,,UEB ,,TE*NICAL ,ALGEBRA & ,GEOMETRY ,- ,BASIC PRES5T$ BY ,W5DY ,B5CKHUYS51 ,COMMITTEE ,VICE-,*AIR ,NOVEMB] #BJ1 #BJBJ ,ONL9E1 ,VIRTUAL ,3F];E ,,,NA;NAL BRL ASSOCIA;N,' #IE ,ALL5S ,CREEK ,ROAD1 ,BUILD+ #A1 ,SUITE #BJB1 ,RO*E/]1 ,,NY #ADFAH ^C ,? MAT]IAL MAY N 2 REPRODUC$ )\T ! WRITT5 3S5T ( ! ,NA;NAL ,BRL ,ASSOCIA;N1 ,9C4 ,9 #A ,VOLUME ,BRL PAGES T#A-T#B1 P#A-P#B1 & #A-#DG ,PR9T PAGES I-AII & #C-A#CB T#A ,,TRANSCRIB]',S ,,NOTES ,MO/ EXAMPLES T >E ,,PR9T$ 9 SIMBRL >E PREC$$ BY ! H1D+ ,2G9N+ ( ,EXAMPLE 5CLOS$ 9 TRANSCRIB]'S NOTE 9DICATORS4 ,COM;T>Y TO S* EXAMPLES IS PREC$$ BY ! H1D+ ,COM;T>Y TO ! ,PREC$+ ,EXAMPLE1 5CLOS$ 9 TRANSCRIB]'S NOTE 9DICATORS4 T#B ,3T5TS I-II ,9TRODUC;N """""""""""""""""""""""""" #C ,SUP]SCRIPTS """""""""""""""""""""""" #D .=9 & 8IN0 ,- GRADE #A 9DICATORS "" #D ,SCOPE ( A ,SUP]SCRIPT ,9DICATOR "" #F ,H[ TO MAKE YR SUP]SCRIPT LA/ L;G] """""""""""""""""""""""""""" #F ,? APPLIES TO ,,SUBSCRIPTS1 ,,TOO6 """""""""""""""""""""""""" #G ,COMMON ,MODIFI]S """"""""""""""""""" #H ,SCOPE ( A ,COMMON ,MODIFI] """"""" #I 8,B>S & DOTS ETC40 & GRADE #A 9DICATORS """""""""""""""""""""" #AJ ,L9E ,NOTA;N """"""""""""""""""""" #AA ,%APE ,SYMBOLS & ! ,%APE ,T]M9ATOR #AB ,9ITIAL ,%APE ,9DICATORS """"""""" #AB ,SPECIFIC ,%APE ,SYMBOLS """"""""" #AB .=$ & 8$0 ,- GRADE #A 9DICATORS "" #AD ,%APE ,T]M9ATOR """""""""""""""""" #AE .=: & .1,%APE .1,MODE ,- NO GRADE #A 9DICATORS """"""""""""" #AF ,%APES = ,M1SURE;T OR ,ID5TIFICA;N #AG ,"S ,EXAMPLES = ,4CUS.N """""""""" #AH P#A AII ,! ,B1UTY ( ,PR9T """""""""""""""""" #BA ,IGNORE ,TYPE=M = ,V>IABLES """""" #BA ,FOLL[ ,,BANA ,=MATT+ ,GUIDEL9ES #BB ,O!R ,3SID]A;NS """""""""""""""""" #BC ,,GTM ,SEC;N #C3 ,SIGNS ( ,OP]A;N & ,COMP>ISON """"""""""""""""""" #BE ,OP]A;N ,SIGNS @& ,COMP>ISON ,SIGNS """"""""""""""""""""""""" #BE ,SPAC+ """"""""""""""""""""""""""" #BF ,M9US """""""""""""""""""""""""""" #BG ,POSITIVE & ,NEGATIVE ,NUMB]S """" #BH ,! ,HOLL[ ,DOT """"""""""""""""""" #CJ ,! ,A/]ISK """"""""""""""""""""""" #CA ,3CEPTS = ,ALGEBRA & ,GEOMETRY """"" #CB ,CLOS+ ,^WS """""""""""""""""""""""" #CB P#B ,,UEB ,,TE*NICAL #C ,ALGEBRA & ,GEOMETRY ,- ,BASIC ,9TRODUC;N ,! GOAL ( ? "W%OP IS TO DRAW ATT5;N TO & CL>IFY "S SEC;NS ( ! ,RULES ( ,,UEB "<9CLUD+ ! ,GUIDEL9ES = ,TE*NICAL ,MAT]IAL"> T (T5 COME 9TO PLAY :5 TRANSCRIB+ ALGEBRA & GEOMETRY MAT]IAL4 ,F/1 WE W T1SE \ J #E 3CEPTS1 Z \TL9$ 9 ? DOCU;T'S TABLE ( 3T5TS4 @.<,! L9K = ! "UL9$ TEXT 9 ! FOLL[+ P>AGRAPH IS3 HTTP3_/_/ICEB4" ORG_/UEB4HTML@.> ,NEXT1 WE W /UDY ,,GTM ,SEC;N #C1 8,SIGNS ( ,OP]A;N & ,COMP>ISON10 A NEW V].N ( : 0 PUBLI%$ ON ! _7,,UEB PAGE ( ,,ICEB'S WEBSITE_' 9 ,OCTOB] #BJAH "<,,ICEB IS AN A2REVIA;N = ,9T]NA;NAL ,C\NCIL ON ,5GLI% ,BRL">4 ,? "W%OP IS N 9T5D$ TO 2 A C]TIFICA;N-/YLE C\RSE 9 TRANSCRIB+4 ,X IS 9T5D$ TO 2 A SUPPORT TO ! /UDY ( #A ! PRIM>Y RES\RCES4 A#C ,? "W%OP DOES N REPLACE OR SUP]S$E ANY ,,BANA OR ,,ICEB PUBLICA;N4 --------------------------------------#D ,SUP]SCRIPTS ,A SUP]SCRIPT IS A LR1 FIGURE1 OR SYMBOL WRITT5 OR PR9T$ ABV ! L9E4 "<,OX=D"> ,S9CE WE _C *ANGE ! PHYSICAL %APE OR V]TICAL POSI;N ( BRL1 WE USE BRL SYMBOLS TO GIVE 9=MA;N AB PR9T L9E POSI;N4 ,"S ( ! BRL SYMBOLS WE USE TO D ? >E %[N 2L4 ,SUP]SCRIPT " .=9 ,OP5+ BRL GR\P+ 9DICATOR .=< ,CLOS+ BRL GR\P+ 9DICATOR .=> "<,! DOT LOCATOR = M5;N .= %D PREC$E EA* SYMBOL ON A ,SPECIAL ,SYMBOLS ,PAGE2 ? C HELP A BRL R1D] TO FIGURE \ ": ! LI/$ SYMBOL FALLS )9 A BRL CELL4"> ,9 O!R ^WS1 IF WE PUT ! #B 8,SUP]SCRIPT "0 A#D 9DICATOR 2F A NUMB]1 WE >E SAY+ 8X IS A SUP]SCRIPT0 & 8X IS PR9T$ ABV ! L9E40 @.<,2G9N+ ( ,EXAMPLE@.> ,I WD R W9 #AJ9#AJ DOLL>S ?AN #AJ9#B4 @.<,COM;T>Y TO ! ,PREC$+ ,EXAMPLE@.> ,! NUM]IC 9DICATOR M/ 2 REP1T$ AF ! SUP]SCRIPT 9DICATOR1 2C NUM]IC MODE _C 3T9UE OV] A LEVEL *ANGE 9DICATOR4 "<,,RUEB ^S#F4C4A"> @.<,2G9N+ ( ,EXAMPLE@.> ;;;,E "7 MC9#B;' @.<,COM;T>Y TO ! ,PREC$+ ,EXAMPLE@.> ,TO GET ! GRADE #A E6ECTS ": NEC1 ! TRANSCRIB] *OSE TO USE A GRADE #A PASSAGE4 ,? EXPRES.N CD AL 2 TRANSCRIB$ ;,E "7 MC;9#B .=9 & 8IN0 ,- GRADE #A 9DICATORS ,! SUP]SCRIPT 9DICATOR HAS ! SAME #C DOT 3FIGURA;N Z ! L[] ^WSIGN & L[] B#D GR\PSIGN 8IN40 ,S1 :AT'S A TRANSCRIB] TO D8 ,WE M/ MAKE SURE TO USE ! SUP]SCRIPT 9DICATOR 9 ^7GRADE #A MODE4^' ,O!RWISE1 X W M1N 8IN04 ,! NUM]IC 9DICATOR E/ABLI%ES GRADE #A MODE4 #E9X #AJ9#H --------------------------------------#E ,GRADE #A MODE C AL 2 E/ABLI%$ BY US+ GRADE #A 9DICATORS1 %[N 2L4 ,GRADE #A SYMBOL 9DICATOR .=; ,GRADE #A ^W 9DICATOR .=;; ,GRADE #A PASSAGE 9DICATOR .=;;; X9#B"6Y9#B "7 ,C SAYS 8X9#B"6Y9#B "7 ,C04 @.<;X 9 #B PLUS ;Y-SQU>$ EQUALS ,CAN@.> ,H["E1 X;9#B"6Y9#B "7 ;,C SAYS @.<;X-SQU>$ PLUS ;Y-SQU>$ EQUALS ;,C@.>4 #D X;9#B #CX9#B #D;A9#B #E9#B A#E X;9#B"6Y9#B"6Z9#B ,M ON *OOS+ : WAY ( E/ABLI%+ GRADE #A MODE W COME UP Z WE EXPLORE M EXAMPLES 9 ? "W%OP4 --------------------------------------#F ,SCOPE ( A ,SUP]SCRIPT ,9DICATOR ,L O!R BRL 9DICATORS1 ! SUP]SCRIPT 9DICATOR'S E6ECT HAS LIMITS4 ,! AM.T ( MAT]IAL ON : A SUP]SCRIPT C H AN E6ECT ,- XS SCOPE ( 9FLU;E1 IF Y W ,- IS DEF9$ 9 ,,GTM SEC;N #G4A4 ,A SUP]SCRIPT 9DICATOR C A6ECT AN ^1ITEM4 ,AN ITEM IS DEF9$1 BRIEFLY1 Z ANY ( ! FOLL[+ IF !Y COME IMMLY AF ! LEVEL *ANGE 9DICATOR3 #E #A4 ,AN 5TIRE NUMB]1 : 9CLUDES A#F "EY?+ 9 ! E/ABLI%$ NUM]IC MODE "ATOR SPACES1 & SIMPLE NUM]IC FRAC;N L9ES">4 A4 ,^! >E ALL EXAMPLES ( 5TIRE NUMB]S3 #E #DB #C4ADAEI #A/B #E1BHJ #C4ADAEIBFECE"HIGICBCHDF"BFDCCHCBGI #B4 ,AN 5TIRE G5]AL FRAC;N1 5CLOS$ 9 FRAC;N 9DICATORS4 #C4 ,AN 5TIRE RADICAL EXPRES.N1 5CLOS$ 9 RADICAL 9DICATORS4 #D4 ,AN >R[4 #E4 ,AN >BITR>Y %APE4 #F4 ,ANY EXPRES.N 5CLOS$ 9 MAT*+ PAIRS ( R.D P>5!SES1 SQU>E BRACKETS OR CURLY BRACES4 #G4 ,ANY EXPRES.N 5CLOS$ 9 ! BRL GR\P+ 9DICATORS4 #H4 ,IF N"O ( ! =EGO+ APPLY1 ! ITEM IS SIMPLY ! NEXT 9DIVIDUAL SYMBOL4 A4 ,^! >E ALL EXAMPLES ( 9DIVIDUAL SYMBOLS3 "9 "7 #= #F ,H[ TO MAKE YR SUP]SCRIPT B#F LA/ L;G] ,WE C EXP& ! SCOPE ( 9FLU;E ( A SUP]SCRIPT BY US+ BRL GR\P+ 9DICATORS4 ,S1 :5 "S?+ " IS 8SUP]SCRIPT$0 & IS N AN ITEM BY ANY ( ! O!R DEF9I;NS ABV1 BRL GR\P+ 9DICATORS C MAKE X " 9TO AN ITEM4 @.<,2G9N+ ( ,EXAMPLE@.> X;9"-#B @.<,COM;T>Y TO ! ,PREC$+ ,EXAMPLE@.> ,)\T ANY BRL GR\P+ 9DICATORS1 ! BRL SAYS1 8;X SUP]SCRIPT M9US 444 & !N TWO40 @.<,2G9N+ ( ,EXAMPLE@.> ;;X9<"-#B> @.<,COM;T>Y TO ! ,PREC$+ ,EXAMPLE@.> ,) BRL GR\P+ 9DICATORS1 ! BRL SAYS1 8;X SUP]SCRIPT M9US-TWO40 #G ,? APPLIES TO #G ,,SUBSCRIPTS1 ,,TOO6 ,! TE*NIQUE = MAK+ A SUP]SCRIPT LA/ L;G] "WS J ! SAME = SUBSCRIPTS "<& AL = COMMON MODIFI]S">4 @.<,2G9N+ ( ,EXAMPLE@.> X;5#B"6K @.<,COM;T>Y TO ! ,PREC$+ ,EXAMPLE@.> ,)\T ANY BRL GR\P+ 9DICATORS1 ! BRL SAYS1 8;X SUBSCRIPT TWO 444 & !N PLUS ;K40 @.<,! "UL9$ TEXT 2L HAS ! FOLL[+ L9K3 HTTP3_/_/BRAILLEAU?OR;Y4ORG_/" UEB4HTML_?GUIDE@.> ,A GRADE #A SYMBOL 9DICATOR IS ONLY NE$$ )9 ! F/ ?REE SYMBOLS ( ! SYMBOLS-SEQU;E1 S ! TRANSCRIB] *OSE TO USE T SOLIT>Y GRADE #A SYMBOL 9DICATOR E>LY ON "<& N USE A GRADE #A ^W 9DICATOR = ! :OLE SYMBOLS-SEQU;E">4 "<_?#E 9 ,,BANA'S _7,PROVI.NAL ,GUID.E = ,TRANSCRIB+ ,MA!MATICS 9 #H ,,UEB_'"> A#G @.<,2G9N+ ( ,EXAMPLE@.> ;;X5<#B"6K> @.<,COM;T>Y TO ! ,PREC$+ ,EXAMPLE@.> ,) BRL GR\P+ 9DICATORS1 ! BRL SAYS1 8;X SUBSCRIPT TWO-PLUS-;K40 ,BO? ! SUBSCRIPT 9DICATOR & ! OP5+ BRL GR\P+ 9DICATOR NE$ TO 2 9 GRADE #A MODE1 S ! TRANSCRIB] *OSE TO USE A GRADE #A ^W 9DICATOR = ! :OLE SYMBOLS-SEQU;E "<9/1D ( US+ TWO GRADE #A SYMBOL 9DICATORS1 "O = ! .=5 & ANO!R = ! .=<">4 "<_?#E 9 ,,BANA'S ,PROVI.NAL ,GUID.E = ,TRANSCRIB+ ,MA!MATICS 9 ,,UEB"> @.<,2G9N+ ( ,EXAMPLE@.> ;$#C:5 @.<,COM;T>Y TO ! ,PREC$+ ,EXAMPLE@.> ,PL1SE NOTE T NO 3TRAC;NS >E US$ 9 ! ^W 8REGUL>10 2C GRADE #A MODE 0 SET E>LI] 9 ! SYMBOLS-SEQU;E4 ,! CLOS+ BRL #I GR\P+ 9DICATOR AF ! ^W 8POLYGON0 B#G HAS A GRADE #A SYMBOL 9DICATOR1 2C ! SPACE 2F ! ^W T]M9AT$ GRADE #A MODE .4 ,? CD AL 2 TRANSCRIB$3 ;;;$#C:5;' ,BRL GR\P+ 9DICATORS >E AL US$ = MULTIPLE LEVELS ( SUP]SCRIPTS1 SUBSCRIPTS1 & MODIFI]S Z WELL Z = MULTI-^W DESCRIP;NS ( A TRANSCRIB]-DEF9$ %APE1 B ^? USES >E \TSIDE ! SCOPE ( ? "W%OP4 --------------------------------------#H ,COMMON ,MODIFI]S ,COMMON MODIFI]S S* Z ! B>1 >R[1 DOT1 TILDE1 HAT OR >C >E TR1T$ SEP>ATELY F SUP]SCRIPTS & SUBSCRIPTS4 "<,!Y'RE S COMMON_/FREQU5T T !Y H SPECIAL D$ICAT$ SYMBOLS ALL _! [N4"> ,^! COMMON MODIFI]S >E COV]$ 9 ,SEC;N #AB ( ! ,,GTM4 ,WE >E GO+ TO FOCUS 9 ? "W%OP ONLY ON COMMON MODIFI]S T >E .1ABV ! ITEM #AJ !Y MODIFY4 ,"! IS A :OLE SET ( A#H COMMON MODIFI]S T G .1"U ! ITEM !Y MODIFY1 B !Y >E \TSIDE ! SCOPE ( ? BASIC "W%OP4 ,B> OV] PREVI\S ITEM .=: ,SIMPLE "R-PO9T+ >R[ OV] PREVI\S ITEM .=^: ,DOT OV] PREVI\S ITEM .=^4 ,TILDE OV] PREVI\S ITEM .=_: ,HAT OV] PREVI\S ITEM .=": ,>C OV] PREVI\S ITEM .=._: ,OP5+ BRL GR\P+ 9DICATOR .=< ,CLOS+ BRL GR\P+ 9DICATOR .=> "<,ON A ,SPECIAL ,SYMBOLS ,PAGE1 ! DOT LOCATOR = M5;N .= %D PREC$E EA* SYMBOL4"> ,B;: B> ,G;^: >R[ #C^4 DOT X_: TILDE Y;": HAT ,A._: >C #AA ,SEC;N #AB ( ! ,GUIDEL9ES = B#H ,TE*NICAL ,MAT]IAL GIVES A FULL LI/ ( ! BRL SYMBOLS = COMMON MODIFI]S1 9CLUD+ ^? T >E 2L ! ITEM !Y MODIFY4 --------------------------------------#I ,SCOPE ( A ,COMMON ,MODIFI] @.<,! "UL9$ TEXT 2L HAS A L9K TO PR9T PAGE #F ( ? "W%OP4@.> ,! E6ECT ( A COMMON MODIFI] APPLIES ONLY TO ! ^1ITEM T IMMLY PREC$ES X4 ,! DEF9I;N ( AN ITEM TO : A COMMON MODIFI] APPLIES IS ! SAME Z ! DEF9I;N ( AN ITEM T DET]M9ES ! _7SCOPE ( A SUP]SCRIPT_'4 ,H[ 3V5I5T6 ,IF ! COMMON MODIFI] APPLIES TO "S?+ M OR LESS ?AN ! ITEM T PREC$ES X1 !N ! SCOPE ( ! COMMON MODIFI] IS *ANG$ BY US+ BRL GR\P+ 9DICATORS4 ,? C 2 "PICUL>LY P]T95T 9 GEOMETRY = ?+S L3 #AB @.<,2G9N+ ( ,EXAMPLE@.> A#I ;;<,,EF>^: >R[ OV] ,,EF @.<,COM;T>Y TO ! ,PREC$+ ,EXAMPLE@.> ,! BRL GR\P+ 9DICATORS MAKE ! SIMPLE "R-PO9T+ >R[ APPLY TO ! ;,E & ;,F TGR 9/1D ( ONLY TO ! ;,F4 ,A GRADE #A ^W 9DICATOR PREC$ES ! SYMBOLS-SEQU;E = ;;<,,EF>^:1 2C O!RWISE X WD M1N 8<,,EF>^:0 @.<,2G9N+ ( ,EXAMPLE@.> ;;<,,BC>: 8,,BC B>0 OR B> OV] ,,BC @.<,COM;T>Y TO ! ,PREC$+ ,EXAMPLE@.> ,! BRL GR\P+ 9DICATORS MAKE ! B> APPLY TO ! ;,B & ;,C TGR 9/1D ( ONLY TO ! ;,C4 ,A GRADE #A ^W 9DICATOR PREC$ES ! SYMBOLS-SEQU;E ;;<,,BC>:1 2C O!RWISE X WD M1N 8<,,BC,'>:0 @.<,2G9N+ ( ,EXAMPLE@.> ;;<,,BA>._: >C ,,BA #AC @.<,COM;T>Y TO ! ,PREC$+ B#I ,EXAMPLE@.> ,! BRL GR\P+ 9DICATORS MAKE ! >C APPLY TO BO? ! ;,B & ,A 9/1D ( J ! ,A4 ,A GRADE #A ^W 9DICATOR PREC$ES ! SYMBOLS-SEQU;E ;;<,,BA>._:1 2C O!RWISE X WD M1N 8<,,BA> 4440 -------------------------------------#AJ @.<,2G9N+ ( ,EXAMPLE@.> #A4<#C>^4 #A4C ) A DOT OV] ! #C @.<,COM;T>Y TO ! ,PREC$+ ,EXAMPLE@.> ,! BRL GR\P+ 9DICATORS MAKE ! DOT APPLY TO J ! #C 9/1D ( TO ! 5TIRE NUMB] #A4C4 ,NO GRADE #A 9DICATORS >E US$1 2C ! NUM]IC 9DICATOR AT ! 2G9N+ ( ! SYMBOLS-SEQU;E SETS GRADE #A MODE = ! :OLE ?+4 ,A NUM]IC 9DICATOR IS US$ 2F ! #C1 2C ! OP5+ BRL GR\P+ 9DICATOR T]M9ATES ! E6ECT ( ! NUM]IC 9DICATOR 2F ! #A4 #AD 8,B>S & DOTS ETC40 & A#AJ GRADE #A 9DICATORS ,Z WE H SE5 9 ! EXAMPLES ABV1 GRADE #A 9DICATORS >E (T5 NEC :5 BRL GR\P+ 9DICATORS >E 9VOLV$1 2C BRL GR\P+ 9DICATORS CORRESPOND TO ! 3TRAC;NS = 8GH0 & 8AR40 ,9 ADDI;N1 MO/ ( ! COMMON MODIFI]S H A GRADE #B M1N+1 S GRADE #A MODE M/ 2 E/ABLI%$ S !Y >E N MISR1D4 -------------------------------------#AA ,L9E ,NOTA;N ,"! IS "O NOTA;N T IS COMMON 9 GEOMETRY T ,,UEB DOES N CLASSIFY ) ! 8COMMON MODIFI]S40 ,T IS ! 8BIDIREC;NAL >R[ OV]10 : C D5OTE A L9E4 @.<,2G9N+ ( ,EXAMPLE@.> ;;,A.9\WRO @.<,COM;T>Y TO ! ,PREC$+ ,EXAMPLE@.> ,! LA/ F\R BRL CELLS ABV MAKE UP ! #AE COMMON HORIZONTAL BIDIREC;NAL A#AA >R[4 ,! TWO BRL CELLS 2F ! COMMON HORIZONTAL BIDIREC;NAL >R[ IS ! SYMBOL = 8EXPRES.N DIRECTLY ABV40 ,NO BRL GR\P+ 9DICATORS >E NEC1 2C ! S+LE LR ,A IS AN ITEM1 & T IS :AT ! MODIFI] A6ECTS4 ,A GRADE #A ^W 9DICATOR PREC$ES ! SYMBOLS-SEQU;E ;;,A.9\WRO1 2C O!RWISE X WD M1N 8,A ) 8\WRO0 OV] X40 @.<,2G9N+ ( ,EXAMPLE@.> ;;<,,AZ>.9\WRO @.<,COM;T>Y TO ! ,PREC$+ ,EXAMPLE@.> ,! BRL GR\P+ 9DICATORS MAKE ! BIDIREC;NAL >R[ APPLY TO BO? ! ,A & ;,Z 9/1D ( J ! ;,Z4 ,A GRADE #A ^W 9DICATOR PREC$ES ! SYMBOLS-SEQU;E ;;<,,AZ>1 2C O!RWISE X WD M1N 8<,,AZ>0 ,AL1 )\T GRADE #A MODE1 ! OP5+ >R[ 9DICATOR WD J M1N ! 3TRAC;N 8OU40 #AF ,%APE ,SYMBOLS & ! ,%APE #AB ,T]M9ATOR ,N[ T WE H T\*$ ON L9E NOTA;N1 COMMON MODIFI]S1 & SUP]SCRIPTS1 LET'S TALK AB %APES4 ,GEOMETRY MAT]IAL USES A .1LOT ( %APES4 ,BOY-OH-BOY1 C WE "E .1N DRAW LL %APES )9 ! BRL L9E4 ,S1 WE USE BRL SYMBOLS TO GIVE 9=MA;N AB ! LL %APE T APPE>S 9 PR9T4 ,9ITIAL ,%APE ,9DICATORS ,! K9D ( 9=MA;N WE GIVE AB A %APE IS BASICALLY 8:AT %APE IS X80 & 8:AT D XS 9SIDES LOOK L80 ,! SECOND "Q "<:AT D XS 9SIDES LOOK L8"> IS ANSW]$ BY ! 9ITIAL %APE 9DICATOR US$4 ,%APE 9DICATOR .=$ ,FILL$ " %APE 9DICATOR .=_$ ,%AD$ %APE 9DICATOR .=.$ #AG ,SPECIFIC ,%APE ,SYMBOLS A#AB ,! F/ "Q "<:AT %APE IS X8"> IS ANSW]$ BY :AT COMES AF ! 9ITIAL %APE 9DICATOR4 ,,UEB GIVES U SPECIFIC SYMBOLS = A P>ALLELOGRAM1 A CIRCLE1 & ANY %APE ) SIDES ALL ! SAME L5G?4 P>ALLELOGRAM .=$@#D CIRCLE .=$= 7777777777777777777777777777777777777777 ,:AT IS A P>ALLELOGRAM8 A FLAT %APE ) OPPOSITE SIDES P>ALLEL & EQUAL 9 L5G? ,-MA?ISFUN4COM GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG @.<,2G9N+ ( ,EXAMPLES@.> _$@#D .$@#D ;$@#D @.<,COM;T>Y TO ! ,PREC$+ ,EXAMPLES@.> ,! F/ ITEM ABV IS A SOLID #AH " %APE .=_$ T IS A B#AB P>ALLELOGRAM .=@#D ,! SECOND ITEM ABV IS A %AD$ %APE .=.$ T IS A P>ALLELOGRAM .=@#D ,! ?IRD ITEM ABV IS A . %APE .=$ T IS A P>ALLELOGRAM .=@#D @.<,2G9N+ ( ,EXAMPLES@.> _$= .$= ;$= -------------------------------------#AC ,= ANY ^7%APE ) SIDES ALL ! SAME L5G?^' "0 %APES">1 WE ANSW] ! "Q 8:AT %APE IS X80 ) A NUMB] T CORRESPONDS TO ! NUMB] ( SIDES T MAKE UP ! %APE4 ,? 9CLUDES SQU>ES ;$#D:1 EQUILAT]AL TRIANGLES ;$#C:1 HEXAGONS "91 ETC4 REGUL> %APE ) .- NUMB] ( SIDES .=$# @. @.<,2G9N+ ( ,EXAMPLES@.> ;$#C @. #AI ;$#D @.E@.> A#AC ;$#E @. ;$#F @. ;$#AB @. ,ALL SIDES ( A _$#D >E ! SAME L5G?4 -------------------------------------#AD .=$ & 8$0 ,- GRADE #A 9DICATORS ,! 9ITIAL %APE 9DICATOR = A %APE T IS HOLL[ HAS ! SAME DOT 3FIGURA;N Z ! /R;G GR\PSIGN 8$40 ,S1 :AT'S A TRANSCRIB] TO D8 ,WE M/ MAKE SURE TO USE ! 9ITIAL %APE 9DICATOR = A %APE T IS HOLL[ 9 ^7GRADE #A MODE4^' ,O!RWISE1 X W M1N 8$40 ,! NUM]IC 9DICATOR E/ABLI%ES GRADE #A MODE4 ,! MODE C AL 2 E/ABLI%$ BY GRADE #A 9DICATORS "4 @.<,2G9N+ ( ,EXAMPLE@.> ,LABEL ! ;$#C Z ^7EQUILAT]AL1 "R1 SCAL5E1^' OR ^1ISOSCELES4 #BJ @.<,COM;T>Y TO ! ,PREC$+ A#AD ,EXAMPLE@.> ,! FILL$ %APE 9DICATOR & ! %AD$ %APE 9DICATOR _C 2 ANY?+ O!R ?AN 9ITIAL %APE 9DICATORS1 REG>D.S ( :E!R !Y >E 9 GRADE #A OR GRADE #B MODE4 ,S1 GRADE #A MODE DOES N NE$ TO 2 =C$ = EI .=_$ OR .=.$4 @.<,2G9N+ ( ,EXAMPLE@.> ,PLACE A _$= AT COORD9ATES "<#C1 #D">4 -------------------------------------#AE ,%APE ,T]M9ATOR ,WE USE "O ( ! 9ITIAL %APE 9DICATORS TO E/ABLI% T WE >E GIV+ 9=MA;N AB A %APE4 ,B H[ IS A R1D] TO "K :5 WE H /OPP$ GIV+ 9=MA;N AB T %APE & MOV$ ON TO O!R ?+S8 ,%APE T]M9ATOR .=: ,! %APE T]M9ATOR TELLS !M :5 X IS OV]4 #BA ,,USE X :5 444 ANO!R SYMBOL A#AE FOLL[S IMMLY AF ,IF ! %APE SYMBOL IS FOLL[$ BY PUNCTUA;N OR IS UNSPAC$ F A FOLL[+ SYMBOL1 !N ! %APE T]M9ATOR M/ 2 US$4 "<,,GTM #AD4A4B"> @.<,2G9N+ ( ,EXAMPLES@.> _$#D:"6X "7 #EB ;$#C:,,ABC ,IS X A ;$#C:1 ;$#D:1 OR ;$=:8 -------------------------------------#AF ,L1VE X ,,(F :5 444 A BLANK CELL DEF9ES ! 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PR9T SYMBOL IS ALR COV]$ ELSE": 9 ! CODE4 ,! DEF9I;NS ( ALL %APE SYMBOLS %D 2 AVAILABLE TO ! R1D] 9 EI A TRANSCRIB]'S NOTE OR ON A SPECIAL SYMBOLS PAGE40 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG -------------------------------------#AG ,%APES = ,M1SURE;T OR ,ID5TIFICA;N ,RULES ( ,,UEB "<,,RUEB"> ^S#AF4A4C SAYS1 8,D N USE L9E MODE ^7:5 ! ATTRIBUTES ( ! L9ES OR _! RELA;N%IP ) "O ANO!R IS IMPORTANT1^' S* Z 9 ! /UDY ( GEOMETRY OR ! M1SURE;T ( ANGLES40 " ,SIMIL>LY1 :5 ! M1SURABLE ATTRIBUTES ( A %APE &_/OR XS RELA;N%IP TO O!RS #BD IS ! R1SON ! %APE IS 9CLUD$ 9 ! A#AG TEXT1 .7!N ! %APE 9DICATORS J 4CUSS$ >E N APPROPRIATE4.' ,= EXAMPLE1 IF ! /UD5T IS EXPECT$ TO _4 C.T ! SIDES ( A %APE 9 ORD] TO ID5TIFY X _4 ID5TIFY A TRIANGLE Z EQUILAT]AL1 ISOSCELES1 OR SCAL5E _4 /UDY ! M1SURE;T ( AN ANGLE _4 F9D ! COORD9ATES ( A %APE !N A TACTILE GRAPHIC IS A BETT] OP;N ?AN EI %APE 9DICATORS OR L9E MODE4 ,AG1 :5 ! M1SURABLE ATTRIBUTES ( A %APE &_/OR XS RELA;N%IP TO O!RS IS ! R1SON ! %APE IS 9CLUD$ 9 ! TEXT1 ! /UD5T OR R1D] NE$S A DETAIL$1 M1SURABLE REPRES5TA;N ( ! %APE 9 ORD] TO /UDY XS ATTRIBUTES4 #BE ,"S ,EXAMPLES = ,4CUS.N #AH ,ANGLES ) M1SURE;TS @.<,PR9T %[S A "W%EET 5TITL$ 8,,ANGLES ,,TO #IJ^J0 & ITEMS #A & #B1 : >E BO? SIMPLE DRAW+S ( A "R ANGLE DIVID$ 9TO TWO ANGLES ) "O ( ^? LABEL$ EI #CE^J OR #DE^J4 ,TEXT 2F ! ITEMS SAYS1 8,"W \ ! MISS+ ANGLES1 ,REMEMB] T A "R ANGLE IS EQUAL TO #IJ^J4 ,! ANGLES >E N DRAWN TO SCALE1 S D N TRY TO M1SURE !M60@.> ,PLOTT$ L9E @.<,PR9T %[S ! EQUA;N ;;;,SLOPE "7 (,.DY./,.DX);' & A ,C>TESIAN GRID ) A L9E PLOTT$ ON X4 ,! L9E CROSSES ! ;Y-AXIS AT #E & ! ;X-AXIS J ! LEFT ( #G4 ,XS SLOPE IS LABEL$ Z #D TO ! "R & "-#C D[N4@.> #BF ,%APE ) M1SURE;TS PR9T$ NEXT #AI TO XS SIDES @.<,PR9T %[S ! TEXT 8,:AT IS ! ^1P]IMET] ( ! RECTANGLE 9 T]MS ( ;B80 !N A DRAW+ ( A RECTANGLE ) XS TOP1 L;G SIDE LABEL$ #F;B"-#G & XS LEFT1 %ORT SIDE LABEL$ #D;B4 ,AF ! RECTANGLE IS ! TEXT 8,:AT IS ! ^1>EA ( ! RECTANGLE 9 T]MS ( ;B80@.> ,CLASSIFY+ TRIANGLES @.<,PR9T %[S A "W%EET 5TITL$ 8,CLASSIFY+ TRIANGLES " ,GRADE #D ,GEOMETRY ,"W%EET40 ,! DIREC;NS SAY 8,CLASIFY ! TRIANGLES40 ,ITEMS #A & #B EA* 3SI/ ( A L9E DRAW+ ( A TRIANGLE & A BLANK L9E4@.> -------------------------------------#BJ ,CLASSIFY+ ANGLES @.<,PR9T %[S A "W%EET 5TITL$ 8,K#E ,LE>N+ ,CLASSIFY+ ANGLES " ,GRADE #D ,GEOMETRY ,"W%EET40 ,! DIREC;NS SAY1 #BG 8,CLASSIFY ! ANGLES Z ACUTE1 A#BJ OBTUSE OR "R40 ,ITEMS #A1 #B1 & #C EA* 3SI/ ( A SIMPLE L9E DRAW+ ( AN ANGLE & A BLANK L9E4@.> 8,": ! TE*NOLOGY IS AVAILABLE1 X IS (T5 BETT] TO REPRES5T L9ES 9 DIAGRAMS ) TACTILE GRAPHICS40 ,-,,RUEB ^S#AF4A4E -------------------------------------#BA ,! ,B1UTY ( ,PR9T ,=MATT+ IS N :AT ? "W%OP IS AB1 S WE W N G 9TO GRT DEP? AB =MATT+4 ,N"O!.S1 WE AC"KL$GE T "O ( ! 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FOLL[+ L9K3 HTTP3_/_/BRAILLEAU?OR;Y4ORG_/UEB4" HTML_?GUIDE@.> ,! =MATT+ GUIDEL9ES = A ,,UEB ,MA?_/,SCI;E TRANSCRIP;N 9 ! ,U4,S4 & ,CANADA COME F ,BRL ,=MATS #BJAF & ,,BANA'S 8_7,PROVI.NAL ,GUID.E = ,TRANSCRIB+ ,MA!MATICS 9 ,,UEB4_'0 ,2L IS A BRIEF SUMM>Y ( ! =MATT+ GUID.E GIV5 9 T ,,BANA DOCU;T4 _4 #C-#A " P>AGRAPHS ONLY _4 ,4PLAY$ LIT]>Y TEXT IS =MATT$ AC TO ,,BF#BJAF1 EXCEPT = P>AGRAPH =MAT _4 ,MA!MATICAL EXPRES.NS >E 4PLAY$ AC TO ,,BF#BJAF1 US+ ! =MULA3 _4 BLANK L9E _4 ADD TWO TO PREC$+ RUNOV] POSI;N _4 ADD TWO M = 4PLAY$'S RUNOV] #CJ POSI;N A#BB _4 BLANK L9E _4 #A-#C C 2 US$ = A BIG EXPRES.N 9 HI<] MA? _4 ,DIREC;NS USE M>G9S #E-#E1 #G-#E _4 ,EX]CISES >E =MATT$ AC TO ,,BF#BJAF " _4 ,A2REVIA;NS /AY ON A BRL L9E ) _! RELAT$ NUMB] @.<,9 ! P>AGRAPH T FOLL[S1 ! "UL9$ TEXT HAS ! FOLL[+ L9K3 HTTPS3_/_/WWW4NA;NALBRAILLE4ORG_/" RES\RCES_/WEB9>S->*IVE_/@.> ,,BANA'S 8,PROVI.NAL ,GUID.E = ,TRANSCRIB+ ,MA!MATICS 9 ,,UEB0 IS COMPLETELY 4CUSS$ 9 ! ,,NBA WEB9> _7,,UEB ,PROVI.NAL ,GUID.E ,WALK"?_' T IS = SALE ON ,,NBA'S WEBSITE4 #CA ,O!R ,3SID]A;NS #BC ,SPAC+ ,G5]ALLY1 SPACE SIGNS ( COMP>ISON & UNSPACE SIGNS ( OP]A;N4 ,IF X HELPS1 WE C ?9K ( ? Z OP5+ UP "S 4T.E "<9 ORD] TO H 8P]SPECTIVE0"> :5 ?+S >E COMP>$ & CLOS+ ! SPACE TO GET PROXIM;Y = P]=M+ AN OP]A;N "4 @.<,2G9N+ ( ,EXAMPLES@.> X"6Y "7 ;Z #IJ^J"-#FJ^J "7 #CJ^J ;;;<,,AD>:"6<,,BC>: "7 <,,AC>:;' ;;;X "7 ("-B_6%B9#B"-#D;AC+./#B;A);' ,! 8:Y0 ( ? SPAC+ DIRECTIVE IS T\*$ ON 9 ! .1,NOTE AT ! 2G9N+ ( ! LATE/ SEC;N #C4A 9 ,,GTM4 ,X SAYS1 8,NOTE3 ,! PRES;E OR ABS;E ( SPACES 9 BRL IS AN IMPORTANT AID TO P>S+ MA!MATICAL EXPRES.NS & EQUA;NS4 ,PR9T SPAC+ IS (T5 SIMPLY A MATT] ( PR9T+ /YLE40 ,BLUNTLY1 SPAC+ IS M IMPORTANT 9 BRL ?AN X IS 9 PR9T4 ,S1 /AY 3SI/5T 9 #CB BRL1 REG>D.S ( PR9T'S /YLI/IC A#BC SPAC+ *OICES4 -------------------------------------#BD ,BLANKS ,FOLL[ PR9T1 US+ ! L1/ COMPLEX EQUIVAL5T Y C GET AWAY )4 ,= EXAMPLE1 USE "O "USCORE 9/1D ( A C]TA9 L5G? ( "USCOR+ "ATE "USCORES">4 ,SIMIL>LY1 9/1D ( TRANSCRIB+ A 8BLUE RECTANGLE10 USE A RECTANGLE "E N MULTIPLE COLORS ( RECTANGLE">4 @.<,2G9N+ ( ,EXAMPLE@.> ,FILL 9 ! BLANK3 ;Y "7 MX"68 @.<,2G9N+ ( ,EXAMPLE@.> ,FILL 9 ! BLANK3 ;Y "7 MX"6.- @.<,2G9N+ ( ,EXAMPLE@.> ,9S]T ! ?REE MISS+ NUMB]S3 #C4AD.-.-.- @.<,T IS ! 5D ( ! EXAMPLE4@.> #CC ,A QUOTE F ! REC5T ,,ICEB A#BD ,G5]AL ,ASSEMBLY1 8,YES1 BOXES >E CLUNKY40 444 ,&1 .7IF !Y >E NEC1.' WE USE !M1 REG>D.S ( CLUNKI;S4 @.<,2G9N+ ( ,EXAMPLE@.> ,FILL 9 ! BLANK3 ;;;Y "7 MX"6+;' @.<,2G9N+ ( ,EXAMPLE@.> @.<,! SYMBOL .=@_$REC IS US$ = A BLUE RECTANGLE4@.@> ,FILL 9 ! CIRCLE & ! RECTANGLE3 _$= "7 MX"6@_$REC @.<,T IS ! 5D ( ! EXAMPLE4@.> @.<,9 ! P>AGRAPH T FOLL[S1 ! "UL9$ TEXT HAS ! FOLL[+ L9K3 HTTPS3_/_/WWW4NA;NALBRAILLE4ORG_/" RES\RCES_/WEB9>S->*IVE_/@.> ,=MATT+ IS AL 4CUSS$ 9 ! #AE-M9UTE WEB9> 8,,UEB ,TE*NICAL - ,=MAT0 9 ! S]IES ( WEB9>S ON ,,UEB ,TE*NICAL ,MAT]IAL1 : IS "P ( A _1WEB9> _1>*IVE T IS FREE TO ,,NBA MEMB]S4 #CD ,,GTM ,SEC;N #C3 #BE ,SIGNS ( ,OP]A;N & ,COMP>ISON ,! MO/ CURR5T V].N ( ,SEC;N #C 9 ! ,GUIDEL9ES = ,TE*NICAL ,MAT]IAL "<,,GTM"> 0 APPROV$ 9 ,OCTOB] #BJAH4 ,X IS ! F/ COMPLET$ SEC;N ( A REVIS$ ,,GTM4 ,A FULL LI/ ( UPDATES TO ,,UEB RULES C ALW 2 F.D AT HTTP3_/_/ICEB4ORG_/UEB4HTML4 ,LET'S REVIEW ! HIISON ,SIGNS ,SEC;N #C PROVIDES TWO 9=MATIVE TABLES AT XS V 2G9N+4 ,^! TABLES N ONLY LI/ SIGNS ( OP]A;N @& COMP>ISON & _! BRL SYMBOLS2 !Y AL GIVE3 #A"> A COPY_/PA/ABLE "* = EA* SIGN "1 S Y CD PA/E X "R 9TO ! PR9T 9PUT >EA ( A BRL TRANSCRIP;N PROGRAM & GET A #CE USE;L BRL TRANSCRIP;N A#BE #B"> ! NUM]IC ,UNICODE VALUE = EA* SIGN1 & #C"> A V>IETY ( "NS = EA* SIGN "* ! FILE Y >E M LIKELY TO F9D :AT Y >E LOOK+ = ON ! F/ TRY & S Y CD USE A SE>* 5G9E TO F9D M 9=MA;N AB A SIGN">4 ,:AT IS A ,UNICODE VALUE1 & H[ C ,I USE X8 ,UNICODE IS AN 9T]NA;NAL 5COD+ /&>D = USE ) DI6]5T LANGUAGES & SCRIPTS1 9 : EA* LR1 DIGIT1 OR SYMBOL IS ASSIGN$ A UNIQUE NUM]IC VALUE T APPLIES ACR DI6]5T PLAT=MS & PROGRAMS4 ,BLUNTLY1 ,UNICODE IS A SY/EM 9 : A SPECIFIC NUMB] CORRESPONDS TO A V SPECIFIC SYMBOL4 ,A P]SON C USE A ,UNICODE NUMB] TO 5T] A SYMBOL 9 A V>IETY ( PROGRAMS4 -------------------------------------#BF ,SPAC+ ,9 ? "W%OP1 WE H ALR T\*$ ON ! #CF 3CEPT ( SPAC+4 ,! ,,GTM A#BF "<,GUIDEL9ES = ,TE*NICAL ,MAT]IAL"> BASICALLY SAYS1 9 ! ABS;E ( O!R 9/RUC;N1 UNSPACE SYMBOLS ( OP]A;N1 & SPACE SYMBOLS ( COMP>ISON4 ,:5 9 D\BT AB :E!R A SIGN IS A SYMBOL ( OP]A;N OR COMP>ISON1 LOOK TO ! TABLES AT ! 2G9N+ ( ,,GTM ,SEC;N #C ,- "O IS FULL ( SIGNS ( OP]A;N & ! O!R IS FULL ( SIGNS ( COMP>ISON6 @.<,2G9N+ ( ,EXAMPLES@.> #AB4EY "7 #G"-X #FC "7 X"8#I ;Y "7@: #J #AJA @> ;Z #DE^J"68 "7 #IJ^J ;,,AB #L ,,WX 7777777777777777777777777777777777777777 ,D :AT IS BE/ = ! /UD5T ,! ,GUIDEL9ES SAY1 8,SIGNS ( OP]A;N MAY 2 SPAC$ :5 !Y >E F/ TAUN+ !M4 ,AG & Z ALW1 D :AT IS BE/ = ! /UD5T IF Y C F9D T \4 ,A SPAC$ SIGN ( OP]A;N WD LIKELY MAKE M NUM]IC & GRADE #A 9DICATORS NEC4 ,X IS UNLIKELY T A /UD5T /UDY+ ALGEBRA OR GEOMETRY IS F/ LE>N+ SIGNS ( OP]A;N4 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG @.<,9 ! P>AGRAPH T FOLL[S1 ! "UL9$ TEXT HAS ! FOLL[+ L9K3 HTTPS3_/_/WWW4NA;NALBRAILLE4ORG_/" RES\RCES_/WEB9>S->*IVE_/@.> ,SPAC+ IS AL 4CUSS$ 9 ! #AE-M9UTE WEB9> 8,,UEB ,TE*NICAL - ,SPAC+0 9 ! S]IES ( WEB9>S ON ,,UEB ,TE*NICAL ,MAT]IAL1 : IS "P ( A _1WEB9> _1>*IVE T IS FREE TO ,,NBA MEMB]S4 ,T WEB9> 9CLUDES 4CUS.N ( EXCEP;NS = SPAC+ SIGNS ( COMP>ISON :5 #A"> !Y APPE> 9 AN EXPRES.N T IS N ON ! BASE L9E & #B"> TO AVOID DIVID+ AN EXPRES.N 2T BRL L9ES4 #CH #C4A4E #BG 8,SIGNS ( OP]A;N MAY 2 SPAC$ TO 5H.E ! P>S+ ( AN EXPRES.N : 9CLUDES SPACES 2T QUANTITIES & _! UNITS40 @.<,2G9N+ ( ,EXAMPLE@.> ;;;L FT "8 W FT "8 H FT "7 ,A FT9#C;' @.<,COM;T>Y TO ! ,PREC$+ ,EXAMPLE@.> ,! A2REVIAT$ UNITS ( M1SURE;T " >E SPAC$ AWAY F BO? ! V>IABLE TO : !Y APPLY & AL F ! SIGN ( OP]A;N T FOLL[S2 ? MISE "4 #C4A4F 8,FOLL[ PR9T SPAC+ = SIGNS ( OP]A;N & COMP>ISON :5 ! ADJAC5T TEXT IS N A :OLLY MA!MATICAL EXPRES.N40 ,9 O!R ^WS1 ! DIRECTIVE TO SPACE SIGNS ( COMP>ISON & UNSPACE SIGNS ( OP]A;N IS M1NT TO APPLY )9 MA!MATICAL EXPRES.NS1 N )9 N>RATIVE S5T;ES4 #CI @.<,2G9N+ ( ,EXAMPLE@.> A#BG ,JOSEPH HAS _6#E ACRES = SALE4 @.<,COM;T>Y TO ! ,PREC$+ ,EXAMPLE@.> ,X WD N 2 MA!MATICALLY A3URATE1 NOR WD X 2 HELP;L1 TO H ! _6 UNSPAC$ F ! ^W 8HAS0 9 ? N>RATIVE S5T;E4 ,M9US #C4B'S ,NOTE ,A M9US 9 PR9T LOOKS A LOT L A HYPH54 @.<,2G9N+ ( ,EXAMPLE@.> FIFTY-FIVE"-TW5TY-TWO "7 ?IRTY-?REE @.<,T IS ! 5D ( ! EXAMPLE4@.> 7777777777777777777777777777777777777777 ,9 .1EXCELL5TLY =MATT$ PR9T1 AN ACTUAL M9US SIGN MAY H A DI6]5T ,UNICODE VALUE " ?AN A HYPH5 "">4 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG #DJ #C4B4A #BH 8,X IS P]MISSIBLE TO USE A BRL HYPH5 = A M9US : IS 9DI/+UI%ABLE F A HYPH5 9 PR9T40 ,9 O!R ^WS1 IF Y _C TELL ! DI6];E F ! PR9T1 !N X IS BETT] TO MAKE NO 4T9C;N 2T ! HYPH5S & M9USES ?AN TO 9T]PRET ! MAT]IAL & IMPOSE YR [N 4T9C;N = ! BRL US]4 @.<,2G9N+ ( ,EXAMPLE@.> "O-"T-OPPORTUN;Y - FE> "7 SU3ESS IS Z SIMPLE Z #B"6#B "7 #D4 ,POSITIVE & ,NEGATIVE ,NUMB]S #C4C4A 8,USE A SUP]SCRIPT 9DICATOR :5 A PLUS OR M9US1 9DICAT+ A POSITIVE OR NEGATIVE NUMB]1 IS 9 ! SUP]SCRIPT POSI;N40 @.<,2G9N+ ( ,EXAMPLE@.> #D"-9"-#B "7 #F #DA @.<,COM;T>Y TO ! ,PREC$+ A#BH ,EXAMPLE@.> ,! M9US SIGN T IS SUP]SCRIPT$ 9 PR9T IS AL 9 ! SUP]SCRIPT POSI;N 9 BRL4 ,? EXPRES.N DOES N REQUIRE ANY GRADE #A 9DICATORS1 2C NUM]IC MODE SETS GRADE #A MODE4 @.<,2G9N+ ( ,EXAMPLE@.> #J"-#CB "7 ;9"-#CB^J,F @.<,COM;T>Y TO ! ,PREC$+ ,EXAMPLE@.> ,! M9US SIGN 9 ! SUP]SCRIPT POSI;N 2F ! SECOND #CB IS BRLD 9 ! SUP]SCRIPT POSI;N4 ,! SUP]SCRIPT 9DICATOR AF A SPACE IS N 9 NUM]IC MODE2 X NE$S TO H GRADE #A MODE APPLI$ TO X4 ,S1 ! TRANSCRIB] *OSE TO USE A GRADE #A SYMBOL 9DICATOR 2F ! SUP]SCRIPT 9DICATOR T FOLL[S A SPACE4 -------------------------------------#BI #C4C4A'S ,NOTE 8,X IS P]MISSIBLE TO DESCRIBE ! #DB SUP]SCRIPT POSI;N 9 A A#BI TRANSCRIB]'S NOTE 9/1D ( US+ A SUP]SCRIPT 9DICATOR40 ^1,IF ! SUP]SCRIPT POSI;N DOES N ADD ANY 9=MA;N AB ! SIGN ( OP]A;N1 !N X ^1MAY 2 IGNOR$ 9 BRL4 @.<,2G9N+ ( ,EXAMPLE@.> @.<,9 ! FOLL[+ P>AGRAPHS1 PR9T USES A SUP]SCRIPT PLUS = A POSITIVE NUMB] & A SUP]SCRIPT M9US = A NEGATIVE NUMB]4 ,! SUP]SCRIPT POSI;N IS N %[N 9 BRL4@.@> ,JANE SD1 8,I _C ABIDE WAT] ABV "6#AF^J,C40 8,T'S NO?+4 ,I ONLY TAKE MY WAT] SUP]COOL$ TO "-#DH4C^J,C10 REPLI$ ,JOHN4 @.<,COM;T>Y TO ! ,PREC$+ ,EXAMPLE@.> ,A TRANSCRIB]'S NOTE 2F ! TEXT SAYS1 8,IN ! FOLL[+ P>AGRAPHS1 PR9T USES A SUP]SCRIPT PLUS = A POSITIVE NUMB] & A SUP]SCRIPT M9US = A NEGATIVE NUMB]4 ,! SUP]SCRIPT POSI;N IS N %[N 9 #DC BRL40 B#BI -------------------------------------#CJ ,! ,HOLL[ ,DOT #C4D4A 8,USE ! HOLL[ DOT TO REPRES5T ! MA!MATICAL SIGN ( OP]A;N40 ,! HOLL[ DOT IS N AN UN%AD$1 UNFILL$ CIRCLE1 L ! "O US$ Z A BULLET4 ,NOR IS ! HOLL[ DOT ! DEGREE SIGN4 @.<,2G9N+ ( ,EXAMPLE@.> ,3SID] ! FOLL[+ LI/3 ;$= #BG^J ;,C IS D>N$ HOT4 ;$= "" C 2 SD Z 8;F-COMPOSE-;G ( ;X40 @.<,COM;T>Y TO ! ,PREC$+ ,EXAMPLE@.> ,AT ! 2G9N+ ( EA* LI/$ ITEM1 PR9T IS FOLL[$ = ! BULLETS1 : >E HOLL[ CIRCLES4 ,AF ! #BG1 ! DEGREE SYMBOL IS US$ #DD = ! PR9T$ DEGREE SIGN4 A#CJ ,9 ! MA? EXPRES.N1 ! R+ OP]ATOR " IS US$ = ! HOLL[ DOT 9 ! FUNC;N4 -------------------------------------#CA ,! ,A/]ISK #C4E4A 8,USE ! BRL A/]ISK TO REPRES5T ! PR9T MIDL9E A/]ISK US$ Z A SIGN ( OP]A;N 9 MA!MATICS4 ,X IS G5]ALLY BRLD UNSPAC$40 ,! MIDL9E A/]ISK SIGN ( OP]A;N IS N ! SAME SIGN Z ! A/]ISK US$ TO M>K NOTES1 9DICATE EMPHASIS1 ETC4 444 ?\< BO? SYMBOLS D H ! SAME BRL SYMBOLS4 @.<,2G9N+ ( ,EXAMPLE@.> 8,I AM "9NOT"9 R1DY YET4 ,I NE$ #C"9#C " H\RS TO F9I% GETT+ R1DY60 SD ,C>LA"9 "333333 "9,C>LA IS N A PATI5T P]SON4 #DE ,3CEPTS = #CB ,ALGEBRA & ,GEOMETRY #A4 ,SUP]SCRIPTS & SIMIL> 9DICATORS " C H ! SCOPE ( _! 9FLU;E ADJU/$ ) BRL GR\P+ 9DICATORS4 #B4 ,COMMON MODIFI]S H _! [N SPECIFIC SYMBOLS & >E COV]$ 9 SEC;N #AB ( ! ,,GTM4 #C4 ,%APE SYMBOLS "W BY ANSW]+ TWO "QS3 8:AT %APE IS X80 & 8:AT D XS 9SIDES LOOK L80 #D4 ,%APES = M1SURE;T OR ID5TIFICA;N %D N 2 TRANSCRIB$ US+ %APE SYMBOLS4 #E4 ,WE M/ N FALL PREY TO ! SIR5 S;G ( ! B1UTY ( PR9T4 ,WE IGNORE TYPE=M = PRACTICALLY ALL V>IABLES1 & WE >E 3SI/5T ) \R SPAC+ EV5 :5 PR9T IS N4 #F4 ,GRADE #A M/ 2 US$ TO KEEP SYMBOLS F 2+ MISR1D4 ,H[ T MODE IS APPLI$ V>IES BAS$ ON ! EXPRES.N4 #DF ,CLOS+ ,^WS A#CB ,?ANK Y = SP5D+ "S ( YR V VALUABLE "T & ATT5;N ON ? "W%OP4 ,5D ( ! MAT]IAL = ,ALGEBRA & ,GEOMETRY ,- ,BASIC "<,,UEB ,TE*NICAL"> @.<,! ,5D@.> #DG