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;,C4 ,SPATIAL ,LAY\T & ,DIAGRAMS """ #AJ
  ,PRACTICE ;,C """""""""""""""""""" #AJ
;,D4 ,FRAC;NS """""""""""""""""""""" #AD
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#AJ4 ;C SUP 8M9US #C;D0
#AA4 ,FE SUP 8,,III0 ,CL SUB #C
#AB4 ;M SUB ;X SUP ;Y
  8;M SUP ;Y0 SUB ;X
  ;M SUB 8;X SUP ;Y0
#AC4 SUP M9US #C PLUS SUP PLUS #G EQUALS
    SUP PLUS #D
#AD4 #B4G "TS #AJ SUP #G DEGREES,F
#AE4 ! SUM F 8;X EQUALS #A0 TO #E ( ;X
    SUB ;N SUP #H ) SUMMA;N LIMITS
    DIRECTLY 2L & ABV A CAPITAL SIGMA4
#AF4 ;,V SUB C"O EQUALS "O-HALF PI ;R
    SQU>$ ;H

         ,ANSW]S ,,PRACTICE ;,E

#A4 ,A "7 #C4ADR9#B ;;B9#C ;;,C,O5#B
#B4 ;;P9#CQ ;;P9<#CQ> ;;A9<#C;B>
#C4 ;;M9#C"6N ;;M9<#C"6N>
  ;;M9<#C"6N>"-#F
#D4 ;;Y9#C/E ;;(Y9#C./#E)
#E4 ;;(X9#B"6Y9#B./Z9#C)
#F4 ;;;P "7 Q9(R./S)T;'
            ;,E PRACT & ANS          #BJ
#G4 ;;X9<Y9#C> ;;X9"<Y9#C">
#H4 #B9<#B9<#B9#B>>
#I4 ;;,V5<I9#B> ;;,V9<I5#B>
#AJ4 ;;C9<"-#C;D>
#AA4 ;;,FE9<,,III>,CL5#C
#AB4 ;;M5X9Y ;;M9Y5X ;;M5<X9Y>
#AC4 ;;;9"-#C"69"6#G "7 9"6#D;'
#AD4 #B4G"8#AJ9#G ^J,F
#AE4 ;;,.S.5<X"7#A>.9#EX5N9#H
#AF4 ;;,V5<CONE> "7 #A/B.PR9#B;H
     ;;;,V5<CONE> "7 #A/B.PR9#B;H;'
     .<OR.>
     ,V;5;<C"O;> "7 #A/B.PR9#B;H

        ;,,,F4 SQU>E ROOTS & O!R
           RADICALS,' .<#H.>

  #H4A EXPLA9S ! ME?OD ( TRANSCRIB+
SQU>E ROOTS4 ,REF] TO #H4B = !
TRANSCRIP;N ( A RADICAL 9DEX4 ,NOTE A
NE/$ RADICAL IS %[N 9 ! LA/ EXAMPLE (
#H4B4
  #H4C ILLU/RATES ! SYMBOL = ! SQU>E
ROOT SIGN )\T A V9CULUM4
               ;,F ROOTS             #BA
             ,,PRACTICE ;,F

#A4 SQU>E ROOT ( 8;X SQU>$ PLUS #A0
#B4 #C SQU>E ROOT ( 8;X OV] ;Y0 PLUS #B
#C4 CUBE ROOT ( #B
#D4 8;M PLUS N0? ROOT ( 8;P PLUS ;Q0
#E4 SQU>E ROOT ( 8SQU>E ROOT ( ;X0
#F4 ,USE @.<SQU>E ROOT SIGN@.> = SQU>E
    ROOTS4

         ,ANSW]S ,,PRACTICE ;,F

#A4 ;;%X9#B"6#A+
#B4 #C%(X./Y)+"6#B
#C4 ;;%9#C#B+
#D4 ;;%9<M"6N>P"6Q+
#E4 ;;%%X++
#F4 ,USE "% = SQU>E ROOTS4






            ;,F PRACT & ANS          #BB
         ;,G4 ,,FUNC;NS .<#I.>

  ,FOLL[ #I4C = ! SPAC+ ( FUNC;N "NS4
,NOTE T 3TRAC;NS >E US$ UN.S GRADE #A
MODE IS 9 E6ECT1 S* Z FOLL[+ A NUM]IC
9DICATOR "<SEE ! F9AL EXAMPLE 9
#I4C4C">4

             ,,PRACTICE ;,G

#A4 S9 #CJ DEGREES1 COS ;X1 TAN !TA
#B4 A CSC ;X1 #C S9 #DE DEGREES1 COS SUP
    8M9US #A0 #J4B
#C4 #B LOG SUB #D #H1 LOG SUB A ;X1 LOG
    SUB #H ;X
#D4 S9 ;,A EQUALS M9US 8#A OV] SQU>E
    ROOT ( #B0
#E4 ;Y EQUALS M9US #C S9 "<#B ;X PLUS
    PI"> M9US #A1 M9US PI IS LESS ?AN OR
    EQUAL TO ;X IS LESS ?AN OR EQUAL TO
    #B PI



          ;,G FUNC;NS & PRACT        #BC
         ,ANSW]S ,,PRACTICE ;,G

#A4 S9#CJ^J1 COS ;X1 TAN.?
#B4 A CSC ;X1 #CSIN#DE^J1
  ;;COS9<"-#A>#J4B
#C4 #BLOG5#D#H1 ;;LOG5AX1 ;;LOG5#HX
#D4 ;;;SIN,A "7 "-(#A./%#B+);' .<OR.>
    S9,A "7 "-;(#A./%#B+)
#E4 ;Y "7 "-#CSIN"<#BX"6.P">"-#A1
  "-.P _@< ;X _@< #B.P

     ,,,H4#A SET !ORY1 GR\P !ORY &
            LOGIC,' .<#AJ.>

  ,USE ! APPROPRIATE SYMBOLS4 ,SYMBOLS (
COMP>ISON >E SPAC$ & SYMBOLS ( OP]A;N >E
UNSPAC$ "<SEE ! EXAMPLES">4

     ,,,H4#B MISCELLANE\S SYMBOLS,'
                .<#AA.>

  ,NOTE : SYMBOLS C 2 F.D "H E4G4 9F9;Y1
9TEGRAL1 A/]ISK1 ANGLE4 ,"S SIGNS >E N[
M ?OR\<LY COV]$ 9 ! REVIS$ ,SEC;N #C4
        ;,G ANS & ;,H SETS" MISC     #BD
             ,,PRACTICE ;,H

#A4 ,A 9T]SEC;N ;,B1 ;,X IS A SUBSET (
    ;,Y
#B4 "<,A & N ;,B"> 3TA9S "<N ;,X OR
    ;,Y">
#C4 9TEGRAL F 8;X EQUALS A0 TO 8;X
    EQUALS ;B0 ( F"<X">DX
#D4 ! SUM F 8;N EQUALS #J0 TO 9F9;Y ( A
    SUB ;N ) SUMMA;N LIMITS DIRECTLY 2L
    & ABV A CAPITAL SIGMA
#E4 "!=E ANGLE ,,ABC IS LESS ?AN #IJ
    DEGREES
#F4 _<! SET ( "<;X1 ;Y"> S* T ;X EQUALS
    ABSOLUTE VALUE ( ;Y_>
#G4 ;N FACTORIAL OV] 8;R FACTORIAL "<;N
    M9US ;R"> FACTORIAL0

         ,ANSW]S ,,PRACTICE ;,H

#A4 ,A.8,B1 ;,X ^< ;,Y
#B4 "<,A@8@?,B"> ^> "<@?,X@6,Y">
#C4 ;;!5<X"7A>9<X"7B>F"<X">DX
#D4 ;;,.S.5<N"7#J>.9#=A5N
            ;,H PRACT & ANS          #BE
#E4 ;,* _[,,ABC @< #IJ^J
#F4 ;;;_<"<X1 Y"> _\ X "7 _\Y_\_>;'
#G4 ;;(N6./R6"<N"-R">6)

    ,,,I4 B>S & DOTS ETC4 OV] & "U,'
                .<#AB.>

  ,^! SYMBOLS FOLL[ ! 8ITEM0 : !Y >E OV]
OR "U4 ,NOTE T S"EAL ( ^! SYMBOLS H
3TRACT$ M1N+S & W NE$ TO 2 9 GRADE #A
MODE4 ,! DEF9I;N ( AN ITEM IS REP1T$ 9
#AB4A4

             ,,PRACTICE ,I

  .7,TRANSCRIBE "Q #F Z A SPATIAL
>RANGE;T4.'
      @.<,9 "Q #B1 S"EAL ITEMS FOLL[ "O
    ANO!R ON ! PR9T L9E SEP>AT$ ONLY BY
    SPACES4 ,!Y H BE5 PLAC$ ON SEP>ATE
    L9ES 9 ! V]BALIZA;NS 2L = CL>;Y4@.>
#A4 ;Y B> OV] IS N EQUAL TO #J
#B4 #A4DE ) A B> OV] DIGITS #DE
  #A4DE ) DOTS OV] DIGITS #D & #E
          ,I B>S1 DOTS & PRACT       #BF
  ,,DEF ) A HAT OV] ;,E
#C4 ;X ) TILDE "U
#D4 ;V ) "R >R[ OV]
#E4 8;,,AB0 B> OV] SQU>$
#F4 8#C OV] #H ) #H C.ELL$ & #B 2L0 "TS
    8#D OV] #G ) #D C.ELL$ & #A ABV0
    EQUALS 8#C OV] #AD0

         ,ANSW]S ,,PRACTICE ,I

#A4 ;;Y: "7@: #J
#B4 #A4<#DE>: #A4<#DE>^4 ;;,D,E":,F
#C4 X,_:
#D4 ;;V^:
#E4 ;;<,,AB>:9#B
#F4

           #A
   #C     #D@:    #C
  "333 "8 "333 "7 "33
  #H@:     #G     #AD
   #B


                 ,I ANS              #BG
          ;,J4 ,,>R[S .<#AC.>

  ,SIMPLE >R[S >E DEF9$ & _! TRANSCRIP;N
IS EXPLA9$ 9 #AC4A4 #AC4B D1LS ) >R[S )
UNUSUAL %AFTS & #AC4C LI/S SYMBOLS =
UNUSUAL TIPS4 ,IF X IS NEC TO DET]M9E !
DIREC;N ( ! >R[1 FOLL[ ! PROVI.NS AT !
BOTTOM ( PAGE #FB4 ,! ORD] = TRANSCRIB+
! ELE;TS ( AN UNUSUAL >R[ IS GIV5 AT !
TOP ( PAGE #FC4

             ,,PRACTICE ;,J

#A4 ;X T5DS TO @.<"R ARR[@.> 9F9;Y
#B4 LIMIT1 Z !TA T5DS TO #J1 ( COS !TA
#C4 8O!RWISE ORD9>Y UPW>D >R[1 ) TWO H1D
    TIPS0 8COMMON V]TICAL BIDIREC;NAL
    >R[0
#D4 ;X IS N EQUAL TO ;Y 8D\BLE %AFT$
    HORIZONTAL BIDIREC;NAL >R[0 N "<;X
    EQUALS ;Y">
#E4 ;X 8"R >R[ ) UPP] HALF B>B0 ;Y


           ;,J ARR[S & PRACT         #BH
         ,ANSW]S ,,PRACTICE ;,J

#A4 ;X ;\O #=
#B4 ;;LIM.5<.?\O#J>COS.?
#C4 ;\33RR+ ;\WR+
#D4 ;;;X "7@: Y \W77RO @?"<X "7 Y">;'
#E4 ;;;X \@RO Y;'

    ;,,,K4 %APE SYMBOLS & COMPOSITE
           SYMBOLS,' .<#AD.>

  ,! %APE 9DICATORS >E LI/$ 9 #AD4 ,NOTE
! LI/ ( SPECIFIC %APES4 ,= A RECTANGLE1
! SYMBOL = P>ALLELOGRAM MAY 2 US$4 ,REF]
TO #AD4A TO DET]M9E :5 A T]M9ATOR IS
REQUIR$ = A %APE4 ,ONCE 9 %APE MODE1
GRADE #A 9DICATORS >E N REQUIR$4
  ,FOLL[ #AD4B = A TRANSCRIB]-DEF9$
%APE4 ,REF] TO #C4BF 9 ! ,RULEBOOK TO
DET]M9E :5 ! USE ( A TRANSCRIB]-DEF9$
.1SYMBOL IS PREF]R$ TO A TRANSCRIB]-
DEF9$ .1%APE4
  ,! USE ( COMPOSITE SYMBOLS IS DESCRIB$
9 #AD4C4 ,NOTE T EA* IS %[N ) A GRADE #A
          ;,J ANS & ;,K %APES        #BI
SYMBOL 9DICATOR PREC$+ X4
  ,(T5 CALCULATOR KEYS >E %[N 5CLOS$ )9
A BOX4 ,! PREF]R$ ME?OD = _! TRANSCRIP;N
IS GIV5 9 #C4E ( ,,GTM #BJAD4
  ,SEE #C4F ( ,,GTM #BJAD = A SQU>E US$
Z A M>K ( OMIS.N4

             ,,PRACTICE ;,K

#A4 #I M9US #E SQU>E #D
#B4 CIRCLE 8SOLID P5TAGON0 8%AD$ SQU>E0
#C4 ;,H SUB #B ,O 8"R >R[ OV] LEFT >R[0
    #B,H PLUS ,O
#D4 />
#E4 ,PRESS CALCULATOR KEYS 8SQU>E ROOT
    SIGN 9 BOX0 8#D 9 BOX04
#F4 "<B9OMIAL COE6ICI5T ;N OV] #J">
    EQUALS "<B9OMIAL COE6ICI5T ;N OV]
    ;N"> EQUALS #A

         ,ANSW]S ,,PRACTICE ;,K

#A4 #I"-#E ;$#D #D
#B4 ;$= _$#E .$#D
            ;,K PRACT & ANS          #CJ
#C4 ;;;,H5#B,O \O]\[ #B,H"6,O;'
#D4 @$S .<OR1 AM;G S"EAL OP;NS.>
    @$STAR
#E4 ,PRESS CALCULATOR KEYS _2"% _2#D4
#F4 ;;;"<N]#J"> "7 "<N]N"> "7 #A;'

      ;,,,L4 MATRICES & VECTORS,'
                .<#AE.>

  ,US+ ! 5L>G$ GR\P+ SYMBOLS F #E1 FOLL[
! PROVI.NS 9 #AE = MATRICES .<#AE4B.>1
DET]M9ANTS .<#AE4C.> & VECTORS
.<#AE4F.>4 ,NOTE T #AE4D D1LS ) OMIS.N
DOTS1 #AE4E GIVES GUID.E ON WIDE
MATRICES & #AE4G %[S ! USE ( 5L>G$ GR\P+
SYMBOLS = GR\P+ ( EQUA;NS4
  ,IF A GRADE #A PASSAGE 9DICATOR IS
US$1 X MAY 2 PLAC$ ON A L9E BY XF
"<REPLAC+ ! BLANK L9E"> PREC$$ BY ! DOT
LOCATOR = 8USE0 "<DOTS #E-#E-#ABCDEF">4
,SEE #C4AD 9 ! ,RULEBOOK4 ,! GRADE #A
T]M9ATOR WD AL 2 PLAC$ ON A L9E BY XF
FOLL[+ ! >RANGE;T & PREC$$ BY ! DOT
LOCATOR = 8USE04
              ;,L MATRICES           #CA
             ,,PRACTICE ;,L

      @.<,COMMAS 9DICATE A NEW PR9T
    L9E4@.>
#A4 @.<MATRIX3@.> "<#A 8M9US #B01 8M9US
    #C0 #D">
#B4 @.<MATRIX3@.> .<8M9US ;M0 ;N1 ;P
    #CQ.>
#C4 @.<MATRIX3@.> _\8A SUB #AA0 8A SUB
    #AB0 ELLIPSIS 8A SUB #AN01 8A SUB
    #BA0 8A SUB #BB0 ELLIPSIS 8A SUB
    #BN01 DOT DOT ELLIPSIS DOT1 8A SUB
    R#A0 8A SUB R#B0 ELLIPSIS 8A SUB
    RN0_\
#D4 8,,XY0 ) "R >R[ OV]
  8,,XY0 ) B> "U
#E4 ^2;V EQUALS .<;R1 8ANGLE !TA0.>
#F4 F"<N"> EQUALS _<8;N PLUS #E IF ;N IS
    EV501 8;N M9US #E IF ;N IS ODD





               ;,L PRACT             #CB
         ,ANSW]S ,,PRACTICE ;,L

#A4 ,"<  #A "-#B,">
    ,"<"-#C   #D,">

#B4 ,.<"-M ;N ,.>
    ,.< ;P #CQ,.>

#C4
""=;;;
  ,_\A5#AA   A5#AB   444 A5<#AN>,_\
  ,_\A5#BA   A5#BB   444 A5<#BN>,_\
  ,_\  4       4     444    4   ,_\
  ,_\A5<R#A> A5<R#B> 444 A5<RN> ,_\
""=;'

#D4 ;;<,,XY>^: ;;<,,XY>,:

#E4 ^2;V "7 ,.<R   ,.>
            ,.<_[.?,.>

#F4 F"<N"> "7 ,_<N"6#E IF ;N IS EV5
              ,_<N"-#E IF ;N IS ODD

                ;,L ANS              #CC
         ;,M4 ,,*EMI/RY .<#AF.>

  ,:5 TRANSCRIB+ *EMI/RY1 REF] TO #AF4B
= CAPITALIZA;N4 ,SUBSCRIPTS &
SUP]SCRIPTS = ATOMIC MASS NUMB]S >E 9
#AF4C & = ELECTRONIC 3FIGURA;N >E 9
#AF4D4 ,EXAMPLES ( *EMICAL EQUA;NS >E
%[N 9 #AF4E4 ,PR9T USES V>I\S ME?ODS (
%[+ ELECTRONS : MAY 2 REPRES5T$ BY !
CORRESPOND+ ,,UEB SIGNS Z ILLU/RAT$ 9
#AF4F4 ,/RUCTURAL =MULAE >E COV]$ 9
#AF4G4 ,NOTE T "! >E ,,UEB SYMBOLS GIV5
9 #AF : >E US$ = L9E BONDS4 ,REF] TO
#AF3 ,L9E ,MODE 9 ! ,RULEBOOK = !
TRANSCRIP;N ( L9ES 9 /RUCTURAL =MULAE4

             ,,PRACTICE ;,M

#A4 8;,H SUB #B ,O0 8;,H L9E BOND ,O L9E
    BOND ;,H0
#B4 ,FE SUP 8#B PLUS0 PLUS #B ;E SUP
    M9US "R >R[ ,FE


          ;,M *EMI/RY & PRACT        #CD
#C4 ;,R EQUALS #H4CA;DM SUP #C
    @.<MULTIPLICA;N DOT@.> K,PA SLA% MOL
    @.<MULT4 DOT@.> ;,K
#D4 8SUB #ID0 8SUP #BDD0 ,PU =
    ,PLUTONIUM
#E4 ,BR L9E BOND ,BR EQUILIBRIUM >R[ #B
    ,BR @.<) D\BLE DOT ON LEFT1 D\BLE
    DOT ABV1 S+LE DOT ON "R1 D\BLE DOT
    2L@.>
#F4 ,ACETIC ACID "<V9EG>">3 @.<SEE ANSW]
    = /RUCTURAL =MULA@.>
#G4 @.<SEE ANSW] = /RUCTURAL =MULA@.>
#H4 @.<^W 8H1T0 IS OV] "R >R[@.> ;,H SUB
    #B ,O "R >R[ #B,H PLUS ,O

         ,ANSW]S ,,PRACTICE ;,M

#A4 ;;,H5#B,O ;;,H,-,O,-,H
#B4 ;;;,FE9<#B"6>"6#B;E9"- \O ,FE;'
#C4 ;,R "7 #H4CA;DM9#C"4K,PA_/MOL"4,K
#D4 ;5#ID9#BDD,PU = ,PLUTONIUM



            ;,M PRACT & ANS          #CE
                      ."4
#E4 ,BR,-,BR ^_7 #B."4,BR"4
                      ."4

#F4 ,ACETIC ACID "<V9EG>">3
""=;;;
            ,O
           >>
  ,C,H5#C,-,C,-,O,H
""=;'
#G4
""=;;;
  ,BR
   _
   ><
  >  <
  _  _
  <  >
   <>
   _
  ,C"<,C,H5#C">5#C
""=;'


                ;,M ANS              #CF
#H4
""=;;;
         HEAT
  ,H5#B,O \O #B,H"6,O
""=;'

    ;,,,N4 COMPUT] NOTA;N,' .<#AG.>

  #AG4A GIVES A DEF9I;N ( COMPUT] NOTA;N
& EXPLA9S :AT IS M1NT BY 84PLAY$0 &
89L9E04 ,! L9E >RANGE;T = 4PLAY$ COMPUT]
NOTA;N & XS SPAC+ >E 4CUSS$ 9 #AG4B4
,USE UNCONTRACT$ BRL = 4PLAY$ COMPUT]
NOTA;N & ANY ASSOCIAT$ EXC]PTS
.<#AG4C.>4

             ,,PRACTICE ;,N

      @.<SEE ANSW]@.>

         ,ANSW]S ,,PRACTICE ;,N

  ,? EXAMPLE ( A ,C"6"6 PROGRAM 0 F.D AT
HTTP3_/_/WWW4CS49DIANA4$U_/@9SABRY_/"
           ;,N COMPUT] NOTA;N        #CG
T1*+_/9TRO_/FA#IF_/CODE_/PRIME4,C4 ,X IS
US$ TO *ECK IF A NUMB] IS PRIME4

""=;;;
_?INCLUDE @<IOSTREAM4H@>

INT SMALLDIV "<INT N"> _<
  INT COUNT2
  COUNT "7 #B2

  WHILE "<COUNT @< N @&@& N .0 COUNT""
      6"7 #J"> _<
    COUNT "7 COUNT "6 #A2
  _>
  RETURN"<COUNT">2
_>

INT MAIN "<"> _<
  INT N2
  COUT @<@< ,7,ENTER A NATURAL NUMBER3""
      ,72
  CIN @>@> N2
  IF "<N "7"7 SMALLDIV"<N">"> _<
    COUT @<@< N @<@< ,7 IS A PRIME""
                ;,N ANS              #CH
      NUMBER,7 @<@< ENDL2
  _>
  ELSE _<
    COUT @<@< N @<@< ,7 IS NOT A PRIME""
      NUMBER,7 @<@< ENDL2
  _>
  ,RETURN"<#J">2
_>
""=;'

                ,,! ,,5D













                ;,N ANS              #CI