@L|}6CD l0C)HCC WhL/h `CmCDiD`  R@W1  c0@R !L` D  C D     )16CS R)  C)D1 p p 0 C9DI pCDL~CiCDiD`!"jINLINETRANSLATLOOFLSALDN(@#@6@@##26}-@6-@<;$,;,F((6.D:GBBD:HBBD:IBBD:JBBD:KBBD:LCCd;AU,;,@8@@2}R1:;NO TRANSLATE,,@6@@R1:-@$&@6.7<%&@,} @@$$@@R1:"7,@@@R1:7START IO,} @A6@@ @A-@@@@STOP IO0 }4$$$$$$A D @N b$$@@R1:l7,@@@R1: }7START IOv @A $$@@R1:7,@@@R1:7 }START IO @A@STOP IO@  D:G1@@##26\G. Special TrianglesMake sure you know these theorems&definitions and assumptions.~RA~SB~SP266095224095224031266095~S }H1335s~SH0736h~SF`A. The 30*& 60*& 90* Triangle.1. The side(s) oppositethe 30* angle equalsone-half the hypotenuse (h)}.` s = h/22. The side(s) oppositethe 60* angle equalsone-half the hypotenuse (h)` _times \/3.` h } _` s = - \/3` 2~RA~SB~SH1433s~SH0729s s~SH0934a~SP182095266095224031182095~SP22403122409522409522409}5~SF3. The altitude (a) ofan equilateral triangleequals one-half the` _side(s) times \/3.` s _}` a = - \/3` 2~RA~SB~SH0733h s~SH1134s~SP210079258079258031210079~SF`B. The 45*& 45*& 90* Triangle1. T}he side(s) opposite the45* angle equals one-half` _the hypotenuse (h) times \/2.` h _}` s = - \/2` 22. The hypotenuse (h) _equals the side (s) times \/2.` _` h = s\/2~RA~SB~S}H1134s~SH0730s d s~SH0434s~SP210079258079258031210079~SP258031210031210079210079~SF3. The side of a square(s)equal}s half the diagonal (d)` _times \/2.` d _` s = - \/2` 24. The diagonal (d) of asquare equa}ls the side(s)` _times \/2.` _` d = s \/2~RA~SD~Q1. Find the altitude of an equilateraltriangle }whose side is 10.` _ _(a) 5 (b) 5\/2 (c) 5\/3` _ _(d) 10\/2 (e) 10\/3~RCC` } _1. (c) 5\/3 Ans.Note~ Draw an altitude (a) to create a30*& 60*& 90* triangle.` 1 _` a = -10\/3` } 2` _` a = 5\/3 Ans.~RA~Q~SB~SH0729s s~SH09336~SH1326A s B~SH0333C~SP1820952}66095224024182095~SP224024224096224095224095~SF2. Find the side s ofequilateral triangle ABCwhose altitude is 6.` } _ _(a) 3 (b) 2\/3 (c) 3\/3` _ _(d) 4\/3 (e) 6\/3~RCD` _2. (d) 4\/3 Ans.Altitud}e of an equilateral` S _triangle equals -\/3` 2` S _` -\/3 = 6` 2` _` S \/3 = 1}2` _` 3S = 12\/3` _` S = 4\/3 Ans.~RA~Q~SB~SH0330A~SH1329B~SH1029D C~SP203024203}096238078203024~SP203078238078238078238020~SF3. In {ABC& AC = 8} and } 45*~RATherefore& {CEF is an isosceles righttriangle in which the sides are 1}. Thehypotenuse EC = 2s` ?} = 2 (1})` = 2} Ans.~ET~ETorems&definitions and assumptions.~RA~SB~SP266095224095224031266095~S3~SB~SP182063224063196016182063~SP196016196063196063196063~SP238063259063245040238063~SP245040245063245063245063~SH0927AA}'D' B'A D B~SH0229C'~SH0629h'~SH0536C~SH0836h~SFJ.Similar Figures.Make sure you know thesetheorems& definitions andB}assumptions.1. Corresponding lines&sides& and perimeters (p)of similar polygons arein proportion.` h s pthC}en& -- = -- = --` h' s' p'~RA~SD2. Areas (A) of similar polygons are toeach other as the squares ofcorrespondD}ing lines& sides& andperimeters.` {ABC is similar to {A'B'C'` then~` 2 2 2` A h s pE}` - = --- = --- = ---` 2 2 2` A' h' s' p'~RA3. In any two circles~` C r d` -- = F}-- = --` C' r' d'` 2 2 2` A r d C` - = --- = --- = ---` 2 2 2` G}A' r' d' C'~RAExample~Given~ Circle O is 4 times as large ascircle O'. Radius OP = 10}.Find~ Length of radius O'H}P'.Let O' P' = ya) In circles O and O'&` 2` A OP` - = -----` 2` A' I} O'P'~RA` 2` 4 10b) then~ - = ---` 2` 1 y` 2` 4y = 100` J} 2` y = 25` y = 5} Ans.~RA~Q1. The sides of two similar polygonsare in the ratio 4~1. TheircorresK}ponding perimeters are in theratio~(a) 4~1 (b) 8~1 (c) 12~1 (d) 16~1(e) 2~1~RCA1. (a) 4~1 Ans.` p s` -- = L}--` 1 1` p s` p 4` -- = - Ans.` 1` p 1~RA~Q2. The areas of two similar trianglesare in the raM}tio 4~9. Theircorresponding sides are in the ratio~(a) 16~81 (b) 4~9 (c) 2~9/2 (d) 2~3(e) 3~2~RCD2. (d) 2~3 Ans.`N} 2` s A` ---- = --` 2` 1 1` (s ) A` 2` s 4` ---- = -` 2` 1` (s ) 9~RA` O} _` s \/4` -- = ---` 1 _` s \/9` s 2` -- = - Ans.` 1` s 3~RA~Q3. The circumferences oP}f two circlesare 4#} and 9#}& respectively. Theirareas are in the ratio~(a) 4~9 (b) 2~3 (c) 8~18 (d) 16~81(e) 16#~81Q}~RCD3. (d) 16~81 Ans.` 2` c a` ----- = --` 2` (c') a'` R} 2` (4#r) a` ------ = --` 2` (9#r) a'` 2 2` 16# r a` ----S}-- = -- Ans.` 2 2` 81# r a'~RA~Q~SB~SP217016217095252095217016~SP238064238095238095238095~SH0831yT}~SH13333 2~SH10344~SF4. Find y in the diagram~(a) 10 (b) 6 (c) 2.5(d) 1.5 (e) 5~RCA4. (a) 10 Ans.` y 4`--U}--- = -`(3+2) 2` y` - = 2` 5` y = 10 Ans.~ET~ET063245040238063~SP245040245063245063245063~SH0927AIK. Volumes.Make sure you know these theorems&definitions and assumptions.Volume is the measure in cubic units ofthe sp W}ace contained in or occupied byan object.1. Rectangular Solid.` Volume = Bh = lwh2. Cube.` 3` X} Volume = e~RA3. Right Circular Cylinder.` 2` Volume = Bh = #r h~RA4. Sphere` Y} 3 3` Volume = 4/3#r = 1/6#d~RAExample~A cylindrical bar of metal having acircular base of radius 5 Z} inches and aheight of 3 inches weighs 1000 grams.What would a cylindrical bar of thesame metal weigh if its circular base [}has a radius of 3 inches and its heightis 5 inches?~RA` 2 2` V = #r h V' = #r \}h` 2 2` V = 5 x 3# V' = 3 x 5#` V = 75# V' = 45#` Dire ]}ct proportion` V W` -- = --` V' W'` 75# 1000` --- = ----` ^} 45# y` 75y = 45000` y = 600 grams Ans.~RA~Q1. A tank 8' x 6' x 5' is filled with _}aliquid weighing 120 lbs. What would bethe weight of a quantity of this liquidwhich fills a tank 4' x 3' x 1'?(a) 20 lbs `}. (b) 12 lbs. (c) 10 lbs.(d) 6 lbs. (e) 4 lbs.~RCD1. (d) 6 lbs. Ans.` V W` -- = --` 1 1` V W a}` 8x6x5 120 lbs.` ----- = --------` 1` 4x3x1 W` 240 120` --- = ---` 1` 12 b}W` 1` W = 6 Ans.~RA~Q2. A cylinder with base diameter of 10}and height of 6} weighs 15 lbs. Whatwould a cylin c}der of base diameter 6}and height of 10} weigh if it is madeof the same material?(a) 90# lbs. (b) 360# lbs. (c) 25 lbs. d}(d) 9 lbs. (e) 3# lbs.~RCD2. (d) 9 lbs. Ans.` V W` -- = --` 1 1` V W e}` 2` #(5) (6) 15` ----- ---- = --` 2 1` #(3) (10) W` 150# 15 lbs.` ---- = f}-------` 1` 90# W` 1` W = 9 lbs. Ans.~RA~Q3. Find the edge of a cub g}e whose volumeis 64 cu. in.(a) 4 in. (b) 8 in. (c) 10 2/3 in.(d) 21 1/3 in. (e) 2 in.~RCA3. (a) 4 in. Ans.` h} 3` V = e` 3` 64 = e` 4 in. = e Ans.~RA~Q4. A sphere is inscr i}ibed in a cube 6}on an edge. The difference in volumebetween the cube and the sphere incubic inches is~(a) 432# (b) 180 j}# (c) 216 (d) 36#(e) 216 - 36#~RCE4. (e) 216 - 36# Ans.` Cube Sphere` e = 6 r = 3` k} 3 4 3` V = e V = -#r` 3` 3 4` l} V = 6 V = -(27)#` 3` V = 216 V = 36#Difference = 216 - 36# Ans.~RA m}~Q5. A rectangular swimming pool is 50ft. by 120 ft. Water is entering at therate of 1750 gallons per minute. Howmany hou n}rs will it take to fill thepool to a depth of 7 feet?(7 1/2 gallons = 1 cu. ft.)(a) 1 4/5 (b) 3 (c) 3 1/5 (d) 180(e o}) 2 1/2~RCB5. (b) 3 Ans.V = 1whV = (120) (50) (7)V = 42&000 cu. ft. x 7 1/2 gal/cu.ft.` = 315&000 gal1750 Gal/min p} x 60 min/hr.=` 105&000 gal./hr.` 315&000 gal.` -------------- = 3 hr. Ans.` 105&000 gal/hr~ET }~Q1. The wheel of a bicycle is 28 inchesin diameter. Compute the number of feetthat will be covered in six turns ofthe wr}heel of this bicycle.(use # = 22/7)(a) 14 ft (b) 44 ft (c) 88 ft(d) 308 ft (e) 528 ft~RCB~Q2. A circle has a diames}ter that is 20inches longer than the diameter ofanother circle. If the radius of thesmaller circle is r& the circumferencet}of the smaller circle is to thecircumference of the larger as~` 2r 2r r(a) ------ (b) ------ (cu}) -------` r + 10 r + 20 2r + 20` r r(d) ------ (e) ------` r + 20 r + 10~RCE~Q3. Tv}he angles of {LMN are y*& y/2 + 10*and 3y - 10*. Find y.(a) 20 (b) 30 (c) 40 (d) 110(e) 120~RCC~Q4. The two legs ow}f a right triangle are.6} and .8}& respectively. The numberof inches in the hypotenuse is~(a) .14} (b) 1} (c) .10} (d)x} 14}(e) .2}~RCB~Q~SB~SP196024259024259070196070~SP196070196024197024210070~SH0328D~SH0338C~SH1028A E~SH1038B~SFy}5. The area of rectangleABCD is equal to 48 sq.in. and AE~EB as 1~3.The number of sq. in.in {ADE is~(a) 6 (b) 12 (c) z}16(d) 24 (e) 8~RCA~SD~Q6. The radius of a circular playgroundis 4 times the radius of a circularpool with the same c{}enter. The ratio ofthe area of the pool to the area of theplayground is~(a) 2~1 (b) 1~2 (c) 4~1 (d) 16~1(e) 1~16~RC|}E~Q7. A boat sailed 35* due east along aparallel of latitude. If it startedfrom a port situated on 22* westlongitude& it}}s new position is~(a) 57* west long.(b) 57* east long.(c) 13* west long.(d) 13* east long.(e) 0* east long.~RCD~Q8. ~}The diagonal of a square divides itinto two triangles each 32 sq. in. inarea. The length of the diagonal ininches is~` } _ _(a) 16\/2 (b) 16 (c) 8\/2` _ _(d) 32\/2 (e) 4\/2~RCC~Q9. The scale of a map is }1 in. = 50miles. The actual area in square milesof a circle 2 inches in diameter is~(a) 50# (b) 100# (c) 200# (d) 2500}#(e) 10&000#~RCD~Q10. A rectangle is 4 inches longer thanit is wide. Its perimeter is 20 inches.The number of square i}nches in its areais~(a) 96 (b) 32 (c) 21 (d) 12 (e) 36~RCC~Q11. Through how many degrees does thehour hand of a cl}ock move in 150minutes?(a) 2 1/2* (b) 25* (c) 75* (d) 150*(e) 256/#*~RCC~Q~SB~SH0927A B~SH0533C~SH033}7D~SP259024189064266064227040~SF12. AC = 10}&