~ ~r _______________________________________________ _

-~ Geom~try amp Calculus ~o 1 bull The sum of two numbers Is 40 Express Ihelr product as emiddotmiddot1tIFlnd the lenoth of the shortest ladder that wlll reach over

fU(l~tlor of one of the numbersmiddot an 8-ft high fence to a large wall which Is 3 ft behind the AI 40x- C 40-4X fence r- l

l 1 ~h 1shy 20x-4x DOy+x2 A 1 64 ft amp 1667 ft I _ bullbull_ B 077 ft ~499 ft (xmiddot~)middotmiddot

2 The product of two numbers Is 32 Find a function that repre$enls the sum of t~elr squares 13 The talJestlnhabiled bllllding In the world 15 the Sears

A 2x-32x C 32~-1~ TQwer In Chicago if the observation tower Is 1450 feei ( 6) ~ + (32J)2 D 2-3 ~X above ground Ievel how far can a pef8l)n standlllg 1n-tIle

observation tower see (with the aid of a tele$cope) ~e ~ A farmer ha$ 1500 feet of farmlnlln his barn He wishes 39~~lles for the radius of Earth

to encl05e a rectangula- pen subdivided Into two regions NoQmlJe 5260 feet by a $ectlon of fflnce duwn the middle parallel to one 466~ ml C 3626 mi side C)f the recUlngle Express the area enclosed by the B 3558 mi D 53 48 ml pervesa function of Its width x

W 750x - 32 bull C 1500xmiddot3 middot14 middotThe width ola rectangle Is four feet less than the length B 450xmiddot3 D 23)2~1500X3 The perimeter Is 16 ft FInd the width

h 1 C 3 ~ A piece of wire 12 Inches long Is to be used to form a ~ 2 D4

sruare andlor a circle Determine a function that expres$es the combined a~e~ middot of both figures 4( 1 ] 1 r 1 15 The length of a rectangular box Is 3 less than 3 times the

A 4X2+6X+2 C ~ + (6 - 2X)2 c Z width The perimeter Is 74 ft Find the length of the box B 36-4xmiddot2 D y+2+41 11 ] ~ or ~_ ( A 5 C15

~ I ~ 10 middotIi l~- D 20 5 A 1 mile racetrack ha$ two semicircular ends connected V

bull by straight lines Expresll the area enclosed by the track t6 One angle of e triangle Is three times another The third as a lunctlon of Its semicircular radius angle Is 45 degrees greater than tile smallest Find the

A rTH Gm2+TTr measure of the $mallest angle B Cr-TTr 13) 252THmiddotr A ~

8 72 lt3127 Jx l

- x -I 01101-----middot- 17 SUPP068 that a box has a base with a width 01 x a lenglh

6 Computo ~I Xl - 4 - of x+l arid a height of 2 Inches It Is cut Irom a A 010 CC)114 1 rectangular sheet of material with an area of 166 Inches2

B 6 No limit find the dimension of the box 1 ~-I [11 bullbull l_ 4 bull J ~ 8 x 7 C 9 x 8 I

xmiddot -81 6 10xS _ D11x10I1m

7 Corp~te ~ 2x - 5x - ) ilB middot The dimensions of a garden are In whole numbef8 If1h-e A 1087 C

length Is reduced by 3 and the width reduced by 1 ~B 256 D Undefined the area Is reduced by half What Is area of the original

I 1 rectangla r _r ( ( )A 30 CI36 ltshy-+shyB 42 038tim~

8 Calyul te --1 x + 8 f) -148 G 526 io One of the angles of a triangle Is equal to the sum of the

other two angles If the ratio of the other two angles IsB 3128 D Canit solve 45 find the smallest angle of the triangle

A 50 C45 ~ -n+bX lxgt2 B30 IQ~ 40 1 bull 1S0f(x J If x 2 --gt X)ll bull

9 Consider tha funclon b - cu 1 x lt2 20 Which parabola Intersects the xmiddotaxls In two distinct

Determine the values of constantmiddots a and b such that points IA yz(X+5)2

exists and Is equal to f(2) B y=(2+16 lim f (x)

A middot13 and 53 C 23 anc 43 21 Given that twIce the complement Is three-fifths the B 23 and-l3 D 43 and -13 supplement Find the measure of the angle

b 60 C M 34 10 A ractangular piece of paper Is 12 Inc-hes high and six (~ 5143 D7155

Inches wide The lower rlghtmiddothand corner Is folded over so as to reach the leftmost Eldge of the paper Find the 22 Given the sum of two numbers Is thirty and that twice the minimum length of the resulting crea~e first number Is 3 more than the second find the largest

A 679 In C 679 In ~ ~ number C3J779 In D 687 In 1( j A 11 C21

IS) 19 D15- 1middot1 Car B Is 30 mites dlrectjy east of Car A and begins

moving west it gO mph At ttlamp sarna moment car A 23 If 1 gallon of paint covers 400 square feei about hOW begins moving north at 80 mph What time td6es the many gallons of paint are needed to P3lnt the ~utslde or Ii minimum distance betweanltSsrA and Car eoccur - spherical tank of diameter 20 fe~t l 4

A 023 min C 138 min A 2 C4 B 2496 min D 2077 min B 3 D5middot

1- ~ I ~

1 of 5 t bullbull

I 1ampor61amp r ll r J 110 IlIHj(lrllurn orOLl 01 ~ roctun~ltt clrcumacrlbed (luout D fixed rectangle of length 6 IIld width 4 A (13)(e3

- (7J9)xe 3 (227)e3 C A 64 In

2 C 81 In2B (23)le- (13)xe (127e3 + C

(8) 72middot In2 D 54 In2c (29)e3 - (23)xe3

(5l7)e3 C D (213)(e3bull - (9)116 3bull (22Z)e3l C

35 A ladder 10 ft long Is res ling against the side of a building If the foot of the ladder slips away from the wall 25 If x items of a commodity are suld to a wholesaler the at ihe rate of 2 tVmln how fast la the anale between theprice per Item Is P500 - 2x - 01)2 Compute the ladder and the building changtng whon Iho rool or thomiddot middot

marginal rellenue derhed fJPYIhe sale of the 11 unit ladder Is 6 tt aWlY from th~lIdlng A 4659 ~30 Po ~ radlmln rsx Yo radmin B 4197 0417 B 13 radmln D 213 radmin

26 Boyles law states that when a gas Is compressed at 36 Two sides of a triangle are 31n and 4 In 10JI If the anQfe constant temperature the product of Its pressure and between them Is Increasing at the nite of 2 per second volume remains constmt If the prossure of a gas Is 60 how faat Is the area of the triangle Increasing when the Iblin2 when the volume Is 40 In3

flnltl the rate of change of anglA-l~ 450 prJs~Je with respect to volumElhen the volume Is 20~ Iagt 0148 In2s C 0154 In2s

6 0234 In2s D 0315 In2sml 2 2 ) pj-e1r A middot8 Iblln per In C 24 Ibll~ i er 111 3 ( ~ I 0

I ~ 8 6 Iblln2 per Inl O middot12 Ibltn per In 37 A television camera Is located 5000 tt from the base of a ~ ~+LI rock8tlaunchlng pad The camer I delgnod to rollow

the vertical path of the rocket If the rockets spe8d Is 500 2~Arectangle Is to be Inscribed In tho olilpse WO SO _ tVsec when It has risen 200~ how fast Is the carner Determine Its maximum poslble area _ 1- )( 1) angle of elevation changln this Instant 1- y A 360 C 150 bull bull v_ r Po 395 degreeasec 194 degreeslsec

(_t3~) 200 D 250 gt ~ r J v B 267 degreessec D 587 degreessec I I 3

26 A closed cylindrical can must have a volume of 1000 In 38 A lighthouse (s situated 2 km aw~y from a b8ach lnd ~ Its lateral surface Is to be constructed from a rectangular beacon revolves at the rate of 3 revoluUons per minutepiece of metal and Its top and bottoM are to be stamp~d P Is the point on the beach nearest the lighthouse howfrom square pieces of rnetnl and the rest of the square fast Is the beam of light moving along the beach when Itdiscorded What helohtmiddotNII mlnlhllze the amount of metal

Is I km from P7needed In the construction of the call

A 12n kmlmin pound 14n kmlmlnA 30n In C 50m In B 13n kmlmin G 15n kmlmin~~~~) 40n In rJ 60m In -_~ r

Two corrldora of widths a and b Interaect at right angles 29 A closed cylindrical can must have a volurtle of 10do In 39 What Is he length of the longest pipe that can be carried

Wha( radius will mlnlml~e ItampSJrface area tr -t l bj (1 ~) horizontally around the corner F 2I31fl Po 1084 In ~42 In PI - II bull 1 Po (a 113 + b2tl)312 Ca2tl + b ) B 767 In 0 1267 In f 11 I~th B (a2tl +iJ1(3)312 D (a2tl b2IJ)12

30 A publisher wants to prlQt a book whose pages are each 40 A painting of height 3 ft hangs on a wall with the botto) to have an area of 96 In The margins are to be lin on of the painting 6 ft above the flopr How far from the woJJeach of three sides and 2 In on the fourth side to allow should Llnpsay whose fives are 5 ft from the floor atand room for binding What dimensiongt wilL allow the In order to get the bost view of the painting (The bestmiddotmaximum area offor the prmlld region view occurs when the angle of vision from the bottom to A 24 In x 4 in C)12 In x 6 In the top of the palnlIng Is maximized) B161nx61n 0192Inx5 In ~ 1 ft C 3 ft

(8 J 2 ft O 4 ft31 A runner and his trainer are standing together on a circular track of radlus 100 meters When the trainer 4f A r~aclI~e su~alance has a mall$ of 100 mg After 10gives a signal the runnfr starts to run around tho track at years It has decayed to a mass of 75 mg What will thea speed of 10 mla How faat la the distance Ielween the

ma~f the ublance be after another 10 yearsrunner and the trainer Inmiddoteaalng when the runner has rUr1 Po 5625 mg C 4934 mg Yo of he way around the track bull 3436 mg D 6312mg Po 22 mJs e 42 mls B 32 mls ~2 fills 42 The halfmiddotflfe ofC (carbon-14) Is 5730 years How lon5

willI taka a 100-mg sample of HC to decay to 90 mg 32 A man at poInt A on the shore 6f a circular lake of radls

A 67645 year~ C 76096 years ~ ~ _ ~ 1 mile wantll to reach point B on the shore diametrically B 99029 years D 63094 years opposite A If he can row a boat 3 mllh and jog 6mllh at what angle ewith tbe diameter shculd he ro~ in cmiddotrder to lOe reactimiddot~ In the shortet POSSible Ume

A) 0524 rad C 0223 rad 43 How old Is a fossil whose iiC rallo Is 10 percent of that It 0325 rad 00113 rad found In the atmosphere today

A 16 000 years old C 18 000 years old 33 Two vehicles A and B btart at point P and travel aast at B 17 000 years old (Ql19 000 yeara old

ratell of 10 kmlh and 30 kmlh respectively M obllerver at Q 1 km north of P Is able to obs~rve bothvehlcles 44 How iong will It take money tOdouble if It Is compounded What Is the maximum allgll3 of Sight betwean the contlnuoualy at an annual rate of 5 percent observers IIlew of A anti B 1245 years C 1526 years

A 150 C45deg s 1386 years D 1478 years B 300

- D 600 ~ - I_shy ~ I 2t Ill ~ -e ~ __ 2 of 5 T

~

ltn

~ 156lT3 C 254lTJ3 t( I -- _) ~ i _

46 According 0 New1ons law of cooling the t~mperature of middotmiddot~)256lT3 O 356lTJ3 J Ii middot an object changes at a rate proportional to the (jlfference in temperature between the object and the outsIde 08 A hole of radIus 2 Is drmed through the axIs of a sphere medIum I an object Vlhose tempsratuTIl Is 700 radius 3 Compute the volume of the remaining solid Fahrenheit Is placed In a medlum whoso temperature Is A 46-632 C 36234 - 200 and is found to bt 400 after 3 minutes what will Its B 35235 D50234 ( ~-

I rtemperatureobe after 6 minutes a h( - 1 iiI -i () II cost 005(1 + 6x + 100 dollars to produce )( pounds OfA 25 F27F7middot middott-

B 26 OF D 8 OF I ( ] shy soap Because of quantity discounts each pound sellsjCr vI 1= 09gt 12 015x dollars Compu1BJre marginal revenue

4 7 _10 mg of a radioactive substance with a half-life of 20 A 7 IQ~ hours Is Injected Into a patlents bloodstream The patient B 9 D6 returns to the medlral facility after 24 hourlgt and a technician determlnes that there are 2 mg of the 60 The cost of manufacture x baseballs IsC(x) 005x2 + substance In the patients pancreas How much of the 05x + 50 How much will It cosi to produce the 101 base substance Is In the remainder of the patlentmiddots body ball I middot tmiddot - t

A 435 mg C 315 mg A 106 C 115 bull Ej 235 mg D 135 mg B 11 6 ~ D 1055

46 An Egyptian paEyrus Ii discoverod and It Is found that the 61 The cost C(x) In thousands of dollars of a full-page rallo of c to I C 11 6i percent ct the known raUo of c advtllllsement In a magazine Is related to Its monthly 10 12C In the air today The half-life ofC Is 5730 years Howald is the papyrus middott 11 circulation by the function C(x) 5VX -900 We

A 3465 years old C 4321 years old ~ yt r ~)II j~ assume x30 where x is the circulation In thousands 01 i B) 3561 years old D 3536 years old C copies sol9 If the clrculation Is Increasing at the rate at -- 30()1) copies per month how fast Is the cost of advertlslrg

middot 49 On a day when the temperature Is 300 Celsius a cool IncreaSing when 50000 ~la are belng sold _drink is taken from a rtJrlgerator whose temperature Is A 13650 C 750 5deg If he tempeatur~ of th~rlnk Is 200 after 10 minutes t +1 1 ~ B 14675 16450 what willits temperature b fter 20 minutes J) Ii

A 24 negrees 26 negrees _ jLt 62 Find the eCjuation of the perpendicular bisector of the B 25 degrees D 27 degrees ~hi 1~ -1 t segment Joining the points (26) and (-43) l+2u -( ~

A 2x-4y+50 C4x+2y-5aOmiddot J 50 Find the area of the reglon~ounded by yX - 5x + 6 the B 2x + 4y - 5 0 D 5x - 2y 4 0

x axis and the vertical lines ~ 0 and x 4 A 143 ~63 ~ I f31 63 Find the radius of the circle circumscribing an Isosc~(~B 153 b 1713 0 Ylt1)( ~ 0 ~y right triangle having an areIO162 sq cm f ~~J~

~ oJ -I J( A 1123 ~C 1273 51 Determine the area of the region bounded by the B 10~3 6~ 1527 ~ ~

parabQla y9 - x2and the line x + y 7 )(- -11 4i ~- 92 C32 middot 64 The sides of the triangle are 40 cm 50 cm and 60 cm

B 52 D 72 J 1 lt ~ 1_bt -1) How far Is the pOint of Intersection of the perpendicular -I bisector of the sides of tHe triangle to any of Its vertex

52 Find the volume of tho olld revolution obtained by A 3024 C 2354 revolving the region bounded hy )X_)(2 and the x axis B 1527 D 4013 about the x axis JI bull I

A Tl15 CAr30 rr (gt -x ) 41 e~~Flnd the area of a regular polygon whose aide la 25 m B Tl45 D lT60 () ancrthom Is 172 m

A 1075 C1175 53 Find tho volume obtained If the region bounded by y = x 925 D1275

Rnd y =2x Is rotated about the x axis l) ) Jf- 6 6 A 34TT15 C 5tr5 1 ( ) ( ~ )1 -~ po Find the area of a hexagon with a square having an ~eO

~ 34TT15 D 14TT5 ~ ij of 72 sq cm Insclbed In a circle which Is Inscribed In cl I hexwn

54 Determine the aroa of the r~gloTl bounded by the curvey A 12477 sq cm C 15035 sq em = )(3 _ 4(1 + 3x and the x ~ 0 S x S 3) I i 15026 sq cm D 13077 sq em

AS _94 D 37112 bullbull + J l 94 1713 V J 67 Two cylinders are equal radius 3 m have their axes at

right angles Flndl the volume of the common part 55 Determine the area of the region bounded by ~e curves y A 122 cu cm C 154 cu cm

2 B 144 middotcu cm D 134 cu cm It - x and y (1- 1middot J I JA ) bull A 1613 C 154 )( omiddot

i O) 1615 0173 r 68 A solid has a ctrculer base of radius 20 cm Find the votume of the solid If every plane sectlon perpendicular-tO

56 Fi ld Ihe area of the regon bounded by tha parabola y a certain diameter Is an equilateral triangle x2

the tangent Une to the parabola at the point (2 4) and A 1847521 cm3 C 1277521 cln3

the )( Ilxls B 2047531 cm3 0 2147521 cm

middot ~ middot Geometry amp Calculus 45 How much money should Arlel invest In a bal)k ccount

paying 8 percent annuallnteresl compounded continuously If she wants to use the money to buy a $200~ car In 4 years

lt A $1452298 C $1866764 (p- ~G) B $1300732 D $1278005 shy

J 1 I- ~- -Ji i r~ 13 0 middot C 1 amp~3 0 43

57 Compute the volume of the solid obtained by rotating the 2C reglon bounded by y (I y 8 - x and the y axis about

the x axIs bull 1

3 of 5

I 1ampor61amp r ll r J 110 IlIHj(lrllurn orOLl 01 ~ roctun~ltt clrcumacrlbed (luout D fixed rectangle of length 6 IIld width 4 A (13)(e3

- (7J9)xe 3 (227)e3 C A 64 In

2 C 81 In2B (23)le- (13)xe (127e3 + C

(8) 72middot In2 D 54 In2c (29)e3 - (23)xe3

(5l7)e3 C D (213)(e3bull - (9)116 3bull (22Z)e3l C

35 A ladder 10 ft long Is res ling against the side of a building If the foot of the ladder slips away from the wall 25 If x items of a commodity are suld to a wholesaler the at ihe rate of 2 tVmln how fast la the anale between theprice per Item Is P500 - 2x - 01)2 Compute the ladder and the building changtng whon Iho rool or thomiddot middot

marginal rellenue derhed fJPYIhe sale of the 11 unit ladder Is 6 tt aWlY from th~lIdlng A 4659 ~30 Po ~ radlmln rsx Yo radmin B 4197 0417 B 13 radmln D 213 radmin

26 Boyles law states that when a gas Is compressed at 36 Two sides of a triangle are 31n and 4 In 10JI If the anQfe constant temperature the product of Its pressure and between them Is Increasing at the nite of 2 per second volume remains constmt If the prossure of a gas Is 60 how faat Is the area of the triangle Increasing when the Iblin2 when the volume Is 40 In3

flnltl the rate of change of anglA-l~ 450 prJs~Je with respect to volumElhen the volume Is 20~ Iagt 0148 In2s C 0154 In2s

6 0234 In2s D 0315 In2sml 2 2 ) pj-e1r A middot8 Iblln per In C 24 Ibll~ i er 111 3 ( ~ I 0

I ~ 8 6 Iblln2 per Inl O middot12 Ibltn per In 37 A television camera Is located 5000 tt from the base of a ~ ~+LI rock8tlaunchlng pad The camer I delgnod to rollow

the vertical path of the rocket If the rockets spe8d Is 500 2~Arectangle Is to be Inscribed In tho olilpse WO SO _ tVsec when It has risen 200~ how fast Is the carner Determine Its maximum poslble area _ 1- )( 1) angle of elevation changln this Instant 1- y A 360 C 150 bull bull v_ r Po 395 degreeasec 194 degreeslsec

(_t3~) 200 D 250 gt ~ r J v B 267 degreessec D 587 degreessec I I 3

26 A closed cylindrical can must have a volume of 1000 In 38 A lighthouse (s situated 2 km aw~y from a b8ach lnd ~ Its lateral surface Is to be constructed from a rectangular beacon revolves at the rate of 3 revoluUons per minutepiece of metal and Its top and bottoM are to be stamp~d P Is the point on the beach nearest the lighthouse howfrom square pieces of rnetnl and the rest of the square fast Is the beam of light moving along the beach when Itdiscorded What helohtmiddotNII mlnlhllze the amount of metal

Is I km from P7needed In the construction of the call

A 12n kmlmin pound 14n kmlmlnA 30n In C 50m In B 13n kmlmin G 15n kmlmin~~~~) 40n In rJ 60m In -_~ r

Two corrldora of widths a and b Interaect at right angles 29 A closed cylindrical can must have a volurtle of 10do In 39 What Is he length of the longest pipe that can be carried

Wha( radius will mlnlml~e ItampSJrface area tr -t l bj (1 ~) horizontally around the corner F 2I31fl Po 1084 In ~42 In PI - II bull 1 Po (a 113 + b2tl)312 Ca2tl + b ) B 767 In 0 1267 In f 11 I~th B (a2tl +iJ1(3)312 D (a2tl b2IJ)12

30 A publisher wants to prlQt a book whose pages are each 40 A painting of height 3 ft hangs on a wall with the botto) to have an area of 96 In The margins are to be lin on of the painting 6 ft above the flopr How far from the woJJeach of three sides and 2 In on the fourth side to allow should Llnpsay whose fives are 5 ft from the floor atand room for binding What dimensiongt wilL allow the In order to get the bost view of the painting (The bestmiddotmaximum area offor the prmlld region view occurs when the angle of vision from the bottom to A 24 In x 4 in C)12 In x 6 In the top of the palnlIng Is maximized) B161nx61n 0192Inx5 In ~ 1 ft C 3 ft

(8 J 2 ft O 4 ft31 A runner and his trainer are standing together on a circular track of radlus 100 meters When the trainer 4f A r~aclI~e su~alance has a mall$ of 100 mg After 10gives a signal the runnfr starts to run around tho track at years It has decayed to a mass of 75 mg What will thea speed of 10 mla How faat la the distance Ielween the

ma~f the ublance be after another 10 yearsrunner and the trainer Inmiddoteaalng when the runner has rUr1 Po 5625 mg C 4934 mg Yo of he way around the track bull 3436 mg D 6312mg Po 22 mJs e 42 mls B 32 mls ~2 fills 42 The halfmiddotflfe ofC (carbon-14) Is 5730 years How lon5

willI taka a 100-mg sample of HC to decay to 90 mg 32 A man at poInt A on the shore 6f a circular lake of radls

A 67645 year~ C 76096 years ~ ~ _ ~ 1 mile wantll to reach point B on the shore diametrically B 99029 years D 63094 years opposite A If he can row a boat 3 mllh and jog 6mllh at what angle ewith tbe diameter shculd he ro~ in cmiddotrder to lOe reactimiddot~ In the shortet POSSible Ume

A) 0524 rad C 0223 rad 43 How old Is a fossil whose iiC rallo Is 10 percent of that It 0325 rad 00113 rad found In the atmosphere today

A 16 000 years old C 18 000 years old 33 Two vehicles A and B btart at point P and travel aast at B 17 000 years old (Ql19 000 yeara old

ratell of 10 kmlh and 30 kmlh respectively M obllerver at Q 1 km north of P Is able to obs~rve bothvehlcles 44 How iong will It take money tOdouble if It Is compounded What Is the maximum allgll3 of Sight betwean the contlnuoualy at an annual rate of 5 percent observers IIlew of A anti B 1245 years C 1526 years

A 150 C45deg s 1386 years D 1478 years B 300

- D 600 ~ - I_shy ~ I 2t Ill ~ -e ~ __ 2 of 5 T

~

ltn

~ 156lT3 C 254lTJ3 t( I -- _) ~ i _

46 According 0 New1ons law of cooling the t~mperature of middotmiddot~)256lT3 O 356lTJ3 J Ii middot an object changes at a rate proportional to the (jlfference in temperature between the object and the outsIde 08 A hole of radIus 2 Is drmed through the axIs of a sphere medIum I an object Vlhose tempsratuTIl Is 700 radius 3 Compute the volume of the remaining solid Fahrenheit Is placed In a medlum whoso temperature Is A 46-632 C 36234 - 200 and is found to bt 400 after 3 minutes what will Its B 35235 D50234 ( ~-

I rtemperatureobe after 6 minutes a h( - 1 iiI -i () II cost 005(1 + 6x + 100 dollars to produce )( pounds OfA 25 F27F7middot middott-

B 26 OF D 8 OF I ( ] shy soap Because of quantity discounts each pound sellsjCr vI 1= 09gt 12 015x dollars Compu1BJre marginal revenue

4 7 _10 mg of a radioactive substance with a half-life of 20 A 7 IQ~ hours Is Injected Into a patlents bloodstream The patient B 9 D6 returns to the medlral facility after 24 hourlgt and a technician determlnes that there are 2 mg of the 60 The cost of manufacture x baseballs IsC(x) 005x2 + substance In the patients pancreas How much of the 05x + 50 How much will It cosi to produce the 101 base substance Is In the remainder of the patlentmiddots body ball I middot tmiddot - t

A 435 mg C 315 mg A 106 C 115 bull Ej 235 mg D 135 mg B 11 6 ~ D 1055

46 An Egyptian paEyrus Ii discoverod and It Is found that the 61 The cost C(x) In thousands of dollars of a full-page rallo of c to I C 11 6i percent ct the known raUo of c advtllllsement In a magazine Is related to Its monthly 10 12C In the air today The half-life ofC Is 5730 years Howald is the papyrus middott 11 circulation by the function C(x) 5VX -900 We

A 3465 years old C 4321 years old ~ yt r ~)II j~ assume x30 where x is the circulation In thousands 01 i B) 3561 years old D 3536 years old C copies sol9 If the clrculation Is Increasing at the rate at -- 30()1) copies per month how fast Is the cost of advertlslrg

middot 49 On a day when the temperature Is 300 Celsius a cool IncreaSing when 50000 ~la are belng sold _drink is taken from a rtJrlgerator whose temperature Is A 13650 C 750 5deg If he tempeatur~ of th~rlnk Is 200 after 10 minutes t +1 1 ~ B 14675 16450 what willits temperature b fter 20 minutes J) Ii

A 24 negrees 26 negrees _ jLt 62 Find the eCjuation of the perpendicular bisector of the B 25 degrees D 27 degrees ~hi 1~ -1 t segment Joining the points (26) and (-43) l+2u -( ~

A 2x-4y+50 C4x+2y-5aOmiddot J 50 Find the area of the reglon~ounded by yX - 5x + 6 the B 2x + 4y - 5 0 D 5x - 2y 4 0

x axis and the vertical lines ~ 0 and x 4 A 143 ~63 ~ I f31 63 Find the radius of the circle circumscribing an Isosc~(~B 153 b 1713 0 Ylt1)( ~ 0 ~y right triangle having an areIO162 sq cm f ~~J~

~ oJ -I J( A 1123 ~C 1273 51 Determine the area of the region bounded by the B 10~3 6~ 1527 ~ ~

parabQla y9 - x2and the line x + y 7 )(- -11 4i ~- 92 C32 middot 64 The sides of the triangle are 40 cm 50 cm and 60 cm

B 52 D 72 J 1 lt ~ 1_bt -1) How far Is the pOint of Intersection of the perpendicular -I bisector of the sides of tHe triangle to any of Its vertex

52 Find the volume of tho olld revolution obtained by A 3024 C 2354 revolving the region bounded hy )X_)(2 and the x axis B 1527 D 4013 about the x axis JI bull I

A Tl15 CAr30 rr (gt -x ) 41 e~~Flnd the area of a regular polygon whose aide la 25 m B Tl45 D lT60 () ancrthom Is 172 m

A 1075 C1175 53 Find tho volume obtained If the region bounded by y = x 925 D1275

Rnd y =2x Is rotated about the x axis l) ) Jf- 6 6 A 34TT15 C 5tr5 1 ( ) ( ~ )1 -~ po Find the area of a hexagon with a square having an ~eO

~ 34TT15 D 14TT5 ~ ij of 72 sq cm Insclbed In a circle which Is Inscribed In cl I hexwn

54 Determine the aroa of the r~gloTl bounded by the curvey A 12477 sq cm C 15035 sq em = )(3 _ 4(1 + 3x and the x ~ 0 S x S 3) I i 15026 sq cm D 13077 sq em

AS _94 D 37112 bullbull + J l 94 1713 V J 67 Two cylinders are equal radius 3 m have their axes at

right angles Flndl the volume of the common part 55 Determine the area of the region bounded by ~e curves y A 122 cu cm C 154 cu cm

2 B 144 middotcu cm D 134 cu cm It - x and y (1- 1middot J I JA ) bull A 1613 C 154 )( omiddot

i O) 1615 0173 r 68 A solid has a ctrculer base of radius 20 cm Find the votume of the solid If every plane sectlon perpendicular-tO

56 Fi ld Ihe area of the regon bounded by tha parabola y a certain diameter Is an equilateral triangle x2

the tangent Une to the parabola at the point (2 4) and A 1847521 cm3 C 1277521 cln3

the )( Ilxls B 2047531 cm3 0 2147521 cm

middot ~ middot Geometry amp Calculus 45 How much money should Arlel invest In a bal)k ccount

paying 8 percent annuallnteresl compounded continuously If she wants to use the money to buy a $200~ car In 4 years

lt A $1452298 C $1866764 (p- ~G) B $1300732 D $1278005 shy

J 1 I- ~- -Ji i r~ 13 0 middot C 1 amp~3 0 43

57 Compute the volume of the solid obtained by rotating the 2C reglon bounded by y (I y 8 - x and the y axis about

the x axIs bull 1

3 of 5

ltn

~ 156lT3 C 254lTJ3 t( I -- _) ~ i _

46 According 0 New1ons law of cooling the t~mperature of middotmiddot~)256lT3 O 356lTJ3 J Ii middot an object changes at a rate proportional to the (jlfference in temperature between the object and the outsIde 08 A hole of radIus 2 Is drmed through the axIs of a sphere medIum I an object Vlhose tempsratuTIl Is 700 radius 3 Compute the volume of the remaining solid Fahrenheit Is placed In a medlum whoso temperature Is A 46-632 C 36234 - 200 and is found to bt 400 after 3 minutes what will Its B 35235 D50234 ( ~-

I rtemperatureobe after 6 minutes a h( - 1 iiI -i () II cost 005(1 + 6x + 100 dollars to produce )( pounds OfA 25 F27F7middot middott-

B 26 OF D 8 OF I ( ] shy soap Because of quantity discounts each pound sellsjCr vI 1= 09gt 12 015x dollars Compu1BJre marginal revenue

4 7 _10 mg of a radioactive substance with a half-life of 20 A 7 IQ~ hours Is Injected Into a patlents bloodstream The patient B 9 D6 returns to the medlral facility after 24 hourlgt and a technician determlnes that there are 2 mg of the 60 The cost of manufacture x baseballs IsC(x) 005x2 + substance In the patients pancreas How much of the 05x + 50 How much will It cosi to produce the 101 base substance Is In the remainder of the patlentmiddots body ball I middot tmiddot - t

A 435 mg C 315 mg A 106 C 115 bull Ej 235 mg D 135 mg B 11 6 ~ D 1055

46 An Egyptian paEyrus Ii discoverod and It Is found that the 61 The cost C(x) In thousands of dollars of a full-page rallo of c to I C 11 6i percent ct the known raUo of c advtllllsement In a magazine Is related to Its monthly 10 12C In the air today The half-life ofC Is 5730 years Howald is the papyrus middott 11 circulation by the function C(x) 5VX -900 We

A 3465 years old C 4321 years old ~ yt r ~)II j~ assume x30 where x is the circulation In thousands 01 i B) 3561 years old D 3536 years old C copies sol9 If the clrculation Is Increasing at the rate at -- 30()1) copies per month how fast Is the cost of advertlslrg

middot 49 On a day when the temperature Is 300 Celsius a cool IncreaSing when 50000 ~la are belng sold _drink is taken from a rtJrlgerator whose temperature Is A 13650 C 750 5deg If he tempeatur~ of th~rlnk Is 200 after 10 minutes t +1 1 ~ B 14675 16450 what willits temperature b fter 20 minutes J) Ii

A 24 negrees 26 negrees _ jLt 62 Find the eCjuation of the perpendicular bisector of the B 25 degrees D 27 degrees ~hi 1~ -1 t segment Joining the points (26) and (-43) l+2u -( ~

A 2x-4y+50 C4x+2y-5aOmiddot J 50 Find the area of the reglon~ounded by yX - 5x + 6 the B 2x + 4y - 5 0 D 5x - 2y 4 0

x axis and the vertical lines ~ 0 and x 4 A 143 ~63 ~ I f31 63 Find the radius of the circle circumscribing an Isosc~(~B 153 b 1713 0 Ylt1)( ~ 0 ~y right triangle having an areIO162 sq cm f ~~J~

~ oJ -I J( A 1123 ~C 1273 51 Determine the area of the region bounded by the B 10~3 6~ 1527 ~ ~

parabQla y9 - x2and the line x + y 7 )(- -11 4i ~- 92 C32 middot 64 The sides of the triangle are 40 cm 50 cm and 60 cm

B 52 D 72 J 1 lt ~ 1_bt -1) How far Is the pOint of Intersection of the perpendicular -I bisector of the sides of tHe triangle to any of Its vertex

52 Find the volume of tho olld revolution obtained by A 3024 C 2354 revolving the region bounded hy )X_)(2 and the x axis B 1527 D 4013 about the x axis JI bull I

A Tl15 CAr30 rr (gt -x ) 41 e~~Flnd the area of a regular polygon whose aide la 25 m B Tl45 D lT60 () ancrthom Is 172 m

A 1075 C1175 53 Find tho volume obtained If the region bounded by y = x 925 D1275

Rnd y =2x Is rotated about the x axis l) ) Jf- 6 6 A 34TT15 C 5tr5 1 ( ) ( ~ )1 -~ po Find the area of a hexagon with a square having an ~eO

~ 34TT15 D 14TT5 ~ ij of 72 sq cm Insclbed In a circle which Is Inscribed In cl I hexwn

54 Determine the aroa of the r~gloTl bounded by the curvey A 12477 sq cm C 15035 sq em = )(3 _ 4(1 + 3x and the x ~ 0 S x S 3) I i 15026 sq cm D 13077 sq em

AS _94 D 37112 bullbull + J l 94 1713 V J 67 Two cylinders are equal radius 3 m have their axes at

right angles Flndl the volume of the common part 55 Determine the area of the region bounded by ~e curves y A 122 cu cm C 154 cu cm

2 B 144 middotcu cm D 134 cu cm It - x and y (1- 1middot J I JA ) bull A 1613 C 154 )( omiddot

i O) 1615 0173 r 68 A solid has a ctrculer base of radius 20 cm Find the votume of the solid If every plane sectlon perpendicular-tO

56 Fi ld Ihe area of the regon bounded by tha parabola y a certain diameter Is an equilateral triangle x2

the tangent Une to the parabola at the point (2 4) and A 1847521 cm3 C 1277521 cln3

the )( Ilxls B 2047531 cm3 0 2147521 cm

middot ~ middot Geometry amp Calculus 45 How much money should Arlel invest In a bal)k ccount

paying 8 percent annuallnteresl compounded continuously If she wants to use the money to buy a $200~ car In 4 years

lt A $1452298 C $1866764 (p- ~G) B $1300732 D $1278005 shy

J 1 I- ~- -Ji i r~ 13 0 middot C 1 amp~3 0 43

57 Compute the volume of the solid obtained by rotating the 2C reglon bounded by y (I y 8 - x and the y axis about

the x axIs bull 1

3 of 5

hmiddot Geometry amp Calculus

If Ihe edge of a cube is increased by 30 by how much6fJ I

~~I

is Ihe surface orea inGretlse~ A 30 ( G 69 8 21 -D33

Imiddot 70 If sin3x~cos6y then

A l( -2y 30 0+2Y==30 B x + Y 180 O x + y = 90

71 Compute the angle between I~e line 2y - 9x - 18 == the x axis

A 64 54 0

8 450

72 A hul has a parabolic crossmiddotsectlon whose height Is 30 ni and whose base ls 60 m wide If a ceiling 40 m wide Is to be placed Inside th~ hut how high will It be above the base

A 1667 m C 1447 m 8 1548 m 01985 m

73 An ellipse has an eccentdclty of 13 Compute the distance between directrices If the distance betwfen foci middot Is 4 ) C 2

1 18 C32 eo ~ B 36 O 38 gt c

rt 74 The area of an Isosceles triangle Is 36 m2 witt1 the

smallest angle aqua to one third of Ihe other angle Find thft Iftngth of the shortest side

A 1298 m C 457 m) 8 573 m O 6B4 m

75 Compute the area of bimiddotrectangular spherical triangle havil)g an angle of 600 and a radius of 8 m

A 7656 m2 C 5634 m2 2S 4565 m2 06702 m

76 Two balls one 6 cm In diameter and the olhe4 cm In diameter are plactld In a cylindrical Jar 9 cm In diameter Find the volume of water necersary to cover them

A 23444 cm3 C 36233 cm3

B 25722 cm1 D 26222 cmJ

77 The langsnl and a secant to a circle are from the same external point If the tanoent Is 6 Inches arid the external segment of the secant I~ 3 Inchus cClmpute the length of tho secant

A 10 C12 B lJ 011

7H Two circles with rndll 8 and 3 ale tangent to each other extornally What Is the distance betwflen the points of tangency of onfl of their common uxternal tangents

A 78 m C 107 m B 98 m D 67 m

79 The diameters of tile two clrcles middotthat are tangent Internally are 18 and 8respuctlvely What Is the length of the tangent segment fom the centsr of the larger circle to the smaller circle

A 2 C 3 S 4 05

80 Three Identical circles are iang~nt to each other externally If the area of the curvilinear triangle enclosed between thll poInts of tangency of the 3 circles Is 16 13 compute the radius of each circle

A Ul cm C 9cm 8 ~ 13cm D15cm

Two men A and B starting at the same point at tle same circumference of a circle walked at the same rate of 60 illmin if A walks towards the center and B W31ks around tt]e circumference and the rsdlufl of the circle Is 800 m

find Ihe distance betwoen the two men A and B after 5 minutes

A 28367 m C 32150 m 8 41256 m D26160m

82 Given a solid right circular cone having a height of 8 cm has a volume equal to 4 times the volume of the smaller cone that could be cut from the same cone having the SalJlli-S~ls Compute the height of the smaller cone

IA- 504 em C 445 cm 8 J25 cm D 232 cm

83 The diameter of a sphere and the base of a cone ere equal What percentage of that diameter must the canas height be so that both volumes are equal

A 100 C 50 B 20Q (95 400

64 The volume of a regular pyramid whose base Is a regular hexagon Is 156 m3

bull If the altitude of the pyramid Is 5 m find the sides of thebase I~

A 4m 19 6m B 8m O3m

85 The base of a cylinder Is a hexagon Inscribed In a circle If the difference In the circumference of the clrclll and thlJ porlmetllr of the hexagon Is 4 em find the volume oftN t cyllnder if It has an altitude of 20 cm

J J A 10367 middotcm C10123 cm

middot B 12239cmJ D11231cmJ I I) I ~

86 A solid has a circular base of diameter 040 em Find the volume of the s)lid If every section perpendicular to a fixed diameter Is an Isosceles right triangle

A 32223 56 C1066667 ~ B 1255560 D1204448

87 The volume of a truncated prism wlih an equilateral triangle a~ Its horizontal base Is equal to 3600 cm3

bull The vertical edgeli at each corners are 4 6 and 8 cm respectively Find one sld~lthe base

A 2237 (G ~722 bull B 2543 U-1789

ltJj

88 Find the area of a pentagonal spherical pyramid the angles of whose base are 105deg 126deg 134~ 146~ and 1Sfo on the sphere of radius 12 m

A 32421 C 22234 B 34356 043367

BD How mllny odoos arether~ a regular octahedron - A 8 ~2

B 20 030

90 Philippine Air Lines flew from Tokyo whose latitude Is 140 36N and longitude of 121 00SE on a course S300W and maintaining a uniform altitude What will be Its course at the point where It crosses the eQuator

A S28036W C~ Sl1012W B S250 15W D S320 05W

91 Compute thelt[1gLeQC(ncilnalon of the IIAe 2y - 9x - J6 l 0 0 ---middot middot middot0

~ middotmiddotf427 C 6744 ~74700 54360

92 The difference of the distances ot a moving point from (10) and (-10) Is 1 Find the equation of Its locus

A 4x2 -121 3 C12-4l 3 B 3 - 4Y = 12 D 4 - 9Y 3

93 A locus of a point whose difference of the distances frorn two fixed points Is consta(gt

A Ellipse C Hyperbola B Parabola Circle

J

0 and

I

4 of 5

0

-

Geometry amp Calculus Find the shortest dlstal1ce frorr (3 8) to the curvell +

+4x-6y12 A 121 C 409 B i 207 0373

95 Find the volume of the pyramid fonned In the octant by the plane 6x + 1 Oy + 5z - 30 = 0 and the coordinate axes

A 13 C 14 I r rr bull B 12 D 15 j ~I ( J

bull ~ I L bull

06 Wht conic section is described by the equation r -G(4-3cosO)

A Circle C Hyperbola B Ellipse D Parabola

97 What is the new equation of the lint) 5x+4y+3=0 If the origin Is translated to tile point (12)7

A 4x + 3y + 16 0 C 5x - 4y - 16 0 B 5x+4y+16iJ D6xmiddot+6y-160

Oil Detrmino the equation of the perpendicular bisector of the segment PQ if P (-Z 3) and Q (4 -5) rYir

A 3y -3x + 7 =0 C4x - 3y + 7 = 0 1) dfiln ~ B 6x - 8y - 14 OcJx - 4y - 770

go n ellipse has lis center at (OO) with lis axis horizontal 7he distance between the vertlcos Is 8 and Its eccentricity is 05 Compute the length of the longest foltal radius from point (23) on the curve

A 3 C4 8 5 0 6

1uOFind lle area of the triangle whose vertices have polar coordinates ot OOmiddot) (620middot) and (850middot)

A 9 sq units C 12 sq units B 16 sq units D 15 sq units

5 of 5

1 A 2 B 3 A 4 C 5 D 6 C 7 A 8A 9C 10 B

41 A 42C 43D 44 B 45 A 46D 47B 4B B 49C 50D

B1 B 82B 83 A 84C 85A B6A 87C 88 D

89C 90 D

ANSWER KEY Geometry amp Caluculus

t

1113 21 B 12lt 22 B 13D 23 A 14A 24 D 15B 25C 16 D 26 A 17C 278 lB C 2B B 19 D 29C 20C 30 C

51 A 61 D 52C 62 C 53 B 63C 54C 64 C 55 B 65 B 56 B 66 A 57B 67 A 58 D 68 D 59C 69 B 60 D 70 C

91 B 92B 93C 94D 95C 96B 97A 9B D 99C 100 A

31 D 32A 33 B 34 B 35C 36A 37C 38 D 39C 30 B

71C 72 D 73 A 74 D 75C 76 A 77 D 7BC 79B BO B

1 A 2 B 3 A 4 C 5 D 6 C 7 A 8A 9C 10 B

41 A 42C 43D 44 B 45 A 46D 47B 4B B 49C 50D

B1 B 82B 83 A 84C 85A B6A 87C 88 D

89C 90 D

ANSWER KEY Geometry amp Caluculus

t

1113 21 B 12lt 22 B 13D 23 A 14A 24 D 15B 25C 16 D 26 A 17C 278 lB C 2B B 19 D 29C 20C 30 C

51 A 61 D 52C 62 C 53 B 63C 54C 64 C 55 B 65 B 56 B 66 A 57B 67 A 58 D 68 D 59C 69 B 60 D 70 C

91 B 92B 93C 94D 95C 96B 97A 9B D 99C 100 A

31 D 32A 33 B 34 B 35C 36A 37C 38 D 39C 30 B

71C 72 D 73 A 74 D 75C 76 A 77 D 7BC 79B BO B