TECHNOLOGICAL INSTITUTE OF THE PHILIPPINES MANILA PRE BOARD EXAM DAY 3 STUDENT NAME & NUMBER __________________________________________________ _________________________________ _________________ DATE: OCTOBER 11, 2013 DIRE DIRECT CTIO IONS NS::
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1. What part part of 90% alcohol must be removed removed and replaced replaced by an eual amount of pure alcohol to ma!e 95% alcohol solut"on# a. 5% or less b. bet$een 5% and 10% c. 5% d. 50% . & man $ants to sell h"s scooter. 'here are t$o offers( one at )s. 1(000 cash and the other a cred"t of )s. 1(**0 to be pa"d after * months( money be"n+ at 1*% per annum. Wh"ch "s the better offer# &. 1(000 "n cash ,. 1(**0 at cred"t -. ,oth are eually +ood . & companys mar+"nal mar+"nal revenue funct"on "s +"ven by d)/d 1000/√ 21( $here 31 "s the number of "tems manufactured. "nd the total revenue ) "n terms of ( "f ) 1(000 $hen 6 a. ) 1000/√ 21 000 b. ) 1000/√ 2 1 000 c. ) 000/√ 2 1 000 d. N7'8 4. 'he euat"on of mot"on of a part"cle start"n+ from rest alon+ a stra"+ht l"ne "s t3 t 2 5. 'he rat"o of the accelerat"ons after 5 sec and sec $"ll be &. ,. -. 4 :. 5 5. & man buys a $atch for ;hp 1950 "n cash and sells "t for ;hp 00 at a cred"t of 1 year. ho hours -. * hours :. 14 hours >. '"c!ets numbered 1 to 0 are m"ed up and then a t"c!et "s dra$n at random. What "s the probab"l"ty that the t"c!et dra$n has a number $h"ch "s a mult"ple of or 5# &. ? ,. /5 -. */15 :. 9/0 0*.. @uppose that a corpse $as d"scovered "n a motel room at 0* m"dn"+ht and "ts temperature $as *0°. 'he temperature of the room "s !ept constant at 60°. '$o '$o hours later the temperature of the corpse dropped to>5 °. "nd the t"me of death. Note= 'he temperature of a l"ve person "s 9*. 6°. a. *=0 ;A b. >=0 ;A c. 9=00 ;A d. N 7 ' 8 9. When eual and oppos"te forces appl"ed to a body( tend to elon+ate "t( the stress so produced( "s " s called &. shear stress ,. compress"ve stress -. tens"le stress :. transverse stress. 10. :eterm"ne the resultant of the l"ne load act"n+ on the beam sho$n "n the f"+ure. a. ; 105 KN b. ;>5 KN c. ;90 KN d. ;45 KN 15 KN/m
10 KN/m
4m
Figure 10
6m
11. 'oms 'oms ret"rement account "n a company currently totals ;hp416(*4. What perpetual "ncome can 'om 'om and h"s h" s he"rs
rece"ve per year "f he ret"res no$ and t he money "s "nvested "n an annu"ty earn"n+ 6% "nterest# B&C ;hp0(9*0 B,C ;hp(9*0 B-C ;hp4(9*0 B:C ;hp6(9*0 1. 1. & con"c has the l"nes y and y 5 as d"rectr"ces and the po"nt B1( 6C as a focus. What are the coord"nates of the verte closest to the +"ven focus# a. B1(11C b. B( 11C c. B( *C d. N7'8 1. 'he l"nes y DB5/1C are asymptotes of a hyperbola $hose foc" are 6 un"ts apart. Wh"ch -&NN7' be a verte of the hyperbola# a. B1( 0C b. B0( 5C c. B0( 1C d. B1( 0C 14. "nd the centro"d of a hem"sphere of rad"us ) revolv"n+ about the a"s. a. 5/* from center b. /5 from center c. /5 from center d. /* from center 15. Eo$ many !"lo+ram of su+ar cost"n+ ;hp. 9 per !+ must be m"ed $"th > !+ of su+ar cost"n+ ;hp. > per !+ so that there may be a +a"n of 10% by sell"n+ the m"ture at ;hp. 9.4 per !+# &.6 !+ ,.4 !+ -.54 !+ :.6 !+ !" 16. 'he solut"on for dy/d e $hen yB0C 0 a. y e 2 B1C b. y e 2 B1C 2 c. y e B B1C 1 d. N 7 '8 1>. 8"ven the force vectorsF & *" 4G ! and the pos"t"on vectors , G 6! m and - " 2 G 4! m( the dot product of & and , "s a. 2 4N.m b. 2 .>1 N.m c. 2 4.5 N.m d. >. N.m 11*. 5 B-C ;hp(415 B:C ;hp(4*5 0. & man $ants to fence a rectan+ular area as "nepens"vely as poss"ble. 5.6 m"/h . '$o forces ;I and ;) of ma+n"tudes 5.0 !+ and *.0 !+( respect"vely( acts at a po"nt ;. 'he d"rect"on of ;I "s N0J( and the d"rect"on of ;) "s N65J. &ppro"mate the ma+n"tude ma+n"tude and d"rect"on of the resultant ;@. aC 11. !+( N4o bC 1.1 !+( N4*o cC 14.1 !+N>o dC 15.1 !+.N>o . Hou are cons"der"n+ "nvest"n+ "n a 5yr -:Bcert"f"cate of depo depos" s"tC tC $"th $"th an annu annual al y"el y"eld d of 6.5% 6.5% and and mo mont nthl hly y compound"n+. % B:C 6.*% 4. "nd the euat"on of the hyperbola $"th vert"ces at B D(0C and asymptotes y D a. 4 2 6y 144 b. 6 2 4y 144
c. 9 2 4y 6 d. 4 2 9y 6 5. "nd the len+th of the latus rectum of a hyperbola $hose euat"on "s #"2$ %2 '("$ )# y 2 11 0. a. / b. 4/ c. */ d. 16/ 6. 'he beam sho$n "n the net f"+ure "s supported by a h"n+e at & and a roller at ,. 'he react"on )& of the h"n+ed support & of the beam( "s &. 10.* t ,. 10.6 t -. 10.4 t :. 10. t
"+ure 6
>. 'he ma"mum veloc"ty of a body v"brat"n+ $"th a s"mple harmon"c mot"on of ampl"tude 150 mm and freuency v"brat"ons/sec( "s &. 1**.5 m/sec ,.1*.*5 m/sec -. 1.**5 m/sec :.0.1**45 m/sec *. 'he vert"cal react"on at the support & of the structure sho$n "n belo$ f"+ure( "s &.1 t ,. t -. t :..5 t.
6.
>. & rectan+ular beam 0 cm $"de "s subGected to a ma"mum shear"n+ force of 10( 000 !+( the correspond"n+ ma"mum shear"n+ stress be"n+ 0 !+/cm. 'he depth of the beam "s &. 15 cm ,. 0 cm -. 5 cm :. 0 cm. *. or a +"ven mater"al Houn+s modulus "s 00 8N/m and modulus of r"+"d"ty "s *0 8N/m. 'he value of ;o"ssons rat"o "s &. 0.15 ,. 0.0 -. 0.5 :. 0.40 9. 'he force "n member U L of the truss sho$n "n belo$ f"+ure( "s &.10 ' tens"on ,.10 ' compress"on -.Lero :.15 ' compress"on.
F* -. 3%
0.5 µ C
9. 'he total surface of t$o cubes "s 150 s. m( 'he total len+th of the"r ed+es "s *4 cm. "nd the ed+e of the lar+er cube. a. 4 b. 5.5 c. 6.4 d. >. 0. "nd the po"nt on the curve y * 2 1 $here the tan+ent l"ne "s parallel to the a"s a. B4( 6C b. B 4( *C c. B 4( *C d. N7'8 1. 'he an+le of elevat"on of a hot a"r balloon( cl"mb"n+ vert"cally( chan+es from 5 de+rees at 10=00 am to 60 de+rees at 10=0 am. 'he po"nt of observat"on of the an+le of elevat"on "s s"tuated 00 meters a$ay from the ta!e off po"nt. What "s the up$ard speed( assumed constant( of the ball oon# a. .5 m/s b. .>6 m/s c. .16 m/s d. .*9 m/s . 'he present $orth of ;hp 1404 due "n t$o eual half yearly "nstallments at *% per annum s"mple "nterest "s= &. ;hp 15 ,. ;hp 100 -. ;hp 150 :. ;hp 1500 . "nd the centro"d of the sem"c"rcular area "ns"de y a $"th y +reater than or eual to Lero. a. B0(a/MC b. B0(a/5M c. B0(4a/MC d. B0(5a/MC 4. 'he masses of t$o balls are "n the rat"o of = 1 and the"r respect"ve veloc"t"es are "n the rat"o of 1 = but "n oppos"te d"rect"on before "mpact.
0.% µ C
40. '$o char+es( one of and the other of ( attract each other $"th a force of 100 N. Eo$ far apart are they# a. mm b. 4 mm c. 0 mm d. 40 mm 41. & part"cular moon roc! "s analyLed and "t "s found to conta"n eual amounts of ;otass"um19 and &r+on1*( $h"ch are denoted as "sotope that can decay to
( respect"vely. . Note that
potass"um decay and that the y"eld of
"s a rad"oact"ve for "s about 11% B".e.
about 1 out of every 9 atoms decays to C. &ssum"n+ that the "n"t"al amount of ar+on $as Lero and that all of the ar+on "s the result of potass"um decay( est"mate the a+e of the moon roc!. a. b"ll"on years b. 4. b"ll"on years c. 5. b"ll"on years d. N7'8 40°
4. & shell "s f"red at an an+le above the hor"Lontal at a veloc"ty of 00 m/s. What "s the t"me of fl"+ht# a. 9 s b. 41 s c. 4 s d. 45 s 4. Ar. 'homas "nvested an amount of ;hp 1(900 d"v"ded " n t$o d"fferent schemes & and , at the s"mple "nterest rate of 14% p.a. and 11% p.a. respect"vely. 00 :. ;hp >500 44. & parabola has "ts focus at B>( 4C and d" rectr" H . "nd the euat"on a. O2 1O 2 14H 61 0 b. O2 14O 2 1H 61 0 2 c. O 2 1O 14 H 61 0 d. O2 2 14O 1 H 61 045. red balls and 5 $h"te balls# aC 14>00 bC 1>400 cC 4>100 dC 10>40 46. 'he tens"le force reu"red to cause an elon+at"on of 0.045 mm "n a steel rod of 1000 mm len+th and 1 mm d"ameter( "s B$here 106 !+/cmC &. 166 !+ ,. 10 !+ -. 04 !+ :. >4 !+
4>. &t $hat rate of compound "nterest per annum $ "ll a sum of ;hp 100 become ;hp 14*. "n years# &. 6% ,. 6.5% -. >% :. >.5% 4*. 'he compound "nterest on )s. 0(000 at >% per annum "s )s. 44>. 'he per"od B"n yearsC "s= &. ,. ? -. :. 4 4950. & t"re manufacturer uses 10(000 tons of spec"al add"t"ve un"formly throu+hout the year. >> B,C *>> B-C 9>> B:C 10>> 50. Eo$ freuently should orders be placed# B&C6 days B,C * days B-C 0 days B:C days 51. & r"+ht tr"an+le has a f"ed hypotenuse of 0 cm and the other t$o s"des are allo$ed to vary. :eterm"ne the lar+est poss"ble area of the tr"an+le. a. 5 s.cm b. 4 s. cm c. 4 s. cm d. 16 s. cm %0°C
5. & total of 0.* !+ of $ater at "s placed "n 1 !W electr"c !ettle. Eo$ lon+ a t"me "s needed to ra"se the 100 °C
temperature of $ater to . a. .5 m"n b. 4.5 m"n c. 5.5 m"n d. 6.5 m"n 5. & ba+ conta"ns s" $h"te( f"ve red( and four blue balls. m b. ' 4. KN( E *.>> m c. ' >4. KN( E 5.>> m d. ' 94. KN( E 6.>> m "+ure 56
5>. @tress "n members of stat"cally determ"nate s"mple frames( can be determ"ned by &. method of Go"nts ,. method of sect"ons -. +raph"cal solut"on :. all the above 5*. Hou purchase 1(000 shares of stoc! at ;hp15.00 per share. 'he stoc! pays uarterly d"v"dends of ;hp15 for t $o years at $h"ch t"me you sell the stoc! at the trad"n+ pr"ce of ;hp16.50 per share. 'he yearly return on your "nvestment "s most nearly= B&C % B,C 4% B-C 6% B:C *% 1 59. "nd the l"m"t of the seuence an B1 n C/B 2 n 2C( n 1( P. a. b. 1 c. d. N7'8 60. '$o forces of 6 Ne$tons and * Ne$tons $h"ch are act"n+ at r"+ht an+les to each other( $"ll have a resultant of &. 5 Ne$tons ,. * Ne$tons -. 10 Ne$tons :. 1 Ne$tons. 61. & company produces transm"ss"on +ears used by several farm tractor manufacturers. 'he base cost of operat"on "s
;hp596(>00 per year. 'he cost of manufactur"n+ "s ;hp1*.40 per +ear. .90 each( ho$ many +ears must be sold each year to brea! even# B&C 15(>40 B,C 1*(400 B-C 0(600 B:C (40 6. & man dra$s 1 card from each of separate dec!s. What "s the probab"l"ty that the card from the f"rst dec! "s an ace and the one from the second dec! a face card# aC 14/169 bC /169 cC16/169 dC /169 6. &n elevator system for a 0yr old h"+hr"se off"ce bu"ld"n+ cost ;hp400(000 $hen f"rst "nstalled. 'he system $as des"+ned to last 0 years( $"th salva+e at 10% of "n"t"al cost. :eprec"at"on "s stra"+ht l"ne. 'he allo$able deprec"at"on char+e per year "s= B&C ;hp1(000 B,C ;hp1( B-C ;hp1*(000 B:C ;hp0(000 64. "nd the euat"on of the ell"pse $"th foc" at BD1( 0C and maGor sem" 2a"s a. 9 *y > b. 4y 1 c. 4 y 1 d. * 9y > 65. &n archeolo+"sts d"scovered some anc"ent obGects $ h"ch had or+an"c rema"ns. Ee found that 60% of the or"+"nal amount of - 2 14 rema"ns and the d"sappearance of -14 obeys the f"rstorder decay la$( +"ve an est"mat"on for the a+e of the obGects +"ven the half l"fe of -14 "s appro"mately 5600 years( determ"ne the a+e of the foss"l. a. 41>. 01 yrs. b.405.6 yrs. c. 4569.5 yrs. d. N7'8 66. &n open bo "s made from a suare p"ece of cardboard Bof s"de 1C by cutt"n+ out four eual Bsmall suaresC at the corners and then fold"n+. Eo$ b"+ should the small suares be "n order that the volume of the bo be as lar+e as poss"ble# a. 1/* b. 1/10 c. 1/6 d. N7'8 6>. 0. 1. & spr"n+ scale "n a stat"onary l"ft sho$s a read"n+ of 60 !+ for a man stand"n+ on "t. !+ :. N7'8 >. & 50 !+ boy cl"mbs up a * m rope "n +ymnas"am "n 10 sec. 'he avera+e po$er developed by the boy "s appro"mately &. 400 $atts ,. 500 $atts -. 4000 $atts :. none of these >. 8"ven part of an ar"thmet"c seuence B 1( QQQ( QQQ( 1>4C and t)0 1160( $hat "s the value of the 6th term a. 4* b. 56 c. 6> d. >4 >4. 5.
