ZXTape! 0Created with Ramsoft MakeTZXALG1  [  N0:0:0::236099\,502:0:0:0 q$="y"x -z$="  " K12 ,10 ;1;4;"PLEASE WAIT";0;0 "" .a=07:a,0;1;z$:a (H12 ,6;4;1;" LOADING PROGRAM ";:0 -*18,5;" " .13 ,0; / 0 2 "file" <*:15,0;"Leave tape running" F"" P*15,0;"Stop and rewind tape" R"clear (y/n) ?";q$ Tq$="y""address ? ";x ZJ17,0;"Type in file name in ";1;"UPPER CASE";0 n"Filename",a$ o015,0;"Recording " p517,0;" " x a$10 "logo"16384@,2304  '10 ,5;"Load main program" )12 ,5;"SAVE""file"" LINE 2" Z&  QnAALG1E$logo @ ??80?߀????>?#|?~???|?|~?8???1???<???????<?0~|??~?~|?|~?>??#???8??????1???????~<?|??|~?|?|~?|?|~???9??>?? ?????8<0p??>?x?~file s&s_Ms :del=30:star=8580!:scroll=8550f!:arrow=85004!:table=8480 !:inchar=8360 :get=8350 :innum=82400 :mdown=8200 :clear=8180:delay=8160:msnd=8130:buck=8090:mach=8000@ d(x)=x/2 a(x )=x+3 s(x)=x-4 rflg=0 2I0:0:0:0:0:6:l=12 :clear < 9000(# nEintop=8600!:outbot=8700!:s$="":pmach=8800`":pmach xX17,0;" This is a machine that turnsold numbers into new ones.":star ,l=2:c=22:table:flag=0 l=6:clear M17,0;" Type in a number between 1 and9 and see what happens." d$="..":innum "dd<1dd>9 160 C4+flag,22;"";dd:l=4+flag:c=24:arrow $intop:msnd:dd=dd*2:outbot 4+flag,29;"";dd flag=flag+1 l=6:clear Eflag=117,0;" Try another number.":160 ?flag=217,0;"And another...":160 jj$="":17,0;" What do you think the machineis doing to the numbers you putin?":inchar s$=""240 l=6:clear s$<5280 z=1̱s$-5 s$(zz+4)="doubl"s$(zz+4)="times"s$(zz+4)="multi"17,0;"Yes, it doubles the number youput in.":300, z C17,0;"No,in fact it doubles the numberyou put in." ,star:l=6:clear 617,0;" We must now find a way for youto enter your answers so thatI can understand you easily.":star:clear @17,0;" Look at the machine above, itactually multiplies the numberyou put in by two.We could writethis as: 2 times your number." J star:clear T17,0;" But this is too long, so let'sstart by replacing 'your number'by the letter'x'.Which gives us:"''" 2 times x." ^ star:clear hv17,0;" Now we can replace the word'times' by the 'x' sign.To give:"''" 2 x x" r star:clear |17,0;" However , this is confusingbecause it has too many x's. Therefore we must remove thefirst 'x' to leave:"'" 2x"  star:clear X17,0;" Therefore the rule 2 times x isthe same as the rule 2x." l=20:star:clear c5,0;" What do you think the rule isfor a machine that multiplies anumber by 3?" j$="F":inchar 5s$="3x"10 ,5;"Correct !":460 \10 ,0;" No,the rule would be 3x, since3x is the same as 3 times x." star:l=20:clear L5,0;" Now five questions for you toattempt.":star:clear +sc=0:1,25;"SCORE 0" c=15 %nm=(*8)+2:a$=nm+"x" }l=19:clear:5,0;" What do you think the rule isfor a machine that multipliesa number by ";nm;"?" j$="F":inchar \s$=a$sc=sc+1:10 ,5;"Correct !";1,31;"";sc:550& /10 ,0;"No, the rule is ";a$;"." &star 0c :l=20:clear D5,0;" Now you have completed thefirst part of lesson one youshould attempt exercise 1a inthe instruction booklet beforeproceeding with the second part." N19,0;"Press any key when you havecompleted the exercise and Iwill begin the second part ofLesson One." Xget bq$="divides by":subtext=2000:t$="div":u$="sha":k$="hal":r$=" Yes, it halves the number youput in.":w$=" No,in fact if halves the numberyou put in.":rflg=1:l=21:clear gflag=0 ls$="":pmach vl=2:c=22:table l=5:clear bflag2=0:17,0;" Type in a whole number between1 and 9 and see what happens." d$="..":innum "dd<1dd>9 660 *0,6;" " U4+flag2,22;"";dd:l=4+flag:l=4+flag2:c=24:arrow  intop:msnd q$(1)="d"dd=d(dd) q$(1)="a"dd=a(dd) q$(1)="s"dd=s(dd) outbot 13 ,16;"";s$ !4+flag2,29;"";s$ flag2=flag2+1 l=5:clear Eflag2=117,0;"Try another number.":660 @flag2=217,0;"And another...":660 V17,0;" What do you think the machinedoes to the number you put in?" j$="L":inchar s$=""760  s$21150~  q$="adds" isubtext=2030:k$="add":t$="plu":u$="sum":r$="Yes, it adds 3.":w$="No, in fact it adds 3." rflg=0:620l L$q$="subtracts":subtext=21004 V_t$="tak":u$="min":k$="sub":r$="Yes, it subtracts 4.":w$="No, in fact it subtracts 4." ` 620l ~l=20:clear u3,0;" Now you have completed lessonone you should attempt exercise1b in the instruction booklet." Q20,0;" PRESS ANY KEY WHEN YOU HAVE COMPLETED EXCERCISE ONE." get:l=21:clear: 20,11 ;5;1;"LESSON ONE" 85,1;6;"That completes Lesson One." ؿ6;7,1;"If you would like to go over"'" Lesson One again, ";10 ,13 ;2;6;"PRESS R":'" otherwise:-";12 ,13 ;6;1;"PRESS S" =""1260 ="r"Ŧ="R"5 ="S"Ŧ="s"1300  1260 l=21:clear 5,0;5;" When you are ready to begin thenext lesson, type NEW followedby-";7;1;9 ,10 ;"LOAD ~ALG2~" (23636T\,255:   subtext1 M'" To halve a number you mustdivide by two,therefore we couldwrite:" #'" your number divided by 2" g'" But this is too long, so wecould start by replacing 'yournumber'by the letter'x',to give:" '" x divided by 2"  star:clear 3,0;" However,this still contains toomany words, so let's replace'divided by' by the '/' symbol.Which is obtained by holdingSYMBOL SHIFT and pressing V.Thisleaves us with:" '" x/2" _17,0;" Remember,the rule 'x divided by2' is the same as the rule x/2." star:  subtext2 ]3,0;" To describe what the lastmachine was doing we couldwrite:" " x plus 3" '" Where 'x' is the number you putin. But this is still a littlelong, so we could replace theword 'plus' with the '+' sign,which is obtained by holdingdown SYMBOL SHIFT and pressingthe K key." _17,0;"So, the rule 'x plus 3' is thesame as the rule 'x+3'.":star: 4 subtext3 >R3,0;" To describe what the lastmachine did we could write:" H" x minus 4" R'" Where 'x' is the number you putin. But this is still a littlelong, so we could replace theword 'minus' with the '-' sign,which is obtained by holdingdown SYMBOL SHIFT and pressingthe J key." \n17,0;" This means that the rule 'xminus 4' is the same as the rule'x-4'.":star: ? Jdl-5,c+8;"";l-4,c-1;" ";l-3,c-1;" " Tl-2,c;"";l-1,c;"";l,c;"";l+1,c+6;" " ^5s$""l-1,c+2+(4-s$);"";s$ h buck ;l-1,c-1;" ";l,c-1;"": msnd ̠.3,-40(:.2~L,-29:.3,-37%:.8L,-20:.25~,-34":.2~L,-30:.5,-35#:.1}L,-5  delay z=1del:z: clear l>21l<1 23659k\,l+3:"": mdown #del=del-0.5:l,c;"";s$ 9x=ll+n:x,c;"";s$:delay:x,c;" "(csp):x: 0innum D%dd=0:l=1:x$="":clear N'21,0;"N";8; Xz=1̱d$ ]get b%s$=13 x$""dd=x$:clear: ls$=12 8260D vs$<"0"s$>"9"8285] "s$;"N";8;:x$=x$+s$ z:dd=x$:l=1:clear: get s$="" ""8351 =""8354 s$=:.01z# =,5: j$=""j$="L" x$="":l=1:clear 21,0;j$;8; get $s$=13 s$""clear:s$=x$: s$=12 8370 x$=x$+s$:s$;j$;8; 8390 ! table !*nl,c;"x y":7;c*8,166-(l*8):7;64@,0:c=c+2:arrow: !4arrow !>x=c*8:y=171-(l*8):7;x,y:7;31,0:7;-3,3:7;x+31,y:7;-3,-3: !fscroll !p"z=1l:zz=3582 :z: !star !?1;21,31;"*":15:=""8590! !21,31;" ": !intop !Y13 ,16;" ":csp=2:l=2:c=9 :n=5:s$=dd:mdown: !hcsp=3:l=11 :c=16:n=2:s$=dd:8900":mdown:13 ,16;s$+" ": "`pmach "j=l=10 :c=9 :mach:l=14:c=15:buck: " rflg "(q=dd*2:q/2=(q/2) "q=1s$="": "s$=((q/2))+"": " #-6:0:0: #2x=010 :l$:5,0+x*3;l$:.05|L,40(-(2*x):x:"F","U","N","D","A","M","E","N","T","A","L" #<7,2;" " #A*3;14,11 ;"LESSON ONE" #Fstar:l=21:clear #Z %21,31;" ": &"":5 &+"file"9899&:"usr""a",168: ' "":"" AF B`Nl m .L,nNa *e!m'! \je %'^m'\&fFg! @G f Ɔfa `ƃ ]&E^) 'E e e%F '^)e e% %FF @Ffˀ^Ff '_`&f@@Ml!B@ơ@ &%NLnd ΌA&#m'! F@^m!&NLndʈD m΍-άGn$'b@N$DY}fF '`f& (@2*gA@]&f@2 a`A@{dDfb Z@@ #%"WR BZPP "" Z`` "4 Zpp "u3 "ZÀ "C 0ZÐÐ#BR dZ À%tr#Z0À$ P ``ZppPPh(p(iphPh`K Ap(HhXp0h@h[qpch CqIAE)SiI[HhXph0Ypӹv_aph CqI CN_aphXap0hph hpiphtְ88 x8숀뭤8084 XL884 Pְ88,x8쉍XnXbbw`vDDu\dX`Xl Xbbw`vDDuXnXbbw`vDDu\dXbd ,zj ubf`xHzL^HzddlbIbn``x|L^Hxhp`^H|jnrn``x~{`H&HzDZEn`p^[tPR|`xb|rn``xnb`^[tPR|`xj |rn``x&z`hb`uXbdXb`w`vD@@@DuXXfw`vD@@D>XVbXfw`v@@dTHzbfd@u\`bGzXuhzrbbub`uXVbXb`vHuXXb`w`vD@@@D|$\hXl @@bd```|`uXbn"XhvD@@@@@@@@@@@@@@@@@@@@@D0n``xD,zdubf`N(HzD^Eb`j`4X(HzDTEb```\(HzDVEb`n`\b(HzDZEb`p`plul``n`v,zj ubf`p``@.zbbb``Xbr&XhvD@@@@@@@@@@@@@@@@@@@@@Dun``x(HzD^Eb`j`4(HzDTEb```(HzDZEb`p`p(HzDVEb`n`\,zdubf`ul``,zj u130 0:800  L=11100L  b=a*v b$=b  b=a/v b$=b $ 1500 ) .b=a+v 3b$=b 7 8b=a-v Bb$=b K L'5,19;0;"x y" V)6,18;0;" ---------" `S=2:130 j95,21;0;"PPPp":S=5:130 t2U=U+2:U,19;0;a;" ";b$ ~S=2:130 U,21;0;"PPPp" S=5:130  clear Pc=1521:c,0;0;" ":c  i=210-1 8i,0;0;" " (i 2 xF$(5,4,1) { 1430 }D=25 N=1D-1  F$(D,N) N D )"&","[","_","]","&","^","{","|","}","@"  S=5:130 N=((b-b)*v+.5) b-(b)=01515 b=01530  1520 b$=b:1540 b$=b+F$(v,N)  1540  b$=F$(v,N)  @concatenation J-A$="":I=1̱R$:R$(I)=" "1630^ T $/y4 sm}x xx xv7$z&"'"z'"'*")#''" xvAlvHxvAz;;;;;;;;;;;;;;;;;;;xvA'z*4440642:40103'"7:294:7'" vvdvX+z*<240;727:212;02lz 029;040829lv^ xvt$ xvA+x,l.v,8 xvA= lv?xvA@xB xvBDxvAGvLvdQvXVIlz+027<:445:426424273:7:427:29<028::434:74w;};eV[vX[z(027$099<$27:22902<"4<642762:427:2w<8:4<}9>":0:700 ^'G:v=2:b=a+v:b$=b:600X _0:800  ` 0:U=6:1100L a%5:0:C$="+":900 b 1200 c16,2;"In this case, the MACHINE is obviously adding TWO to the numbers you are putting in. So we can write it's RULE as ....":2:21,13 ;"x+2":0:300, d 200 e 1200 f16,2;"If the MACHINE was adding 5 to your number x , then we would write the RULE as:-";:2:20,13 ;"x + 5":0:300, g 200 h 1200 i_16,2;0;"What is the RULE that adds 3 to:427:29w09v } <e7} e4vXz '744v8vXz ,:4094:vvdmvXnlz)4:62:9<:73427:42)*":1<:42&$"4:4237673"21lz *42202:492(49lvvd mv xxxvzˋxx͏msv  xvA΅vH xvA xvz"xxxxxxvzv 4z 2<0742527&$"v技mv 3z <<z xvA眀z (((8xvA lvH蘀xxlmsz+027<:445:44&$"27酀vvdJz *44:4*<240;727:212;02lz 029;040829l xv^xxxv, xvAv xv&xvBvXz$:441:42&$"4126<lz0373lz:427:29<028::434);1;4249)*"0lz lvvdvXLz$:42&$";9:9043397<:42;;2;42:42)*"0lz <lvvdvXz+04:42)*"370&$":40:0397:427:29w09v  } <eu} esz '7:42)*";vvvXz,:4094:vvdxxxvzvXlz)4:62:9<:73427:42)*":1<:42&$"4:4237673"21lz *42202:492(49lvvdsmv vHxvzv 5z'71272337:7&2*;::7:78002;5:497"21vvd!z"7373:71206<099v vd%lzeta!crolf!rro4!abl !ncha e nnu0 dow leaelasnucac@fll 2#LLusr X??@DHT*B`0 8x||x8?>x``x>?x<?NWo :star=8580!:scroll=8550f!:arrow=85004!:table=8480 !:inchar=8360 :get=8350 :innum=82400 :mdown=8200 :clear=8180:delay=8160:msnd=8130:buck=8090:mach=8000@ 1del=30:pmach=8700!:thru=8800`" 2I0:0:0:0:0:6:l=12 :clear < 9000(# n3,0;" In this lesson we are going toput two machines together andthen see what happens.":star:l=20:clear xt$="":b$="":pmach l=2:c=22:table t$="2*x":b$="x+1" l=5:clear Nflag=0:17,0;" Type in a whole number between 1 and 9." 2d$="..":innum:dd<1dd>9 160 C4+flag,22;"";dd:l=4+flag:c=24:arrow &thru:4+flag,29;"";dd flag=flag+1 *flag=1m$="Try another number." %flag=2m$="And another..." flag=3250 3l=5:clear:17,0;m$:160 l=5:clear 17,0;" As you have probably realized,the top machine doubled yournumber x, while the bottom onethen added 1." star:l=5:clear v17,0;" So,the rule for the top machineis  2x and the rule for thebottom machine is x+1." 65,5;"2x";11 ,12 ;"x+1" " star:clear ,d17,0;" Therefore, if we could combinethe two macines its rule wouldbe 2x+1." 6 star:clear @17,0;" However we had better checkthis."'" But, before we do, copy theresults table onto a piece ofpaper." Jstar:l=20:clear T'l=7:c=4:s$="2x+1":mach ^Jflag=0:l=11 :c=10 :buck:l=2:c=23:table `13 ,0;" This machine has the rule 2x+1,so we will test to see if itdoes the same as the last twomachines, by putting in the samenumbers.":star:l=9 :clear hk15,0;" Use your list to enter the samenumbers in the same order. Startwith the first now:" r2d$="..":innum:dd<1dd>9 370r wC4+flag,23;"";dd:l=4+flag:c=25:arrow |P10 ,11 ;" ":s$=dd:l=1:c=4:n=3:mdown:msnd Zs$=(2*dd+1):l=8:c=11 :n=2:mdown:10 ,11 ;s$  4+flag,30;"";s$ %l=7:clear:flag=flag+1 flag>2450 +flag=1m$="Now the next number." $flag=2m$="Now the last." !15,0;m$:370r l=7:clear n15,0;" Did you get the same results asyou did with the two machines?"'"Press Y or N." 8j$="L":d$=".":inchar:s$"y"s$"n"470 l=7:clear s$="y"17,0;" Good, that proves that thismachine does the same as thelast two joined together.":510 V17,0;" You must have entered differentnumbers, try again.":330J star:l=7:clear S15,0;" Suppose you made x equal 11.What would the y number be?" d$="...":innum dd=0530 &l=7:clear 0Ldd=2315,0;" Correct, let's try another.":580D :r15,0;" No, it should be 23, because 2times 11 is 22, plus 1,makes 23.Let's try another example." Dl=7:star:clear N215,0;"If x is 15 what will y be?" X(d$="...":innum:dd=0600X bOl=7:clear:dd=3115,0;"That's right!":630v lP15,0;" No, it would be 31, since 2x15is 30, plus 1, makes 31." vstar:l=20:clear N17,0;" Let's try two more machinesjoined together.":star 3pmach:l=2:c=23:table:flag=0 l=5:clear o17,0;" The rule for the top machine is3x and the rule for the bottommachine is x-2." 65,5;"3x";11 ,12 ;"x-2" ,t$="3*x":b$="x-2":star:l=5:clear @17,0;" Type in a whole number between1 and 9." 2d$="..":innum:dd<1dd>9 710 I4+flag,23;"";dd:l=4+flag:c=25:arrow:thru  4+flag,30;"";s$ %flag=flag+1:l=5:clear flag>2800  *flag=1m$="Try another number." %flag=2m$="And another..."  !17,0;m$:710  l=5:clear:16,0;" What do you think the rulewould be if the two machineswere replaced by one that doesthe same job?" *"d$=".....":j$="F":inchar 4s$=""810* 9l=5:clear >Hs$="3x-2"17,0;"Correct, it would be 3x-2.":850R H-17,0;"No, it would be 3x-2." Rstar:l=20:clear \El=7:c=4:s$="3x-2":mach:l=11 :c=10 :buck f13 ,0;" Here is a machine with the rule3x-2. Now suppose x was 11 whaty value would the machineoutput?" p(d$="...":innum:dd=0880p z$20,0;"Let's see..." 7l=1:c=4:s$="11":n=3:mdown:msnd 2l=8:c=11 :n=2:s$="31":mdown star:l=8:clear `dd3116,0;"No, it was 31 because, 11 times3 is 33, minus 2, makes 31." C20,0;" Let's try another.":star:l=8:clear D16,0;"If x is 15, what will y be?":d$="...":innum $18,0;"Let's see..." il=1:c=4:s$="15":n=3:mdown:msnd:l=8:c=11 :n=2:s$="43":mdown l=7:clear wdd43+16,0;" First you multiply 15 by 3which makes 45,then you subtract2,which leaves 43." star:l=20:clear u3,0;" Try an exercise of 10 questionslike the ones you have justdone.":star:l=20:clear  scr=0 i=110 A1,1;"QUESTION ";i;1,24;"SCORE ";scr ~w$=".x+.":>.5w$(3)="-":w$(1)=((*4)+5):w$(4)=((*4)+1):1100L $Jw$(1)=((*5)+2):w$(4)=((*7)+2) Lnm=(*15)+2 Vl=19:clear `k5,0;" A machine has the rule ";w$;"."'"What will its output be if"'"x is ";nm;"?" j)d$="...":innum:dd=01130j t'ans=(nm*w$(1))+(w$(3)) ~Fdd=ans15,5;"Correct !":scr=scr+1:1200 815,0;"No, the output would be ";ans;"." 1:100d:i l=20:clear 5,0;" Now that you have completedlesson two you should doexercise 2 in the instructionbooklet." _20,0;" PRESS ANY KEY WHEN YOU HAVE COMPLETED EXCERCISE TWO":1:get L=20:CLEAR 20,11 ;5;1;"LESSON TWO" 85,1;6;"That completes Lesson Two." 6;7,1;"If you would like to go over"'" Lesson Two again, ";10 ,13 ;2;6;"PRESS R":'" otherwise:-";12 ,13 ;6;1;"PRESS S" =""2050  ="R"Ŧ="r"5 ="S"Ŧ="s"21004  2050 4l=21:clear H5,0;5;" When you are ready to begin thenext lesson, type NEW followedby-";7;1;9 ,10 ;"LOAD ~ALG3~" \23636T\,255: ? @mach Jfl-5,c+8;"";l-4,c-1;" ";l-3,c-1;" " Tl-2,c;"";l-1,c;"";l,c;"";l+1,c+6;" " ^5s$""l-1,c+2+(4-s$);"";s$ h buck ;l-1,c-1;" ";l,c-1;"": msnd ̠.3,-40(:.2~L,-29:.3,-37%:.8L,-20:.25~,-34":.2~L,-30:.5,-35#:.1}L,-5  delay &del=del-.3:q=1del:q: clear l>21l<1 23659k\,l+3:"": mdown %l,c;"";s$:z=0:20 9z=ll+n:z,c;"";s$:delay:z,c;" "(̱s$):z: 0innum D%dd=0:l=1:x$="":clear N'21,0;"N";8; Xz=1̱d$ ]get b%s$=13 x$""dd=x$:clear: ls$=12 8260D vs$<"0"s$>"9"8285] "s$;"N";8;:x$=x$+s$ z:dd=x$:clear: get s$="" ""8351 =""8354 s$=:.01z# =,5: inchar j$=""j$="L" x$="":l=1:clear 21,0;j$;8; z=1̱d$ get $s$=13 s$""clear:s$=x$: s$=12 8370 x$=x$+s$:s$;j$;8; z:s$=x$:clear: ! table !*nl,c;"x y":7;c*8,166-(l*8):7;64@,0:c=c+2:arrow: !4arrow !>x=c*8:y=171-(l*8):7;x,y:7;31,0:7;-3,3:7;x+31,y:7;-3,-3: !fscroll !p"z=1l:zz=3582 :z: !star !?1;21,31;"*":15:=""8590! !21,31;" ": !pmach "#s$="":l=6:c=2:mach "$s$="":l=12 :c=9 :mach "l=15:c=15:buck "$ "`thru "jO14,16;" ":x=dd:s$=x:l=1:c=2:n=2:mdown "tmsnd "~x=t$:s$=x "(l=7:c=9 :n=2:mdown "msnd "x=b$:s$=x "dl=13 :c=16:n=1:mdown:14,16;" ";14,16;s$:dd=s$: #-6:0:0: #2x=010 :l$:5,0+x*3;l$:.05|L,40(-(2*x):x:"F","U","N","D","A","M","E","N","T","A","L" #<7,2;" " #A*3;14,11 ;"LESSON TWO" #Fl=21:star:clear #Z %21,31;" ": &"":5 &-"ALG2"9899&:"code2""a",168: ' "":"" AF B`Nl m .L,nNa *e!m'! \je %'^m'\&fFg! @G f Ɔfa `ƃ ]&E^) 'E e e%F '^)e e% %FF @Ffˀ^Ff '_`&f@@Ml!B@ơ@ &%NLnd ΌA&#m'! F@^m!&NLndʈD m΍-άGn$'b@N$DY}fF '`f& (@2*gA@]&f@2 a`A@{dDfb Z@@ #%"WR BZPP "" Z`` "4 Zpp "u3 "ZÀ "C 0ZÐÐ#BR dZ À%tr#Z0À$ P ``ZppPPh(p(iphPh`K Ap(HhXp0h@h[qpch CqIAE)SiI[HhXph0Ypӹv_aph CqI CN_aphXap0hph hpiphtְ88 x8숀뭤8084 XL884 Pְ88,x8쉍XnXbbw`vDDu\dX`Xl Xbbw`vDDuXnXbbw`vDDu\dXbd ,zj ubf`xHzL^HzddlbIbn``x|L^Hxhp`^H|jnrn``x~{`H&HzDZEn`p^[tPR|`xb|rn``xnb`^[tPR|`xj |rn``x&z`hb`uXbdXb`w`vD@@@DuXXfw`vD@@D>XVbXfw`v@@dTHzbfd@u\`bGzXuhzrbbub`uXVbXb`vHuXXb`w`vD@@@D|$\hXl @@bd```|`uXbn"XhvD@@@@@@@@@@@@@@@@@@@@@D0n``xD,zdubf`N(HzD^Eb`j`4X(HzDTEb```\(HzDVEb`n`\b(HzDZEb`p`plul``n`v,zj ubf`p``@.zbbb``Xbr&XhvD@@@@@@@@@@@@@@@@@@@@@Dun``x(HzD^Eb`j`4(HzDTEb```(HzDZEb`p`p(HzDVEb`n`\,zdubf`ul``,zj u130 0:800  L=11100L  b=a*v b$=b  b=a/v b$=b $ 1500 ) .b=a+v 3b$=b 7 8b=a-v Bb$=b K L'5,19;0;"x y" V)6,18;0;" ---------" `S=2:130 j95,21;0;"PPPp":S=5:130 t2U=U+2:U,19;0;a;" ";b$ ~S=2:130 U,21;0;"PPPp" S=5:130  clear Pc=1521:c,0;0;" ":c  i=210-1 8i,0;0;" " (i 2 xF$(5,4,1) { 1430 }D=25 N=1D-1  F$(D,N) N D )"&","[","_","]","&","^","{","|","}","@"  S=5:130 N=((b-b)*v+.5) b-(b)=01515 b=01530  1520 b$=b:1540 b$=b+F$(v,N)  1540  b$=F$(v,N)  @concatenation J-A$="":I=1̱R$:R$(I)=" "1630^ T $/y4 sm}x xx xv7$z&"'"z'"'*")#''" xvAlvHxvAz;;;;;;;;;;;;;;;;;;;xvA'z*4440642:40103'"7:294:7'" vvdvX+z*<240;727:212;02lz 029;040829lv^ xvt$ xvA+x,l.v,8 xvA= lv?xvA@xB xvBDxvAGvLvdQvXVIlz+027<:445:426424273:7:427:29<028::434:74w;};eV[vX[z(027$099<$27:22902<"4<642762:427:2w<8:4<}9>":0:700 ^'G:v=2:b=a+v:b$=b:600X _0:800  ` 0:U=6:1100L a%5:0:C$="+":900 b 1200 c16,2;"In this case, the MACHINE is obviously adding TWO to the numbers you are putting in. So we can write it's RULE as ....":2:21,13 ;"x+2":0:300, d 200 e 1200 f16,2;"If the MACHINE was adding 5 to your number x , then we would write the RULE as:-";:2:20,13 ;"x + 5":0:300, g 200 h 1200 i_16,2;0;"What is the RULE that adds 3 to:427:29w09v } <e7} e4vXz '744v8vXz ,:4094:vvdmvXnlz)4:62:9<:73427:42)*":1<:42&$"4:4237673"21lz *42202:492(49lvvd mv xxxvzˋxx͏msv  xvA΅vH xvA xvz"xxxxxxvzv 4z 2<0742527&$"v技mv 3z <<z xvA眀z (((8xvA lvH蘀xxlmsz+027<:445:44&$"27酀vvdJz *44:4*<240;727:212;02lz 029;040829l xv^xxxv, xvAv xv&xvBvXz$:441:42&$"4126<lz0373lz:427:29<028::434);1;4249)*"0lz lvvdvXLz$:42&$";9:9043397<:42;;2;42:42)*"0lz <lvvdvXz+04:42)*"370&$":40:0397:427:29w09v  } <eu} esz '7:42)*";vvvXz,:4094:vvdxxxvzvXlz)4:62:9<:73427:42)*":1<:42&$"4:4237673"21lz *42202:492(49lvvdsmv vHxvzv 5z'71272337:7&2*;::7:78002;5:497"21vvd!z"7373:71206<099v vd%lzta!crolf!rro4!abl !ncha e nnu0 dow leaelasnucac@emac!hr`"l 2#LAcode2 X !??@DHT*B`0 8x||x8?>x``x>?x<?9 170 C4+flag,22;"";dd:l=4+flag:c=24:arrow Cs$=y$:thru:15,16;dd;4+flag,29;"";dd flag=flag+1 flag=3245 5flag=1m$="Try another number.":150 "m$="And another...":150 l=4:clear flag2500 |18,0;" As you probably realised, thesecond machine changes the newnumber back into the originalone." l=4:star:clear v17,0;" It does the opposite of ";a$;", sowhat do you think the rule isfor the second machine?" "j$="F":d$=".....":inchar "rl=4:clear:s$=b$18,0;"Yes, the rule for the bottommachine is ";b$;".":320@ ,:18,0;" No, the rule would be ";b$;"." @star:l=4:clear Jt18,0;" When a rule undoes what anotherrule has done, then we say thatit is an INVERSE rule.":star Tl=4:clear ^W18,0;" So, the inverse rule to ";a$;" is";b$;".":star:clear ccounter0410 hq18,0;" What do you think the inverserule to x+5 is?":d$=".....":inchar:s$=""360h ml=4:clear rXs$="x-5"18,0;"That's right, the inverse ruleis x-5.":400 |@18,0;" No, the INVERSE rule would bex-5." l=4:star:clear 18,0;" Let's try another. In this casethe first machine has the rule";c$;" so the inverse rule shouldbe ";e$;".";5,5;"";c$:star:clear 18,0;" So, let the rule for the secondmachine be  ";e$;" and see what"'"happens.";12 ,12 ;"";e$:star:clear _flag=0:z=46:z,22;" ":z:flag2=1:y$=c$:145 l=4:clear 18,0;" So, just as ";b$;" is the inverse"'"rule of ";a$;", ";e$;" is the inverse"'"rule to ";c$;".":star:l=20:clear counter=counter+1 counter>1600X gl=20:clear:3,0;"  Now try another chain of machines.":star 'a$="2x ":b$="x/2":c$="x/2":e$="2x" &l=20:clear:110n Xl=20:clear v5,0;" Now that you have completedlesson three, you should attemptexercise 3 in the instructionbooklet." T20,0;" PRESS ANY KEY WHEN YOU HAVE COMPLETED EXCERCISE THREE."  get:clear 40,10 ;5;1;"LESSON THREE" :5,1;6;"That completes Lesson Three." 6;7,1;"If you would like to go over"'" Lesson Three again, ";10 ,13 ;2;6;"PRESS R":'" otherwise:-";12 ,13 ;6;1;"PRESS S" =""760 ="R"Ŧ="r"5  ="S"Ŧ="s"800   760  l=21:clear *5,0;5;" When you are ready to begin thenext lesson, type NEW followedby-";7;1;9 ,10 ;"LOAD ~ALG3~" 423636T\,255 W Xpmach bGl=6:c=2:s$="":mach:l=13 :c=9 :s$="":mach ll=16:c=15:buck v thru 15,16;" " "h$=s$:h$(3)=" "s$="2*x" Gx=dd:f$=(s$):s$=dd:l=1:c=2:n=2:mdown:msnd Uh$="x/2"dd/2ɺ(dd/2)f$=((dd/2))+"":f$(1)="0"f$="" 5s$=f$:l=7:c=9 :n=3:mdown:msnd 2s$=dd:l=14:c=16:n=1:mdown  s$=h$: ? @mach Jfl-5,c+8;"";l-4,c-1;" ";l-3,c-1;" " Tl-2,c;"";l-1,c;"";l,c;"";l+1,c+6;" " ^5s$""l-1,c+2+(4-s$);"";s$ h buck ;l-1,c-1;" ";l,c-1;"": msnd ̠.3,-40(:.2~L,-29:.3,-37%:.8L,-20:.25~,-34":.2~L,-30:.5,-35#:.1}L,-5  delay &del=del-.3:z=1del:z: clear l>21l<1 23659k\,l+3:"": mdown l,c;"";s$:20 9x=ll+n:x,c;"";s$:delay:x,c;" "(̱s$):x: 0innum D%dd=0:l=1:x$="":clear N'21,0;"N";8; Xz=1̱d$ ]get b%s$=13 x$""dd=x$:clear: ls$=12 8260D vs$<"0"s$>"9"8285] "s$;"N";8;:x$=x$+s$ z:dd=x$:clear: get s$="" ""8351 =""8354 s$=:.01z# =,5: inchar x$="":l=1:clear j$=""j$="L" 21,0;j$;8; z=1̱d$ get $s$=13 s$""clear:s$=x$: s$=12 8370 x$=x$+s$:s$;j$;8; z:clear:s$=x$: ! table !*nl,c;"x y":7;c*8,166-(l*8):7;64@,0:c=c+2:arrow: !4arrow !>x=c*8:y=171-(l*8):7;x,y:7;31,0:7;-3,3:7;x+31,y:7;-3,-3: !fscroll !p"z=1l:zz=3582 :z: !star !?1;21,31;"*":15:=""8590! !#21,31;8;" ": #-6:0:0: #2x=010 :l$:5,0+x*3;l$:.05|L,40(-(2*x):x:"F","U","N","D","A","M","E","N","T","A","L" #<7,2;" " #A,3;14,10 ;"LESSON THREE" #Fstar:l=21:clear #Z %21,31;" ": &"":5 &-"ALG3"9899&:"code3""a",168: ' "alg1/3c":10 ' "":"" AF B`Nl m .L,nNa *e!m'! \je %'^m'\&fFg! @G f Ɔfa `ƃ ]&E^) 'E e e%F '^)e e% %FF @Ffˀ^Ff '_`&f@@Ml!B@ơ@ &%NLnd ΌA&#m'! F@^m!&NLndʈD m΍-άGn$'b@N$DY}fF '`f& (@2*gA@]&f@2 a`A@{dDfb Z@@ #%"WR BZPP "" Z`` "4 Zpp "u3 "ZÀ "C 0ZÐÐ#BR dZ À%tr#Z0À$ P ``ZppPPh(p(iphPh`K Ap(HhXp0h@h[qpch CqIAE)SiI[HhXph0Ypӹv_aph CqI CN_aphXap0hph hpiphtְ88 x8숀뭤8084 XL884 Pְ88,x8쉍XnXbbw`vDDu\dX`Xl Xbbw`vDDuXnXbbw`vDDu\dXbd ,zj ubf`xHzL^HzddlbIbn``x|L^Hxhp`^H|jnrn``x~{`H&HzDZEn`p^[tPR|`xb|rn``xnb`^[tPR|`xj |rn``x&z`hb`uXbdXb`w`vD@@@DuXXfw`vD@@D>XVbXfw`v@@dTHzbfd@u\`bGzXuhzrbbub`uXVbXb`vHuXXb`w`vD@@@D|$\hXl @@bd```|`uXbn"XhvD@@@@@@@@@@@@@@@@@@@@@D0n``xD,zdubf`N(HzD^Eb`j`4X(HzDTEb```\(HzDVEb`n`\b(HzDZEb`p`plul``n`v,zj ubf`p``@.zbbb``Xbr&XhvD@@@@@@@@@@@@@@@@@@@@@Dun``x(HzD^Eb`j`4(HzDTEb```(HzDZEb`p`p(HzDVEb`n`\,zdubf`ul``,zj u130 0:800  L=11100L  b=a*v b$=b  b=a/v b$=b $ 1500 ) .b=a+v 3b$=b 7 8b=a-v Bb$=b K L'5,19;0;"x y" V)6,18;0;" ---------" `S=2:130 j95,21;0;"PPPp":S=5:130 t2U=U+2:U,19;0;a;" ";b$ ~S=2:130 U,21;0;"PPPp" S=5:130  clear Pc=1521:c,0;0;" ":c  i=210-1 8i,0;0;" " (i 2 xF$(5,4,1) { 1430 }D=25 N=1D-1  F$(D,N) N D )"&","[","_","]","&","^","{","|","}","@"  S=5:130 N=((b-b)*v+.5) b-(b)=01515 b=01530  1520 b$=b:1540 b$=b+F$(v,N)  1540  b$=F$(v,N)  @concatenation J-A$="":I=1̱R$:R$(I)=" "1630^ T $/y4 sm}x xx xv7$z&"'"z'"'*")#''" xvAlvHxvAz;;;;;;;;;;;;;;;;;;;xvA'z*4440642:40103'"7:294:7'" vvdvX+z*<240;727:212;02lz 029;040829lv^ xvt$ xvA+x,l.v,8 xvA= lv?xvA@xB xvBDxvAGvLvdQvXVIlz+027<:445:426424273:7:427:29<028::434:74w;};eV[vX[z(027$099<$27:22902<"4<642762:427:2w<8:4<}9>":0:700 ^'G:v=2:b=a+v:b$=b:600X _0:800  ` 0:U=6:1100L a%5:0:C$="+":900 b 1200 c16,2;"In this case, the MACHINE is obviously adding TWO to the numbers you are putting in. So we can write it's RULE as ....":2:21,13 ;"x+2":0:300, d 200 e 1200 f16,2;"If the MACHINE was adding 5 to your number x , then we would write the RULE as:-";:2:20,13 ;"x + 5":0:300, g 200 h 1200 i_16,2;0;"What is the RULE that adds 3 to:427:29w09v } <e7} e4vXz '744v8vXz ,:4094:vvdmvXnlz)4:62:9<:73427:42)*":1<:42&$"4:4237673"21lz *42202:492(49lvvd mv xxxvzˋxx͏msv  xvA΅vH xvA xvz"xxxxxxvzv 4z 2<0742527&$"v技mv 3z <<z xvA眀z (((8xvA lvH蘀xxlmsz+027<:445:44&$"27酀vvdJz *44:4*<240;727:212;02lz 029;040829l xv^xxxv, xvAv xv&xvBvXz$:441:42&$"4126<lz0373lz:427:29<028::434);1;4249)*"0lz lvvdvXLz$:42&$";9:9043397<:42;;2;42:42)*"0lz <lvvdvXz+04:42)*"370&$":40:0397:427:29w09v  } <eu} esz '7:42)*";vvvXz,:4094:vvdxxxvzvXlz)4:62:9<:73427:42)*":1<:42&$"4:4237673"21lz *42202:492(49lvvdsmv vHxvzv 5z'71272337:7&2*;::7:78002;5:497"21vvd!z"7373:71206<099v vd%lzta!crolf!rro4!abl !ncha e nnu0 dow leaelasnucac@ehrmacXl 2#Ax+2Bx-2Cx-2Ex+2ountecylaSLLycode3 Xɀ[??@DHT*B`0 8x||x8?>x``x>?x<?"If it outputs the number ";y;", whatis the input number x?" 'q=1q=2q=4a=nm+y q=3q=5a=y-nm (d$="...":innum:dd=0430 a=dd3:216,67C:4,-4:12 ,16:7:.2~L,0:.2~L,10 :scr=scr+1:500 ‡3:216,63?:16,16:232,63?:-16,16:7:.2~L,0:.2~L,-15 .12 ,0;"No, it would be ";a;"." 82,27;"";scr:star:l=18:clear:q l=20:clear 3,0;" You probably did most of thequestions in that exercise byintelligent guess work,but thereis a more mathematical way." Z'" The idea is to use the inverserule and put in the number wewere given as output." ''" Here is an example:-" &star:l=20:clear 0F3,0;" Suppose the rule is '3x' andthe output is 12." :,''" Well, the inverse rule will be'x/3'." D5'" So, 12 divided by 3 is 4."''" Therefore x=4." N star:clear X/3,0;" Now one for you to try..." bBnm=(*5)+2:y=(*5)+3:nm=y610b lB'''" A machine has the rule x-";nm;" and the output is ";y;"." n '" Find the input number x." v!'''"What is the inverse rule ?" !d$="....":j$="F":inchar s$=""640 12 ,0; @s$="x+"+nm"Yes, the inverse rule is x+";nm;".":680 '"No, the inverse rule is x+";nm;"." 0'"Now let x be ";y;" and work out theanswer." d$="..":innum 8dd=nm+y18,0;" Correct !!!":720 T17,0;" No, the answer is ";nm+y;" since ";y;"+";nm;"=";y+nm;"." *" Now five questions for you totry..." star:l=20:clear ques=735:800  ques Ql=20:clear:1,0;"Question ";q;". Score ";scr;"." 6'''"  The rule is ";r$;" and the output is ";y;"." &''"First, what is the inverse rule." !d$="....":j$="F":inchar s$=""744 Ms$=i$12 ,0;"Yes, ";i$;",now what is the answer?":770 B12 ,0;" No, it is ";i$;",so what is the answer ?" (d$="...":innum:dd=0770 dd=a3:232,11 :4,-4:12 ,16:.2~L,0:.2~L,10 :7:scr=scr+1:780   3:232,8:16,16:248,8:-16,16:7:.2~L,0:.2~L,-15:18,0;" No, the answer is ";a;"."  71,27;"";scr:star:l=19:clear:  scr=0:q=15 *1nm=(*7)+2:y=(*7)+2 4.q=1q=3y/nmɺ(y/nm)810* 66q=1q=3r$=nm+"x":i$="x/"+nm:a=y/nm 87q=2q=4r$="x-"+nm:i$="x+"+nm:a=nm+y >$q=5y-nm<1810* H-q=5r$="x+"+nm:i$="x-"+nm:a=y-nm  ques:q l=20:clear Y3,0;" We can write these questions ina slightly different but shorterway." q'" Instead of asking ""What is xif the output from the rule x+3is 5?"" we write, ""What is x ifx+3=5?""." U'" We call 'x+3=5' an EQUATION. Wecall it an equation because ofthe equals sign." U'" Sometimes we ask the samequestion by saying 'Solve theequation x+3=5'."  '" Let's try some examples..."  star:clear )scr=0:ques=980:1100L A1,0;"Question ";q;".";19;"Score ";scr;"." Tq/2=(q/2)6,0;"Solve the equation, ";e$;".":1000 )6,0;"What is x if ";e$;"?" d$="...":innum dd=01000 dd=ascr=scr+1:3:232,12 :4,-4:12 ,16:7:.2~L,0:.2~L,10 :1030 10 ,0;"No, it would be ";a;".":3:232,8:16,16:248,8:-16,16:7:.2~L,0:.2~L,-15 1,25;"";scr star:l=19:clear: Lq=110 V1nm=(*7)+2:y=(*7)+2 `Eq=1q=4q=6q=9 e$="x-"+nm+"="+y:a=y+nm j/q=2q=5y/nmɺ(y/nm)1110V l-q=2q=5e$=nm+"x="+y:a=y/nm t2q=7q=10 e$="x/"+nm+"="+y:a=y*nm ~/q=3q=8y-nm<11110V 1q=3q=8e$="x+"+nm+"="+y:a=y-nm  ques:q:l=20:clear 5,0;" Now that you have completedlesson four you should attemptexercise four in the instructionbooklet, before continuing." [20,0;"  PRESS ANY KEY WHEN YOU HAVE COMPLETED EXCERCISE FOUR.":get: 30,10 ;5;1;"LESSON FOUR" 95,1;6;"That completes Lesson Four." 6;7,1;"If you would like to go over"'" Lesson Four again, ";10 ,13 ;2;6;"PRESS R":'" otherwise:-";12 ,13 ;6;1;"PRESS S"  =""2060  ="R"Ŧ="r"5  ="S"Ŧ="s"21004 * 2060  4l=21:clear H5,0;5;" When you are ready to begin thenext lesson, type NEW followedby-";7;1;9 ,10 ;"LOAD ~ALG5~" \23636T\,255: Lthru Q10 ,11 ;" " V6s$="x":l=1:c=4:n=3:mdown:msnd `4s$=(v$):l=8:c=11 :n=2:mdown t2.1}L,-15:10 ,11 ;"";s$: ? Jfl-5,c+8;"";l-4,c-1;" ";l-3,c-1;" " Tl-2,c;"";l-1,c;"";l,c;"";l+1,c+6;" " ^5s$""l-1,c+2+(4-s$);"";s$ h buck ;l-1,c-1;" ";l,c-1;"": msnd ̠.3,-40(:.2~L,-29:.3,-37%:.8L,-20:.25~,-34":.2~L,-30:.5,-35#:.1}L,-5  delay o=1del:o: clear l>21l<1 23659k\,l+3:"": mdown ,del=del-0.5:l,c;"";s$:csp=s$ 9z=ll+n:z,c;"";s$:delay:z,c;" "(csp):z: 0innum D%dd=0:l=1:x$="":clear N'21,0;"N";8; Xz=1̱d$ ]get b%s$=13 x$""dd=x$:clear: ls$=12 8260D vs$<"0"s$>"9"8285] '"";s$;"N";8;:x$=x$+s$ z:dd=x$:l=1:clear: get s$="" ""8351 =""8354 s$=:.01z# =,5: j$=""j$="L" x$="":l=1:clear 21,0;j$;8; get $s$=13 s$""clear:s$=x$: s$=12 8370 x$=x$+s$:"";s$;j$;8; 8390 ! table !*nl,c;"x y":7;c*8,166-(l*8):7;64@,0:c=c+2:arrow: !4arrow !>xx=c*8:y=171-(l*8):7;xx,y:7;31,0:7;-3,3:7;xx+31,y:7;-3,-3: !fscroll !p"z=1l:zz=3582 :z: !star !?1;21,31;"*":15:=""8590! !21,31;" ": !intop !Y13 ,16;" ":csp=2:l=2:c=9 :n=5:s$=dd:mdown: !hcsp=3:l=11 :c=16:n=2:s$=dd:8900":mdown:13 ,16;s$+" ": "`pmach "j=l=10 :c=9 :mach:l=14:c=15:buck: " #-6:0:0: #2x=010 :l$:5,0+x*3;l$:.05|L,40(-(2*x):x:"F","U","N","D","A","M","E","N","T","A","L" #<7,2;" " #A+3;14,10 ;"LESSON FOUR" #Fstar:l=21:clear #Z %21,31;" ": &"":5 &-"ALG4"9899&:"code4""a",168: ' "":"" AF B`Nl m .L,nNa *e!m'! \je %'^m'\&fFg! @G f Ɔfa `ƃ ]&E^) 'E e e%F '^)e e% %FF @Ffˀ^Ff '_`&f@@Ml!B@ơ@ &%NLnd ΌA&#m'! F@^m!&NLndʈD m΍-άGn$'b@N$DY}fF '`f& (@2*gA@]&f@2 a`A@{dDfb Z@@ #%"WR BZPP "" Z`` "4 Zpp "u3 "ZÀ "C 0ZÐÐ#BR dZ À%tr#Z0À$ P ``ZppPPh(p(iphPh`K Ap(HhXp0h@h[qpch CqIAE)SiI[HhXph0Ypӹv_aph CqI CN_aphXap0hph hpiphtְ88 x8숀뭤8084 XL884 Pְ88,x8쉍XnXbbw`vDDu\dX`Xl Xbbw`vDDuXnXbbw`vDDu\dXbd ,zj ubf`xHzL^HzddlbIbn``x|L^Hxhp`^H|jnrn``x~{`H&HzDZEn`p^[tPR|`xb|rn``xnb`^[tPR|`xj |rn``x&z`hb`uXbdXb`w`vD@@@DuXXfw`vD@@D>XVbXfw`v@@dTHzbfd@u\`bGzXuhzrbbub`uXVbXb`vHuXXb`w`vD@@@D|$\hXl @@bd```|`uXbn"XhvD@@@@@@@@@@@@@@@@@@@@@D0n``xD,zdubf`N(HzD^Eb`j`4X(HzDTEb```\(HzDVEb`n`\b(HzDZEb`p`plul``n`v,zj ubf`p``@.zbbb``Xbr&XhvD@@@@@@@@@@@@@@@@@@@@@Dun``x(HzD^Eb`j`4(HzDTEb```(HzDZEb`p`p(HzDVEb`n`\,zdubf`ul``,zj u130 0:800  L=11100L  b=a*v b$=b  b=a/v b$=b $ 1500 ) .b=a+v 3b$=b 7 8b=a-v Bb$=b K L'5,19;0;"x y" V)6,18;0;" ---------" `S=2:130 j95,21;0;"PPPp":S=5:130 t2U=U+2:U,19;0;a;" ";b$ ~S=2:130 U,21;0;"PPPp" S=5:130  clear Pc=1521:c,0;0;" ":c  i=210-1 8i,0;0;" " (i 2 xF$(5,4,1) { 1430 }D=25 N=1D-1  F$(D,N) N D )"&","[","_","]","&","^","{","|","}","@"  S=5:130 N=((b-b)*v+.5) b-(b)=01515 b=01530  1520 b$=b:1540 b$=b+F$(v,N)  1540  b$=F$(v,N)  @concatenation J-A$="":I=1̱R$:R$(I)=" "1630^ T $/y4 sm}x xx xv7$z&"'"z'"'*")#''" xvAlvHxvAz;;;;;;;;;;;;;;;;;;;xvA'z*4440642:40103'"7:294:7'" vvdvX+z*<240;727:212;02lz 029;040829lv^ xvt$ xvA+x,l.v,8 xvA= lv?xvA@xB xvBDxvAGvLvdQvXVIlz+027<:445:426424273:7:427:29<028::434:74w;};eV[vX[z(027$099<$27:22902<"4<642762:427:2w<8:4<}9>":0:700 ^'G:v=2:b=a+v:b$=b:600X _0:800  ` 0:U=6:1100L a%5:0:C$="+":900 b 1200 c16,2;"In this case, the MACHINE is obviously adding TWO to the numbers you are putting in. So we can write it's RULE as ....":2:21,13 ;"x+2":0:300, d 200 e 1200 f16,2;"If the MACHINE was adding 5 to your number x , then we would write the RULE as:-";:2:20,13 ;"x + 5":0:300, g 200 h 1200 i_16,2;0;"What is the RULE that adds 3 to:427:29w09v } <e7} e4vXz '744v8vXz ,:4094:vvdmvXnlz)4:62:9<:73427:42)*":1<:42&$"4:4237673"21lz *42202:492(49lvvd mv xxxvzˋxx͏msv  xvA΅vH xvA xvz"xxxxxxvzv 4z 2<0742527&$"v技mv 3z <<z xvA眀z (((8xvA lvH蘀xxlmsz+027<:445:44&$"27酀vvdJz *44:4*<240;727:212;02lz 029;040829l xv^xxxv, xvAv xv&xvBvXz$:441:42&$"4126<lz0373lz:427:29<028::434);1;4249)*"0lz lvvdvXLz$:42&$";9:9043397<:42;;2;42:42)*"0lz <lvvdvXz+04:42)*"370&$":40:0397:427:29w09v  } <eu} esz '7:42)*";vvvXz,:4094:vvdxxxvzvXlz)4:62:9<:73427:42)*":1<:42&$"4:4237673"21lz *42202:492(49lvvdsmv vHxvzv 5z'71272337:7&2*;::7:78002;5:497"21vvd!z"7373:71206<099v vd%lzhrLeta!crolf!rro4!abl !ncha e nnu0 dow leaelasnucac@l 2#laVx+2P+2cySxns lLLocode4 XԀA??@DHT*B`0 8x||x8?>x``x>?x<?20nm>20795 *&q=2q=6y21l<1 23659k\,l+3:"": 0innum D%dd=0:l=1:x$="":clear N'21,0;"N";8; Xz=1̱d$ ]get b%s$=13 x$""dd=x$:clear: ls$=12 8260D vs$<"0"s$>"9"8285] '"";s$;"N";8;:x$=x$+s$ z:dd=x$:clear: get s$="" ""8351 =""8354 s$=:.01z# =,5: inchar x$="":l=1:clear j$=""j$="L" 21,0;j$;8; z=1̱d$ get $s$=13 s$""clear:s$=x$: s$=12 8370 x$=x$+s$:"";s$;j$;8; z:clear:s$=x$: !fscroll !p"z=1l:zz=3582 :z: !star !?1;21,31;"*":15:=""8590! !#21,31;8;" ": #-6:0:0: #2x=010 :l$:5,0+x*3;l$:.05|L,40(-(2*x):x:"F","U","N","D","A","M","E","N","T","A","L" #<7,2;" " #A+3;14,10 ;"LESSON FIVE" #Fstar:l=21:clear #Z %21,31;" ": &"ALG5"5: '"" AF B`Nl m .L,nNa *e!m'! \je %'^m'\&fFg! @G f Ɔfa `ƃ ]&E^) 'E e e%F '^)e e% %FF @Ffˀ^Ff '_`&f@@Ml!B@ơ@ &%NLnd ΌA&#m'! F@^m!&NLndʈD m΍-άGn$'b@N$DY}fF '`f& (@2*gA@]&f@2 a`A@{dDfb Z@@ #%"WR BZPP "" Z`` "4 Zpp "u3 "ZÀ "C 0ZÐÐ#BR dZ À%tr#Z0À$ P ``ZppPPh(p(iphPh`K Ap(HhXp0h@h[qpch CqIAE)SiI[HhXph0Ypӹv_aph CqI CN_aphXap0hph hpiphtְ88 x8숀뭤8084 XL884 Pְ88,x8쉍XnXbbw`vDDu\dX`Xl Xbbw`vDDuXnXbbw`vDDu\dXbd ,zj ubf`xHzL^HzddlbIbn``x|L^Hxhp`^H|jnrn``x~{`H&HzDZEn`p^[tPR|`xb|rn``xnb`^[tPR|`xj |rn``x&z`hb`uXbdXb`w`vD@@@DuXXfw`vD@@D>XVbXfw`v@@dTHzbfd@u\`bGzXuhzrbbub`uXVbXb`vHuXXb`w`vD@@@D|$\hXl @@bd```|`uXbn"XhvD@@@@@@@@@@@@@@@@@@@@@D0n``xD,zdubf`N(HzD^Eb`j`4X(HzDTEb```\(HzDVEb`n`\b(HzDZEb`p`plul``n`v,zj ubf`p``@.zbbb``Xbr&XhvD@@@@@@@@@@@@@@@@@@@@@Dun``x(HzD^Eb`j`4(HzDTEb```(HzDZEb`p`p(HzDVEb`n`\,zdubf`ul``,zj u130 0:800  L=11100L  b=a*v b$=b  b=a/v b$=b $ 1500 ) .b=a+v 3b$=b 7 8b=a-v Bb$=b K L'5,19;0;"x y" V)6,18;0;" ---------" `S=2:130 j95,21;0;"PPPp":S=5:130 t2U=U+2:U,19;0;a;" ";b$ ~S=2:130 U,21;0;"PPPp" S=5:130  clear Pc=1521:c,0;0;" ":c  i=210-1 8i,0;0;" " (i 2 xF$(5,4,1) { 1430 }D=25 N=1D-1  F$(D,N) N D )"&","[","_","]","&","^","{","|","}","@"  S=5:130 N=((b-b)*v+.5) b-(b)=01515 b=01530  1520 b$=b:1540 b$=b+F$(v,N)  1540  b$=F$(v,N)  @concatenation J-A$="":I=1̱R$:R$(I)=" "1630^ T $/y4 sm}x xx xv7$z&"'"z'"'*")#''" xvAlvHxvAz;;;;;;;;;;;;;;;;;;;xvA'z*4440642:40103'"7:294:7'" vvdvX+z*<240;727:212;02lz 029;040829lv^ xvt$ xvA+x,l.v,8 xvA= lv?xvA@xB xvBDxvAGvLvdQvXVIlz+027<:445:426424273:7:427:29<028::434:74w;};eV[vX[z(027$099<$27:22902<"4<642762:427:2w<8:4<}9>":0:700 ^'G:v=2:b=a+v:b$=b:600X _0:800  ` 0:U=6:1100L a%5:0:C$="+":900 b 1200 c16,2;"In this case, the MACHINE is obviously adding TWO to the numbers you are putting in. So we can write it's RULE as ....":2:21,13 ;"x+2":0:300, d 200 e 1200 f16,2;"If the MACHINE was adding 5 to your number x , then we would write the RULE as:-";:2:20,13 ;"x + 5":0:300, g 200 h 1200 i_16,2;0;"What is the RULE that adds 3 to:427:29w09v } <e7} e4vXz '744v8vXz ,:4094:vvdmvXnlz)4:62:9<:73427:42)*":1<:42&$"4:4237673"21lz *42202:492(49lvvd mv xxxvzˋxx͏msv  xvA΅vH xvA xvz"xxxxxxvzv 4z 2<0742527&$"v技mv 3z <<z xvA眀z (((8xvA lvH蘀xxlmsz+027<:445:44&$"27酀vvdJz *44:4*<240;727:212;02lz 029;040829l xv^xxxv, xvAv xv&xvBvXz$:441:42&$"4126<lz0373lz:427:29<028::434);1;4249)*"0lz lvvdvXLz$:42&$";9:9043397<:42;;2;42:42)*"0lz <lvvdvXz+04:42)*"370&$":40:0397:427:29w09v  } <eu} esz '7:42)*";3vvvXz,:4094:vvdxxxvzvXlz)4:62:9<:73427:42)*":1<:42&$"4:4237673"21lz *42202:492(49lvvdsmv vHxvzv 5z'71272337:7&2*;::7:78002;5:497"21vvd!z"7373:71206<099v vd%lzicrrosl@ta!crolf!ncha e nnu0 leal 2#LL ALGT 4f&hec6f :tick=7300:cross=7350:answer=7200 :cls=7000X:star=8580!:scroll=8550f!:inchar=8360 :get=8350 :innum=82400 :clear=8180 r(x ,y)=((*x))+y  7500L 2I0:0:0:0:0:6:l=12 :clear < 9000(# n 7 x2,0;" This Post Test contains ninequestions which are matched tothe minimum objectives, set outin the instruction booklet." '" Your answer to each question ischecked. At the end, you will betold which questions you gotwrong and the objectives thathave not been achieved. Based onthis you will be given a guideto further study." '" Because this program producesdifferent questions each time itis loaded, it can be used togreat advantage in your revisionwork." star:cls &2,1;"Question one." qp=qp+1 d4,0;" What rule does a machine haveif its input x and output y areas shown below?" nm=r(10 ,3):''' "  x  y" " " '" 1 ";nm $'" 2 ";nm*2 $'" 3 ";nm*3 "a$=nm+"x":j$="F":answer star:cls 52,1;"Question two.":qp=qp+1 n1=r(7,2):n2=r(5,5):a$=n1+"x"+("+"n2>0)+n2:a$(4)="0"a$(4)="1":n2=1 4,0;" Two machines are joinedtogether. The rule for the firstmachine is ";a$(2);" and the rule forthe other is ";a$(2);".The table belowshows three input numbers x andthree output values y." ' " x  y" " " &'" 3 ";3*n1+n2 &'" 4 ";4*n1+n2 &'" 5 ";5*n1+n2 "7'" What is the rule for thecombined machine?" ,answer 6 star:cls @7qp=qp+1:2,1;"Question three." Esn1=r(7,2):n2=r(5,5):k$=n1+"x"+("+"n2>0)+n2:k$(4)="0"k$(4)="1" J?7,0;" The combined rule for a machineis ";k$;"." TD''" What is the output y, if x=";:no=r(9 ,1):no;" ?" ha$=((no*n1)+n2) |j$="N":answer  star:cls 6qp=qp+1:2,1;"Question four." no=r(15,1) H'''" The rule for a machine is ";no;"x."''"What is the inverse rule?" #j$="F":a$="x/"+no:answer  star:cls 6qp=qp+1:2,1;"Question five." Dk$="x-.":k$(3)=(r(15,2)):a$="x+"+k$(3) T''''" The rule for a machine is ";k$;"."'''" What is the inverse to this rule?" j$="F":answer  star:cls 5qp=qp+1:2,1;"Question six." Dn1=r(8,2):n2=n1*r(5,2):k$=n1+"x="+n2 Dn3=r(8,2):n4=n3*r(5,2):l$=n3+"x="+n4 a$=(n2/n1)+(n4/n3) 44,0;" (a) Solve the equation ";k$;"." j$="N":innum:v$=dd 9d$="...":8,0;" (b) What is x if ";l$;" ?" j$="N":innum v$=v$+dd:s$=v$:72204 & star:cls 07qp=qp+1:2,1;"Question seven." :En1=r(5,1):n2=r(5,5):k$="x+"+n1+"="+n2 ?En3=r(5,1):n4=r(5,5):l$="x+"+n3+"="+n4 @a$=(n2-n1)+(n4-n3) D&'''" (a) Solve the equation ";k$;"." Nj$="N":innum:v$=dd X/10 ,1;"(b) What is x if ";l$;" ?" binnum lv$=v$+dd:s$=v$:72204 v star:cls 7qp=qp+1:2,1;"Question eight." Tno=r(10 ,6):cost=r(40(,502):cost/noɺ(cost/no)650 35,0;" ";no;" apples cost ";cost;"p." 2''" What is the cost (in pence) of one apple ?" %a$=(cost/no):j$="N":answer  star:cls 6qp=qp+1:2,1;"Question nine." 1n1=r(8,2):n2=r(10 ,2) J'''" A number divided by ";n1;" is equalto ";n2;". What is the number?" #a$=(n1*n2):j$="N":answer  star:cls ;1,1;"RESULTS";2,1;"" 33,0;" You scored ";nr;" out of 9." Um$="You got all the questions wrongso I suggest you do all thelessons again." Cnr1m$="Not so good, you got all thesequestions wrong." Mnr4m$="Not too bad but you still gotall these questions wrong." Cnr6m$="Well done, but you did get thesequestions wrong."  9nr=8m$="This was the question you gotwrong."  nr=9 6,0;" Well done, you got all thequestions right. You are nowready to start the second partof ~Fundamental Algebra~." :1000  5,0;"";m$ '' z=19  q$(z)="1"900 %" (";z;") "; *z=1m$="objective 1." ,z=2m$="objective 2." .z=3m$="objective 3." 0z=4m$="objective 4." 2z=5m$="objective 4." 4z=6m$="objective 5." 6z=7m$="objective 5." 8z=8m$="objective 6." :z=9 m$="objective 6." <"Which tested ";m$ z &star:cls:1,1;" " 4,0;" That ends this Post Test.It maybe a good idea to have anotherlook at the lessons you do notfully understand." star:l=21:clear 40,9 ;5;1;"POST TEST (1)" =4,1;"That completes the Post TestPart One." 6;7,1;"If you would like to go over"'" the Post Test again, ";10 ,13 ;2;6;"PRESS R":'" otherwise:-";12 ,13 ;6;1;"PRESS S" $=""1060$ .="R"Ŧ="r"5 8="S"Ŧ="s"1100L B 1060$ Ll=21:clear V5,0;5;" When you are ready to begin thenext lesson, type NEW followedby-";7;1;9 ,10 ;"LOAD ~ALG6~" `23636T\,255: W Xcls b00,27;" ":l=20:clear:  answer !w=1̱j$ "#j$(w)="F"d$=".....":7210* #=j$(w)="L"d$="...............................":7210* $1j$(w)="N"d$="....":innum:s$=dd:72204 %w *inchar:s$=""7210* 4*s$=a$q$(qp)="1":nr=nr+1:tick: > cross: tick |3;232,154:3;4,-4:3;12 ,16:.2~L,0:.3,-5: cross 3;232,154:3;16,16:3;247,154:3;-16,16:.2~L,-10 :.3,-20: Lsetup V*q$="000000000":qp=0:nr=0: ? clear l>21l<1 23659k\,l+3:"": 0innum D%dd=0:l=1:x$="":clear N'21,0;"N";8; Xz=1̱d$ ]get b%s$=13 x$""dd=x$:clear: ls$=12 8260D vs$<"0"s$>"9"8285] '"";s$;"N";8;:x$=x$+s$ z:dd=x$:clear: get s$="" ""8351 =""8354 s$=:.01z# =,5: inchar x$="":"" j$=""j$="L" #1;j$;8; z=1̱d$ get s$=13 "":s$=x$: s$=12 8370 )x$=x$+s$:#1;"";s$;j$;8; z:s$=x$:"": !p"z=1l:zz=3582 :z: !star !?1;21,31;"*":20:=""8590! !#21,31;8;" ": #-6:0:0: #2x=010 :l$:5,0+x*3;l$:.05|L,40(-(2*x):x:"F","U","N","D","A","M","E","N","T","A","L" #<7,2;" " #A,3;14,9 ;"POST TEST (1)" #Fstar:l=21:clear #Z %21,31;" ": &"":5 &-"ALGT"9899&:"codet""a",168: ' "":"" AF B`Nl m .L,nNa *e!m'! \je %'^m'\&fFg! @G f Ɔfa `ƃ ]&E^) 'E e e%F '^)e e% %FF @Ffˀ^Ff '_`&f@@Ml!B@ơ@ &%NLnd ΌA&#m'! F@^m!&NLndʈD m΍-άGn$'b@N$DY}fF '`f& (@2*gA@]&f@2 a`A@{dDfb Z@@ #%"WR BZPP "" Z`` "4 Zpp "u3 "ZÀ "C 0ZÐÐ#BR dZ À%tr#Z0À$ P ``ZppPPh(p(iphPh`K Ap(HhXp0h@h[qpch CqIAE)SiI[HhXph0Ypӹv_aph CqI CN_aphXap0hph hpiphtְ88 x8숀뭤8084 XL884 Pְ88,x8쉍XnXbbw`vDDu\dX`Xl Xbbw`vDDuXnXbbw`vDDu\dXbd ,zj ubf`xHzL^HzddlbIbn``x|L^Hxhp`^H|jnrn``x~{`H&HzDZEn`p^[tPR|`xb|rn``xnb`^[tPR|`xj |rn``x&z`hb`uXbdXb`w`vD@@@DuXXfw`vD@@D>XVbXfw`v@@dTHzbfd@u\`bGzXuhzrbbub`uXVbXb`vHuXXb`w`vD@@@D|$\hXl @@bd```|`uXbn"XhvD@@@@@@@@@@@@@@@@@@@@@D0n``xD,zdubf`N(HzD^Eb`j`4X(HzDTEb```\(HzDVEb`n`\b(HzDZEb`p`plul``n`v,zj ubf`p``@.zbbb``Xbr&XhvD@@@@@@@@@@@@@@@@@@@@@Dun``x(HzD^Eb`j`4(HzDTEb```(HzDZEb`p`p(HzDVEb`n`\,zdubf`ul``,zj u130 0:800  L=11100L  b=a*v b$=b  b=a/v b$=b $ 1500 ) .b=a+v 3b$=b 7 8b=a-v Bb$=b K L'5,19;0;"x y" V)6,18;0;" ---------" `S=2:130 j95,21;0;"PPPp":S=5:130 t2U=U+2:U,19;0;a;" ";b$ ~S=2:130 U,21;0;"PPPp" S=5:130  clear Pc=1521:c,0;0;" ":c  i=210-1 8i,0;0;" " (i 2 xF$(5,4,1) { 1430 }D=25 N=1D-1  F$(D,N) N D )"&","[","_","]","&","^","{","|","}","@"  S=5:130 N=((b-b)*v+.5) b-(b)=01515 b=01530  1520 b$=b:1540 b$=b+F$(v,N)  1540  b$=F$(v,N)  @concatenation J-A$="":I=1̱R$:R$(I)=" "1630^ T $/y4 sm}x xx xv7$z&"'"z'"'*")#''" xvAlvHxvAz;;;;;;;;;;;;;;;;;;;xvA'z*4440642:40103'"7:294:7'" vvdvX+z*<240;727:212;02lz 029;040829lv^ xvt$ xvA+x,l.v,8 xvA= lv?xvA@xB xvBDxvAGvLvdQvXVIlz+027<:445:426424273:7:427:29<028::434:74w;};eV[vX[z(027$099<$27:22902<"4<642762:427:2w<8:4<}9>":0:700 ^'G:v=2:b=a+v:b$=b:600X _0:800  ` 0:U=6:1100L a%5:0:C$="+":900 b 1200 c16,2;"In this case, the MACHINE is obviously adding TWO to the numbers you are putting in. So we can write it's RULE as ....":2:21,13 ;"x+2":0:300, d 200 e 1200 f16,2;"If the MACHINE was adding 5 to your number x , then we would write the RULE as:-";:2:20,13 ;"x + 5":0:300, g 200 h 1200 i_16,2;0;"What is the RULE that adds 3 to:427:29w09v } <e7} e4vXz '744v8vXz ,:4094:vvdmvXnlz)4:62:9<:73427:42)*":1<:42&$"4:4237673"21lz CI\*]\!U*a\7R`in ͸y=((+[S\U"S\*a\++*I\p+q+s+râ K SR P n (*Q\##0*Q\^#V,ɇo&\^#Vz *O\"Q\0####N!-^KSP0M d*e\!K\>^#VR0 r+s##= RDM~ V#^*c\+U##Ca\#*Y\6 "[\#6#"a\*a\"c\*c\"e\!\"h\[Y\#~ȹ# 78 N#Fq#p*O\ ###N!N KSP͔8!\O N#F+8x(*O\ ###~K(S(P ]s#r 3z <<z xvA眀z (((8xvA lvH蘀xxlmsz+027<:445:44&$"27酀vvdJz *44:4*<240;727:212;02lz 029;040829l xv^xxxv, xvAv xv&xvBvXz$:441:42&$"4126<lz0373lz:427:29<028::434);1;4249)*"0lz lvvdvXLz$:42&$";9:9043397<:42;;2;42:42)*"0lz <lvvdvXz+04:42)*"370&$":40:0397:427:29w09v  } <eu} esz '7:42)*";vvvXz,:4094:vvdxxxvzvXlz)4:62:9<:73427:42)*":1<:42&$"4:4237673"21lz *42202:492(49lvvdsmv vHxvzv 5z'71272337:7&2*;::7:78002;5:497"21vvd!z"7373:71206<099v vd%lzicrosnswe lXta!crolf!ncha e nnu0 leaQ 000000000l 2#LLA4xJF!D.....XLcodet XhY>BB<DHpHDB@@@@@~BfZBBBBbRJFB