' +JJJJ ?\>m0M='+l> /+l   d]@ŵLҦ]]LF L}BBL]렮 鷎귭෍ᷩ췩緈JJJJx Lȿ L8ᷭ緍췩 緍i 8 `巬 췌`x (`(8`I`B` ``>J>J>VU)?`8'x0|&HhHh VY)'&Y)xꪽ)' `Hh`V0^*^*>&` aI꽌ɪVɭ&Y&&Y& 꽌ɪ\8`&&꽌ɪɖ'*&%&,E'зЮ꽌ɪ`+*xS&x'8*3Ixix&& 8  '  & x)*++`FG8`0($ p,&"ųųೳŪŪųųij  !"#$%&'()*+,-./0123456789:;<=>?   1 '" *"( (9"1 ( ,.(0# 2  /#0/#0 *?'#07#00/0/'#07#0:"4<*55/**5/*%5/)1/)1/)1/)'#0/#0*5/*75/**5/*:5//#0/#0'#07#0:::*::'#07#0"):$(%"%:$(%"%$$2%4%$$2%4%$(2()!)E(!8b $!H(+ "@H !D)"E` @ $ C ` DQ &J80^݌Hh ü ü݌ ռ ռ ռA ļD ļ? ļAEDE?HJ>h Լ ռ ռ ռ`HJ>݌h Hh݌`葠葠ȔЖȔЖȠHIHHHHhHH݌hHhHh݌H6 VDP (ED Z $0x8x D- ܸDD# H8`?E Vk *f???0xE Hh D#-EEE8` D ܸx D - ܸx8`-0ݩ?ʥD EEE`   LDcpq` [` ~  LӜu`".Q`pNФbptťܥm2<(-Py0\|e<6e<g< JJJJj귍hI  aUL@ kU8  L  Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( R \ZLl8 ўR HH\`\Z[YS6`LxQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭ͲLɍ [LLĦ__ ^ 9 LҦ3 9 a   0LjLY u< (_9 ˭ɠuɠK_9 ?LˆʎõĵL õ ĵµ aµ`` L̦µ_bJLuLz`  ȟ QlXJ̥KlV  ȟ QlV eօ3L e3L &RL &QL d L4 Ne)n `@-eff L f`L . tQLѤ LҦL` OPu d L Ne)noon 8ɍ` ^f\õL ^NR  RΩLҦ)\Z ʽ LHv 3h`0L [L NС õ`A@` ŵL^Lõ`  \ 濭0 \  ȟ Q ^\lZl^?cqH şch`fhjõĵ@OAP`u@`@&`QR`E Ls  @DAE@u`8` %@ @A@`@`@A`Mµ ) LЦ`8@AWc@8@-@HAȑ@hHȑ@ȑ@hHȑ@Ȋ@ch8&ȑ@Hȑ@Ah@LHȑ@ȑ@ htphso`hMhL`9V8U897T6S67`INILOASAVRUCHAIDELETLOCUNLOCCLOSREAEXEWRITPOSITIOOPEAPPENRENAMCATALOMONOMOPRINMAXFILEFINBSAVBLOABRUVERIF!pppp p p p p`" t""#x"p0p@p@@@p@!y q q p@  LANGUAGE NOT AVAILABLRANGE ERROWRITE PROTECTEEND OF DATFILE NOT FOUNVOLUME MISMATCI/O ERRODISK FULFILE LOCKESYNTAX ERRONO BUFFERS AVAILABLFILE TYPE MISMATCPROGRAM TOO LARGNOT DIRECT COMMANč$3>L[dmx- ( " Ϡ@跻~!Wo*9~~~~ɬƬ~_ j ʪHɪH`Lc (L ܫ㵮赎 ɱ^_ J QL_Ls贩紎 DǴҵԵƴѵӵµȴ 7 ַ :ŵƴѵǴҵȴµ納贍﵎ٵ്ᵭⳍڵL^ѵ-I `  4 ò-յ!  8صٵ紭ﵝ 7L (0+BC  7L HH`LgL{0 HH` õL H hBL BH [ h`Lo õ ڬL B ڬ LʬH hB@ յյ [L (ȴ) ȴ 7L L ( L (ȴL{ƴѵ洩ƴǴҵ 7 ^* B0 HȱBh ӵԵ 8 L8 ݲ` ܫ  / / ED B / / ]ƴS0Jȴ ȴ)  紅D贅E B ƴ  / 0L Ν `HD٤DEEhiHLGh ` ŵBѵ-` ѵB-` ܫ XI볩쳢8 DH E𳈈췍Ȍ X0 · JLǵBȵC`,յp` 䯩 R-յյ`յ0` K R-յյ`ɵʵӵԵ` 4 K ( ѵҵLBȱBL8` DBHBH : ַ޵BȭߵBhhӵԵ RBܵmڵ޵ȱBݵm۵ߵ` 䯩LR˵̵ֵ׵`êĪLR E( 8` R` ELRŪƪ`췌 յյI뷭鷭귭ⵍ㵍跬ª 뷰` Lf ݵܵߵ޵ ^`8ܵ i B8` 4L ֵȱB׵ ܯ䵍൭嵍 ` DȑB׵Bֵ  ַ յյ`굎뵎쵬 뵎쵌``õĵBCõĵ`µµ`L õBĵCصص Qƴ0"Bƴ 󮜳` 0۰ϬBƴ8`i#`ЗLw!0>ﵭ` m ﳐ 7i볍 8 ЉLw`H h ݲL~ `浍국䵍뵩嵠Jm赍嵊mjnnn浈ۭm浍浭m䵍䵩m嵍`"L ŵ8ŵH ~(`# d ֠Ġz#ILoLHllLŌŒlaHŒ\LŒ\KH\HLHlaH\朻\\LŒ\\HFlHHHHCHlaClLŒ\霿gLŒ\Č,[ELOL` u`50 ^1920^5030292.^DN250508^1920B^5030^5030RT$RT$P$:P$;:44100]?(RT$)1RT$"":4418A]ART$(RT$,1)Y]B(8)" "(8);:4410i]DNP(RT$):{] MAIN LOOP ]400]4400]250]AD1]:TPTP1:"Problem #"TP;:23(E$)2:E$]780]292]990]292^DN250305\GF0:\\0m\5:9:N$", how many problems would you like to do (1-50)? ";:RT$"":16368,0\:P$:(P$(8)P$(127))(RT$)4415:P$(13)(RT$)4420:P$"0"P$"9"4410:(RT$)0(P$"0"P$"9")(RT$)24410:(RT$P$)504410]<270[DGFSG".":4270[" "N$", you are incorrect. Multiplying by 1 will not simplify the equation.":WT4040:WT1:CCCC1[302:[ GET GREATEST COMMON FACTOR \GF0:T921:AT(AT)BT(BT)CT(CT)DT(DT)GFT:T2::4are incorrect.":WT4190:WT1:4270\Z^WT0:" The correct answer is ";:T14230,4240,4250ZhAGFSG14210:AGFSG14220:AGFSG"X.":4270Zr"X.":4270Z|"-X.":4270ZBGFSG".":4270[CGFSG14210:CGFSG14220:CGFSG"X.":4,DD(GFSG)'Y6 MAKE NEW EQUATION Y@368:E$A$(FA(A))X1$((A$)0)SP$((B$)0A0)S$((B$)0A0)B$" = "C$(FA(C))X1$(C0)SP$((D$)0C0)S$((D$)0C0)D$:YJ MULTIPLY THROUGH ERROR MESSAGES #ZTCCCC1:(37)2:" "N$", you :IP1:ML5:50:RT$(CGFSG)"X"RT$"-X"CGFSG1RT$"X"CGFSG14120:T3:4170:4110zXVTVT2:WT0:CC(GFSG)X"D04150:VT:958:" Solve ("D") ("SN(GFSG)"/"GFSN(GF)")";:21:": ";:IP2:ML5:50:RT$(DGFSG)4140:T4:4170:4130 YT0:AA(GFSG)WB04110:VT:958:" Solve ("B") ("SN(GFSG)"/"GFSN(GF)")";:21:": ";:IP2:ML5:50:RT$(BGFSG)4100:T2:4170:4090WVTVT2:WT0:BB(GFSG)]XC04130:VT:958:" Solve ("C"X) ("SN(GFSG)"/"GFSN(GF)")";:21:": ";"/"(GFSN(GF))")":IN(RT$):308:DISPLAY NEW EQUATIONVA04090:7:958:" Solve ("A$(FA(A))"X) ("SN(GFSG)"/"GFSN(GF)")";:21:": ";:IP1:ML5:50:RT$(A(GFSG))"X"RT$"-X"AGFSG1RT$"X"AGFSG14080:T1:4170:4070WVTVT2:Wu are incorrect.":WT4040:WT1:4050cU" The correct multiplier is ";:WT0:A1ĺ"-1/1";:4043UA1ĺSN(A)"/"GFSN(A);:4043USN(A)"/"GFSN(A);U"."UCCCC1:302:DV14020::VSG(DV):WT0:VT7:E$"("E$") ("(SN(GFSG))OUGH BY THE 1/-GCF OR 1/GCF %TWT0T292:7:" Enter term to multiply equation by.":10::"TERM";::": ";:IP3:ML10:50:DV1İ4260:4020TDV1A14030:DV1A1GF1:4060TDV1GFA14060TDV1GFA14060%U11:" "N$", yoN(A))") = 1X":L2$"1X = X"lS WR$(DA):R1$"("(D)") ("(SN(A))"/"(ASN(A))") = "(DA):R2$""S W$"X = "(DA):E$"("A$(FA(A))"X) ("(SN(A))"/"(ASN(A))") = ("(D)") ("(SN(A))"/"(ASN(A))")"S T" MULTIPLY THRtiplying by one will not simplify the equation. "FR WT0WT1:3040}R WT0:"The correct answer is "SN(A)"/"SN(A)A"."R CCCC1:302:3010R GENERATE SIMPLIFICATION ERROR MESSAGESS 368:WL$"X":L1$"("A$(FA(A))"X) ("(SN(A))"/"(ASFLAG, CLEAR SCREEN, AND REARRANGE A AND C}Q 7:" Enter term to multiply both sides by. "::"TERM";::": ";:IP3:ML8:50Q DV1A3050Q " "N$", you are incorrect. You must multiply by the reciprocal of the coefficient of X. "1R DV1ĺ"MulP BIN".":2770BP CIN12710:CIN12720:CIN"X.":2770UP DIN".":2770P " "N$", you are incorrect. Dividing by 1 will not simplify the equation.":WT12540:WT1:2550P 302:P MULTIPLICATION P WT0)Q CN2:292:358:SET )D$:,On DIVIDE THROUGH ERROR MESSAGES tOx CCCC1:(37)2:" "N$", you are incorrect.":WT12690:WT1:2770O WT0:" The correct answer is ";:T2700,2730,2740,2750O AIN12710:AIN12720:AIN"X.":2770O "X.":2770P "-X.":2770958:" Solve ("D")/("IN")";:18:": ";:IP2:ML5:50:RT$(DIN)2640:T4:2670:2630bNP DDIN}NZ MAKE NEW EQUATION Od 368:E$A$(FA(A))X1$((A$)0)SP$((B$)0)S$((B$)0A0)B$" = "C$(FA(C))X1$(C0)SP$((D$)0C0)S$((D$)0C0RT$(BIN)2600:T2:2670:25908M( VTVT2:WT0:BBINM2 C02630:VT:958:" Solve ("C"X)/("IN")";:18:": ";:IP1:ML5:50:RT$(CIN)"X"2620:CIN1RT$"X"2620:CIN1RT$"-X"2620:T3:2670:2610M< VTVT2:WT0:CCINWNF D02660:VT:02590:7:958:" Solve ("A$(FA(A))"X)/("IN")";:18:": ";:IP1:ML5:50:RT$(AIN)"X"2580:AIN1RT$"X"2580:AIN1RT$"-X"2580:T1:2670:2570L VTVT2:WT0:AAIN M B02610:VT:958:" Solve ("B")/("IN")";:18:": ";:IP2:ML5:50:K 11:" "N$", you are incorrect.":WT2540:WT1:2550]K " The correct divisor is ";:WT0qK A1ĺA;:2545K A1ĺGF;:2545K GF;K "."K CCCC1:302:2520K WT0:VT7:E$"("E$") / "RT$:IN(RT$):308:DISPLAY NEW EQUATIONL A"JT0T$(T)"X"JCJ " DIVIDE THROUGH BY GCF OR -GCF LJ WT0J 292:7:" Enter term to divide equation by.":10::"TERM";::": ";:IP2:ML5:50:IN(RT$):IN12760:IN02530J ((INGF)A0)(IN1A1)2560J INGFA025607racting "T$" from both sides will not simplify the equation. Please try again.":WT1:302:2210I2170:WT0:(37)2:" "N$", you are incorrect. You may subtract the following: ":2177IT1T$"-X":2299IT1T$"X":2299JT0T$(T)"XBX0B0T$(B):TB:368:2095: SUBTRACT BdHTCXC0TC:2290:368:2125:SUBTRACT CHTDDOD0X0T$(D):TD:368:2085: SUBTRACT DH SUBTRACTION ERROR MESSAGES aICCCC1:WT0Ģ(37)2:" "N$", you are incorrect. SubtT$"X"T1GT$"-X"T1HGIF T$ = "-X" THEN T$ = "-1X":T = - 1jGAD1DO0((TCX)TB)2204GT1XA12202G(TDX0)(B0C0)2203G((TDX0)(TAX))(B0C0)2203GTAXA0TA:2290:368:2115: SUBTRACT A2HTEnter term to subtract from both sides. "::"TERM";::": ";:IP1:ML5:50mFCHECK FOR AN X IN THE ANSWERFT$RT$:X0:T1(T$):(T$,T,1)"X"XT:T(T$)FFHAS THE CORRECT TERM BEEN SPECIFIED OR HAS IT BEEN SUBTRACTED ALREADY GT(T$):n if you were to "AS$(AS);T$;AS$(AS2)"both sides";:WT2205:WT1:2188E". The best choice is to "AS$(AS)((1(AS0))(AS1))A"X "(8)AS$(AS2)"both sides";:WT0:2188E SUBTRACTION AXIOM EAS1:CN1:WT0:ADAD1:AD2DN1KF292:7:" correct; however, an extra step would be added to the process of solving this equation if you were to "AS$(AS);T$;AS$(AS2)"both sides";:2188HE" "N$", that is correct; however, an extra step would be added to the process of solving this equatioB0ĺC"X";CT2D0ĺA"X";0CT2A0ĺD;:C2188OCA1ĺ"X";:2188`CA"X";:2188C" "N$", that is correct; however, I cannot move the variable to the other side of the equation. Please use another term";:2188D" "N$", that is (AD2)(DO0)22190,2199;BA0A1A1ĺA"X";:2183PBA1ĺ"X";:2183[B"-X";mBB0ĺ", "B;BC0C1C1ĺ", "C"X";:2187BC1ĺ", X";:2187B", -X";BD0ĺ", "D;B".":302:AS2210:2010BT1C0ĺB; CT1on. Please try again.":WT1:302:2010vAzT(B0C0)(A0D0DO)2:AS02175:: LEFT (1) OR RIGHT (2) COLLECTIONAWT0:(37)2:" "N$", you are incorrect. You may add the ";::"OPPOSITE";::" of the following: ":"PRINT ALL CORRECT TERMSB(A$)0)B$" "T$" = "C$(FA((C$)))X1$((C$)0)SP$((C$)0)S$(((D$)0)(C$))D$SP$((D$)0)T$p@k@p ADDITION ERROR MESSAGES &AuCCCC1:WT0Ģ(37)2:" "N$", you are incorrect. Adding "T$" to both sides will not simplify the equatiS$(D0)D$SP$(D0)"= "D$" +0":R2$D$" +0 = "D$z?RW$AC$(FA(AC))"X"SP$((B$)0)S$(B0)B$" = "D$:AAC:C0?W SET UP NEW EQUATION AND T$ FOR SIMPLIFICATION ?\T$S$(T0)T$j@fE$A$(FA((A$)))X1$((A$)0)SP$((B$)0)S$((B$)0>MWL$AC$(FA(AC))"X"S$(B0)B$:WR$D$:L1$"("A$(FA(A))X1$(A0)S$(C0)NC$(FA(C))X1$(C0)") "S$(B0)B$SP$((B$)0)"= "AC$(FA(AC))"X"SP$((B$)0)S$(B0)B$5?OL2$"":R1$"("C$(FA(C))X$(C0)S$(C0)NC$(FA(C))X1$(C0)") "+0"=EL2$B$" +0 = "B$:R1$"("C$(FA(C))X$(C0)S$(A0)NA$(FA(A))X1$(A0)") "S$(D0)D$SP$(D0)"= "CA$(FA(CA))"X"SP$(D0)S$(C0D0)D$:R2$""=HW$B$" = "CA$(FA(CA))"X"SP$(D0)S$(D0)D$:CCA:A0:2135>K SUBTRACT C 0)C)(DB):R2$""j<4W$A$(FA(A))X$(A0)"= "C$(FA(C))X$(C0)S$((DB0)C)(DB):DDB:B0:2135}<> SUBTRACT A =CWL$B$:WR$CA$(FA(CA))"X"S$(D0)D$:L1$B$" "S$(B0)"("A$(FA(A))X$(A0)S$(A0)NA$(FA(A))X1$(A0)") = "B$" 0)C)(DB):L1$A$(FA(A))X$(A0)S$(A0)"("B$" "S$(B0)(B)") = "A$(FA(A))X$(A0)"+0"<1L2$A$(FA(A))X$(A0)"+0 = "A$(FA(A))X1$(A0):R1$C$(FA(C))X$(C0)S$(C0)"("D$SP$(D0)S$(B0)(B)") = "C$(FA(C))X$(C0)S$((DB") = "C$(FA(C))X$(C0)"+0":R2$C$(FA(C))X1$(C0)" +0 = "C$(FA(C))X1$(C0):*W$A$(FA(A))X$(A0)S$((BD0)(A0))(BD)" = "C$(FA(C))X$(C0):BBD:D0:2135:- SUBTRACT B f;/WL$A$(FA(A))X1$(A0):WR$C$(FA(C))X1$(C0)S$((DB9%WL$A$(FA(A))X1$(A0)S$((BD0)(A0))(BD):WR$C$(FA(C))X1$(C0):L1$A$(FA(A))X$(A0)S$(A0)"("B$" "S$(D0)(D)") = "A$(FA(A))X$(A0)S$((BD0)(A0))(BD)T:'L2$"":R1$C$(FA(C))X$(C0)S$(C0)"("D$" "S$(D0)(D)0C0)220368((TDX0)(TAX))(B0C0)2203^8TAA0Xİ368:2110:SUBTRACT A8 TCC0Xİ368:2125:SUBTRACT C8TBB0Xİ368:2095:SUBTRACT B8TDDOD0Xİ368:2085:SUBTRACT D82160:ERROR8  SUBTRACT D (T$,T,1)"X"XT:T(T$) 7k7HAS THE CORRECT TERM BEEN SPECIFIED OR HAS IT BEEN SUBTRACTED ALREADY7T(T$):T$"X"T$"X":T17T$"-1X"T$"-X"7T$"-X"T17AD1DO0((TCX)TB)22047T1X1A12202 8(TDX0)(Bz#?     Ҡ Ϡ ɠ#ӮϠ" ïàҮʠҠŮXAA$"N"1890 AA$"Y"370J:"Sample problem: 8X +14 = -10"Q6 "The first step is to get the constants on one side. To do this, we can either add or subtract a term from both sides. For this example, we will add a term to both2290:AA$"R"300h:12:"Do you wish to try a sample problem?":20:14:"Type ";::"Y";::" or ";::"N ";::4:" or ";::"R";::" to reread the previous page.";m12:38rAA$:AA$(8)370:(AA$)96AA$((AA$)32)wAA$"R"330| computational error will occur if you calculate something incorrectly. For example, if you try to add 7X to both sides of an equation at a point "^"where adding 8X would be more appro- priate, you will be charged with a computational error.":ng the problem. For example, trying to add a term to "@"both sides at a point where multiplying or dividing would be more appropriate is a procedural error.":2290:AA$"R"290J:2:"The second kind is ";::"COMPUTATIONAL";::". "T"A2290:AA$"R"270V":12:4:"I know about two kinds of errors.":2290:AA$"R"280,:2:"The first kind is ";::"PROCEDURAL";::". "96"A procedural error occurs when the oper- ation you choose will not lead you along the best path to solvi are incorrect. If you make the same mis- take twice, I'll tell you the correct answer.":2290:AA$"R"240:10:"I will give you a summary of your errors after each problem. After a set of problems, I will give you a total error analysis.":$"N"P$"n"231:P$"Y"P$"y"240:18901 "To solve an equation, you will have to choose operations from the following list:" ::2070:2290:AA$"R"130o :8:"If you make a mistake while solving a problem, I will tell you why you"in solving linear equations with one". ] "variable. Equations will take the form"c "AX + B = C -- where A, B, and C are integers. The solution, X, will be an integer. Do you want instructions (Y/N)?";+ P$:P$"Y"P$"y"P************************";:1,450:106 <T13000:K FFL0:2330:F$N${ ZL(F$):801,L:T1L:801T,((F$,T,1)): nN$F$ xA(78)(79):AA:X(A) :3 "Hi, ";N$;"!" "This program will give you practice" ( :12:"Design by Don Ross":T112:912::34,12 (23:14:"Copyright 1984":T19:912::34,14:23:4:"Microcomputer Workshops Courseware":T17:912::& 210:1:1:"****************************************":1,4539:23:1:"****************N!1 "I Last update:10/4/84 by Kevin Vessio l (800)255N$"":T1(801):N$N$((801T))::240::23:13:"Linear Equations":13:"================":T116:912:1 34,8:23:9:"Program by Mark S. Appel":T114:912::34,10:23            @ : CLEAR SCREEN;@230,32:3086: CLEAR PAGE 1c@(13)(4);"BLOAD CBS.LOGO,A$2000"@49236,0: DISPLAY PAGE 1@#T13500:T@(::@2(13)(4)"RUN COVER"2GPRINT CHR$(13)CHR$(4)"(34)"RUN COVER"(34)9 16:" pZ (13)(4)"BRUNUC/LC DVR.OBJ"::8:17:"Loading":10:13:"Linear Equations":800,0o(13)(4)"RUNI"N0"NAA$"I"240%"XAA$"P"1850="b LOAD EQUATIONS II"l:8:17:"Loading":10:13:"Linear Equations":(13)(4)"RUNE.2""v" SAMPLE SCREEN ENTRY ROUTINE"16368,0"X(36): HORIZ POSITION"Y(37): VERTI POSITION<#(24):age." !D!"Press ";::"I";::" to review the instructions."J!!"Press ";::"P";::" to proceed with actual problems."!16368,0!&(23)!0(16):"Choice: ";!:AA$:AA$(8)1850!D(AA$)96AA$((AA$)32)"IAA$"R"156 |A$"-3"(13) 1920- AA$"R"14703 g 2320:(5):(9):" X = -3 ":(9) "Congratulations, "N$"!"   "You have reached the correct solution."  !"Press ";::"R";::" to reread the previous pType ";::"X";::" and press ";::"RETURN";::".";:(8)A,`6"Enter new left side : ";q@A$"X"(13){J1920TAA$"R"1470^(22):9:"Type ";::"-3";::" and press ";::"RETURN";::".";:(10)hr"Enter new right side: ";0 2320;"We must now enter the new left and"AW"right sides. ""In this case, the new left side is X,""and the new right side is -3."2290:AA$"R"14002320:5:9:" (8X)/8 = (-24)/8":12;"22:9:""11407d2320:(5):(9):" (8X)/8 = (-24)/8":(12)gn"Now we must again simplify the equation."s2290:AA$"R"1270x2320:2070(22):16:"Type ";::"5";::".";:(19)(16):"Choice: ";A$"5"1920AA$"R"138AA$"R"103092320:5:9:" 8X = -24 ":7d"Enter term to divide both sides by." 22:6:" Type ";::"8";::" and press ";::"RETURN";::".";:(8)("TERM";2<": ";FA$"8"(13)P1920ZAA$"RAA$"R"950t2320~!L"Now we have to enter the divisor of"Ru"both sides of the equation."{"In this case, we want to divide by 8":"because 8 is the coefficient of the":"variable X." 2290: by a term. For this example, we will divide both sides by a term.":2290:AA$"R"800h2320:(5)9:" 8X = -24 "$2070.22:16:"Type ";::"4";::".";8(19)BL(16):"Choice: ";VA$"4"`1920 j11):"I am going to rearrange the equation"1V"using the symmetric property."f2210:23205:1:958:9:" 8X = -24 "Y9:"In order to undo the coefficient of X, we can either multiply or divide both sides of the equation\1920fAA$"R"750ap22:6:" Type ";::"-24";::" and press ";::"RETURN";::".";kz(10)q"Enter new right side: ";A$"-24"(13)1920AA$"R"7502320:(5)1010(10):" -14 = -14X "+(nter the new right and left sides of the equation."L2290:AA$"R"670u 2320:5:10:"8X +14 -14 = -10 -14"*(22):6:" Type ";::"8X";::" and press ";::"RETURN";::".";4(8)>H"Enter new left side : ";RA$"8X"(13)070:(22)+16:"Type ";::"5";::".";5(19);P16:"Choice: ";[A$"5"e1920vAA$"R"6502320::"Simplification involves collecting the" "like terms on each side."5" In order to simplify, we must e." X(9)#b:"TERM";::": ";6lA$"-14"(13)@v1920QAA$"R"5102320:(3):(7)::"YOUR EQUATION NOW READS:":::(10):"8X +14 -14 = -10 -14":(9)(12):" Now we must simplify the equation."2290:AA$"R"560 2320:2"4002320:11>"Now we have to enter the term to be"D`"added to both sides."w&2290:AA$"R"43002:1:958:7:"Enter term to be added to both sides."DN22:8:"Type ";::"-14";::" and press ";::"RETURN";::" sides. ";m"As an alternative we could have divided both sides by 2 or multiplied both sides by 1/2."2290:AA$"R"3602320:207022:16:"Type ";::"1";::".";(19)16:"Choice: ";A$"1"1920AA$"Rs@`p0  80`@p300p0030\xppฮ|@@`p8p`p|Օ@p`p8`p p pxฮB|p p `?``Օa@: @@8`7 7 S S S S 0p06 p@9 `88 0<710 @# Ff@@~~" 8p`@@@@@@`p0? @@@`p8@s0`@xy?``? 80p``@@@@@``00 x x x8` |  c``ag# #  ??# g``c```g7  LLOLLL  XpxC `0 @!~cffc```@x | Cx q33s3331!`?@xx윀@8yյCp@0800OꚆa`8~ 0`@``յC@@`0 ``Ꚇa F~~8`8`ccffc``agCffCaGqCf`fC`xN<8`@?`@@@ppqx@|뛇p``0 ?`?@յ|?``?px x xꚆaxx x @@յC?`xppꚆ` ! S S pp07 8`: @p9 8>30 @$ FfF@ #  0`@@@@`0? @@`0 a303a `08  0p`@q30p0031 Xp   L(L$):L97L(L$)32:L$(L)5) (N$)102370M) N$N$L$:L$;:2370TL$:L$;:2370T2370- (32 * ASC (L$) > = 97))[(` L$(8)(N$)1ĺ(8);(32);(8);:N$(N$,1,(N$)1):2370(j L$(8)(N$)1ĺ(8);(32);(8);:N$"":2370(t (L$)96L$((L$)32)(~ L$"A"L$"Z"2370( (N$)0L(L$):L97L(L$)32:L$(L)!) (N$)0me (up to ten letters) and press RETURN. Last name: ";:2370'8 5:" Please type your first name (up to ten letters) and press . ":10:"Name: ";'B L$:L$(8)2370:L$(13)(N$)0ı'L L$(127)L$(8)(V L$ = CHR$ ( ASC (L$) to continue.":24:4:"Press ";::"R";::" to reread previous page.";:16368,0&A(16384):AA(A224)32:A141A2102300& AA$(A128):16368,0:& (1):(6):958:(7):& &$ N$"":FL0ė>'. FL1Ģ12:" Please type your last na%z"%"5) Simplify both sides"(%.%R% INSTRUCTIONS->SAMPLE SCREENa%(24):(8)%"Press ";::"RETURN";::" to continue.";%16368,0%A(16384)%A1412250%16368,0%R&(22):(8):"Press ";::"RETURN";::" wish to use:"3$ "-----------------------------"9$*c$4"1) Add the same term to both sides"i$>$H"2) Subtract same term from both sides"$R$\"3) Multiply both sides by the same term"$f$p"4) Divide both sides by the same term"(1):" Press ";::"R";::" to reread the previous page.";M#(Y1):36,X\#X1(A$)b##AA$:AA$(8)2000:(AA$)02000#(AA$)96AA$((AA$)32)#AA$"R"ı#AA$(A$,X,1)1990#AA$;#X# $"Pick the rule you INPUT ! HT(36)1:VT(37)1N 868:RT$"":S0:N0:N00:N10:16368,0i P$:P$(127)P$(8){ P$(13)162 P$(8)(RT$)0150 (RT$)ML132 P$"/"(SN0)132:P$"/"S(RT$)1HP$"-"((N01N1)(S0N00(RT$)0)("-"(P$"0"P$"9")1020 nP$"-"(RT$)0102C p(RT$)ML102\ rRT$RT$P$:P$;:102} t(RT$)1ĺ(8)" "(8);:100 v(RT$)0102 xRT$(RT$,1,(RT$)1):(8)" "(8);:102 z(RT$)1RT$"-"102 |RT$((RT$)): ~ MULTIPLICATION;:56 Z(RT$)1RT$"-"567 [RT$"X"RT$"-X"96X \RT$((RT$)):XRT$RT$"X"p ]RT$"-1X"RT$"-X" ^RT$"1X"RT$"X" ` b DIVISION INPUT dRT$"":16368,0 fP$:P$(127)P$(8) hP$(13)122 jP$(8)116 lP$"X"X56( FP$"0"P$"9"X56:NN18 HP$"X"X1P LRT$RT$P$:P$;:56p N(RT$)1ĺ(8)" "(8);:54 P(RT$)056 RP$(RT$,1):T(P$"X")((P$"0"P$"9")2):T84,86 S88 TX0:88 VNN1 XRT$(RT$,1,(RT$)1):(8)" "(8) : MAX LEN. ! 3IP198,126,174' 4I 6RT$"":X0:N0:NG0:16368,0d 8P$:P$(127)P$(8)w :P$"x"P$"X" <P$(13)90 >P$(8)78 ?(RT$)ML56 @P$"-"P$"X"(P$"0"P$"9")56 BP$"-"(RT$)056:P$"-"NG1 DP$U 5000, WRITTEN BY MARK S. APPEL q "E.2 REVISION 1 LAST UPDATE: 11/21/84 By Kevin Vessio w(-20(T$)2:T$: 2 ALL INPUT ROUTINES BELOW IP=1 : ADDITION IP=2 : DIVISION IP=3 : MULTIPLICATION IP=4 : SIMPLIFICATION ML                          (0 Zнй`)JJ & & f)``STL)L "  ??" g```c```g6 : ?`@`?p@6 6 S 2aՀ  p333s3330?`C@`?x@!`yp`p 00``@@@@@``p08 p ppp@ |  accca``cf"aՀ `p8꺎C  LLLOLLL \xp ս Հ x~~`p8~C @agfga```@@p | x8p@?`@@`??`@`?`88`8axxx켌@yYa8`8008O@ฮ꺎C @p~8p`@@@@ ꊂx ՟~||p@p@1ƚagfga``cfgfgccg`g@p|9408:PC0:((P5)56(P7)24)((P5)72(P7)72)((P23)201(P55)207(P76)234)PC1:"CHECK FOR A PRINTER CARDN5:"Press ";::"M";::" to do more problems. "P6:"Press ";::"R";::" to review the instructions."$R7:"Press ";A)))PA;:31:ZZPA:348T@" Computational ....."3((CA)))CA;:31:ZZCA:348A:5:"Total .............";3((CAPA)))CAPA;:31:ZZCAPA:348BP$" problems.":TP1P$" problem."D" This is your analysis for "TP;P$F19|HP4EADS:":::868:T$E$:40:98 TOTAL ERROR ANALYSIS c:::::10:"TOTAL ERROR ANALYSIS":<:30:"Average":32:"per":5:"Error";:23:"Total";:30:"Problem":5:"-----";:23:"-----";:30:"-------";>" Procedural ........"3((PE6Ģ6(958:+* BLANK ROWS 8-24 :,8:958:N. GET RETURN 024:1:958:9:"Press ";::"RETURN";::" to continue.";:16368,02P$:P$(13)306:24:1:958:4 PRINT EQUATION CENTERED 63:7::"YOUR EQUATION NOW R D > 0 THEN D$ = "+" + D$(D0D$""DAN(DB)(AC):ANSWER cB$(B):A$(A):A1A$""tA1A$"-"C$(C):C1C$""C1C$"-" B0B$"+"B$"E$A$"X "B$" = "D$:AOA:BOB:COC:DOD:$ BLANK SCREEN &1:8:C=0:D=6:GOTO268+A((1)18)9:A0256mC0:C = INT ( RND (1) * 18) - 9: ON C = 0 OR C = A GOTO 258BOAC:P((1)12)6:G1PBOB((1)201)10:B0260P3P1BG1 DG1B:BDD0260 4280:GCFD$(D): IF(RT$,N1P,(RT$)N1P1):S1$"-X"S$((L3$)0)L3$:244:10-XL3$(RT$,PN11):R3$(RT$,N1P,(RT$)N1P1):S1$((R3$))"X"S$((L3$)0)L3$:10-2X GENERATE RANDOM EQUATION CC0:CP0:GF0:DN0:AS0:DC0:AD0A=-1:A$="-X":B=4:1PN1L3$(RT$,PN11):R3$(RT$,N1P,(RT$)N1P1):S1$((R3$))"+"L3$:244:X-10fX10244(RT$,X11,1)"+"L3$(RT$,PN11):R3$(RT$,N1P,(RT$)N1P1):S1$"X"S$((L3$)0)L3$:244:10+X=(RT$,X11,1)"-"L3$(RT$,PN11):R3$3$)(R3$)):244:10-20XX1(RT$,2)"-X"PN1L3$(RT$,PN11):R3$(RT$,N1P,(RT$)N1P1):S1$((R3$))S$((L3$)0)L3$:244:3X-10(RT$,2)"-X"PN1L3$(RT$,PN11):R3$(RT$,N1P,(RT$)N1P1):S1$((R3$))L3$:244:-X-10XX"-1X"RT$"-"(RT$,(RT$)2):PP(1(P0)):N1N1(1(N10)):XX1N1PN1P(RT$)2(RT$,2)"1X"RT$(RT$,N1P)"X":X1X11RT$"-X"RT$"X"ıXX1PN10244XX10PN10L3$(RT$,N1P1):R3$(RT$,N1P,(RT$)N1P1):RT$((L:212P$"+"P0@RT$(RT$,(RT$)1):(8)" "(8);:178tP$(RT$,1):(RT$)0RT$"-"P$"-"P$"+"178FORMAT THE RETURN STRINGS (RT$, S1$, S2$)(RT$,2)"1X"RT$(RT$,(RT$)1):PP(1(P0)):N1N1(1(N10)):XX1D(RT$,3)"(RT$)0178:P$"0"NX10M$"-"M$"+"M$"X"NN1:198I178bRT$RT$P$:P$;:178(RT$)0178:(RT$)1ĺ(8)" "(8);:176P$(RT$,1):(P$"0"P$"9")NN1:212P$"X"X1X10:212P$"X"XX0:212P$"-"N10"X"X1X0PN10X(RT$)1:198JP$"X"X1X0PN1X1(RT$)1:198cP$"-"(RT$)0198P$"-"(NX)N10P0N1(RT$)1:198P$"+"(NX)P0N10P(RT$)1:198M$(RT$,1):(P$"1"P$"9")X10M$"X"NN1:198@P$"0n by zero is not allowed.";:302:1:VT1:958:HT:VT:130IDVNMDDOf SIMPLIFICATION RT$"":S1$"":S2$"":X0:X10:P0:N0:N10:16368,0P$:P$(127)P$(8)P$(8)200:P$(13)214:(RT$)ML178:P$"x"P$"X"!P$")2)((P$"-")3):T154,156,158.S0:160=NN1:160FN10sRT$(RT$,1,(RT$)1):(8)" "(8);:132(RT$,1)"/"(RT$,1)"-"RT$"-"(RT$)1132S0DV(RT$):172NM((RT$,S1)):DD((RT$,(RT$)S))<DD0ĺ" DivisioSN10(RT$)S)(N01N10S0)(N1N00S))132:P$"-"(RT$)0N01dP$"-"S(RT$)SN11P$"/"P$"-"(P$"0"P$"9")132:P$"0"P$"9"NN1RT$RT$P$:P$;:132(RT$)1ĖHT:130!P$(RT$,1):T(P$"/")((P$"0"P$"9on.": GOTO 925Z-zDN1G13CN0ĺ" To undo the coefficient of X, use rule 3 or rule 4."m-302:292:795- BRANCH TO APPROPRIATE AXIOM SUBROUTINE THEN PRINT THE NEW EQUATION -368:G12000,2206,3000,1270,1470,2500,4000.308:DISPLAY NEW Euce fractions in the equation.":925c,pDN1CN2ĺ" The only thing left to do is simplify.":925-u IF GF = 0 AND DN = 0 AND (G1 = 3 OR G1 = 4) THEN PRINT " It is usually preferable to undo addition and subtraction before multiplication and divisi of all the terms is 1, dividing by anything except 1 or -1 will produce fractions in the equation.":925$,nG13GF0DN0ĺ" Since the greatest common factor of all the terms is 1, multiplying by the reciprocal of anything except 1 or -1 will prod(A0C1)(C0A1))G14Ģ7:" Division is unnecessary at this point. The coefficient of X already equals one. The next step is addition or subtraction.":925*kN$", that's not the best choice."k+mG14GF0DN0ĺ" Since the greatest common factor", you are incorrect.":40:10:3:"The next step is simplification.":925)a((A0C1)(C0A1))G13Ģ7:" Multiplication is unnecessary at this point. The coefficient of X already equals one. The next step is addition or subtraction.":925*f( THROUGH!)8(HCN0DN0(G11G12)ı:ADD OR SUBTRACT~(R292:CPCP1:CLEAR SCREEN AND INCREMENT PROCEDURAL ERROR COUNTER(WCN0G15Ģ8:T$N$", you are incorrect.":40:10:6:"There is nothing to simplify.":925K)\CN(DN0DN1)G15Ģ8:T$N$F)A1)DN0CN0((AAOCOCCOAO)(BBODODDOBO))G16::"DIVIDE THROUGH'9G13((GF)A1)DN0CN0((AAOCOCCOAO)(BBODODDOBO))G17::"MULTIPLY THROUGH'>CNG15ı:SIMPLIFY (CCN0DN1(G13G14)ı:MULT OR DIV (NOT term to both sides 2) Subtract same term from both sides 3) Multiply both sides by the same term 4) Divide both sides by the same term 5) Simplify both sides"&*24:15:"Choice: ";:16368,0:P$:G1(P$):G11G15810:24:1:958T'4G14((GKeep trying, you'll get it.":CM$(10)"Don't get discouraged. You'll do better on the next one."f%%  PRINT AXIOM OPTIONS AND GET INPUT %9:958:8% " Pick the rule you wish to use: -----------------------------"&%" 1) Add the samemework."S$CM$(3)"Too bad your teacher can't see this.":CM$(4)"Very well done."$CM$(5)"Well, we can't all be perfect.":CM$(6)"That was a good try."$CM$(7)"You almost made it on that one.":CM$(8)"These problems are not so easy."`%CM$(9)"(2)"-":S$(1)"+":X1$(0)"X":X$(0)"X ":SP$(1)" ":AS$(0)"add ":AS$(1)"subtract ":AS$(2)" to ":AS$(3)" from ":TP0:CA0:PA0#FA(A)((A)1)((A1)2)#SN(A)((A0)2)1$CM$(1)"Very impressive.":CM$(2)"I see you've been doing your ho:D$(D):AC$(1)(AC):CA$(1)(CA):A0A$"":A$(1)""G"tB0B$""_"vC0C$"":C$(1)""n"xD0D$""t"z" INITIAL VARIABLE SET-UP "CZ0:N$"":T1(801):N$N$((801T)):#A$(2)"-":NA$(2)"-":C$(2)"-":NC$(2)"-":AC$(2)"-":CA$n using the symmetric property.":302:8:958:364:!jN!lAD1AD2:DN1a!mA1DANDN2!n368:E$A$(FA(A))X$((A$)0)"= "D$:308:!p MAKE STRINGS OUT OF NUMERICS 8"rA$(A):A$(1)A$:NA$(1)(A):B$(B):C$(C):C$(1)C$:NC$(1)(C)"0"P$, _XX1(P$):(P$,XX,1)"."352:F `XX(P$)1P$P$"0"d aXX(P$)2P$(P$,XX2)w b(P$)5ĺP$: c5(P$))P$: d f REARRANGE THE A AND C VARIABLES 4!hA0AC:C0:DB:B0:8:958:"I am going to rearrange the equatioprogram. Press RETURN to reboot the disk.":20:16368,0ZP$:P$(13)346:(42204)238(42205)16(42206)192Č47731: PP 1.5 BOOT[(43626):\P$"":ZZ0P$"0.00":355]ZZZZTP:P$(ZZ):ZZ(ZZ)P$P$".00" ^(P$,1)"."P$::"E";::" to exit the program.";wTP$:(P$"M"P$"m")((P$"R"P$"r")2)((P$"E"P$"e")3)5010,342,344:340V:12:11:"Loading Instructions":800,255:(13)(4)"RUNI"=X:10:9:T$"Thank you, "N$".":40:" I hope you enjoyed this (FA(C))X$(C0)S$(A0)NA$(FA(A))X1$(A0)") "S$(D0)D$SP$(D0)"= "CA$(FA(CA))"X"SP$(D0)S$(C0D0)D$:R2$""=HW$B$" = "CA$(FA(CA))"X"SP$(D0)S$(D0)D$:CCA:A0:2135=K SUBTRACT C >MWL$AC$(FA(AC))"X"S$(B0)B$X$(A0)"= "C$(FA(C))X$(C0)S$((DB0)C)(DB):DDB:B0:2135X<> SUBTRACT A U" The correct multiplier is ";:WT0:A1ĺ"-1/1";:4043cUA1ĺSN(A)"/"GFSN(A);:4043|USN(A)"/"GFSN(A);U"."UCCCC1:302:DV14020:VSG(DV):WT0:VT7:E$"("E$") ("(SN(GFSG))"/"(GFSN(GF))")":IN(RT$):308:mT292:7:" Enter term to multiply equation by.":10::"TERM";::": ";:IP3:ML10:50:DV1İ4260:4020TDV1A14030:DV1A1GF1:4060TDV1GFA14060TDV1GFA14060U11:" "N$", you are incorrect.":WT4040:WT1:4050(DA):R1$"("(D)") ("(SN(A))"/"(ASN(A))") = "(DA):R2$""S W$"X = "(DA):E$"("A$(FA(A))"X) ("(SN(A))"/"(ASN(A))") = ("(D)") ("(SN(A))"/"(ASN(A))")"S S" MULTIPLY THROUGH BY THE 1/-GCF OR 1/GCF TWT0 equation. "!R WT0WT1:3040XR WT0:"The correct answer is "SN(A)"/"SN(A)A"."oR CCCC1:302:3010R GENERATE SIMPLIFICATION ERROR MESSAGESR 368:WL$"X":L1$"("A$(FA(A))"X) ("(SN(A))"/"(ASN(A))") = 1X":L2$"1X = X"GS WR$ND CXQ 7:" Enter term to multiply both sides by. "::"TERM";::": ";:IP3:ML8:50iQ DV1A3050Q " "N$", you are incorrect. You must multiply by the reciprocal of the coefficient of X. " R DV1ĺ"Multiplying by one will not simplify theCIN12720:CIN"X.":27700P DIN".":2770P " "N$", you are incorrect. Dividing by 1 will not simplify the equation.":WT12540:WT1:2550P 302:P MULTIPLICATION P WT0Q CN2:292:358:SET FLAG, CLEAR SCREEN, AND REARRANGE A ASSAGES OOx CCCC1:(37)2:" "N$", you are incorrect.":WT12690:WT1:2770O WT0:" The correct answer is ";:T2700,2730,2740,2750O AIN12710:AIN12720:AIN"X.":2770O "X.":2770O "-X.":2770O BIN".":2770P CIN12710:";:IP2:ML5:50:RT$(DIN)2640:T4:2670:2630=NP DDINXNZ MAKE NEW EQUATION Nd 368:E$A$(FA(A))X1$((A$)0)SP$((B$)0)S$((B$)0A0)B$" = "C$(FA(C))X1$(C0)SP$((D$)0C0)S$((D$)0C0)D$:On DIVIDE THROUGH ERROR MEN1L3$(RT$,PN11):R3$(RT$,N1P,(RT$)N1P1):S1$((R3$))"+"L3$:244:X-10aX10244(RT$,X11,1)"+"L3$(RT$,PN11):R3$(RT$,N1P,(RT$)N1P1):S1$"X"S$((L3$)0)L3$:244:10+X8(RT$,X11,1)"-"L3$(RT$,PN11):R3$(RT$,(R3$)):244:10-20XX1(RT$,2)"-X"PN1L3$(RT$,PN11):R3$(RT$,N1P,(RT$)N1P1):S1$((R3$))S$((L3$)0)L3$:244:3X-10(RT$,2)"-X"PN1L3$(RT$,PN11):R3$(RT$,N1P,(RT$)N1P1):S1$((R3$))L3$:244:-X-10SX1PRT$"-"(RT$,(RT$)2):PP(1(P0)):N1N1(1(N10)):XX1N1PN1P(RT$)2(RT$,2)"1X"RT$(RT$,N1P)"X":X1X11RT$"-X"RT$"X"ıXX1PN10244XX10PN10L3$(RT$,N1P1):R3$(RT$,N1P,(RT$)N1P1):RT$((L3$)P$"+"P0;RT$(RT$,(RT$)1):(8)" "(8);:178oP$(RT$,1):(RT$)0RT$"-"P$"-"P$"+"178FORMAT THE RETURN STRINGS (RT$, S1$, S2$)(RT$,2)"1X"RT$(RT$,(RT$)1):PP(1(P0)):N1N1(1(N10)):XX1?(RT$,3)"-1X"T$)0178:P$"0"NX10M$"-"M$"+"M$"X"NN1:198D178]RT$RT$P$:P$;:178(RT$)0178:(RT$)1ĺ(8)" "(8);:176P$(RT$,1):(P$"0"P$"9")NN1:212P$"X"X1X10:212P$"X"XX0:212P$"-"N10:2121X0PN10X(RT$)1:198EP$"X"X1X0PN1X1(RT$)1:198^P$"-"(RT$)0198P$"-"(NX)N10P0N1(RT$)1:198P$"+"(NX)P0N10P(RT$)1:198M$(RT$,1):(P$"1"P$"9")X10M$"X"NN1:198;P$"0"(Rzero is not allowed.";:302:1:VT1:958:HT:VT:130DDVNMDDJa SIMPLIFICATION RT$"":S1$"":S2$"":X0:X10:P0:N0:N10:16368,0P$:P$(127)P$(8)P$(8)200:P$(13)214:(RT$)ML178:P$"x"P$"X"P$"X"X((P$"-")3):T154,156,158)S0:1608NN1:160AN10nRT$(RT$,1,(RT$)1):(8)" "(8);:132(RT$,1)"/"(RT$,1)"-"RT$"-"(RT$)1132S0DV(RT$):172NM((RT$,S1)):DD((RT$,(RT$)S))7DD0ĺ" Division by 0(RT$)S)(N01N10S0)(N1N00S))132:P$"-"(RT$)0N01_P$"-"S(RT$)SN11P$"/"P$"-"(P$"0"P$"9")132:P$"0"P$"9"NN1RT$RT$P$:P$;:132(RT$)1ĖHT:130P$(RT$,1):T(P$"/")((P$"0"P$"9")2)T  HT(36)1:VT(37)1I 868:RT$"":S0:N0:N00:N10:16368,0d P$:P$(127)P$(8)v P$(13)162 P$(8)(RT$)0150 (RT$)ML132 P$"/"(SN0)132:P$"/"S(RT$)1CP$"-"((N01N1)(S0N00(RT$)0)(SN1P$"0"P$"9")102+ nP$"-"(RT$)0102> p(RT$)ML102W rRT$RT$P$:P$;:102x t(RT$)1ĺ(8)" "(8);:100 v(RT$)0102 xRT$(RT$,1,(RT$)1):(8)" "(8);:102 z(RT$)1RT$"-"102 |RT$((RT$)): ~ MULTIPLICATION INPU Z(RT$)1RT$"-"562 [RT$"X"RT$"-X"96S \RT$((RT$)):XRT$RT$"X"k ]RT$"-1X"RT$"-X" ^RT$"1X"RT$"X" ` b DIVISION INPUT dRT$"":16368,0 fP$:P$(127)P$(8) hP$(13)122 jP$(8)116 lP$"-"(56# FP$"0"P$"9"X56:NN13 HP$"X"X1K LRT$RT$P$:P$;:56k N(RT$)1ĺ(8)" "(8);:54| P(RT$)056 RP$(RT$,1):T(P$"X")((P$"0"P$"9")2):T84,86 S88 TX0:88 VNN1 XRT$(RT$,1,(RT$)1):(8)" "(8);:56X LEN.  3IP198,126,174" 4D 6RT$"":X0:N0:NG0:16368,0_ 8P$:P$(127)P$(8)r :P$"x"P$"X" <P$(13)90 >P$(8)78 ?(RT$)ML56 @P$"-"P$"X"(P$"0"P$"9")56 BP$"-"(RT$)056:P$"-"NG1 DP$"X"XV 5000, WRITTEN BY MARK S. APPEL l " REVISION 1 LAST UPDATE: 8/24/84 BY MARK S. APPEL r(-20(T$)2:T$: 2 ALL INPUT ROUTINES BELOW IP=1 : ADDITION IP=2 : DIVISION IP=3 : MULTIPLICATION IP=4 : SIMPLIFICATION ML : MA50 ^1920^5030292.^DN250508^1920B^5030^5030se: -----------------------------"&%" 1) Add the same term to both sides 2) Subtract same term from both sides 3) Multiply both sides by the same term 4) Divide both sides by the same term 5) Simplify both sides"-'*24:15:"Choice: ";:163 one.":CM$(8)"These problems are not so easy."%CM$(9)"Keep trying, you'll get it.":CM$(10)"Don't get discouraged. You'll do better on the next one."%%  PRINT AXIOM OPTIONS AND GET INPUT %9:958:8#& " Pick the rule you wish to u)"Very impressive.":CM$(2)"I see you've been doing your homework."$CM$(3)"Too bad your teacher can't see this.":CM$(4)"Very well done."$CM$(5)"Well, we can't all be perfect.":CM$(6)"That was a good try."/%CM$(7)"You almost made it on that#A$(2)"-":NA$(2)"-":C$(2)"-":NC$(2)"-":AC$(2)"-":CA$(2)"-":S$(1)"+":X1$(0)"X":X$(0)"X ":SP$(1)" ":AS$(0)"add ":AS$(1)"subtract ":AS$(2)" to ":AS$(3)" from ":TP0:CA0:PA0#FA(A)((A)1)((A1)2)#SN(A)((A0)2)1D$CM$(1(C):C$(1)C$:NC$(1)(C):D$(D):AC$(1)(AC):CA$(1)(CA):A0A$"":A$(1)""b"tB0B$""z"vC0C$"":C$(1)"""xD0D$"""z" INITIAL VARIABLE SET-UP "N$"":T1(801):N$N$((801T))::L$"":T1(818):L$L$((818T)):ng to rearrange the equation using the symmetric property.":302:8:958:364U!ji!lAD1AD2:DN1|!mA1DANDN2!n368:E$A$(FA(A))X$((A$)0)"= "D$:308:!p MAKE STRINGS OUT OF NUMERICS S"rA$(A):A$(1)A$:NA$(1)(A):B$(B):C$blem:" `P$" Error Total ----- ----- Procedural ......... "PA" Computational ...... "CA b(13)(4)"PR#0":1002:312 d f REARRANGE THE A AND C VARIABLES O!hA0AC:C0:DB:B0:8:958:"I am goi13)346:(42204)238(42205)16(42206)192Č47731:PP 1.5 BOOTR[(43626):\PC1349::10:" There is no printer card in slot 1.":304:312]:(13);(4);"PR#1":N$" "L$"'s total error analysis for "TP;:P$" problems:" ^TP1P$" pro"P$"p")4)5010,342,344,348:340bV:12:11:"Loading Instructions":800,255:(13)(4)"RUNI"X:10:10:T$"Thank you, "N$".":40:" I hope you have enjoyed this program. Press the RETURN key to reboot the disk.":20:16368,0BZP$:P$(his analysis. "EN5:"Press ";::"M";::" to do more problems. "P6:"Press ";::"R";::" to review the instructions."R7:"Press ";::"E";::" to exit the program.";"TP$:(P$"M"P$"m")((P$"R"P$"r")2)((P$"E"P$"e")3)((P$"Plems.":TP1P$" problem."FD" This is your analysis for "TP;P$NF17HP49408:PC0:((P5)56(P7)24)((P5)72(P7)72)((P23)201(P55)207(P76)234)PC1:"CHECK FOR A PRINTER CARDL4:"Press ";::"P";::" to print out t:::868:T$E$:40:38 TOTAL ERROR ANALYSIS ]:::::10:"TOTAL ERROR ANALYSIS":<" Error Total ----- -----">" Procedural ........ "PA@" Computational ..... "CABP$" prob6(958:&* BLANK ROWS 8-24 5,8:958:H. GET RETURN 024:1:958:9:"Press ";::"RETURN";::" to continue.";:16368,02P$:P$(13)306:24:1:958:4 PRINT EQUATION CENTERED 63:7::"YOUR EQUATION NOW READS:"0 THEN D$ = "+" + D$#D0D$""?AN(DB)(AC):ANSWER ^B$(B):A$(A):A1A$""oA1A$"-"C$(C):C1C$""C1C$"-" B0B$"+"B$"E$A$"X "B$" = "D$:AOA:BOB:COC:DOD:$ BLANK SCREEN &1:8:E6=6:GOTO268&A((1)18)9:A0256hC0:C = INT ( RND (1) * 18) - 9: ON C = 0 OR C = A GOTO 258BOAC:P((1)12)6:G1PBOB((1)201)10:B0260P3P1BG1 DG1B:BDD0260 4280:GCFD$(D): IF D > SAVE YOUR LOGO PROGRAM WITH THE":18:" FILENAME: HELLO."C (22: D 0f0XMaxcsOlfA `׿ժu`z/j+Uj`虢`D 0o0xLa `3X p(RT$)ML102W rRT$RT$P$:P$;:102x t(RT$)1ĺ(8)" "(8);:100 v(RT$)0102 xRT$(RT$,1,(RT$)1):(8)" "(8);:102 z(RT$)1RT$"-"102 |RT$((RT$)): ~ MULTIPLICATION INPU Z(RT$)1RT$"-"562 [RT$"X"RT$"-X"96S \RT$((RT$)):XRT$RT$"X"k ]RT$"-1X"RT$"-X" ^RT$"1X"RT$"X" ` b DIVISION INPUT dRT$"":16368,0 fP$:P$(127)P$(8) hP$(13)122 jP$(8)116 lP$"-"(56# FP$"0"P$"9"X56:NN13 HP$"X"X1K LRT$RT$P$:P$;:56k N(RT$)1ĺ(8)" "(8);:54| P(RT$)056 RP$(RT$,1):T(P$"X")((P$"0"P$"9")2):T84,86 S88 TX0:88 VNN1 XRT$(RT$,1,(RT$)1):(8)" "(8);:56X LEN.  3IP198,126,174" 4D 6RT$"":X0:N0:NG0:16368,0_ 8P$:P$(127)P$(8)r :P$"x"P$"X" <P$(13)90 >P$(8)78 ?(RT$)ML56 @P$"-"P$"X"(P$"0"P$"9")56 BP$"-"(RT$)056:P$"-"NG1 DP$"X"XV 5000, WRITTEN BY MARK S. APPEL l " REVISION 1 LAST UPDATE: 8/28/84 BY MARK S. APPEL r(-20(T$)2:T$: 2 ALL INPUT ROUTINES BELOW IP=1 : ADDITION IP=2 : DIVISION IP=3 : MULTIPLICATION IP=4 : SIMPLIFICATION ML : MA          !!! ! ! ! ! !!!!!!!!!""" " " " " """""""""               se: -----------------------------"&%" 1) Add the same term to both sides 2) Subtract same term from both sides 3) Multiply both sides by the same term 4) Divide both sides by the same term 5) Simplify both sides"-'*24:15:"Choice: ";:163 one.":CM$(8)"These problems are not so easy."%CM$(9)"Keep trying, you'll get it.":CM$(10)"Don't get discouraged. You'll do better on the next one."%%  PRINT AXIOM OPTIONS AND GET INPUT %9:958:8#& " Pick the rule you wish to u)"Very impressive.":CM$(2)"I see you've been doing your homework."$CM$(3)"Too bad your teacher can't see this.":CM$(4)"Very well done."$CM$(5)"Well, we can't all be perfect.":CM$(6)"That was a good try."/%CM$(7)"You almost made it on that#A$(2)"-":NA$(2)"-":C$(2)"-":NC$(2)"-":AC$(2)"-":CA$(2)"-":S$(1)"+":X1$(0)"X":X$(0)"X ":SP$(1)" ":AS$(0)"add ":AS$(1)"subtract ":AS$(2)" to ":AS$(3)" from ":TP0:CA0:PA0#FA(A)((A)1)((A1)2)#SN(A)((A0)2)1D$CM$(1(C):C$(1)C$:NC$(1)(C):D$(D):AC$(1)(AC):CA$(1)(CA):A0A$"":A$(1)""b"tB0B$""z"vC0C$"":C$(1)"""xD0D$"""z" INITIAL VARIABLE SET-UP "N$"":T1(801):N$N$((801T))::L$"":T1(818):L$L$((818T)):ng to rearrange the equation using the symmetric property.":302:8:958:364U!ji!lAD1AD2:DN1|!mA1DANDN2!n368:E$A$(FA(A))X$((A$)0)"= "D$:308:!p MAKE STRINGS OUT OF NUMERICS S"rA$(A):A$(1)A$:NA$(1)(A):B$(B):C$blem:" `P$" Error Total ----- ----- Procedural ......... "PA" Computational ...... "CA b(13)(4)"PR#0":1002:312 d f REARRANGE THE A AND C VARIABLES O!hA0AC:C0:DB:B0:8:958:"I am goi13)346:(42204)238(42205)16(42206)192Č47731:PP 1.5 BOOTR[(43626):\PC1349::10:" There is no printer card in slot 1.":304:312]:(13);(4);"PR#1":N$" "L$"'s total error analysis for "TP;:P$" problems:" ^TP1P$" pro"P$"p")4)5010,342,344,348:340bV:12:11:"Loading Instructions":800,255:(13)(4)"RUNI"X:10:10:T$"Thank you, "N$".":40:" I hope you have enjoyed this program. Press the RETURN key to reboot the disk.":20:16368,0BZP$:P$(his analysis. "EN5:"Press ";::"M";::" to do more problems. "P6:"Press ";::"R";::" to review the instructions."R7:"Press ";::"E";::" to exit the program.";"TP$:(P$"M"P$"m")((P$"R"P$"r")2)((P$"E"P$"e")3)((P$"Plems.":TP1P$" problem."FD" This is your analysis for "TP;P$NF17HP49408:PC0:((P5)56(P7)24)((P5)72(P7)72)((P23)201(P55)207(P76)234)PC1:"CHECK FOR A PRINTER CARDL4:"Press ";::"P";::" to print out t:::868:T$E$:40:38 TOTAL ERROR ANALYSIS ]:::::10:"TOTAL ERROR ANALYSIS":<" Error Total ----- -----">" Procedural ........ "PA@" Computational ..... "CABP$" prob6(958:&* BLANK ROWS 8-24 5,8:958:H. GET RETURN 024:1:958:9:"Press ";::"RETURN";::" to continue.";:16368,02P$:P$(13)306:24:1:958:4 PRINT EQUATION CENTERED 63:7::"YOUR EQUATION NOW READS:"0 THEN D$ = "+" + D$#D0D$""?AN(DB)(AC):ANSWER ^B$(B):A$(A):A1A$""oA1A$"-"C$(C):C1C$""C1C$"-" B0B$"+"B$"E$A$"X "B$" = "D$:AOA:BOB:COC:DOD:$ BLANK SCREEN &1:8:E6=6:GOTO268&A((1)18)9:A0256hC0:C = INT ( RND (1) * 18) - 9: ON C = 0 OR C = A GOTO 258BOAC:P((1)12)6:G1PBOB((1)201)10:B0260P3P1BG1 DG1B:BDD0260 4280:GCFD$(D): IF D > N1P,(RT$)N1P1):S1$"-X"S$((L3$)0)L3$:244:10-XL3$(RT$,PN11):R3$(RT$,N1P,(RT$)N1P1):S1$((R3$))"X"S$((L3$)0)L3$:10-2X GENERATE RANDOM EQUATION CC0:CP0:GF0:DN0:AS0:DC0:AD0 A=-1:A$="-X":B=4:C=0:D6P$"N"P$"n"1966:312+6302:312B6 ADDITION AXIOM h6AS0:CN1:WT0:ADAD1:AD2DN16292:8:"Enter term to be added to both sides.":10::"TERM";::": ";:IP1:ML5:506CHECK FOR AN X IN THE ANSWER7T$RT$:X0:T1(T$): Procedural errors ........ "CP" Computational errors ..... "CCY5T0A4:B1n5T1T2A7:B55T2A10:B8516368,0:T((1)(AB1)B):" "CM$(T):TPNP1978:" Would you like another problem (Y/N)?";5P$:P$"y"P$"Y"ınd "L2$".":164514hR2$""1645:" and "R2$"."U4m(E1L2$"")(E2R2$"")ĺ"."^4oWT0|4rCCCC1:302:E1480,15004 SOLUTION MESSAGES 4CACACC:PAPACP:TCCCP:7:N$", that is the correct solution."H5" Error summary: ", you are incorrect.":WT1615:WT1:1650H3OT$"left":E2T$"right"3T" The "T$" side should read: ";:T$WL$:E2T$WR$3VT$"1X"T$"X"3XT$"-1X"T$"-X"3YT$" because ";:E21630:L1$;:16353^R1$;4cE21640:L2$""1645:" aw right side: ";:IP4:ML10:50}2(CN1(RT$WR$S1$WR$S2$WR$))(CN2(RT$WR$S1$WR$S2$WR$))E2:1610:ERROR2E$W$:(CN2)(DN1A1)(A1C0B0DAN)DN2:DONE2CN0:2J ERROR MESSAGES FOR THE SIMPLIFY ROUTINES *3K" "N$EQUATION 1WT01292k17:958:" Enter new left side : ";:868:IP4:ML10:50:RT$"1X"RT$"X"1RT$"-1X"RT$"-X"1(RT$WL$)(S1$WL$)(S2$WL$)E1:1610:DISPLAY ERROR MESSAGES1 RIGHT SIDE 1WT029:958:" Enter neGENERATE SIMPLIFICATION ERROR MESSAGESk0368:WL$"X":L1$"("A$(FA(A))"X)/"(A)" = 1X":L2$"1X = X"0WR$(DA):R1$"("(D)")/"(A)" = "(DA):R2$""0W$"X = "(DA):E$"("A$(FA(A))"X)/"(A)" = ("(D)")/"(A): 1 SIMPLIFY "::"TERM";::": ";:IP2:ML5:50:IN(RT$)/(INA)1290::" "N$", you are incorrect. You must divide by the coefficient of X.":(INA)ĺ"Not its opposite. "/CCCC1:WT0WT1:302:1275/"The correct divisor is "A".":WT0:302:1275'0 2000,2206,3000,1270,1470,2500,4000B.308:DISPLAY NEW EQUATIONi.(CN0AD2)(CN0DO0AD1)İ358u.4280:. DIVISION .WT0.CN2:292:358:SET FLAG, CLEAR SCREEN, AND REARRANGE A AND C-/7:" Enter term to divide both sides by. addition and subtraction before multiplication and division.": GOTO 925-zDN1G13CN0ĺ" To undo the coefficient of X, use rule 3 or rule 4."-302:292:795- BRANCH TO APPROPRIATE AXIOM SUBROUTINE THEN PRINT THE NEW EQUATION #.368:G1ng by the reciprocal of anything except 1 or -1 will produce fractions in the equation.":925,pDN1CN2ĺ" The only thing left to do is simplify.":925I-u IF GF = 0 AND DN = 0 AND (G1 = 3 OR G1 = 4) THEN PRINT " It is usually preferable to undo e."+mG14GF0DN0ĺ" Since the greatest common factor of all the terms is 1, dividing by anything except 1 or -1 will produce fractions in the equation.":925_,nG13GF0DN0ĺ" Since the greatest common factor of all the terms is 1, multiplyione. The next step is addition or subtraction.":925*f((A0C1)(C0A1))G14Ģ7:" Division is unnecessary at this point. The coefficient of X already equals one. The next step is addition or subtraction.":925+kN$", that's not the best choicothing to simplify.":925)\CN(DN0DN1)G15Ģ8:T$N$", you are incorrect.":40:10:3:"The next step is simplification.":9254*a((A0C1)(C0A1))G13Ģ7:" Multiplication is unnecessary at this point. The coefficient of X already equals ı:SIMPLIFYE(CCN0DN1(G13G14)ı:MULT OR DIV (NOT THROUGH!)s(HCN0DN0(G11G12)ı:ADD OR SUBTRACT(R292:CPCP1:CLEAR SCREEN AND INCREMENT PROCEDURAL ERROR COUNTER)WCN0G15Ģ8:T$N$", you are incorrect.":40:10:6:"There is n68,0:P$:G1(P$):G11G15810:24:1:958'4G14((GF)A1)DN0CN0((AAOCOCCOAO)(BBODODDOBO))G16::"DIVIDE THROUGH'9G13((GF)A1)DN0CN0((AAOCOCCOAO)(BBODODDOBO))G17::"MULTIPLY THROUGH (>CNG15