#ch #s bette5 a' F c"*-"&n+e+ %&atel) c' F c"*-"&n+e+ se*#@ann&all) c' F c"*-"&n+e+ *"nthl) +' F c"*-"&n+e+ c"nt#n&"&sl) 44' A -aab"l#c c&.e has a +escen+#n$ $a+e "! @9'8F wh#ch *eets an ascen+#n$ $a+e "! 9'4F at Sta' 29>919 ' The *a#*&* all"wable chan$e "! $a+e -e 19 *ete stat#"n #s 9'26' Ele.at#"n "! stat#"n 29 > 919 #s 149'39 *' 0hat #s the len$th "! the c&.e5 a' 289 * b' 239 c' 249 +' 219 46' A b&s#ness*an b""we+ P 99,999 an+ a$ees t" +#scha$e h#s "bl#$at#"n b) -a)#n$ a se#es "! 8 e%&al -a)*ents "! P 6744'78 the !#st be#n$ +&e at the en+ "! 6  )eas' #n+ the #nteest ate he #s -a)#n$ #! #t #s c"*-"&n+e+ se*#@ann&all)' a' 4F b' 6F c' 3F +' 7F 43' A se#es "! -e-en+#c&la "!!sets wee ta(en !"* a tans#t l#ne t" a c&.e+ b"&n+a) l#ne' These "!!sets wee ta(en  *etes a-at an+ wee ta(en #n the !"ll"w#n$ "+e =#n *etes? : 1 , '1 , 4, '6 ,6 , 4'6 , 3 , 7 ' C"*-&te the aea &s#n$ S#*-s"nJs One@Th#+ R&le' a' 179'9 *1 b' 189'39 c' 19'6 +' 169'7 47' G#.en the e%&at#"n "! the -aab"la )1  8  4)  19 ; 9 , !#n+ the lat&s ect&*' a' 1 b' 4 c' 3 +' 8 SITUATION 4: "* the !"ll"w#n$ cl"se+ tan.ese+ as !"ll"ws: /INES 2@1 1@ @4 4@2

BEARING N 9 E N 78 E S 1 E @@@@@@@

DISTANCES 219'19 9'19 88'49 @@@@@@@

48' C"*-&te the bea#n$ "! l#ne 4@2' a' N 73 2J E b' N 73 2J 0

c' S 73 2J E

+' S 73 2J 0

4' C"*-&te the +#stance "! the l#ne 4@2' a' 193'9 b' 199'3

c' 199'3

+' 19'93

69' C"*-&te the aea #n hectaes'

a' 238'64

b' 283'46

c' 246'38

+' 263'84

c' 2

+' 1

62' #n+ the l#*#t "! the !"ll"w#n$:

lim ¿ x →∞

( )  y

2

+1

 y

a' 9

b' 

61' #n+ the #n.ese *at# "! the !"ll"w#n$:

[ ] 23 31

a.

[ ] [ ][ ] [ −13

1−2

b.

23

−11

c.

32

−1 1

d.

21 −1− 3

]

6' 0h#ch "! the !"ll"w#n$ state*ents #s A/SE ab"&t the -"ce+&e "! ta-#n$ h"#"ntal +#stances5 a' 0hen a l#ne #s t" be *eas&e+, b"th en+s *&st !#st be *a(e+' b' A stea+) an+ !#* -&ll #s a--l#e+ "n "ne en+ "! the ta-e +&#n$ stetch#n$ +e-en+#n$ "n the we#$ht "! the ta-e' c' D&#n$ the *eas&e*ent, #t #s #*-"tant t" +ete*#ne #n wh#ch the ta-e #s hel+ neal) h"#"ntal' +' In s"*e #nstances, ta-#n$ w"&l+ be +"ne "n a ha+ s&!ace s&ch as c"ncete " as-halt " #n steels "! the a#l"a+' 64' Tw" b"ats le!t the wha! at the sa*e t#*e' One sa#le+ #n the +#ect#"n N 9 E at 49 *-h' The "the sa#le+ +&e East at 16 *-h' H"w !ast wee the) se-aat#n$ at the en+ "! "ne h"& #n *-h5 a' 9 *-h b' 6 c' 49 +' 46 66' #n+ the t"tal len$th "! the c&.e  ; 4=2  s#n L?' a' 23 b' 1 c' 28

+' 19

63' The -"!#t "n a -"+&ct sell#n$ !" P 8'19 #s 29F "! the sell#n$ -#ce' 0hat -ecenta$e #ncease #n -"+&ct#"n c"st w#ll e+&ce the -"!#t b) 39F5 a' 3'37 F b' 7F c' 8'66F +' '23F 67' It +ete*#nes the .al&e "! a c#t#cal !act" at wh#ch ec"n"*#c ta+e@"!!s aea balance+' a' Ann&#t) b' De-ec#at#"n c' Pe-et&#t) +' Bea( E.en Anal)s#s 68' The $e"*et#c *ean an+ ha*"n#c *ean "! tw" n&*bes ae 21 an+ 7'1 , es-ect#.el)' 0hat #s the la$e n&*be5 a' 21 b' 3 c' 14 +' 9 6' #n+ the e*a#n+e "! 4 > 61 >   19 when +#.#+e+ b)  > 1' a'  b' 4 c' 6

+' 3

39' It c"ns#sts "! a&th"#e+ ha&l#n$ #n ecess "! the !ee@ha&l +#stance' a' /#*#t "! Ec"n"*#c Ha&l c' O.eha&l b' C"*-act#"n +' S&b$a+e 32' A c#.#l en$#nee -"cee+ t" +" the sta+#a s&.e) t" w"( t" +ete*#ne the t"-"$a-h) "! a ceta#n aea' The tans#t was set &- at a -"#nt A, e#th the l#ne "! s#$ht h"#"ntal, t""( "+ ea+#n$s !"* the "+s -lace+ at B an+ C wh#ch #s 199 * an+ 39 * !"* A es-ect#.el)' C"*-&te the sta+#a #nte.al !act"' a' 2'66 b' 4'77 c' '68 +' ' SITUATION 6: S&--"se that the +#st#b&t#"n "! *"nthl) ean#n$s !" the &n+ee*-l")e+ w"(es #n a ceta#n c#t) #s (n"wn t" be bell@sha-e+ an+ s)**et#c w#th a *ean "! P 12239 an+ a stan+a+ +e.#at#"n "! P 4669' 31' 0hat -ecenta$e "! the w"(es eane+ less than P 23329 5 a' 21F b' 23F +' 4F 3' 0hat -ecenta$e "! the w"(es ean h#$he than P 219395

+' 6F

a' 6F

b' 3F

c' 7F

+' 8F

34' #n+ the e%&at#"n "! the -e-en+#c&la b#sect" "! the l#ne se$*ent "#n#n$ =1, 4? an+ =@2 ,3?' a' 3  4) ; 27 b'  3  4) ; 27 c' 3 > 4) ; 27 +' @3 > 4) ; 27 36' In !&n+a*entals "! acc"&nt#n$, wh#ch "! the !"ll"w#n$ #s c"ns#+ee+ as c&ent assets5 a' Taes b' M"t$a$e c' In.ent"#es +' E%&#-*ents 33' #n+ the la-lace tans!"* "! !=t? ; t1 a' 
+' 1
38' The G"l+en State 0a#"s h#ts an a.ea$e "! 19 thee -"#nt !#el+ $"als *a+e' 0hat #s the -"bab#l#t) that the the) w#ll h#t 27 .s the Ca.s5 a' 9'973 b' 9'989 c' 9'988 +' 9'97 3' Messa$es when -a#nte+ "n -a.e*ent sh"&l+ be l#*#te+ t" a *a#*&* "!: a' 6 w"+s b' 4 c'  +' 3 79' I! sec1 A #s 6<1 , the .al&e "! c"s 1 A #s: a' 1'6 b' 9'3

c' 2'6

+' 9'4

72' The s&* "! the #nte#" an$les "! a -"l)$"n #s 649 ' #n+ the n&*be "! s#+es' a' 1 b' 14 c' 16 +' 13 71' 0hat #s the e%&at#"n "! the as)*-t"te "! the h)-eb"la 41  )1 ; 35 a' 1  ) ; 9 b'   1) ; 9 c' 1  ) ; 9 +' 1 > ) ; 9 7' The we#$ht "! a *ass "! 29 ($ &s#n$ $ ; '77 *
+' '7 N

74' /"cate the cent"#+ "! the aea b"&n+e+ b) the -aab"la )1 ; 4 , the l#ne ) ; 4 an+ the )@a#s' a' 3<6, b' 1<6, c' 7<4, 3<6 +' 2<4 , <6 76' D&els #n the t"wn "! Hath"#a ae ael) !atal' Thee, each wa#" c"*es at a an+"* *"*ent between 6 a* an+ 3 a* "n the a--"#nte+ +a) an+ lea.es eactl) 6 *#ns late, h"n" se.e+, &nless the "--"nent /#ean a#.es w#th#n the t#*e #nte.al an+ the) (#ll each "the' 0hat !act#"n "! +&els lea+ t" .#"lence5 a' 2<4 b' 2<21 c' 1<244 +' 22<64