after the price of petrol went up by 10

8/9/2019 After the Price of Petrol Went Up by 10

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ANDRO S. REBUYAS BSCE

(MATHEMATICS, SURVEYING & TRANSPO. ENG’G)

1) After the price of petrol went up by 10%, Pedroreduced his petrol consumption by the samepercent. By what percent would his petrol bill bechanged?a) decrease by 10%b) ecrease by 1%

c) !ncrease by 1%d) increase by "%e) !ncrease by #%

#) A s$uare of side A is inscribed in a circle, nd thearea between the circle and the s$uarea) a#&'(#1)b) *& '1)a#

c) &'1)a#

d) &'(+1)a#

e) &'#)a#

-) !t is between - and + ocloc/, and in twentyminutes, the minute hand will be as much after thehour hand as it is by now behind it. hat is thetime?a) -0" +(11

b) -0+ +(11c) -02 +(11d) -03 +(11e) -04 +(11

+) !f 1(5, 1(y, 1(6 are in A.P. nd the 7alue of ya) 56(56b) #56(56c) 65d) 6(1&56)e) #5#6

") 8he $uotient of a two digit number di7ided by thesum of its digit is +. if the number is subtracted fromthe sum of the s$uares of its digits, the di9erence is:, nd the numbera) -2

b) --c) -0d) #4e) -+

2) 8he length of a side of rhombus is "cm. if theshorter diagonal is of length 2cm, nd the area ofthe rhombus?a) -#b) #+c) #4d) -2e) 1#

3) 8here are three short$uestions in math e5ams.;or each $uestion, 1 mar/

will be awarded for a correctanswer and no wor/ for awrong answer. !f theprobability that <arycorrectly answers a $uestion in a test is #(-,determine the probability that <ary gets # mar/s inthe test.a) 4(#3b) #(:c) 1(#3d) "(:e) +(:

4) <aria is -2 yrs old. <aria was twice as old as Annawas when <aria was as old as Anna is now. =ow old

is Anna now?a) ##b) #"c) #+d) #-e) +

:) 8he standard de7iation of two numbers 5 and y,where 5>y is.a) 5y(#b) 5#y#(#c) 5y(#

d) √ x2

− y2

e) 5#y#(#10) etermine the length of the line in meters if there

were - tallies, 4 pins and the last pin was :m fromthe end of the line. the tape used was "0 m. longa) 143"b) 131-c) 1"4+d) 1#-2e) 1:0:

11) 8hese sides of a s$uare lot ha7ing an area of #.#"hectares were measured using a 100 m tape thatwas .0+ m too long. compute the error in the area ins$. metersa) 14b) 10c) 1"d) 1-e) 12

1#) !f 1(5ab and 1(yab nd 5ya) #b(b#a#

b) #a(b#a#

c) b#a#(bd) b#a#(ae) b#a#(a

1-) @ne side of a eld measuring 3" meters is parallelto the centre line of the adoining road. 8he othertwo sides which are both perpendicular to the roadare 1#" and 1"0 m respecti7ely. !f the eld is to bedi7ided into two parts of two e$ual areas by anotherperpendicular line, determine the length of the line.a) 1#:.+1"b) 1#".+1"c) 1+"."++d) 1-4.023e) 1"2.-"+

1+) !n what ratio must tea costing #+ per /g be mi5edwith tea costing -+ per /g so that a prot of #0% ismade by selling the mi5ture at -2 per /ga) #-

b) -#c) 1#d) "-e) +2

1") A line 100 m long was paced by a sur7eyor fourtimes with the following data, 1+#, 1+", 1+".", and1+2. then another line was paced for four timesagain with the following results, 4:-, 4:-.", 4:1,and 4:"."a) 2-".24"b) 213.#-2c) 2"+.1"4

d) 2#4.+#+e) 24:.":4

12) !n a twopeg test

method of a dumpyle7el, the followingobser7ations wereta/en,

!f the line of sight is not in adustment, determine thecorrect rod reading on A with the instrument still set upat B

a) .:1:mb) ."#2c) .4#"d) .22"e) .31"

13) 8ransform r# sin #2 into Cartesian coordinatesa) 5y#

b) 5y-c) 5y+d) 5y"e) 5y2

14) 8he height of the cone is D. it contains water to adepth of #(-=. determine the ration of the 7olume of water to that of the conea) 1:.#3b) #2.#3c) 4#3d) 1#3e) "#3

!nstrument !nstrumentEet up near A Eet up near B

Fod reading onA 1."0" .:-4

Fod reading onA

#.0"+ 1.++:



1:) A boy at 400 am started to wal/ at a rate of +/m(hr for # hrs and +" mins, after which a manfollowed to o7erta/e him with a rate of +." /m(hr forthe rst hour, +.3" /m.hr for the second hour and soon, increasing his rate by a $uarter of /m each hour.nd the time when the man o7ertoo/ the boya) 2+" P<b) 3+" P<c) 4+" P<

d) :+" P<e) 2#" P<#0) Get f&5) &5-) &5+) +. when f&5) is di7ided by &5

/), the remainder is /. nd /a) # or +b) 1 or -c) - or "d) 1 or #e) 1 or 2

#1) 8he daily wage of a technician and an apprenticeare in the ratio #1. !n a day a technician has towor/ 4 hours but an apprentice only in 2 hrs. thehourly wages of a technician and an apprentice is ina ratioa) +-

b) 4-c) #1d) -#e) "-

##) A circular rotunda passes through the three points A&+, -), B &#, 1) and C &#, "). etermine the radiusof the circular rotunda.a) "."4b) -.#2c) 2.1"d) 3.1"e) +.#3

#-) ;ind the e$uations of the tangents to the circle5#y#" which ma/e an angle +" degrees with the5a5is

a) 5yHI10b) 5yHI10c) 5yI10(#d) 5#y#HI10e) 5#y#HI10

#+) 8he point of intersection of the perpendicularbisector of the sides of the trianglea) circumcenterb) centroidc) eulers lined) circul circlee) non of these

#") 8he angle of a sector is 20J and the radius is # cm.what is the area of the sectiona) +(- '

b) 20( 'c) #(- 'd) 1#0e) 1"0

#2) 8he table shows the number of students in twoclasses of a school and their a7erage mar/s in atest.

Class Ko of students A7erage mar/a +0 2"b 5 "0!f the a7erage mar/ of the two classes is "4, nd 5a) -"b) +#c) #4d) -#

e) "##3) Dsing polar coordinates, nd the polar e$uation of

the path of a point which is e$uidistant from thepoints whose polar coordinates are &#a, 0) and &a.'(#)a) r-a(#&#cossin)b) r-a( &#cossin)c) r-a(#&#cos#sin#)d) r-a(&#cossin)

#4) A fruit 7endor goes to mar/et to buy fruits for resaleat her store. Ehe spends half her money formangoes, and 1(- of which remains for bananas.Ehe spends P1"0 for other fruits and still has P#00

left from the amount she originally had. =ow muchmoney did she ha7e at the start?a) 11"0b) 1#"0c) 10"0d) 1110e) 10#"

#:) log10 x x

x x

y nd the 7alue of y

a) y55log105b) y5#log105c) y5# log10&log105)d) y5 log10&log105)e) y5 log10

-0) A haw/er sold 100 eggs. 40 of them were sold at aprot of -0% while the rest were sold at a loss of+0%. hat is the percentage gain or loss on thewhole stoc/?a) a gain of 12%b) a gain of 10%c) a loss of 4%d) a loss of 10%e) a loss of "%

-1) 8he capacities of two hemispherical tan/s are in the

ratio of 2+1#". !f +.4 /g of paint is re$uired to paintthe outer surface of the smaller tan/. 8hen howmany /g of paints would be needed to paint theouter surface of the larger tan/?a) 2.+b) ".-c) 4.2d) :.2e) 3."

-#) 8he bearing of a line from A to B was measured asE. 12J-0 . it was found that there was localattraction at both A and B and therefore a forwardand bac/ward bearing were ta/en between A and apoint C which there was no local attraction. !f the

bearing at AC was E -0J10L and that of CA wasK#4J#0, what is the corrected bearing of AB?a) E 14 #+b) E 14 1" c) E14 #"d) E 14 ##e) E 14 #0

--) !n a throw of two dice, what is the probability ofobtaining a total of 10 or 1#?a) 1(2b) 1(:c) 1(1#d) 1(4e) 1(10

-+) 8he wheel of a car re7ol7es n times while the car

tra7els 5 /m. the radius of the wheel in cm is e$ualto MMMMMMMM a) "00005('nb) #'n5c) #00005('nd) "'n5e) -00005('n

-") A Nuonset 14m long has a parabolic cross section.!ts base is 1# m and its height at the center is 2m. AOat hori6ontal ceiling -.30 m abo7e the base is to be

constructed inside the hut. if the ceiling will consistof wooden boards #" mm thic/, how many cubicmeters of ceiling boards will be re$uired assumingthat 10% of the materials is wasted duringconstruction?a) +."#+b) #.-2"c) ".+"4d) -.31"e) 2.-#2

-2) ;ind the sum of the series 1-"3...&#n1)a) &#n1)#



b) n##nc) &n##n)d) n#

e) n#n-3) A conical funnel is #0 cm wide at the top and "0 cm

deep. Gi$uid is Oowing in at #0 cm-(sec and Oowingout at -0 cm-.sec. ;ind the speed with which theli$uid surface is rising when it is #" cm deep.a) :.31"b) ".11#c) 2.1"#d) 3.+4"e) 4.2"4

-4) A polygon ha7ing 1000 sidesa) $uindecagonb) chillagonc) nonagond) enneagone) icosagon

-:) 8he line /5&-/)y-&1/) passes through a 5edpoint P for a ny 7alue /, nd the coordinates of Pa) -,#b) +,1c) +,#d) -,1

e) #,#+0) ;ind the e$uation of the sphere whose center is &#,

+, -) and which passes through &", 1, -)a) 5#y#6#+54y26410b) 5#y#6##5+y-6+:0c) 5#y#6#251#y46410d) 5#y#6#-5"y26+20e) 5#y#6#"5"y26"00

+1) ABC is a parallelogram in cloc/wise direction. Aline NP as drawn with point P along the side AB.the line NP is the bisector of angle AC and angleNPB is +0J. ;ind the angle BC. point N is outsidethe parallelograma) 40b) 20c) 100d) 1#0e) +0

+#) etermine the e$uation of two lines passing through&#,+) and forming with the a5es of a triangle witharea :a) 5y-, 45y1#0b) 5#y2, 25y1-0c) 5-y2, 45y1"0d) 5y2, 45#y1#0e) 5#y2, 45y1#0

+-) A certain printer charges P100 for e7ery thousandboo/s per page. !f only #000 boo/s are printed. ;ore7ery thousand in e5cess of #000 it will charge #

less. thus if -000 are ordered, the price is:4(thousand, for +000 the price is :2(thousand, etc.nd the total number of boo/s it should print forma5imum income?a) #"000b) #2000c) #+000d) #3000e) #4000

++) A@B is a sector of a circle ha7ing a radius of + cm.QA@B-0J. Point < is located along the radius @B,such that @<<B, nd the area of AB<.a) -(+' 1b) #(-' #c) -(#' #

d) +(-' #e) 1(+' #

+") nd the e$uation of the sphere which passesthrough the origin and whose center is &", 1, #)a) 5#y#6#105#y+60b) 5#y#6#1#5y#60c) 5#y#6#1"5"y260d) 5#y#6#1-5-y460e) 5#y#6#115+y#60

+2) !f &#, +) is the midpoint of &2, 3) and &5,y),determine the 7alue of 5a) :b) 4

c) 10d) 1"e) 10

+3) &5+)#y##" is the e$uation of a circle and &1, +) isthe point at one end of the diameter. nd thecoordinate of the ether end of the diametera) 2,+b) ",-c) 4,-d) +,"e) 3,+

+4) 8here a re + white balls and 2 red balls in a bo5, iftwo balls are ta/en out successfully, the rst ball isnot replaced what is the probability that the ballsare of di9erent colors.a) 3(1"b) -(13c) 4(1"d) "(#3e) 2(1:

+:) A right circular cone is di7ided into - portions A, Band C by planes parallel to the base. the height ofeach portion is = and the base radius of the cone atA is r. determine the ration of the 7olume of A to

that of B.a) 1(3b) 3(1:c) 1(-d) -("e) -(10

"0) A stone contractor has his $uarry 10 /m from P, thenearest point on a straight railway. 8he railroadcompany agrees to haul his stone to E -0 /m alongthe straight trac/ from P for " centa7os per ton per/ilometre. !f the cost of hauling by car from $uarryto the railroad trac/ is 1# centa7os per ton per/ilometre, to what point at then railway should hehaul his stone so that the cost of transportation

from the $uarry to s be minimuma) #.-2b) +.":c) -.+4d) "."4e) 2.#4

"1) Another term for $uadrilateral or $uadranglea) =e5agonb) 8etragonc) Pentagond) 8rape6iume) 8rape6oid

"#) ",#,1 ...are in A.P. nd the sum of the progressionfrom the 11th term to #0th terma) +#"b) #-"c) "#"d) +4"e) -4"

"-) A steel girder 4 m long is mo7ed on rollers along apassageway +.0 m wide and into a corridor at rightangles to the passageway. Keglecting the width ofthe girder how wide must the corridor be?a) #.2b) #.4c) 1.4

d) #.#e) -.#"

"+) ater Oows through a pipe of internal diameter +cm at the rate of 20 cm(sec to a rectangular tan/whose base has a dimension of 140 cm 5 #2+ cm.;ind the time in seconds re$uired to raise the waterle7el by #cm use '##(3a) 1:0b) 1#2c) :-d) 2+e) 1"2



"") 8he top of a ladder 2 m long rests on a 7ertical wallwhile the bottom rests on a hori6ontal Ooor. !f the toslides down at a constant rate of .20 m(secdetermine the rate at which the angle the ladderma/es with the hori6ontal changes when the lowerend is -.2 m from the walla) 1(+ rad(secb) 1(3 rad(secc) 1("

d) 1(4e) 1(2"2) Prietto and ancheta at a distance of /m apart

start simultaneously and tra7el to meet each other.!f their speeds are 5 /ph and y /ph, nd the timeta/en in hours before they meet.a) #(5yb) (5yc) (5yd) #(5ye) (5y

"3) @ne ship was sailing north at 4 /nots, another castat 10 /nots at 1000 A<, the second crossed thecourse of the srt at the point where the rst was at400 A.<. at what rate was the distance between

the ships changing at :00 A.<a) +.+4 /notsb) ".+4c) -.#4d) #.41e) 1.#-

"4) A ship anchored in 3.# m of water. 8he anchor chainpasses through an opening in the ships bow -.2 mabo7e the water surface. !f the chain is pulled in atthe rate 3" mm(sec, how fast is the ship mo7ingwhen 14 m of chain are out?a) :0.+3 mm(secb) 4".++c) :#.1"d) :2."3e) :-.3"

":) A boy 1.# m tallis wal/ing directly away from a lamppost at the rate of .:0 m(sec. !f the lamp is 2mabo7e the ground, nd the rate at which his shadowis lengtheninga) ."2#b) .+1"c) .1"4d) .##"e) .--2

20) !f the surface area of a sphere increases by #1%, its7olume is increased by?a) 1-.-1%

b) --.1%c) -0%d) -+%e) #-.#%

21) ;ind the minimum distance from the point &2,0) tothe parabola y#45

a) + √ #

b) - √ #

c) # √ #

d) + √ # √ #

e) " √ #

2#) !n a group of 30 students, -" are ta/ingmathematics, #" are ta/ing design and 1" areta/ing both subects. !f a student is chosen atrandom, what is the probability that he is ta/ingdesign but not mathematics?a) #("b) 1(3c) -("d) #(3e) -(3

2-) A triangle with all interior angles less than :0

a) Acute triangleb) @btuse trianglec) Rright triangled) Ecalele trianglee) Ecalene

2+) ;ind the length of the common chord of two circlesof radii #" cm and #2 cm respecti7ely if the distancebetween their centers is 13 cma) +4b) +"c) "2d) 2#e) "0.1#

2") 8he surface areas o9 two spheres are #+ cm# and :2cm# respecti7ely. ;ind the ration of their 7olumea) 1(2b) 1("c) *d) 1(4e) 1(:

22) 8he sum to the nth term of a se$uence 4is gi7en byE &n) n &n-). hat is the nth term of these$uence?a) -n#b) #n+c) #n#d) #n+e) -n#

23) 8he mar/ price of a chair is 5 pesos, -0% of thisprice is the prot. !f the chair is sold at a discount of #0% compute the net prota) .o:5b) .#+5c) .105d) .0+5e) .045

24) ;ind the length of the common e5ternal tangent totwo circles of radii "cm and 1# cm respecti7ely. !fthe distance between their centers is #" cma) #2b) #4c) #0d) ##e) #+

2:) Peter bought two cars, one for 20000 and the otherfor +0000. =e sold the rst at a gain of 10n% andthe second at a loss of 1#%. hat is the totalpercentage loss or gain?a) 2%lossb) #."%gain

c) 1.#%gaind) #Slosse) 1.4%gain

30) A chord is #+cm long and its midpoint is 4 cm fromthe midpoint of its shorter arc. ;ind the radius of thecirclea) 1"b) 1#c) 10d) 1+e) 1-

31) Eimplify &1(sinT1(tanT)&1cosT).a) Cos Tb) sinTtanTc) cosT1

d) tan Te) sinT

3#) A cyclic $uadrilateral ABC is inscribed in a circleha7ing a diameter C.AB is parallel to C. !f theangle AB is +0 UV, nd the angle AB.a) #0 Ub) 10c) 1#d) -0e) #"

3-) @ne side of a parallelogram is 10 cm and itsdiagonals are 12 cm and #+ cm respecti7ely. ;ind itsarea



a) 12:.+b) 1+2.1c) 1--.3d) 1"4.2e) 13-.#

3+) 8wo circles of e$ual radii r intersect each other. !fthe center of the circle lies on the circumference ofthe other, nd the perimeter of the resulting gurea) 3(+'rb) -(4'rc) +(3'rd) 4(-'re) +(:'r

3") 8he sides of a triangle are ",3 and 10 respecti7ely,nd the radius of the circumscribed circlea) ".-:b) +."2c) 2.3"d) 3.+"e) -.-#

32) =ow many sides has an e$uiangular polygon if eachof its interior angles is 12" UV?a) #+b) ##c) #0

d) #2e) -0

33) 8he nth term of an A.p. is -n1 where n is a naturalnumber. 8he number of terms of the progressioneach of which is less than 4# isa) 34b) 2c) 4d) #3e) "#

34) ABC is a rectangle. 8he length of the diagonal is -0cm and the acute angle between them is "0V. ;indthe length of the shortest side of the rectanglea) 1-.+#b) 10.+#c) :."2d) 4.1"e) 1#.24

3:) 8he following are the height in cm of : boys,1:0.140,140,110,1-0,100,#00,1"0 and #30. hat isthe median of the distributiona) 1-0b) 100c) 110d) 140e) 1"0

40) 8he sum of three consecuti7e odd integers is 3".;ind the largest integera) W-#b) 1:c) +#d) -4e) #3

41) A semi circle of radius 1+ is formed by a piece ofwire. !f it is bent into a re+ctangle with one sidee$ual to 5 and the other side, nd the 7alue of 5a) 1+."b) 13."c) 1#."d) 12."e) 14."

4#) X 7aries directly as 5 and in7ersely as y#. !f 51 y#and 6#. ;ind 6 when 5- and y+a) #(-b) -(#c) Yd) +(-e)

4-) ;ind the side of a regular octagon inscribed in acircle of radius 10cma) +.1"b) ".2:c) 2.1#d) 3.2"e) -.+"

4+) 1(-, 1(--, 1(-"......is a ZP what is the sum to innity?a) :(10b) -(4

c) :(4d) "(4e) -(10

4") A sector of a circle has a radius F:cm. 8he sectorhas a central angle of 20V. A small circle is inscribedin a sector. etermine the radius of the small circlea) "b) -c) +d) #e) 2

42) 8he length of a side of a s$uare is increased by100%. !ts perimeter is increased bya) 100%b) +00%c) #"%d) #00%e) "0%

43) <ary is three times as old as Fic/y. 8hree years ago,she is four times as old as Fic/y. ;ind the sum oftheir ages.a) -4b) -0c) -2d) +#e) +0

44) A piece of wire of length "# cm is cut into # parts.Lach part is then bent to form a s$uare. !t is foundthat the total area of the two s$uares is :3cm#. ;indthe di9erence in length of the sides of the twos$uares.a) "b) 4c) +d) 10e) 1#

4:) 8he areas of the three faces of a cuboid are 10, 1+

and -". ;ind the 7olume of a cuboid?a) 1+0b) +:c) 10d) -"0e) #+0

:0) A class of +0 students too/ e5amination in Lnglishand Chinese. !f -0 passed in Lnglish, -2 passed inChinese and # failed in both subects, determine thenumber of students passing in both subectsa) #+b) 14c) #2d) #4e) -#

:1) ;our military recruits whose respecti7e shoe si6esare 3, 4, :, and 10 report to the supply cler/ to beissued boots. 8he supply cler/ selects one pair ofboots in each of the four re$uired si6es and handsthem at random to the recruits. hat is theprobability that all recruits will recei7e boots ofincorrect si6es?a) .-4b) .#"c) .+"d) .21e) .3"

:#) 8hree spheres has radii of &r1), r, &r1) respecti7ely.;ind the total 7olume of the three spheres.

a) &r#

#r-.")'b) +'&r-#r)c) -'&r-r)d) F-r#)'e) #'&r#r)

:-) 8he obelis/ of a certain ri6al monument rises tosome height abo7e the dais, the angles of ele7ationof the top and bottom of the obelis/ from the twostations A and B on the same hori6ontal plane asthe base of the dais are +"V and -0V respecti7ely,the corresponding hori6ontal angles to the commoncentre of both dais and obelis/ from the ends of the

after the price of petrol went up by 10

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