+JJJJ  / X5 lӠӠŠϠƠԠҠŠРŠˠҠĠӍ٠٠ϠԮ67988慥ɷ0L`   D(O):CC(O):K14:JZ(K)GDJ(DJ)CJ(CJ)DDJ:CCJ:4600_\:D(O)D:C(O)C::fK15:D(K)1C$(K)(C(K)):5000pC$(K)(C(K))"/"(D(K)):K14:W$(K)C$(KW1)::"R91215,4005,1000,4010,46,6+733:L87eX$"/"D$(1)"SUPPOSE THE PROBLEM IS 4/3"X$"3/5."n720|K521hL1K1:C(L)D(L)C(K)D(K)C(K)C(K)1:MK:K1M:L6:K6::K7İ4500:4100:Z(1)2:Z(2)3:Z(3)5:Z(4)7:OMK1:DM1:K12:C(1)A(1):C(2)A(2):D(1)Y(1):D(2)Y(2):4500:A(1)C(1):A(2)C(2):Y(1)D(1):Y(2)D(2):Q$(A(1))"/"(Y(1)):A$(A(2))"/"(Y(2)):X44004D$"SIMPLIFY "Q$X$A$:4005D$"SIMPLIFY ("Q$")"X$"("A$")"R15:A91:D$::580:E DENOMINATOR) AND MULTIPLY.":D$(4)"THIS CHANGES THE PROBLEM TO":D$(6)"SINCE 4*5=20 AND 3*3=9, THE ANSWER IS:" D$(5)" (4/3)/(3/5) = 4/3*5/3":D$(7)" 4/3*5/3 = 20/9."(13):D$(1)"SUPPOSE THE PROBLEM IS (4/3)/(3/5).":X$"/":M1:K15:4500:4100:47103=12 AND 3*5=15, THE ANSWER IS:" D$(6)" 4/3*3/5 = 12/15.":D$(7)"THIS CAN BE SIMPLIFIED TO 12/15 = 4/5."(13):X$"*":M1:K15:4500:4100:4710:3990p K15:C(K)A(K)Y(K1):D(K)Y(K)A(K1)::D$(2)"THE RULE FOR DIVISION IS TO INVERT":D$(3)"(TH" 4/3-3/5 = 20/15-9/15 = 11/15."(13):M1:K15:4500:4100:4710:3990 K15:C(K)A(K)A(K1):D(K)Y(K)Y(K1)::D$(2)"THE RULE FOR MULTIPLICATION IS TO":D$(4)"DENOMINATORS SEPARATELY.":D$(3)"SIMPLY MULTIPLY THE NUMERATORS AND THE":D$(5)"SINCE 4* X$"+":2010:D$(5)"THEN SIMPLY ADD THE NUMERATORS":D$(7)" 4/3+3/5 = 20/15+9/15 = 29/15."(13):M1:K15:4500:4100:4710:3990G K15:C(K)A(K)Y(K1)Y(K)A(K1):D(K)Y(K)Y(K1)::X$"-":2010:D$(5)"THEN SIMPLY SUBTRACT THE NUMERATORS":D$(7)дC(1)2000,2500,3000,3500Z K15:C(K)A(K)Y(K1)Y(K)A(K1):D(K)Y(K)Y(K1)::2030 D$(2)"FIRST, CONVERT BOTH FRACTIONS TO A":D$(3)"COMMON DENOMINATOR:":D$(6)"AND LEAVE THE DENOMINATOR UNCHANGED:":D$(4)" 4/3*5/5 = 20/15, 3/5*3/3 = 9/15":  ALG2Y INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.103,1:104,8:700:I90:L21:L16:530:C(1)6C9$"E":I90:W11:1030C9$"":I91:W10 P16:L22:L19:530:A(P)C(1):Y(P)C(2)::L21:L14:530:XC(1): SOLVE THE PREVIOUS PROBLEM. "::L89 D$(8)"ASSOCIATIVE MULT.: (AB)C=A(BC)":D$(9)"COMMUTATIVE MULT.: BC=CB"(13):720"+"L$(Y)"="R$(X)"+"R$(Y):W2(Y$) 18W22)Y$::" IDENTIFY THE CORRECT TWO PROPERTIES"::A95:R18:580:R91215,1035,1000,2005,46,6$ 715::"THE FORMULAS BELOW ILLUSTRATE THE BASIC":"RULES OF ARITHMETIC AND MAY HELP YOU ":"SEE HOW TO P(M)XY)(N(M)P(M))(XY)10130 M11022= K1M1v (N(K)P(K)N(M)P(M))(N(K)P(K))(N(M)P(M))K8 :K91013 J(A$(N(M))):W$(M)A$(N(M))","(B$,1,44J)A$(P(M)):& I(A$(X)):W$(I9)A$(X)","(B$,1,44I)A$(Y):Y$L$(X) A$:(A$)999011009 B$" ":K19:A$(K),L$(K),R$(K):D$(K)(A$(K)": ",24)L$(K)"="R$(K): M1W1 L22:L19:530:N(M)C(1):P(M)C(2) (N(M)P(M)3)(N(M)P(M)17)1013" (N(M)ȆP ALG01 INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.i103,1:104,8::700L22:L19:530:XC(1):YC(2)(XY3)(XY17)1003L21:L16:530:UC(1):U41008I94:W13:C9$"BLANK":1009I95:W14:C9$"E"   RS WILL NOT PRINT PROPERLY." 16379,0:20:"DO YOU WANT TO GET PRINTOUTS? (Y/N) ";:16368,0:ZY1:ZX37:R$"N":416:R$"Y"R$"N"3040:R$"Y"Ĺ16379,1 K(ZZ):ZY1:16382,7:6NS YOU SEEON THE SCREEN." :"TO GET A PRINTOUT, FIRST BE SURE YOUR PRINTER IS ATTACHED AND ON-LINE. THEN, SIMPLY TYPE -O TO GET A PRINT- OUT OF THE PROBLEM OR EXPLANATION THAT IS APPEARING ON THE SCREEN." "NOTE THAT GRAPHICS CHARACTEATED."K4ĺ:400:3000`:"PRESS TO RETURN TO BEGINNING OFPROGRAM ";:414:6 (12);::12:" PRINTER OPTION ": 5:"IF YOU HAVE A PRINTER ATTACHED TO YOUR APPLE, YOU CAN GET A PRINTOUT OF THE PROBLEMS OR PROBLEM EXPLANATIOOPY THE"" CONTENTS OF THE SCREEN TO A PRINTER. BE SURE YOUR PRINTER IS ATTACHED AND 'ON-LINE', OR ELSE THE PROGRAM WILL 'HANG' UNTIL"" THE PRINTER IS ACTIVBACK TO THE MAIN MENU, FROM ANYWHERE IN THE PROGRAM."X:" -O ";::" IF YOU ANSWERED 'Y' (YES) TO THE PRINTER OPTION QUESTION, THEN PRESSING -O WILL C EXPLANA-TION OF THE SOLUTION TO THE PROBLEM.";>z23::400h(12);::14::" SPECIAL KEYS "::"WHEN USING THE PROGRAM, TWO KEYS HAVE SPECIAL FUNCTIONS:":R:" ESCAPE KEY ";::" PRESSING THE ESCAPE KEY WILL TAKE YOU . IF YOU PRESS "p"INSTEAD, THE PROGRAM WILL CREATE A RANDOM SEED NUMBER OF ITS OWN IN ORDER TO GENERATE A PROBLEM.":/u"AFTER DOING THE PROBLEM, YOU WILL BE TOLD IF YOUR ANSWER IS CORRECT OR INCORRECT. YOU CAN ALSO SEE ANYPES IN ALL. AFTER YOU SELECT A PROBLEM TYPE, YOU WILL BE ASKED TO ENTER";k"A 'SEED' NUMBER, OR TO PRESS . IF YOU ENTER A SEED NUMBER, THAT NUMBER WILL BE USED TO GENERATE A RANDOM PROBLEM IN THE PROBLEM TYPE AREA YOU SELECTEDRATETHE PROBLEM FROM A 'SEED' NUMBER. YOU CAN ENTER THE SEED NUMBER, OR YOU CAN LET THE PROGRAM CREATE ITS OWN.":a2165Qf"WHEN YOU ENTER PRACTICE MODE, YOU WILL SEE A MENU DISPLAYING THE PROBLEM TYPES YOU CAN WORK ON. THERE ARE 36 PROBLEM TMS IN A PARTICULARTOPIC (PROBLEM TYPE) AREA.":W"WHEN YOU ENTER PRACTICE MODE, YOU SELECTA PROBLEM TYPE FROM THE 36 PROBLEM TYPE AREAS THAT ARE AVAILABLE. THE PROGRAM WILL THEN GENERATE A RANDOM PROBLEM IN"v\"THAT PROBLEM TYPE AREA. IT WILL GENEAS IN WHICH YOU NEED IMPROVEMENT."6H23:1::400M(12);:1::" HOW TO USE INTELLIGENT TUTOR (CONT'D) ":::13::" PRACTICE MODE "::/R"PRACTICE MODE GIVES YOU THE OPPORTUNITY TO SOLVE - AND SEE EXPLANATIONS FOR - A WIDE VARIETY OF PROBLELETED, YOUR RESULTS WILL BE SHOWN. YOU WILL SEE YOUR PERFORMANCE ON EACH PROBLEM, AND ANOVERALL PROFILE OF YOUR AREAS OF STRENGTH AND WEAKNESS. YOU WILL ALSO"$C"SEE WHICH PROBLEM TYPES WILL HELP YOU DEVELOP YOUR SKILLS IN THOSE ARE USE INTELLIGENT TUTOR (CONT'D) "::::15::" TEST MODE "::9"IN TEST MODE YOU CAN TAKE A TEST CONTAINING A VARIETY OF PROBLEMS. BEFORE TAKING THE TEST, YOU CHOOSE THE NUMBER OF PROBLEMS YOU WISH TO DO.":>"WHEN THE TEST IS COMPICES AVAILABLE TO YOU."%:"THE TWO CHOICES YOU WILL PROBABLY SELECT MOST OFTEN ARE 'TEST MODE' AND 'PRACTICE MODE'."*:"TEST MODE AND PRACTICE MODE ARE DESCRIBED ON THE FOLLOWING SCREENS."/23::400@4(12);:1::" HOW TOOBLEM SET MENU'. IT ASKS YOU TO SPECIFY THE PROBLEM SET AREAS IN ALGEBRA THAT YOU WISH TO WORK ON. YOU CAN CHOOSE PARTICULAR AREAS, OR YOU CAN";"WORK ON ALL PROBLEM SET AREAS." :"THE OPTIONS MENU DISPLAYS THE VARIOUS PROGRAM CHOACTERS WILL NOT PRINT PROPERLY." 16379,0:20:"DO YOU WANT TO GET PRINTOUTS? (Y/N) ";:16368,0:ZY1:ZX37:R$"N":402:R$"Y"R$"N"3040:R$"Y"Ĺ16379,1 K(ZZ):ZY1:16382,7:63ATIONS YOU SEEON THE SCREEN." :"TO GET A PRINTOUT, FIRST BE SURE YOUR PRINTER IS ATTACHED AND ON-LINE. THEN, SIMPLY TYPE -O TO GET A PRINT- OUT OF THE PROBLEM OR EXPLANATION THAT IS APPEARING ON THE SCREEN."! "NOTE THAT GRAPHICS CHARK4ĺ:400:3000!2245d:"PRESS TO RETURN TO BEGINNING OFPROGRAM ";:399:3 (12);::12:" PRINTER OPTION ": 5:"IF YOU HAVE A PRINTER ATTACHED TO YOUR APPLE, YOU CAN GET A PRINTOUT OF THE PROBLEMS OR PROBLEM EXPLANE"" CONTENTS OF THE SCREEN TO A PRINTER. BE SURE YOUR PRINTER IS ATTACHED AND 'ON-LINE', OR ELSE THE PROGRAM WILL 'HANG' UNTIL"" THE PRINTER IS ACTIVATED."O THE MAIN MENU, FROM ANYWHERE IN THE PROGRAM."R:" -O ";::" IF YOU ANSWERED 'Y' (YES) TO THE PRINTER OPTION QUESTION, THEN PRESSING -O WILL COPY THNA-TION OF THE SOLUTION TO THE PROBLEM.";8z23::400b(12);::14::" SPECIAL KEYS "::"WHEN USING THE PROGRAM, TWO KEYS HAVE SPECIAL FUNCTIONS:":L:" ESCAPE KEY ";::" PRESSING THE ESCAPE KEY WILL TAKE YOU BACK TYOU PRESS "p"INSTEAD, THE PROGRAM WILL CREATE A RANDOM SEED NUMBER OF ITS OWN IN ORDER TO GENERATE A PROBLEM.":)u"AFTER DOING THE PROBLEM, YOU WILL BE TOLD IF YOUR ANSWER IS CORRECT OR INCORRECT. YOU CAN ALSO SEE AN EXPLAN ALL. AFTER YOU SELECT A PROBLEM TYPE, YOU WILL BE ASKED TO ENTER";k"A 'SEED' NUMBER, OR TO PRESS . IF YOU ENTER A SEED NUMBER, THAT NUMBER WILL BE USED TO GENERATE A RANDOM PROBLEM IN THE PROBLEM TYPE AREA YOU SELECTED. IF E PROBLEM FROM A 'SEED' NUMBER. YOU CAN ENTER THE SEED NUMBER, OR YOU CAN LET THE PROGRAM CREATE ITS OWN.":za2165Kf"WHEN YOU ENTER PRACTICE MODE, YOU WILL SEE A MENU DISPLAYING THE PROBLEM TYPES YOU CAN WORK ON. THERE ARE 36 PROBLEM TYPES IA PARTICULARTOPIC (PROBLEM TYPE) AREA.":W"WHEN YOU ENTER PRACTICE MODE, YOU SELECTA PROBLEM TYPE FROM THE 36 PROBLEM TYPE AREAS THAT ARE AVAILABLE. THE PROGRAM WILL THEN GENERATE A RANDOM PROBLEM IN"p\"THAT PROBLEM TYPE AREA. IT WILL GENERATETH WHICH YOU NEED IMPROVEMENT."0H23:1::400M(12);:1::" HOW TO USE INTELLIGENT TUTOR (CONT'D) ":::13::" PRACTICE MODE "::)R"PRACTICE MODE GIVES YOU THE OPPORTUNITY TO SOLVE - AND SEE EXPLANATIONS FOR - A WIDE VARIETY OF PROBLEMS IN YOUR RESULTS WILL BE SHOWN. YOU WILL SEE YOUR PERFORMANCE ON EACH PROBLEM, AND ANOVERALL PROFILE OF YOUR AREAS OF STRENGTH AND WEAKNESS. YOU WILL ALSO"C"SEE WHICH PROBLEM TYPES WILL HELP YOU DEVELOP YOUR SKILLS IN THOSE AREAS IN NTELLIGENT TUTOR (CONT'D) "::::15::" TEST MODE "::9"IN TEST MODE YOU CAN TAKE A TEST CONTAINING A VARIETY OF PROBLEMS. BEFORE TAKING THE TEST, YOU CHOOSE THE NUMBER OF PROBLEMS YOU WISH TO DO.":>"WHEN THE TEST IS COMPLETED,VAILABLE TO YOU."{%:"THE TWO CHOICES YOU WILL PROBABLY SELECT MOST OFTEN ARE 'TEST MODE' AND 'PRACTICE MODE'."*:"TEST MODE AND PRACTICE MODE ARE DESCRIBED ON THE FOLLOWING SCREENS."/23::400:4(12);:1::" HOW TO USE ISET MENU'. IT ASKS YOU TO SPECIFY THE PROBLEM SET AREAS IN TRIGON-OMETRY THAT YOU WISH TO WORK ON. YOU CAN CHOOSE PARTICULAR AREAS, OR YOU CAN";"WORK ON ALL PROBLEM SET AREAS." :"THE OPTIONS MENU DISPLAYS THE VARIOUS PROGRAM CHOICES ATHIS SCREEN WILL APPEAR AFTER THE TITLE SCREEN. TYPE 'Y' (FOR YES) IF YOU WOULDLIKE TO BE ABLE TO COPY TO A PRINTER THECONTENTS OF ANY OF THE PROGRAM SCREENS." :14::" OPTIONS MENU "::2080:"THE NEXT SCREEN YOU WILL SEE IS THE 'PROBLEM GUIDE FOR LOADING THE PROGRAM.": :" TITLE SCREEN "::"AT THE BOTTOM OF THE TITLE SCREEN IS A MESSAGE TELLING YOU TO TURN THE DISKETTEOVER AND PRESS . YOU MUST DO THIS IN ORDER TO CONTINUE." :10::" PRINTER OPTION SCREEN ":::"T TUTOR / TRIGONOMETRY PROVIDECOMPREHENSIVE COVERAGE OF ALL THJE MAJORTOPICS GENERALLY TAUGHT IN TRIGONOMETRY COURSES."; 23:1::400 (12);:1::" HOW TO USE INTELLIGENT TUTOR (CONT'D) ":::2060" :"FOLLOW THE INSTRUCTIONS IN YOUR USER'S WIDE RANGE OF STIMULATING PROBLEMS. PROBLEM EXPLANATIONS ARE ALSO PROVIDED" "TO HELP YOU UNDERSTAND THE CONCEPTS INVOLVED, AND TO EXPLAIN THE METHODS FORSOLVING THE PROBLEMS.":2040x :"THE 36 PROBLEM TYPE AREAS COVERED BY INTELLIGENHELP YOU IMPROVE YOUR SKILLS AND UNDERSTANDING IN THE SUBJECT OF TRIGONOMETRY, AND DEVELOP YOUR ABILITY TO SOLVE PROBLEMS."R :"THE EMPHASIS OF THE PROGRAM IS ON PROBLEM-SOLVING. INTELLIGENT TUTOR GIVES YOU THE OPPORTUNITY TO SOLVE A   DESCQ INTELLIGENT TUTOR/ALGEBRA ONE (C) 1983 INTELLIGENT SOFTWAREc103,1:104,8(12);:5::" HOW TO USE INTELLIGENT TUTOR "::::8::" OBJECTIVES OF PROGRAM ":: "INTELLIGENT TUTOR / TRIGONOMETRY HAS BEEN DESIGNED TO          A20:A2$"":A30:A3$"":1)oD$(7)"NOTE THAT AX MAY BE A DISTANCE THAT CAN":D$(8)"PLACE THE MAN PAST HIS HOME."(13):731:L88:721$ BETWEEN THE MAN AND HIS HOME"D$(4)(13)" A = THE MULTIPLE OF X THAT THE MAN":D$(5)" MOVED FROM THE ORIGINAL OR CURRENT POSITION"(13):D$(6)" B = THE FINAL DISTANCE BETWEEN THE MAN AND HIS HOME."(13)(13"WHAT IS THE DISTANCE X ?"] A91:K16:A$(K)::R115:580:R91215,1240,1000,4000,46,6)D$(1)(13)" THE PROBLEM TRANSLATES INTO THE":D$(2)"ALGEBRAIC EQUATION "(124)"C-AX"(124)"=B, WHERE:"(13):D$(3)" C = ORIGINAL OR CURRENT DISTANCE MOVES A DISTANCE OF "(A3)" TIMES X":1210n A$(3)(13)"IF HE HAD GONE A DISTANCE OF "(A3)" TIMES X" A$(4)"MILES FROM HIS "R$" POSITION TOWARD":Z4$" MILES":B1Z4$" MILE" A$(5)"HOME, HE WOULD BE "(B)Z4$" FROM HOME.":A$(6)(13):C(1)1R$"CURRENT":A3A31:C(2)1A3A32V A9$"TOWARD":C(2)1A9$"AWAY FROM" A$(1)"A MAN BEGINS "(C)" MILES FROM HIS HOME.":A$(2)(13)"HE THEN MOVES A DISTANCE OF X MILES "A9$" HOME.":R$"ORIGINAL"1200- A$(3)(13)"IF HE NOWK(C2K)A1K(A1K)C2C2K:A1A1K:1120 j:C1(J)C1:C2(J)C2:Z1(J)A:Z2(J)A1::K14:Z2$"/"(Z1(KW1)):Z1(KW1)1Z2$"" ~Z3$"/"(Z2(KW1)):Z2(KW1)1Z3$""- W$(K)(C1(KW1))Z2$" OR "(C2(KW1))Z3$::L22:L12:500:R$"ORIGINAL"C2(1)CB:I1CC:I2CCBB:L28:L119 $530:K14:C1(K1)C(K)8:C2(K1)C(K4)8::K25:C1(K)C2(K)I1C1(K)C2(K)I2K8 B:K91060 LA2A:J15:AA2:A1A2:C1C1(J):C2C2(J):K25 VC1K(C1K)AK(AK)C1C1K:AAK:1110, `C2p  ALG36Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.103,1:104,8:700:L21:L16:530:C(1)6C9$"E":I95:W11:1040C9$"":I91:W10& L21:L15:530:AC(1)1:A3A:L22:L19:530:BC(1):CC(2)9:C1(1)BC: XD$(7)C9$R$T$(4K)A1$" = "(I1)T$(6K)(B(3))" = "(I2)"."(13):L87:720" "C9$T$(5K)A1$R$",":D$(4)"WHERE K IS CONSTANT. FROM THE TWO GIVEN":I1B(2)B(1):K0I1B(2)B(1) D$(5)"VALUES, WE GET K = "(B(2))T$(7K)(B(1))" = "(I1)".":D$(6)"THEREFORE, WHEN "A1$" = "(B(3))", THEN":I2I1B(3):K1I2I1B(3)T$(2),1):T$(4)"":T$(5)"/":D$(1)"LET "A1$"="T$(1)", AND LET "C9$"="T$(2)".":T$(6)"*":T$(7)"/":R$" ":K0:A9$"INVERSE"R$"N ":K1h D$(2)"SINCE WE HAVE A"R$A9$" RELATION, OUR":R$" = K":D$(3)"EQUATION WILL BE "C9$R$T$(4K)A1$", OR)oD$(7)"NOTE THAT AX MAY BE A DISTANCE THAT CAN":D$(8)"PLACE THE MAN PAST HIS HOME."(13):731:L88:721$ BETWEEN THE MAN AND HIS HOME"D$(4)(13)" A = THE MULTIPLE OF X THAT THE MAN":D$(5)" MOVED FROM THE ORIGINAL OR CURRENT POSITION"(13):D$(6)" B = THE FINAL DISTANCE BETWEEN THE MAN AND HIS HOME."(13)(13"WHAT IS THE DISTANCE X ?"] A91:K16:A$(K)::R115:580:R91215,1240,1000,4000,46,6)D$(1)(13)" THE PROBLEM TRANSLATES INTO THE":D$(2)"ALGEBRAIC EQUATION "(124)"C-AX"(124)"=B, WHERE:"(13):D$(3)" C = ORIGINAL OR CURRENT DISTANCE MOVES A DISTANCE OF "(A3)" TIMES X":1210n A$(3)(13)"IF HE HAD GONE A DISTANCE OF "(A3)" TIMES X" A$(4)"MILES FROM HIS "R$" POSITION TOWARD":Z4$" MILES":B1Z4$" MILE" A$(5)"HOME, HE WOULD BE "(B)Z4$" FROM HOME.":A$(6)(13):C(1)1R$"CURRENT":A3A31:C(2)1A3A32V A9$"TOWARD":C(2)1A9$"AWAY FROM" A$(1)"A MAN BEGINS "(C)" MILES FROM HIS HOME.":A$(2)(13)"HE THEN MOVES A DISTANCE OF X MILES "A9$" HOME.":R$"ORIGINAL"1200- A$(3)(13)"IF HE NOWK(C2K)A1K(A1K)C2C2K:A1A1K:1120 j:C1(J)C1:C2(J)C2:Z1(J)A:Z2(J)A1::K14:Z2$"/"(Z1(KW1)):Z1(KW1)1Z2$"" ~Z3$"/"(Z2(KW1)):Z2(KW1)1Z3$""- W$(K)(C1(KW1))Z2$" OR "(C2(KW1))Z3$::L22:L12:500:R$"ORIGINAL"C2(1)CB:I1CC:I2CCBB:L28:L119 $530:K14:C1(K1)C(K)8:C2(K1)C(K4)8::K25:C1(K)C2(K)I1C1(K)C2(K)I2K8 B:K91060 LA2A:J15:AA2:A1A2:C1C1(J):C2C2(J):K25 VC1K(C1K)AK(AK)C1C1K:AAK:1110, `C2p  ALG36Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.103,1:104,8:700:L21:L16:530:C(1)6C9$"E":I95:W11:1040C9$"":I91:W10& L21:L15:530:AC(1)1:A3A:L22:L19:530:BC(1):CC(2)9:C1(1)BC:     XD$(7)C9$R$T$(4K)A1$" = "(I1)T$(6K)(B(3))" = "(I2)"."(13):L87:720" "C9$T$(5K)A1$R$",":D$(4)"WHERE K IS CONSTANT. FROM THE TWO GIVEN":I1B(2)B(1):K0I1B(2)B(1) D$(5)"VALUES, WE GET K = "(B(2))T$(7K)(B(1))" = "(I1)".":D$(6)"THEREFORE, WHEN "A1$" = "(B(3))", THEN":I2I1B(3):K1I2I1B(3)T$(2),1):T$(4)"":T$(5)"/":D$(1)"LET "A1$"="T$(1)", AND LET "C9$"="T$(2)".":T$(6)"*":T$(7)"/":R$" ":K0:A9$"INVERSE"R$"N ":K1h D$(2)"SINCE WE HAVE A"R$A9$" RELATION, OUR":R$" = K":D$(3)"EQUATION WILL BE "C9$R$T$(4K)A1$", OR"WHEN "W$(4C(1))", "W$(5C(1))".":A9$"INVERSE"I92 W$(5)"WHAT IS "T$(2)" WHEN "T$(1)" IS "(B(3))"?":R113:A90:C9$"":L21:L16:500:C(1)0C9$"E" K15:W$(K):::580:R91215,1026,1000,1030,46,6 715:A1$(T$(1),1):C9$($(2)"THEN "T$(1)" VARIES "A9$"LY":W$(3)"WITH RESPECT TO "T$(2)"."S 1017 W$(2)"THEN "T$(1)" IS "A9$"LY":W$(3)"PROPORTIONAL TO "T$(2)"." C(0)0C9$T$(1):T$(1)T$(2):T$(2)C9$: K12:W$(K3)T$(K)" IS "(B(K))::I91:W$(4)B(3)B(2):D91.5:A(4)(B(3)B(2))2B(1):L23:L13:530:K13 T$(C(K))::W$(1)"WHEN "T$(3)" IS FIXED,":A9$"DIRECT":C(3)3A9$"INVERSE" W$(1)"WHEN "T$(3)" IS FIXED,":A9$"DIRECT":C(3)3A9$"INVERSE" L23:L12:500:C(3)01016I WYO ALG35 INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.h103,1:104,8:700:A$:(A$)999301003> L21:L15:500:K03C(1):C9$::L23:L16:530:K13:B(K)C(K)1::A(1)B(3)B(2)B(1):A(2)B(1)B(2)B(3):A(3)B(1):"SUPPOSE THE DOMAIN IS:":R$:R$I:"THEN THE RANGE IS:":R$:R$YK6İ4900:23:1:"PRESS TO CONTINUE ";:414:722$"PRESS TO SEE MORE ";:414:)MORE ";:414: ES THAT X CAN HAVE IS CALLED THE DOMAIN."h:"THE RESULTING SET OF Y VALUES IS CALLED THE RANGE."A$:(A$)999204039R$"--------":R$R$R$R$R$:K16R$:R$"X/3"R$(124)"X"(124)"/3"16:"CONSIDER THE FUNCTION: Y = "R$%E RANGE IS:"1<A91:R115:K15:A$(K):K:580SFR91215,3900,1000,4000,46,6\731:"TO SOLVE THE PREVIOUS PROBLEM, FIND THE""FUNCTION WHICH, WHEN YOU PLUG IN EACH""X VALUE, PRODUCES THE CORRECT Y VALUE.",:"THE SET OF VALU17:C(1)4KB43830/F$",":E$"("F$""KL2(D1$(K)):L22L22E$E$F$(" "D1$(K),L2):V$V$F$(" "(K4),L2):A$(2)V$").":A$(4)E$")."A$(5)"WHAT IS THE FUNCTION?"  A$(1)"THE DOMAIN OF A FUNCTION IS:":A$(3)"TH1(K)B1(K)' C1$"":B1(K)0C1$" "J C2$"/"(G(K)):G(K)1C2$""e D1$(K)(B1(K))C2$:K& K14:C2$(B):B0C2$"+"(B)0 C3$"(":C4$")":B0C2$"":C3$"":C4$"": W$(K)"Y="(H(KW1))"/"C3$"X"C2$C4$:KE$"(":V$"(":KY(KW1))"X":Y(KW1)1C3$"X"E W$(K)"Y="C3$C2$Z4$:K:3800p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o VD1$(K)(D(K))C2$:D(K)0D1$(K)" 0"v [K `K14:C2$"/"(H(KW1)):H(KW1)1C2$"" bB$(E(KW1)) dE(KW1)1B$"-" hE(KW1)1B$"" jW$(K)"Y="B$(124)"X:B1(K)50:K:L21:L14:5309 C(1)1060,2000,2500,3000G $B01040] &J15:FB:K24 (H(J)K(H(J)K)FK(FK)H(J)H(J)K:FFK:1064 *K:E(J)F:J ,K33:ZH(1):YE(1)(K):J24 .YJ(YJ)ZJ(ZJ)YYJ:ZZJ:1070 8  ALG34Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.}103,1:104,8::750:700:I90L21:L16:530:C(1)6C9$"E":I95:W11:1040C9$"":I91:W10L26:L19:530:K15:H(K)C(K):K:BC(6)5 K17         C$(C) 7\B1$"+":B$((B),1):B0B1$"-"MfB0B$"":B1$""YpC$(C)_zN14:AA2:C1C1(J):K27JC1K(C1K)AK(AK)C1C1K:AAK:4540eK:Z1(J)A:C1(J)C1:JK15:Z2$"/"(Z1(K)):Z1(K)1Z2$""V$(K)(C1(K))Z2$:KK14:W$(K)V$(KW1):K:B0B$(B)B0B$"+"(B) B0B$"""NO SOLUTION":Z2$"/"(Z1(4)):Z1(4)1Z2$""SZ3$"/"(Z2(4)):Z2(4)1Z3$""|V$(5)(C1(4))Z2$", "(C2(4))Z3$K14:W$(K)V$(KW1):K:L24:L120:530:K25:C1(K)C(K)10:K:K25C1(K)C1(1)K8K:K94500A2A:J1C1K:AAK:4170GTC2K(C2K)A1K(A1K)C2C2K:A1A1K:4180t^K:C1(J)C1:C2(J)C2:Z1(J)A:Z2(J)A1:JhK13jZ2$"/"(Z1(K)):Z1(K)1Z2$""lZ3$"/"(Z2(K)):Z2(K)1Z3$""|V$(K)(C1(K))Z2$", "(C2(K))Z3$:K.V$(4)."(13)L89:721TL26:L120:530:K13:C1(K1)C(K)7:C2(K1)C(K3)7:K_K24"C1(K)C2(K)C1(1)C2(1)C1(K)C2(K)C1(1)C2(2)K8,K:K941006A2A:J14:AA2:A1A2@C1C1(J):C2C2(J):K27JC1K(C1K)AK(AK)CE: SOLVE "(124)"3-4X"(124)"=7."(13)}D$(6)"REMOVING THE ABSOLUTE VALUE SYMBOL, WE GET THESE TWO EQUATIONS:"D$(7)" 3-4X = 7 AND 3-4X = -7."D$(8)"THESE CAN BE SOLVED TO OBTAIN:"D$(9)" X = -1 AND X = 5/2(124)"AX+B"(124)"=C, THIS WILL BECOME EITHER AX+B=C OR AX+B=-C. THESE TWO" D$(4)R$" EQUATIONS":R$"CAN THEN BE SOLVED SEPARATELY TO FIND" C9$R$" THE TWO POSSIBLE VALUES FOR X."(13):R$"----------"-D$(5)C9$R$R$R$R$"EXAMPL"(124)" CAN NEVER BE"g D$(1)R$" NEGATIVE).":R$"IN ABSOLUTE VALUE PROBLEMS, WE MUST FIRST " D$(2)R$"REMOVE THE ABSOLUTE VALUE SYMBOL":R$"BY THE DEFINITION OF " D$(3)R$"ABSOLUTE VALUE GIVEN ABOVE. IF THE PROBLEM IS"T R$" ""(124)"="C$:3990U "WE ARE GIVEN THE EQUATION:"::" "Z1$::"SOLVE FOR X."i A91:R110:580 R91215,3990,1000,4010,46,6 715:732: R$"IN GENERAL, "(124)"X"(124)"=X IF X>=0 AND "(124)"X"(124)"=-X IF X<0 ("(124)"X4700:Z1$(124)B$B1$A$(124)"="C$:3990e C1(1)CBA:C2(1)1CBA:C1(1)C2(1)İ4500:2040o 4100 A$(A3):A31A$"" L21:L12:530:C(1)2110,2500 >4600:Z1$A$(124)"X"B$(124)"="C$:3990 4700:Z1$A$(124)B$B1$"X25* 530:CC(1)5:C0I94:W10:C9$""J L21:L12:530:C(1)22000 C1(1)CB:C2(1)1(CB):C1(1)C2(1)İ4500:1049 4100 A$(A3)"X":A31A$"X" L21:L12:530:C(1)1060,1500 $4600:Z1$(124)A$B$(124)"="C$:3990- `  ALG33Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.v103,1:104,8:700:I90L21:L16:530:C(1)6C9$"E":I95:W11:1020C9$"":I91:W10 L21:L19:530:AC(1):A3A:L21:L115:530:BC(1)10:L21:L1      C(K1):K011087NA1$"-":K0A1$"+":R$""A1$""ZO(K1K12)(K1)A1$A1$(K)P(K1K12)(K1)A1$A1$((K),2)RR$R$A1$T$(K1)T:~1100:R$""R$"0"OES THE INEQUALITY.":L87P"D$(L81)"WHEN WE PERFORM THIS, WE FIND THAT":1064$L84:R$"NEVER":D(2)0(D(2)0I71)R$"ALWAYS"&D$(3)"SINCE THIS IS "R$" TRUE,"(D$(2)D$(2)"."*D$(L8)"THE ANSWER IS "W$(1)"."(13):720LK112:KI6)T$(4I6):D(1)01060H I61D$(2)D$(2)", OR"T$(3)T$(5)T$(4)r D(1)1L83:D$(2)D$(2)", SO":1066 D$(3)"SINCE THE COEFFICIENT OF X IS NOW "(D(1))"," D$(4)"WE MULTIPLY BY 1/"(D(1))"." L86:D(1)0D$(5)"THIS ALSO REVERS "WHAT IS THE SOLUTION SET OF "::A9$P 580:R91215,1038,1000,1042,46,6 715:R$"":C(1)D(1):C(2)0:1150:T$(3)" "R$" ":R$"":C(2)D(2):C(1)0 1150:T$(4)R$:D$(1)"FIRST, REARRANGE THE INEQUALITY TO GET:" D$(2)" "T$(3I6)T$(5 K12:I1A(K):I19991032: I25:D(2K1)0I26 W$(2K1)"X "T$(I2)" "(I1):W$(2K)"X "T$(11I2)" "(I1):1036 I20:D(2K)0(D(2K)0I70)I21 W$(2KI21)"ALL REAL X":W$(2KI2)"NO REAL X" :A94:C9$"":I91:R18)9$R$")"R T$(1)"X":C(1)B(4):C(2)B(5):1150:T$(3)R$:R$"":C(1)I1B(4)D(1) C(2)I2B(5)D(2):1150:T$(4)R$:L22:L12:500:I6C(1):I7C(2) T$(5)">":T$(6)"<":I71T$(5)">=":T$(6)"<=" A9$" "T$(3I6)" "T$(5I6)" "T$(4I6)" ?"(1)A(2)1004E L23:L15:500:K13:B(K)C(K)2::L22:L111:500{ B(4)C(1)5:B(5)C(2)5:I1B(1)B(2):I2B(1)B(3) R$"":T$(2)"":I10I201020 T$(1)"":C(1)B(1):C(2)0:1100:C9$R$"(":R$"":T$(1)"X":C(1)B(2) C(2)B(3):1100:R$C  ALG32Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.q103,1:104,8:700L24:L123:500:K14:D(K)C(K)9:C(K)18D(K)0:K12:I2999:I1D(2K1):I10I2D(2K)I1 A(K)(I210000.5)10000::A      "X":R$"VERTICAL"I8"SINCE WE HAVE A "R$::"LINE, THE EQUATION WILL"::"BE OF THE FORM "C9$"=C,"::"WHERE C IS A CONSTANT."<:"THEREFORE, WE CAN SEE FROM THE GRAPH"=:"THAT WE MUST HAVE "W$(1)".">::D$(1)"":L81:720 ")-("(B(5))"))/(("(B(2))")-("(B(1))F0:R$")) = "(A(1))"."t1:"SUBSTITUTE THIS INTO Y-Y1=M(X-X1) TO"2:"GET Y-("(B(5))")="(A(1))"*(X-("(B(1))")), AND"4:"REARRANGE TO GET "W$(1)".":10866C9$"Y":R$"HORIZONTAL":A(1)99C9$60$$R91215,1052,1000,1061,46,65%715::1051T&4:1:A(1)99A(1)01078v'"TWO POINTS THAT ARE ON THE"(:"LINE ARE ("(B(1))","(B(5))")"*:"AND ("(B(2))","(B(6))").",:"THEREFORE, THE SLOPE IS"+.R$(13)"M=(("(B(6))OWN AT THE"27)"-4 -2 2 4"34)"+-2":"RIGHT?":34)"+-4" L80:C434.6:R40.8:C534.6:R513:906:C427:R46.5:C540.2:R56.5:906:R46.49B(5)1.35:R56.49B(6)1.35:C434.751.5B(1):C534.751.5B(2):906 R931062 "580#R93R90İ7* W$(K)R$::A94:C9$"":I91:R112:R90 R93ĺ34)"+4"::34)"+2"::28)"+ + + + + "27)"-4 -2 2 4"34)"+-2"::34)"+-4":1053= 34)"+4":"WHICH OF THE FOLLOWING":34)"+2":"EQUATIONS BEST REPRESENTS":28)"+ + + + +THE LINE SHK)(A(K)1000.5)1000::K14S I1A(K):I2A(K4):I199R$"X = "(I2):1048} R$"Y =":C9$" ":I10C9$"-":I1I1 R$R$C9$:C9$"":I10C9$"+":I11R$R$(I1) I10R$R$"X" I20C9$"-":I2I2 I20I10R$R$C9$(I2)3I2I1:I4B(K4)I3B(K):I50:I30I51T A(K)I3:A(K4)I4:I51I399I3:1028~ I3I3:C(K)2I31I3:C(K)0I3I3 A(K1)I3:A(K5)I4::K124 K1K11:A(K)A(K1)A(K4)A(K14)K8 :K9A(K14)A(K14)1:1030 :K18:A(4)I118 :K114:KA(K1)1:K4I34:I42K4:1018V K8I3122K:I44:1018 I34:I4202K:K12I32K28:I44 B(K1)I3:B(K14)I4::L23:L13:500:K11:K132 I1B(K1)B(K):I2B(K5)B(K4):I10I399:I4B(K):I51:1024) I  ALG31Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.v103,1:104,8:750:700I1132:L116L22:530:K1:I2C(2)C(1):I20K2:I2I2A(I11)C(K):A(I1)C(3K):I25I2111006 A(1)A(3)A(2)A(       :1550 R$R$"-"3D$(I64)R$(R((Q3))): R$R$(R((R1)))7R$R$"X":R20R$R$"+":1513ER$R$"-"f(R2)1R$R$(R((R2)))W$(I6)R$"Y = "(R(R3)):I6I61:Q1R1R2:Q3R3R2R$"Y = ":Q10R$"Y = -"(Q1)1R$R$(R((Q1)))R$R$"X":Q30R$R$"+"HEREFORE, THE CORRECT ANSWER IS ("C9$")."(13):L810:D$(7)D$(7)" ":721D$(10)"THEREFORE, THE CORRECT ANSWER IS (E) NONE OF THE ABOVE."(13):L810:D$(7)D$(7)" ":721R$" ":R10R$"-"(R1)1"(X2)","(Y2)")."rD$(8)"TO FIND THE INTERSECTING LINE TO L, SUBSTITUTE THE X VALUE AND SOLVE FOR Y."D$(9)"WHEN THE Y VALUES ARE THE SAME, THE LINES INTERSECT.":C9$"E"C9$"NONE OF THE ABOVE"(C9$,4)"NONE"1485dD$(10)"TEFORE, THE CORRECT ANSWER IS ("C9$")."(13):D$(7)D$(7)"":721D$(L8)R$"THEREFORE, THE CORRECT ANSWER IS "C9$"."(13):D$(7)D$(7)"":721D$(7)"A LINE WHICH INTERSECTS L WILL HAVE A DIFFERENT SLOPE, BUT BOTH WILL HAVE THE POINT (L89R$"":V2V4D$(9)"SINCE THE LINE MUST GO THROUGH ("(X2)","(Y2)"), THE VALUES X="(X2)", Y="(Y2):R$"MUST SATISFY THE EQUATION. ":L810C9$"E"C9$"(E) NONE OF THE ABOVE"(C9$,1)"("1460BD$(L8)R$"THER ":D$(8)"SLOPE = M = "(R(C3C4))". ":L89:1450D$(7)"A LINE THAT IS PERPENDICULAR TO L MUST HAVE A SLOPE OF: ":D$(8)"SLOPE = -1/M = -1/"(R(C3C4))" = "(R(C4C3))" ":"PARALLEL":V2R$"PERPENDICULAR"I236:D$(I2)"ANSWER ("(62I2)") BECOMES: "D$(I2)::D$(6)D$(6)" ":V51470V1410,1410,1420,1420ND$(7)"A LINE THAT IS PARALLEL TO L MUST HAVE A SLOPE OF: HE POINT ";D$(4)dR112:580AiR91215,1300,1000,1400,46,6xD$(3)D$(I15):D$(4)D$(I25):D$(5)D$(I35):D$(6)D$(I45):D$(1)"REWRITE THE PROBLEM AND ANSWERS IN STANDARD FORM: Y=MX+B"(13):D$(2)"LINE L BECOMES: "D$(10)(13):715#zR$"(X2)","(Y2)")?"6 2V1340,1345,1350,1355,1360K <D$(1);"?":1380 A"IS PARALLEL TO L AND PASSES THROUGH THE POINT ";D$(4):1380 FD$(2);"?":1380 K"IS PERPENDICULAR TO L AND PASSES THROUGHTHE POINT ";D$(4):1380P"INTERSECTS L IN TC4:R3R1X2R2Y2:I61:1500B 700:I65:R1C3:R2C4:R3C5:1500l "YOU ARE GIVEN THE LINE L: ";W$(5): ("WHICH OF THE FOLLOWING LINES " -D$(1)"IS PARALLEL TO L":D$(2)"IS PERPENDICULAR TO L" /D$(3)" AND PASSES THROUGH THE POINT ":D$(4)"(`R1R2:R2C1C6:R3C2C5:1500. aV41125G bR1R1:X1X11:1138g eR4R1X1R2Y1:R4R31138s hX1X12 rR3R1X1R2Y1:1500:V21140 sX2X1 tI9V:V51300 vC9$"E"1148 yX2X3:1150 |X2X11:1300 ~I91:R1C1C6:R2C2C5C3X1C4Y1:X3X1:Y2Y1/ LC6C3:E201105U NC6C32:C9$"E":C61C601105a OC6C64 QR1C1C6:R2C1C4:R3C2C5:I61:1500 RV21108 SR1R1:X1X11:1118 TR4R1X4R2Y1:R4R31118 UX1X11 ^R3R1X4R2Y1:1500:X2X4 (2)1 C131035# J101035/ C11C1> J201038J C21C2x L22:L15:530:C3C(1):C4C(2):J101040 C3C3 J201042 C4C4 L23:L13:530:X1C(1):Y1C(2):X4X1C(3):J101050 X1X1 J201060 Y1Y1 $4  ALG30Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.R(Z)(Z)(((((Z)5E4)1000))1000)103,1:104,8555:L19:L21:500:E2C(1) A91:M90:D91:L21:L15:530:VC(1):L22:L13:530:C1C(1)1:C2C         ;:D$(2);" ARE ";:2999522:1:D$(1)"":L80:720L.5:Y5(Y1Y2).5:3160D: D$(1)"C":D$(2)"OF BC":X5X2:Y5Y1:3150lD D$(1)"A":D$(2)"OF AB":X5X1:Y5Y2N "WE DEDUCE THAT THE COORDINATES OF ";D$(1);" ARE ";:2999:X5(X2X5).5:Y5(Y2Y5).5X "THEREFORE, THE COORDINATES OF THE MIDPOINT "2:Y5Y2:2999 12:"THE COORDINATES OF THE MIDPOINT OF A LINE SEGMENT CONNECTING POINTS (X1,Y1) AND (X2,Y2) ARE FOUND BY THE FORMULAS: ":" XM = (X1+X2)/2 AND YM = (Y1+Y2)/2. "& V123120,3130,31400 D$(1)"E":D$(2)"E":X5(X1X2) OF DC IS ";X2X1;","O "THE COORDINATES OF C ARE ";:X5X2:Y5Y1:2999:4999] V23080m 2998:3100 "SINCE THE LENGTH OF DA IS ";Y3;" AND THE":"LENGTH OF DC IS ";Y4;", WE DEDUCE THAT THE"  "COORDINATES OF B ARE ";:X2X1Y4:Y2Y1Y3:X5X 3:1:"THE GIVEN COORDINATES OF D ARE ";:X5X1:Y5Y1:2999:V13010,3030,3060,3060,3060n V1İ2998:3015 "SINCE THE LENGTH OF DA IS ";Y2Y1;"," "THE COORDINATES OF A ARE ";:X5X1:Y5Y2:2999:4999 V1İ2998:3035 "SINCE THE LENGTHA.":D$(2)"C.":D$(3)"E.":D$(4)"THE MIDPOINT OF BC.":D$(5)"THE MIDPOINT OF AB." \"FIND THE COORDINATES OF ";D$(V1):R117:1115 D$(1)"("(X5)","(Y5)")": "THE GIVEN COORDINATES OF B ARE ";:X5X2:Y5Y2 "(";(X5);",";(Y5);").":YX5X1:Y5Y1:2500:R110:C11:L88:T$(8)"":927g >"THE COORDINATES OF":"D ARE ";D$(1);".":V22120} CX5X2:Y5Y2:2500 E"THE COORDINATES OF B ARE ";D$(1);".":2130 H"THE LENGTH OF DA IS ";Y3;",":"AND THE LENGTH OF DC IS ";Y4;"."Q RD$(1)"E20, X5X1E2:Y5Y2E2:2500:W$(1)D$(1)T X5X2E2:Y5Y1E2:2500:W$(2)D$(1) X5.5(X1X2)E2:Y5.5(Y1Y2)E2:2500:W$(3)D$(1) X5X2E2:2500:W$(4)D$(1):I9V1:V152090 %X5.5(X1X2)E2:Y5Y2E2:2500:W$(1)D$(1):I91 *1095/ 4130,46,6 j715:1101A A91:M90:555:L21:L15:530:V1C(1)x L14:L24:500:X1C(1):Y1C(2):X2C(3)5:Y2C(4)5 L21:L12:530:VC(1):V12020 Y3Y2:Y2Y1Y2:Y4X2:X2X1X2 L18:L21:500:E2C(1):E202040 E21:C9$"E":2050 2)1103 NC8382 OL81:R111:C128:R219:C2C8R PL81:R17:C123:R211:C2C8 Q870:L80:R4R1:R5R2:C4C1:C5C2:907:C4C2:C5C1:907:L85:R1(R1R2)2:C1(C1C2)2:926:R933000 TR115:2100 [580:R93R90İ760 ^R91215,1095,1000,16  ALG29Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.q103,1:104,8:750{2000G700:"YOU ARE GIVEN A RECTANGLE ABCD WITH DIAGONALS AC AND BD."I"THE DIAGONALS INTERSECT AT POINT E." MC834:(V1     VERAGE YEARLY PROFIT IS (15+25+35+45+55+65)/6 = 40 MILLION.":D$(4)""eL84:17:1:721Rx733:X117:X(1)1:X(2)2:X(3)3:X(4)4:X(5)5:X(6)6:1362D$(1)"IN THE ABOVE GRAPH 5 OF THE 6 YEARS SHOWA PROFIT OF MORE THAN 15 MILLION."D$(2)"THE RATIO OF THE WORST YEAR'S PROFIT TO THE BEST YEAR'S PROFIT IS 15/65=.23077."PD$(3)"THE AX1:R1R2X(K).5:870:KS ZL88:K16:R1X11:C126K:T$(8)(1977K):926:K \ZZ$"?? 0 10 . . 50 . . 90100":K19:R1(X11)K:C11:T$(8)(ZZ$,K3,3):926:K _R931435 dR118:580:R93R90İ760 jR91215,1300,1000,1400,46,6=TIO OF THE PROFIT IN THE "N H" WORST YEAR TO THAT IN THE BEST YEAR?":1360u K"WHICH IS A GOOD ESTIMATE OF THE" M" AVERAGE PROFIT FOR THE YEARS SHOWN?":D930 PL80:X117 RK111:R10:R2X11K:C14:C240:870:K UK16:C10:C26K:R2YS A COMPANY'S PROFITS"6 "IN MILLIONS OF DOLLARS."Q 2V1340,1345,1350,1355 <"HOW MANY YEARS SHOWED A PROFIT OF MORE THAN ";X4;" MILLION?":1360 A"HOW MANY YEARS SHOWED A PROFIT OF LESS THAN ";X4;" MILLION?":1360 F"WHAT IS THE RAX(1)5:Y2Y1:Y3Y1:K26:Y410X(K)5:Y3Y3Y4? Y1Y41260O Y1Y4:1270_ Y2Y41270i Y2Y4z K:V41280 A(1)Y2Y1:A(2)1A(1):A(3)Y110:A(4)Y210:C9$"E"1300 A(1)Y36:A(2)Y1:A(3)Y2:A(4)2A(1) 700:"THE TABLE DISPLA BV41200 GC9$"E"' V21250] K15:A(K)K1:K:X310X(7):X1X3X(8):X4X310} K16:X210X(K):V21230 X2X11240 1245 X2X11240 1245 A(1)A(1)1 K:A(1)51300 KA(1)1:A(K)0:1300/ D910:Y110f  ALG28Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.s103,1:104,8::750555:L19:L21::500:E2C(1)I91:A90:M90:D91:L21:L14:530:VC(1):L27:L110:500K17:X(K)C(K)::X(8)18E201200       R$((K1),2)0RA9$A9$R$:K1A9$A9$T$(4)8T:T~I72A9$A9$"/"C9$:jA9$C9$"/"A9$:B"SO THE FRACTION IS N/D="(D(3))"/"(D(4))(13)zJD$(10)R$"AND HAS A VALUE OF "(D(3)D(4))"."(13):L810:720LK101:K1C(K):K101108NR$"-":K10R$"+":A9$""R$""O(K11K0)(K11)R$R$(K1)P(K11K0)(K11)R$C(0)C(2):C(1)C(3)::D$(6)"CROSS MULTIPLY TO GET "C9$"="A9$", OR"BC(0)C(4):C(1)C(5):A9$"":D$(8)"SOLVE THIS EQUATION TO OBTAIN"DD$(9)T$(4)" = "(D(5I7))", AND HENCE "T$(3)" = "(D(I72))"."F1100:D$(7)A9$" = 0.":L894HR$IVES US THIS:"A8D$(5)A9$"="(D(1))"/"(D(2))".":C(3)I8:C(2)D(I72)I8D(5I7)D(I74):I72I1D(1):D(1)D(2):D(2)I1<C(4)C(0)D(1)C(2)D(2):C(5)C(1)D(1)C(3)D(2)>I112:C9$A9$:A9$"":C(0)C(0)D(I1):C(1)C(1)D(I1):1100H@7):1100:C9$"("A9$")"V0A1$T$(3)"="A9$", SO OUR FRACTION IS ":A9$T$(4):11502D$(3)A1$A9$".":A9$"":1100:C(0)D(I74):C(1)0:11004C9$"("A9$")":C(1)1:C(0)D(7I7):A9$"":1100:A9$"("A9$")"61150:D$(4)"THE SECOND STATEMENT G THE VALUE OF THE FRACTION?"C(580:R91215,1060,1000,1066,46,6*715:K12:T$(K2)(T$(K),1):D$(K)"LET "T$(K2)"="T$(K):,D$(1)D$(1)" AND "D$(2)".":D$(2)"THE FIRST STATEMENT IS EQUIVALENT TO".A9$"":C(1)I8:C(0)D(I72)I8D(5IL23:L18:I124G 500:I2(C(3)2)2:I3D(2)I2C(2)3:I301052g A(I1)(D(1)I2C(1)3)I3: A(1)D(3)D(4):I91:C9$"":L21:L16:500:C(1)0C9$"E" "R113:A90:D90.5 $"YOU ARE TO FIND A FRACTION:"::K37:T$(K):&:"WHAT ISCHANGE":1046M R$"ADD ":A9$" TO":K10R$"SUBTRACT ":A9$" FROM":K1K1a R$R$(K1)A9$ T$(K4)R$" THE "C9$::T$(5)"IF YOU "T$(5):T$(6)"AND "T$(6)"," R$"THE RESULT IS "(D(1)) D(1)D(2)2R$R$"/"(D(2)) T$(7)R$".":(I72)I8D(5I7):A9$"THE "T$(1)" IS "i C9$" MORE":K0C9$" LESS":KK:K0A9$A9$" EQUAL TO" K0A9$A9$(K)C9$" THAN" D(I7)I8D(3I7)01004 T$(3)A9$:T$(4)R$:K12:C9$T$(I7(32I7)(K1)):K1D(K4) K10R$"DON'T "THE "T$(1)" PLUS TWICE THE ":R$T$(2)" IS ":I82d I2D(I72)I8D(5I7):R$R$(I2)".":1038 I73I7:T$(3I7)T$(I7):T$(I7)"NUMERATOR" I81:R$"":1032 I82:R$"TWICE ":1032 I83:R$"THREE TIMES ") R$R$"THE "T$(2)".":KDI6C(K)3:- D(4)0(D(5)0D(6)0)1004F I72:D(4)D(3)I71t T$(I7)"NUMERATOR":T$(3I7)"DENOMINATOR" L21:L16:500:I8C(1):I81020,1024,1026,1028,1030 A9$"THE SUM OF THE NUMERATOR AND THE":R$"DENOMINATOR IS ":I81:10224 A9$k  ALG27Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.q103,1:104,8:700L24:L18:500:KC(1):D(1)1:D(2)K:K0D(1)3:D(2)2K4D(1)K4:D(2)K3I6(C(2)2)2 K34:D(K2)3C(K):D(K)D(K2)   "")PR$"-":K0R$"+":A9$""R$""LQ(K1A1$"")(K1)R$R$(K)vR(K1A1$"")(K1)R$R$((K),2)TA9$A9$R$A1$V:8:1):C9$A9$K0C(2)0:1100:D$(9)"FACTORING, WE HAVE ("C9$")*("A9$")=0"2R$"SO WE GET "T$(5)"="(A(5))", AND "T$(6)"="W$(0)"="4D$(10)R$(A(6))(13):720LA9$"":I5201:KC(I5):K01110NA1$"":I50A1$T$(5):I52A1$A1$6)"SUBSTITUTE THIS INTO THE AREA FORMULA":W$(0)A9$*D$(7)"TO GET ("A9$")*"T$(5)"="(I6)".":C(2)I2:C(1)A(6)I2A(5),C(0)A(6)A(5):1100:C(1)1:C(0)A(5):C(2)0:C9$A9$:L810 .D$(8)"REARRANGE TO GET "A9$"=0.":1100:C(1)I2:C(0)A(6 WE":I1A(5)A(6):I21C C9$"HAVE 2L+2W="(2I1)", SO ":1062"I70C9$T$(5)"="T$(6)"-"(A(6)A(5))", OR ":I21$D$(4)"THE OTHER STATEMENT, AS A FORMULA, IS"&C(0)A(6)A(5)I2:C(1)I2:C(2)0:1100:D$(5)C9$T$(6)"="A9$"."4(D$(3)"."Q D$(2)"THE AREA OF A "T$(1)" IS "T$(6)"*"T$(5):R$"SO FROM AREA=" R$R$(I6)" WE GET ":I81D$(2)D$(2)"/2":I62I6 D$(3)R$T$(6)"*"T$(5)"="(I6)".":C9$" ":I2I7:I831058D$(4)"THE PERIMETER FORMULA IS P=2L+2W, SO"THE AREA IS "I6"."P :I83ĺ"YOU ARE ALSO GIVEN THAT THE "A9$" IS":R113:x W$(0)::"WHAT IS THE "T$(A(8))"?" 580:R91215,1036,1000,1044,46,6 715:K23:T$(K3)(T$(K),1): D$(1)"LET "T$(5)"="T$(2)", AND LET "T$(6)"="T$(E":I50C9$" LESS":I5I5:I501032D R$(I5)C9$" THAN "R$ W$(0)R$".":L21:L19:500:I9((C(1)1)2):L12:I90I95 500:A(8)C(1)2:A90:C9$"":R111:I83A(4)A(8A(8)) A(I9)A(A(8)3):A(0)0 "YOU ARE GIVEN A "T$(1)"."::(2(A(5)A(6))):1032U I71022,1024,1026:A9$T$(2):R$R$T$(3):I5A(5)A(6):1028 A9$T$(3):R$R$T$(2):I5A(6)A(5):1028 A9$T$(3):R$"TWICE "R$T$(2):I5A(6)2A(5):1028 A9$T$(3):R$"THREE TIMES "R$T$(2):I5A(6)3A(5)' C9$" MOR10 T$(1)"TRIANGLE":I6I62G T$(2)"BASE":T$(3)"ALTITUDE":1014z T$(1)"RECTANGLE":T$(2)"WIDTH":T$(3)"LENGTH" I7C(2):A(5)A(6)I1A(5):A(5)A(6):A(6)I1:1018 I82T$(2)T$(3):T$(3)"BASE" R$"THE ":I83R$R$"PERIMETER IS "  ALG26Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.v103,1:104,8:750:700L26:L110:530:K16:A(K)C(K)1::L22:L14:500I6A(5)A(6):I8C(1):I7C(2) I81008,1012,1012:T$(1)"PARALLELOGRAM":10     :C(4)I1:I2C(2):C(2)C(3):C(3)I2:1166]D$(L7)"BY USING THE FACT THAT BC+CD=BD":L7L71I4B(I1)B(I3):I5D(I1)D(I3):I2I4I4I5I5D$(L7)"SO WE GET "T$(I1)T$(I3)" = "((I2))(13):L7L71K:K9114810501050T$(I1)" TO "T$(I3):L7L71AI1I2I351154,1156,1160,1162{D$(L71)"TRIANGLE ABC: (AB) + (BC) = (AC).":1158D$(L71)"TRIANGLE ABD: (AB) + (BD) = (AD)."D$(L7)"BY USING THE PYTHAGOREAN THEOREM ON":L7L72:1164(K8:C(1)C(4)I3I4I4GzA(1)(I5):A(2)(I3I4):A(3)(2I5):A(4)I3I4:L21:L16{A9$T$(I1)" TO "T$(I2):W$(1)"ABC IS A RIGHT ANGLE":W$(8)""|I1C(1):L71:K12:I2C(K1):I3C(K2)}R$"FIRST":K2R$"SECOND"~D$(L7)R$", FIND THE DISTANCE FROM ":C128:L81:926:R19:L82:926:C134:L83:926:C139EXL84:926:uK13:W$(2K)"":I1C(K):I2C(K1):I3B(I1)B(I2):I4D(I1)D(I2)vW$(2K1)T$(I1)T$(I2)" = "((I3I3I4I4)):xI1C(4):I2C(1):I3(B(I1)B(I2)):I4(D(I1)D(I2)):I5I3)"7*I1D(1)D(I8):I2B(1)B(I8):I3I1I1I2I2:L89e+D$(8)" "("___",((I3))),D$(9)"SO WE GET D = "(14)(I3)" = "((I3))"."(13):721.L8L71:721LI3C(I2):A9$A9$T$(I3)"("(B(I3))","(D(I3))")":5VR13I73R$D$(2):D$(2)D$(4):D$(4)R$:K3J#D$(K)"FIRST":D$(4K)"SECOND"$K132:D$(K)"FROM THE "D$(K)" RELATION WE GET:":&D$(5)(13)"THE DISTANCE FORMULA IS:":R$"______"'D$(6)" _"R$R$R$(D$(7)"D = "(14)"(X1-X2)+(Y1-Y2? 3:1:K18:W$(K):::"WHAT IS THE DISTANCE FROM "A9$"?"d 1110:R114:580:R90R93İ760 R91215,1004,1000,1056,46,6 715:1110::3:1:K18:W$(K)::1004 !R90:R$"----------":R$R$R$R$:I61070'"D$(2)D$(4):D$(4)D$(6):K1:"A TO "T$(I8)V I1B(I8)B(1):I2D(1)D(I8):I3I1I1I2I2:A(1)(I3):A(2)(I32) A(3)(I1I1I2I1):A(5)I1I2:A(4)(A(5)):L21:L14:500 A(C(1)2)A(5):W$(1)"TWO OF THE POINTS ARE:":1050 D91:A90:I91:L21:L16:500:C(1)0C9$"E"A9$" "(I5)R$I I9I92:W$(K11)B$" POINT "T$(I2)".":KI7I3I2 K1K13:D$(I9)T$(I3)" IS ("(B(I3))","(D(I3))").":1034 A9$" ":I2K:1100:A9$A9$" AND ":I2K1:1100:W$(2)A9$ :W$(3)"":W$(6)"":L21:L12:500:I8C(1)3:A9$1032H I2C(K):I3C(K1):I4B(I3)B(I2):W$(K1)"POINT "T$(I3)" IS " I5D(I3)D(I2):R$"RIGHT":A9$"":I40R$"LEFT":I4I4 A9$"":I40W$(K1)W$(K1)(I4)" TO THE "R$:A9$"AND" R$" ABOVE":I50R$" BELOW":I5I5 B$"OF":I50B$13:B(K1)C(K)3::L22:L115Z 500:B(1)0:D(1)C(1)6:K24:D(K)D(1)B(2)::B(2)0 B(4)B(3)B(4):L21:L12:500:I6C(1):L13:500:I7C(1)1 L23:L14:530:C(4)10C(1)C(2)C(3):K14:I61141 K14:B(K)B(K)C(2)8::I92:K13:KI7  ALG25Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.{103,1:104,8:750:700:R90L80:R43:C428.8:R58.3:C528.8:906:C534906:C539:906:R48.3:906:R911052R931057 555:L23:L15:500:K     6580:R91215,1072,1000,1080,46,6.8731`DD$(1)"HERE ARE SOME USEFUL IDENTITIES:":720OL '^'. FOR EXAMPLE, Yx WILL BE SHOWN AS Y^X. ":1C9$"":"YOU MAY ASSUME THAT ALL VARIABLES ARE":"POSITIVE.":2B$""ĺ"YOU ARE ALSO GIVEN THAT "T$(I7)" IS "B$"."::R1174"WHICH OF THE FOLLOWING IS THE SAME AS:"::" "A9$%ZERO.">.W$(3)R$:R$" ONE GIVEN IN THE PROBLEM.":L86/D$(6)"TO SOLVE THE PROBLEM, FIND THE FORM ABOVE WHICH MATCHES THE"R$(13)?0:"NOTE: IN THIS PROBLEM, EXPONENTS ARE REPRESENTED IN A DIFFERENT MANNER, USING THE SYMBA9$R$"^"C9$:I90I92h*W$(1)"0":W$(2)"1":W$(4)"1/"R$:D$(6)" X^(-1) = 1/X IF X IS NON-ZERO.",D$(2)" 0^X = 0 IF X IS POSITIVE.":D$(3)" 1^X = 1 FOR ALL X."-D$(4)" X^1 = X FOR ALL X.":D$(5)" X^0 = 1 IF X IS NON-SIONS."4!D$(9)" = -((-X)^Y) = -(X^Y)"(13)g"D$(5)"THESE RULES CAN BE USED IN COMBINATION"$D$(7)"FOR EXAMPLE, IF Y IS AN EVEN INTEGER,":1072&I9I61:R$T$(I7):C9$"0":I91C9$"1":I94C9$"(-1)"(L86:A9$C9$"^"R$:I90I92D":I93I9FA9$A9$R$"^":R$T$(I7):C(4)1R$"(-"R$")":I52I5A9$A9$R$:I9I9I5:D$(3)"(-X)^Y = X^Y IF Y IS AN EVEN INTEGER":L89D$(2)"X^(-Y) = 1/X^Y":D$(8)"THEN -1/(-X)^(-Y) = -1/(1/(-X)^Y)" D$(6)"TO SIMPLIFY COMPLICATED EXPRES1):C(1)1I92:A9$"- "[ I50:W$(2)"-"W$(1):W$(4)"-"W$(3):C(2)1A9$A9$"1/":I52 D$(4)"(-X)^Y = -X^Y IF Y IS AN ODD INTEGER":R$T$(I6):C(3)01050 R$"(-"R$")":I73I8(T$(I7))2:I8(I8)I93I9 I74B$"EVEN":C(5)1B$"OD = (X^Y)^Z":R$" ONE GIVEN"| D$(7)"TO SOLVE THE PROBLEM, FIND THE FORM ABOVE WHICH MATCHES THE"R$" IN THEPROBLEM." D$(5)" X^(Y-Z) = X^Y/X^Z":D$(8)"":1072 L25:L12:A9$"":C(3)C(4)1038 I91:W$(1)T$(I6)"^"T$(I7):W$(3)"1/"W$($T$(I7):W$(3)"("A1$")^"T$(I7)n W$(1)A1$"/"C9$:W$(2)A1$"*"C9$:W$(4)"NONE OF THE ABOVE":L22:L13 530:I1C(1):D$(4)" X^(Y+Z) = X^Y*X^Z":L88 I2C(2):I36I1I2:D$(2)" (X*Y)^Z = X^Z*Y^Z":D$(3)" (X/Y)^Z = X^Z/Y^Z" D$(6)" X^(Y*Z)95I510):R$"*"I74I63R$""^ A9$"("T$(I6)R$T$(I7)")":I51C9$T$(I8)"^":1026 C9$"^"T$(I8):R$"-":I92I93R$"+":I93I94 A9$A9$C9$:A1$T$(I6)C9$:C9$T$(I7)C9$:W$(3)A1$R$C9$:1028" A9$C9$A9$:A1$C9$T$(I6):C9$C915:530:I6C(1):I7C(2):A94:R91:R115:I11:I22:I33:I44u L21:L17:500:I5(C(1)2):B$"":I51014,1038,1062 I8C(3):L16:500:I9C(1)1:I73I64I1I6:I6I7:I7I1 T$(6)"-":T$(7)"+":T$(8)"*":T$(9)"/":I91I9I92" R$T$(2I5I9Ia  ALG24Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.s103,1:104,8:700:L21:L12:500:I213:T$(I2)(6423C(1)I2):L130:L22:530:I112:T$(I13)(C(I1)1):C(1)C(2)4T$(4)"3"< L23:L   B)):(W$(B),I2,1)(13)IBI2:I2100oI2:W$(0)" "(W$(A),IA1)(" ",(W$(B))2IB)(W$(B),IB)W$(0)W$(0)(W$(A),IA4)" "A1$(W$(B),IB4)(13):(A(I1))PA(I1)1C9$"-"4QI60C9$C9$A9$RIA(C9$)2:I2(R$):R$(" ",1,IA)("________",1,I2)I8$C9$"\/"R$WA(I1)0R$"0":C9$""[W$(I1)R$:A2$"":I21(W$(A)):(W$(A),I2,1)(13)IAI2:I2100%I2:I21(W$((W$(0),(W$(0))1)" ="I8$W$(1):W$(1)W$(2)L85:D$(5)D$(5)(13):7212D$(6)(13)"THEN, SIMPLIFY THE RESULT TO GET:":D$(7)" "W$(1)" ="I8$W$(2)(13):L87:721LR$"":I61R$A9$NB(I1)1R$(B(I1))R$OC9$"":(A(I1))1C9$z# dz dz  dzdz î Dz Dz Dz Dz dz dz dz   DZ Dz Dz!Dz "Dz  Dz Dz  DZ DZ DZ DZDZ  DZDZ  ǰ ǰǰ ǰ  ǰDZDZà̠Ǡǰ ǰ ǰ ǰ  ALG3Y INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.103,1:104,8:700:A91:555:L21:L14:530:VC(1):L24:L110:530:E20:T2C(1)C(3)10:B2C(2)C(4)10 L25:L15:530:K15:I(K)C(K)::530:K15:T3C(K): ӥ膢 \ۈȱ " \<67 L d e8ij v vo> TO RETURN TO BEGINNING OFPROGRAM ";:414 F6N"MULTIPLICATION * A*B (A TIMES B)" 3"DIVISION / A/B (A DIV BY B)EXPONENTIATION ^ A^2 (A SQUARED)" = B"IN THE PROBLEMS PRESENTED ON THE SCREEN"O G"MULTIPLICATION PROBLEMS MAY BE SHOWN IN DIFFERENT WAYS AT DIFFERENIS AN EXPLANATION OF":"THE SYMBOLS USED IN INTELLIGENT TUTOR."E p " OPERATION SYMBOL EXAMPLE" "-------------- ------ ---------------" $"ADDITION + A+B (A PLUS B)" )"SUBTRACTION - A-B (A MINUS B)"+ . SYMBOL 103,1:104,8,(12);d3);::"EXPLANATION OF MATHEMATICAL SYMBOLS";:::"IT IS DIFFICULT TO SHOW CERTAIN MATHE-":"MATICAL SYMBOLS AND EXPRESSIONS ON THE":"SCREEN EXACTLY AS THEY WOULD APPEAR IN"? "A BOOK. SO HERE ::"THIS SCREEN WILL APPEAR AFTER THE TITLE SCREEN. TYPE 'Y' (FOR YES) IF YOU WOULDLIKE TO BE ABLE TO COPY TO A PRINTER THECONTENTS OF ANY OF THE PROGRAM SCREENS." :14::" OPTIONS MENU "::2080:"THE NEXT SCREEN YOU WILL SEE IS THE 'PRSER'S GUIDE FOR LOADING THE PROGRAM.": :" TITLE SCREEN "::"AT THE BOTTOM OF THE TITLE SCREEN IS A MESSAGE TELLING YOU TO TURN THE DISKETTEOVER AND PRESS . YOU MUST DO THIS IN ORDER TO CONTINUE." :10::" PRINTER OPTION SCREEN ":TUTOR / ALGEBRA 1 PROVIDE COMPREHENSIVE COVERAGE OF ALL THJE MAJORTOPICS GENERALLY TAUGHT IN ELEMENTARY ALGEBRA COURSES."; 23:1::400 (12);:1::" HOW TO USE INTELLIGENT TUTOR (CONT'D) ":::2060( :"FOLLOW THE INSTRUCTIONS IN YOUR U WIDE RANGE OF STIMULATING PROBLEMS. PROBLEM EXPLANATIONS ARE ALSO PROVIDED" "TO HELP YOU UNDERSTAND THE CONCEPTS INVOLVED, AND TO EXPLAIN THE METHODS FORSOLVING THE PROBLEMS.":2040~ :"THE 36 PROBLEM TYPE AREAS COVERED BY INTELLIGENT U IMPROVE YOUR SKILLSAND UNDERSTANDING IN THE SUBJECT OF ELEMENTARY ALGEBRA, AND DEVELOP YOUR ABILITY TO SOLVE PROBLEMS."P :"THE EMPHASIS OF THE PROGRAM IS ON PROBLEM-SOLVING. INTELLIGENT TUTOR GIVES YOU THE OPPORTUNITY TO SOLVE A   DESCO INTELLIGENT TUTOR/ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWAREa103,1:104,8(12);:5::" HOW TO USE INTELLIGENT TUTOR "::::8::" OBJECTIVES OF PROGRAM ":: "INTELLIGENT TUTOR / ALGEBRA 1 HAS BEEN DESIGNED TO HELP YO          X1:Q1$(Q2)"/100":Q2X110:V12Q1$(X1X1)"/10000":Q2Q210 `Q1$"THE SQUARE ROOT OF "Q1$:X(1)Q210:X(2)Q2100:X(3)Q21000:X(4)Q210000:X(5)Q22:Y(1)Q210:Y(2)Q2100:Y(3)Q21000:Y(4)Q210000:Y(5)Q22B ~J56I9:L25:L15:530:K15:I11150e .L12:530:V1C(1):Q210X1Y1:Q1$(Q2)"/10":Q3Q2:Q2Q210:V12Q1$(Q3)"/100":Q2Q210 GX(1)Q234:X(2)Q245:X(3)Q256:X(4)Q267:X(5)Q22:Y(1)Q243:Y(2)Q254:Y(3)Q265:Y(4)Q276:Y(5)Q22:1150A VL12:530:V1C(1):Q2X113:530:V1C(1):Q2(10X1Y1)100:V11056,1055,1058X Q2Q210:Q1$(X1Y110):1058r Q2Q2100:Q1$"."Q1$ "Q1$Q1$"%" $X(1)Q210:X(2)Q2100:X(3)Q21000:X(4)Q210000:X(5)Q22:Y(1)Q210:Y(2)Q2100:Y(3)Q21000:Y(4)Q210000:Y(5)Q22:  ALG5Y INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.103,1:104,8:750:700:L22:L19:530:X1C(1):Y1C(2):L21:L13:530:VC(1):L15:530:I9C(1):A90:555:K15:A(K)K1::V1050,1070,11105 Q1$(10X1Y1):L (3)" X * (1/6) = 5/8":D$(4)"OR, X = 5/8 * 6":D$(5)"THE ANSWER IS 30/8 OR 15/4.":D$(6)"":L86:715x 2733::720HR2K:C2(C2)R1C1:R2C2# T: R1G2:R2B2:1105:1100::" HOW MANY ";D$(V);" ARE THERE IN ";D$(6);"?"::R110:580:R91215,1200,1000,1300,46,6h D$(1)"FIND THE NUMBER OF SIXTHS IN THE FRACTION 5/8.":D$(2)"THE EQUATION TO USE IS:":D$ ((N2B2T2).01)1070& "1090D $W$(2)"1":W$(4)"2":1090\ .W$(1)"1":W$(4)"2"k BE201200 GW$(1)"1"W$(1)"1/2":1200 HW$(1)"1":1200 LD$(6)(R1):R21D$(6)D$(6)"/"(R2) O QK129:K10K1:C1R1K RC1(C1)C2":D$(3)"FOURTHS":D$(4)"FIFTHS":D$(5)"SIXTHS":E20C9$"E" N2V1:R1T2N2:R2B2:1105:1100:W$(1)D$(6):R1T2:R2B2N2:1105:1100:W$(2)D$(6):R1B2N2:R2T2:1105:1100:W$(3)D$(6):R1B2:R2T2N2:1105:1100:W$(4)D$(6) ((N2T2B2).01)1060y  ALG4Y INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.103,1:104,8:700:555:L21:L19:500:E2C(1):I91:A91:L22:530:T2C(1):B2C(2):L15:530:VC(1):G2T2T21V1B2VC(2)= D$(1)"HALVES":D$(2)"THIRDS -209)/323=-56/323.":D$(6)"10/14-11/17=(170-154)/238=16/238.":D$(7)"8/18-11/17 =(136-198)/306=-62/306.":R$"SINCE 6/306 IS THE CLOSEST TO ZERO, WE " D$(8)R$"SEE THAT 12/18 IS THE CLOSEST TO 11/17.":L88:715:734:720" 12/18, 16/19, 9/19, 10/14, 8/18. ----------------------------------------TO SOLVE, FIND THE DIFFERENCE BETWEEN EACH FRACTION AND 11/17:":D$(3)"12/18-11/17=(204-198)/306=6/306." D$(4)"16/19-11/17=(272-209)/323=63/323.":D$(5)"9/19-11/17 =(153K15:T4N2(K)D2(K)T9:V212200 T4(T4)> K11230R T4T5V41240f T4T5V41240u T5T4:I9K{  D$(1);D$(V1);D$(6)::C9$"ALL":R17:580:R91215,1300,1000,1400,46,6 xD$(1)"WHICH OF THESE IS CLOSEST TO 11/17?":D$(2)"(D2(K))::T9T2B2:F$(T2)"/"(B2):V11100I GT9(T2B2):F$(T9) LD$(1)"WHICH OF THE FOLLOWING FRACTIONS IS THE ":D$(2)"CLOSEST TO ":D$(3)D$(2):D$(4)"SMALLEST":D$(5)"LARGEST":D$(6)F$"?":V21200 tD$(6)"?" V31210 T90# T3I(K)T3T3, E20N2(K)T2T3:1053< D2(K)T2T3B W E20E21:1035 !K113:K15:((N2(K)D2(K)1)).01D2(K)D2(K)1 #J15 $JKĭ((N2(K)D2(K)N2(J)D2(J))).01D2(J)D2(J)1 &::0 8K15:W$(K)(N2(K))"/"--------------------"p"THE FOLLOWING EXAMPLES ARE SIMILAR TO THOSE SHOWN IN THE PREVIOUS PROBLEM:"::721S2(S):Z0:S214120S21ZZ1:S2S210:41104125S210ZZ1:S2S210:4120E41S2(S21000.5)1000S0HE DECIMAL POINT IN THE NUMBER '1.2' 5 PLACES TO THE RIGHT.":"THE NUMBER .00012 CAN BE WRITTEN IN SCIENTIFIC NOTATION AS 1.2E-4. THE 'E-4'TELLS US TO MOVE THE DECIMAL POINT IN THE NUMBER '1.2' 4 PLACES TO THE LEFT.""-------------------,1000,4010,46,6715::"SCIENTIFIC NOTATION IS A CONVENIENT WAY TO WRITE VERY LARGE AND VERY SMALL NUMBERS. WE'LL EXPLAIN IT THRU EXAMPLES: ">"THE NUMBER 120000 CAN BE WRITTEN IN SCIENTIFIC NOTATION AS 1.2E5. THE 'E5' TELLS US TO MOVE T M09:30004 M18VX:XY:YV:VO:OP(4):P(4)VJ O0V$"-":3517U V$"+"n P(4)0X$"-":3520y X$"+" G$"SIMPLIFY ("(X)"E"V$((O))")"S$"("(Y)"E":F$X$((P(4)))")":A$G$F$:A91<R17:700:A$::580:R91215,39005E-1":D$(2)" (6E+3)/(3E+2) =6000/300= 20 = 2E+1":D$(3)" (4E+1)/(8E+3) = 40/8000=.005 = 5E-3"(13):L83:C(1)3410,3450R SX1Y1:4100z SY1X1:Y2Y1:Y1X1:X1Y2:M18:4100 M093510 A$"SIMPLIFY "(X1)S$((Y1),((Y1))):A91:3900 :4100 SX1Y1:S$"*":D$(1)" (4E+1)*(3E+0) = 40*3 = 120 = 1.2E+2":D$(2)" (7E-2)*(4E+1) = .07*40 = 2.8 = 2.8E+0":D$(3)" (4E-2)*(7E-2) = .04*.07=.0028= 2.8E-3"(13):L83:4100z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g C(K)C(K)4:Y$"+"((C(K)),2) B$(K1)(X)"E"Y$::K14:W$(K)B$(KW1): C(2)0B$".":K$"0":K1(C(2))1:B$B$K$: C(2)0B$B$""(X):2540 B$"":K$"0":K15:X(K)C(1)10(C(K1)3)::C(2)30S$"-":2020A S$"+" A$"EXPRESS AS A DECIMAL NUMBER: "(C(1))"E"S$((C(2)3)):K14:X(KW1)1X(KW1)(X(KW1)) A(K)X(KW1)::D$(1)" 1E+0=1, 3E-2=.03, 4E+3=4000"(13):L81:A90:3900C  ALG6Y INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.103,1:104,8:700:I90:L21:L16:530:C(1)6C9$"E":I95:W11:1040C9$"":I91:W10M02:L21:L14:530:C(1)2000,2500,3000,35006 L26:L19:530:   $(8)"":L88:731:720QE SQUARE ROOT OF (36/100).":D$(8)"":L88:731:720100,1000,1400,46,6 xD$(1)(13)"SEVERAL IMPORTANT ARITHMETIC FACTS ARE ILLUSTRATED BY THE FOLLOWING EQUATIONS:":D$(2)".35% = .0035":D$(3)"3.5% = .035":D$(4)"35% = 0.35":D$(5)"(36/100) = 6/10 = 0.6":D$(6)"(36/10000) = 6/100 = 0.06"D$(7)"":D(K)C(K)::L1J5:L2L1:530:K1J5:X2(I1(K))X(C(K))::J551200s L25:L15:530:KJ515:X2(I1(K))Y(C(K)): C9$"ALL":"HOW MANY OF THE FOLLOWING ARE GREATER":"THAN ";Q1$"?"::K15:(X2(K)1000000.5)1000000" ";:::R19:580:R91215,1242; A(1)I1I4:A(2)I1I4:A(3)I1I3I4:A(4)I1I4:I78` 1110:I82:1150:I83:I91:1058 A(1)I1I3:A(2)I1I3:A(3)I1:A(4)I3:1110:I82:I79:I91:1058 A(1)I1I4I2I3:A(2)I1I4:A(3)I2I3:A(4)I1I4I2I3:I79:1054% A(1)I2I4:A(2A(2)I2I2:A(3)2I2I2:I75S A(4)I1I2:I82:1150:A9$"("A9$")":I91:1060 I82:A(1)I2I3:A(2)I2I3I1I4:A(3)I2I3:I91:T$(5)T$(8)I92 A(4)I2I3I4:1150:1100:I83:I75:1058 A(1)I1I3:A(2)I1I3:A(3)I1I4:A(4)I3:I79:10,T$(I4I3):A L24:L110:500:I114:I2C(I1)4:I21I2I21 D(I1)I2::I1D(1):I2D(2):I3D(3):I4D(4):I81:I60:1110 L23:L18:500:C(1)1028,1032,1038,1040,1046,1050,1052 A(1)2I1I2:A(3)2I1I2:A(2)2I1:I79:1030 A(1)I2I2:O ALG08 INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.m103,1:104,8:750:700:A$:(A$)999031002L21:L15:500:I109C(1):C9$:L22:L13:530:I1C(1):I2C(2):I36I1I2 I4063:T$(I4I1),T$(I4I2)  )1T$(I1)""R$R$(A9):11101RA91R$"-"JSA91A1$""R$"+"`VA1$A1$R$T$(I1)vX:A1$""A1$"0"ZW$(K1)A1$:K1K11:)"THEN, ADDING EACH COLUMN, WE ARRIVE AT OUR ANSWER:":B(1)D(1):B(2)D(2):B(3)D(3):K11:L8A94:1100:D$(L8)" "W$(1)(13):715:720LA1$"":I115:A90:I216:A(I2)I1A9A9B(I2)N:A901112PR$"":A90R$"+":A1$""R$""Q(A9+":I30R$" "<0I30D$(A91)D$(A91)R$(I3)T$(I1)U2R$" +":I40R$" "4I40D$(A92)D$(A92)R$(I4)T$(I1)6I3(D$(A91)):I4(D$(A92)):I3I4D$(A92)D$(A92)(B$,I3I4):I4I3D$(A91)D$(A91)(B$,I4I3)<:D$(A93" R$"THEN,":1062| $D$(A92)"":D$(A9)R$" LINE UP THE TERMS WITH IDENTICAL VARIABLE PARTS IN COLUMNS:":D$(A91)"" &B$" ":I115:I30:I40:I213:A(I2)I1I3I3D(I2) *A(I23)I1I4I4D(I23) ,:I30I401084.R$" ":A9$"+"1060 D$(3)R$" DISTRIBUTE THE MINUS SIGN:":B(1)0:B(2)0:B(3)0:D$(4)" -("W$(7)") = (":K12:1100:D$(4)D$(4)W$(2)")":A95:D$(A92)"":D$(A9)"THEN, LINE UP THE TERMS WITH IDENTICAL VARIABLE PARTS IN COLUMNS, LIKE THIS:":D$(A91)":I91:I41I95v "SIMPLIFY THE FOLLOWING:"::"("W$(6)") "A9$" (";:W$(7)")"::580:R91215,1038,1000,1050,46,6 B(4)D(4):B(5)D(5):B(6)D(6):D$(2)"("W$(6)") "A9$" ("W$(7)")":D$(1)"WE ARE ASKED TO SIMPLIFY THIS:":A93:R$"TO SOLVE, FIRSTB(4)16 1100:B(I3)D(I3):B(4)D(4):D(4)0B(4)2{ 1100:B(4)0:B(5)0:B(6)0:1100:B(1)0:B(2)0:B(3)0:I511034 B(4)D(4):B(5)D(5):B(6)D(6):A9$"+":1036 B(4)D(4):B(5)D(5):B(6)D(6):A9$"-" 1100:A95:R17:W$(I4)W$(5):C9$""L17:500:K16:D(K)C(K)3:B(K)D(K):^ L21:L19:500:I4((C(1)3)2):I50:C(7)2I51 K11:1100:B(5)D(5):D(5)0B(5)1 1100:B(5)D(5):B(6)0:D(6)0B(6)1 1100:B(6)D(6):I31:A(4)A(1)I32 B(I3)D(I3)D(4):B(4)0:D(4)0ĐO ALG07 INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.m103,1:104,8:750:700:A$:(A$)999021002( L21:L15:500:K05C(1):C9$::K15:T$(K)::L23:L15:530:K13:A(K)C(K)::530:K13:A(K3)C(K)::L27:     S2S21E"L25:L19:530:C(1)0:K25:C(K)C(K)5:C(K)0C(K)5p'ZC(K1W1)0W$(ZC(K1W1)):4145)W$"+"((ZC(K1W1)),((ZC(K1W1))))1W$(K1)(S2)"E"W$6:3490"E"W$6:34901000S0S2S212"L25:L(L,C)C(L1):: W963010P L25:IX(L,1)IX(1,1)IX(L,2)IX(1,2)2090Z 2100s *IX(L,3)IX(1,3)L8 4:L92000 >K14:PKW1:EIX(P,1):FIX(P,2):E$(E):E1E$"" ?AAF:4300:F1$"(X"AA$")":AAIX(P,3):4300:F2$"(Y"AA$")":Z2152 C(1)Z(C(1)Z)C(2)Z(C(2)Z)XZ :IX(1,1)X:JX(1,1)C(1):JX(2,1)C(2):L24:L115:530:K25:IX(K,1)C(K1)::C23:L22:L16:530:JX(1,C)C(1):JX(2,C)C(2):C(1)C(2)IX(1,C)C(1):2060 IX(1,C)C(2) L24:L16:530:L25:IX  ALG10Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.103,1:104,8:700:I90:L21:L16:530:C(1)6C9$"E":I95:W11:1040C9$"":I91:W10W98:L21:L13:530:C(1)2000,3000,3300 X1:L22:L130:530:     A9$""R$"";OA91(T$(I2)""(A91A90))R$R$(A9)kRA91(T$(I2)""(A91))R$R$((A9),2)TA9$A9$R$T$(I2)V:W$(I1)A9$:9$:$004 D$(5)"FROM THE ABOVE WE CAN SEE THAT "W$(5)n D$(5)D$(5)(13)"IS A FACTOR OF THESE EXPRESSIONS:" "B(6)I7I7I7:B(7)I8I8I8:1100:D$(8)W$(5)(13):L88:715:720 LA9$"":I217:B(I2)01110 NA9B(I2):B(I2)0:R$"-":A90R$"+":)"CONTAINING THE TERM (A"R$"B) :"K D$(3)"(A"R$"B)=A"R$"2AB+B"} D$(4)"(A"R$"B)(A"C9$"AB+B)=A"R$"B" I15:B(5)I8I8:B(3)I7I7:1100:B(3)I7I7:D$(6)W$(5):B(4)2I7I8 B(5)I8I8:1100:D$(7)W$(5) B(1)I7:B(2)I8:11:"WHICH OF THE FOLLOWING, WHEN FACTORED,":A91Y "HAS A FACTOR OF "W$(5)" ?"::580{ R91215,1032,1000,1040,46,6 D$(1)"THE FOLLOWING ARE SIMPLE FACTORIZATIONS " D$(2)"(A-B)(A+B)=A-B":R$"+":C9$"-":I80R$"-":C9$"+"$ D$(1)D$(1. B(3)I7I7:B(4)2I7I8:B(5)I8I8:1028U B(6)I7I7I7:B(7)I8I8I8:1028 B(3)I7I7:B(4)2I7I8:B(5)I8I8:1028 B(3)I7I7:B(5)I8I8 1100:I1:L21:L19:500:I9(C(1)2)1:W$(I9)W$(5) B(1)I7:B(2)I8:1100:R18:C9$""1 I85 L21:L13:500:I15:L24:L15:C(1)1012,1014V B(3)I7I7:B(5)I8I8:1016| B(6)I7I7I7:B(7)I8I8I8:1016 B(3)I7I7:B(4)2I7I8:B(5)I8I8 1100:530:I114:C(I1)1020,1022,1024,1026 B(3)I7I7:B(4)I7I8:B(5)I8I8:1028O ALG09 INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.m103,1:104,8:750:700:A$:(A$)999041002L21:L15:500:I107C(1):C9$:I117:T$(I1):B(I1)0::L23:L18:500 I7C(1)1:I8C(2)1:C(3)3I8  9$""<~I6I61:I5D(I6):R$"-":I50R$"+":A9$""R$""RI51R$R$(I5)nI51R$R$((I5),2)T$(I8)""(I51I50)R$R$(I5)T$(I8)""I51R$R$((I5),2)A9$A9$R$T$(I8):R$T$(I8):R)"(A+B)=A+2AB+B"E5D$(6)"TO SOLVE THE PREVIOUS PROBLEM, FIRST"6D$(6)D$(6)" MULTIPLY EVERYTHING OUT USING THE "7D$(6)D$(6)"FORMULAS SHOWN ABOVE. THEN, COMBINE LIKETERMS."(13)8L86:715:720LA9$"("A9$")"VC9$A9$:AT$(I7)""ĺ"NSTANT TERM":1068: *"EFFICIENT OF "T$(I7)a ,580:R91215,1062,1000,1072,46,6 0D$(1)"THE FOLLOWING GENERAL FORMULAS MAY BE HELPFUL:" 1D$(2)"A(B+C)=AB+AC" 2D$(3)"A(B+C+D)=AB+AC+AD":D$(4)"(A+B)(C+D)=AC+AD+BC+BD"4D$(5)2I2I4:A(3)I2I4:A(4)I2I4:I75I I82:1150:I81:1100:I82:I91x "1150:C(2)3A9$C9$" * ("A9$")":1060 #A9$"("A9$")"C9$ $D92:C9$"":A90:R19:C(3)0C9$"E" &"YOU ARE GIVEN THIS PRODUCT:"::" "A9$: ("FIND THE CO";:4200 U(1)14300 44001 4170:S$"*"G U(1)U(2)04500X U(1)14600b 4700 4170:S$"/":QC:CD:DQ:U(2)1U(2)2:3520 U(2)1 3005 700:S$"/"ĺ"SIMPLIFY: ("T$") / ("V$")":4010 "SIMPLIFY: "T$" "S$" "V$, ):D1J$""4 V$(C):U(2)1V$V$K$:C1V$K$^ U(2)1J$J$K$:D1J$"("J$")"w !J$""V$V$"/"J$ $L21:L14:530:C(1)2000,2500,3000,3500 4150:S$"+":U(1)U(2)04200 U(1)14300 4400 4150:S$"-":U(1)U(2)0(DK)CCK:DDK:1047 q L12:L21:L12:530:U(L)C(1)::AAX(1):4990:K$"X"AA$:J$(B):B1J$"" T$(A):U(1)1T$T$K$:A1T$K$ U(1)1J$J$K$:B1J$"("J$")" J$""T$T$"/"J$ AAY(1):4990:K$"X"AA$:J$(DL)Y(L)X(K2)Y(K2)X(L)Y(L)X(K2)Y(K2)L8:K28E ::K291035O 4920 X(L)Y(L)X(K2)Y(K2)X(L)Y(L)X(K2)Y(K2)L8:K28 L24:L19:530:AC(1):BC(2):CC(3):DC(4):K29 AK(AK)BK(BK)AAK:BBK:1046 CK(CK)DK$  ALG11Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.103,1:104,8:700:I90:L21:L16:530:C(1)6C9$"E":I95:W11:1035C9$"":I91:W102 J15:L22:L15:530:X(J)C(1):Y(J)C(2)::K225:L1K21:X(     JX(K,1):HJX(K,2):G$(G):G1G$""gAAH:4300:X1$"(X"AA$")":AAJX(K,3):4300:X2$"(Y"AA$")"x H1X1$"X" H0X1$"" JX(K,3)1X2$"Y" JX(K,3)0X2$""X$(K)G$X1$X2$::AA$(" 1",AA1,1):(13)" 4(X)(Y)+6(X)(Y)"(13)(13)"WE GET"(13)(13)" 2(X)(Y) * [2(Y)+3(X)]."(13):D$(7)"NOTICE THAT 2(X)(Y) IS THE"D$(8)"GREATEST COMMON FACTOR IN THE TWO TERMS":D$(9)"OF THE POLYNOMIAL."(13):L89:731:721%K12:G (N+P) N P"(13)"REMEMBER THAT A = A * A ,"D$(3)"AND THAT IN FACTORING MONOMIALS FROM":D$(4)"POLYNOMIALS, THE FACTORS MUST BE":D$(5)"FACTORS OF ALL TERMS OF THE POLYNOMIAL."D$(6)"FOR EXAMPLE, FACTORING THE POLYNOMIAL"(13)* ::L93300)/ L91:C(2)1B$""x4 Q$(2)A$C$D$"+"B$C$D$:A$(1)"FACTOR: "Q$(2):K14:W$(K)Q$(KW1):<K1L9:A$(K):::A91:R19:580:R91215,3900,1000,4010,46,6<D$(1)(13)" IN FACTORING MONOMIALS WE MUST":D$(2)" 1A$"X"" AC(3):BC(4):Z23O AZ(AZ)BZ(BZ)AAZ:BBZ:3312 :C(3)A:C(4)B:B$(C(2)):C$"("(C(3))"X+":C(3)1C$"(X+" D$(C(4))"Y)":C(4)1D$"Y)" Q$(M)"("A$"+"B$")"C$D$::L25:J1L1:Q$(L)Q$(J)J8:L8(13)" ["Q$(2K1W1)"+"Q$(2KW1)"]"(13):l K12:JX(K,1)JX(K,1)IX(1,1):L23:JX(K,L)JX(K,L)IX(1,L):::4100:4000 A$(1)"FACTOR: "X$(1)"+"X$(2):L91:3900  4000:M511:L24:L19:530:AAC(1):4300:A$"(X"AA$")":C(1)JX(K,2):WJX(K,3):U$(U):U1U$""OP AAV:4300:V$"(X"AA$")":V0V$""_R V1V$"X"T AAW:4300:W$"(Y"AA$")":W0W$""V W1W$"Y"X Q$(K)U$V$W$:W0V03162Y 3165Z U1Q$(K)"1"] :W11W127g K14:W$(K)P$"*"  31209 & JX(1,3)JX(2L1,3)JX(2,3)JX(2L2,3)L8I 0 :L93030t : QIX(1,1):TIX(1,2):O$(Q):Q1O$"" ; AAT:4300:O1$"(X"AA$")":AAIX(1,3):4300:O2$"(Y"AA$")":T1O1$"X" = IX(1,3)1O2$"Y"%D P$O$O1$O2$:K110:UJX(K,1):V(K,L)JX(K,L)IX(1,L):: L28:L130:530:K310:JX(K,1)C(K2)::N71:G112:M23:L24:L16:530:L14:JX(2LN7,M)C(L):::N72::L14:JX(1,1)JX(2L1,1)JX(2,1)JX(2L2,1)3090  3120  JX(1,2)JX(2L1,2)JX(2,2)JX(2L2,2)3110F1F1$"X"" AIX(P,3)1F2$"Y" HW$(K)E$F1$F2$::4100:A$(1)"DETERMINE THE GREATEST COMMON FACTOR":A$(2)"BETWEEN THESE TWO MONOMIALS:":A$(3)(13)" "X$(1)","X$(2)::L93:4000:3900 W96:2000 K12:JX(K,1)JX(K,1)IX(1,1):L23:JX)" + ":C9$""; L25:L110:500:K15:C8(K)C(K)::A90O V1$"Y":V2$"X"k ((I(2)I(1))2)1050 I(1)I(1)1:I(1)5I(1)3 J301090 $D$(I(1))"X":I(2)0:(I(1)1)1090 .I(1)31090 8D$(I(1))"/X" BI9I(1):I8I(2):J10D  ALG12Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.s103,1:104,8:700:I60:L23:L12:500:J1C(1):J2C(2):J3C(3)R11:R21:L22:L14:530:I(1)C(1):I(2)C(2):D91 K16:D$(K)""::D$(5)" + ":D$(6     #~AA$(" ",AA1,1)::BBZ:FFZ:4902+,:A$"":A1A$(A)C/B$"":B1B$(B)I2n8W(1)(X(1)Y(1)):G(1)X(1)Y(1)BL24:L19:530:K25:W(K)C(K1):W(K)W(1)K80L:K814930VL24:L19:530:K25:G(K)C(K1):G(K)G(1)K85`:K864950jF$"":F1F$"/"(F)BAAW(KW1):4990:W$(K)A$"X"AA$F$N:3990\K15:O(K)X(K):X(K)Y(K):Y(K)O(K)::4600$FBD:AAD:BBC:Z(1)2:Z(2)3:Z(3)5:Z(4)7:K14:ZZ(K)&AZ(AZ)BZ(BZ)4906(4908*FZ(FZ)AAZ:?K14:AAG(KW1):4990:F$"X"AA$:F1F$"("(F)F$")"[W$(K)A$"/"F$::3990AAC:FBD:BF:C1:D1:4900:K14:X(KW1)Y(KW1)4610A1A$"1"AAW(KW1):4990:F$"X"AA$:F1F$"("(F)F$")"W$(K)A$"/"F$:46121F$"("(F)F$")"U4AAG(KW1):4990:W$(K)"("A$S$B$"X"AA$")/"F$::3990AAC:FBD:BF:C1:D1:4900:U(1)24515F$"":F1F$"/"(F)U(1)24515K14:AAG(KW1):4990:W$(K)A$"X"AA$F$:3990A$""A$"1""("A$S$B$"X"AA$")/"F$):3990F4900:K14:B1B$"1"AAY(KW1):4990:F$"X"AA$:F1F$"("(F)F$")"AAG(KW1):4990:W$(K)"("A$"X"AA$S$B$")/"F$::399004900:A1A$"1"2K14:AAX(KW1):4990:F$"X"AA$:FѭX(KW1)Y(KW1)4230%~B1B$"1"^AAY(KW1):4990:F$"X"AA$:F1F$"("(F)F$")"AAW(KW1):4990:W$(K)"("A$"X"AA$S$B$")/"F$:4236A1A$"1"AAX(KW1):4990:F$"X"AA$:F1F$"("(F)F$")"AAW(KW1):4990:W$(K) ------- = ---- * --- = ---- = --- X/6 3X X 3X X":L88:dhU(1)24220j4900:F$"/"(F):F1F$""xK14:AAX(KW1):4990:N$"("A$"X"AA$S$B$"X":AAY(KW1):4990:W$(K)N$AA$")"F$::3990|4900}K14:5)(13)"EXAMPLE:"(13)(13)"SIMPLIFY: (2/(3X))/(X/6)"(13):D$(6)"TO SOLVE, INVERT THE DIVISOR, THEN MULTIPLY NUMERATORS AND DENOMINATORS."SUD$(7)"THEN, REDUCE THE RESULT TO LOWEST TERMS.":D$(8)" 2/(3X) 2 6 12 4 ALGEBRAIC EXPRESSIONS, MULTIPLY THE NUMERATORS AND THE":D$(2)"DENOMINATORS.":D$(3)(13)"TO DIVIDE, FIRST INVERT THE SECOND EXPRESSION (THE DIVISOR). THEN MULTIPLYNUMERATORS AND DENOMINATORS AS YOU"PD$(4)"WOULD DO IN MULTIPLICATION.":D$(NOMINATOR IS 15X. REWRITING":D$(9)"THE EXPRESSIONS AND COMBINING TERMS WE GET OUR ANSWER:"FD$(10)(13)" 20 27X 20+27X ----- + ----- = ---------- 15X 15X 15X":L810:JD$(1)"TO MULTIPLYT) THE NUMERATORS AND DO NOT";D$(4)"CHANGE THE DENOMINATORS.":D$(5)(13)"EXAMPLE:"(13)" 4 9X":D$(6)"SIMPLIFY: ---- + ----":D$(7)" 3X 5"_BD$(8)(13)"BY INSPECTION, WE FIND THAT THE LEAST COMMON DEA91:R18:580:R91215,3990,1000,4100,46,6? 715:732:7216D$(1)"TO ADD (OR SUBTRACT) ALGEBRAIC EXPRESSIONS, YOU SHOULD FIRST REWRITE":D$(2)"THE EXPRESSIONS SO THAT THEY HAVE THE SAME DENOMINATOR. THEN, SIMPLY ADD":D$(3)"(OR SUBTRAC = (9*8/3)+4"(13)" = 28"(13)(13):L84:733:721DDER THE EQUATION C=K(F-G)/L."(13):D$(2)"THEN, K = CL/(F-G)"(13)" L = K(F-G)/C"(13)" F = (CL/K)+G"(13)" G = F-CL/K"(13)(D$(3)"IF C=9, K=3, G=4, AND L=8,"(13)D<D$(4)" THEN F = (CL/K)+G"(13)" ;D$(V11);" IN TERMS OF THE OTHER"::"VARIABLES.":1250s "THE FOLLOWING VALUES ARE GIVEN:"::K15:KV11245 D$(K);"=";X(K);" ";  ::"FIND THE VALUE OF ";D$(V1);"." R112:580:R91215,1200,1000,1300,46,6D$(1)(13)"CONSI)(X(4)X(5))X(1):1200e A(2)A(1)2X(5):A(3)X(1)X(2)X(3)X(5):A(4)X(1)X(2)X(3)X(4):1200 A(2)X(4)X(1)X(3)X(2):A(3)X(4)X(1)X(3):A(4)X(4)X(1)X(2)X(3) :"YOU ARE GIVEN THE EQUATION C=K(F-G)/L.": V212308 "EXPRESS "(4)X(3):X(1)X(2)(X(4)X(5))X(3):A(1)X(V1):V11140,1150,1160,1170,1180 tA(2)A(1)X(3)X(3):A(3)X(2)(X(5)X(4))X(3):A(4)A(1)X(3):1200 ~A(2)1A(1):A(3)A(1)X(3):A(4)X(1)X(3)(X(5)X(4)):1200 A(2)1A(1):A(3)A(1)X(1)X(1):A(4)X(2)"CL/K+G":W$(2)"CL/K-G":W$(3)"CK/L-G":W$(4)"CLK+G":E20W$(1)"CLK-G"T 41200 8W$(1)"F-CL/K":W$(2)"F+CL/K":W$(3)"F+CLK":W$(4)"F-CLK":E20W$(1)"F+CK/L" >1200K LA90:L15:530:V1C(1):L24:L16:530:X(3)C(1):X(4)C(2):X(5)C(3):X(2)CL14:530:V1C(1):V11050,1060,1070,1080 W$(1)"CL/(F-G)":W$(2)"CL/(G-F)":W$(3)"CL(F-G)":W$(4)"CK/(F-G)":E20W$(1)"CL(F+G)" 1200 $W$(1)"K(F-G)/C":W$(2)"K(F-G)C":W$(3)"K(G-F)C":W$(4)"K(G-F)/C":E20W$(1)"K(F+G)/C" *1200J .W$(1E  ALG13Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.103,1:104,8:700:555:L21:L19:500:E2C(1):I91:A91:D91:L12:530:VC(1):D$(1)"C":D$(2)"K":D$(3)"L":D$(4)"F":D$(5)"G":E20C9$"E"V21100) D$(7)(13)YD$(L84I8)"GATHER ALL THE ADDED AND SUBTRACTED TERMS TO ONE SIDE:"R$"IN THE PREVIOUS PROBLEM, WE HAD DIVISIONBY ZERO, SO THE ANSWER WAS "D$(L81)R$"UNDEFINED.":I80D$(L81)D$(L81)(13)L8L8I7:720EEN SOLVE FOR Y:"UD$(8)" 1/Y = 9/6 = 3/2, SO Y = 2/3":I70D$(8)D$(8)(13)dL88:1490L87:D$(2)" 5 + 6 = 4X - 6":D$(4)" 11 + 6 = 4X"D$(5)" 17 = 4X":D$(6)"THEN SOLVE FOR X:" D$(7)" X = 17/4 = 4.25":I70D$(7)1215,1330,1000,1410,46,6(715:734WD$(1)"SUPPOSE THE PROBLEM IS:":I801460I81:D$(2)" 5 + 6/Y = 3X - 4 WHERE X = 6."D$(3)"SUBSTITUTE IN THE VARIABLE WE KNOW:":D$(4)" 5 + 6/Y = 18 - 4"D$(6)" 6/Y = 14 - 5 = 9":D$(7)"TH(C8(I(1))0)1330 0C9$"E"Q 2"GIVEN THE EQUATION"::""(C8(1))D$(1)D$(5);| <(C8(2))D$(2)" = "(C8(3))D$(3)D$(6); F(C8(4))D$(4)::I801370 P"SOLVE FOR ";V1$;" WHEN ";V2$;" = ";C8(5);".":1380 Z"SOLVE FOR X." dR112:580iR9T9 A(1)0:(C(1)0)1290/ (I91)1300F I71:C9$"E":1300k A(1)(C(3)R2C(4)R1C(2))C(1) A(2)0:T9C(3)R2C(4)C(1):(T90)1320 (I92)1322 I71:C9$"E":1330 ((C(2)0)1305 )A(2)R1C(2)T9 *(I80)1330 .2))C(I(2))C(5)C(5)6 I7I6:A(3)0:(C(3)0)1230H (I93)1240_ I71:C9$"E":1240 A(3)(C(1)R1C(2)R2C(4))C(3) A(4)0:T9C(1)R1C(2)C(3):(T90)1260 (I94)1270 I71:C9$"E":1270 (C(4)0)1245 A(4)R2C(4)$(5)" - ":R11, VJ20D$(6)" - ":R21? j(I(2)0)1210^ tD$(I(2))"X":D$(I(1))"/Y" ~C(I(2))C(I(2))C(5):(I(2)1)1210 (I(2)3)1210 D$(I(2))"/Y":D$(I(1))"X":V1$"X":V2$"Y" I60:(C(5)0)1200 C9$"E":I61:1210 C(I((3):H$(2)W$(6)U5$(2)W$(1)U5$(1)W$(3):H$(3)W$(6)U5$(2)W$(1)U5$(1)W$(4):H$(4)W$(6)U5$(2)W$(2)U5$(1)W$(4):H$(5)W$(5)U5$(2)W$(2)U5$(1)W$(3)4 3600g H$(1)W$(7)U5$(2)W$(9)U5$(1)W$(3):H$(2)W$(7)U5$(2)W$(8)U5$(1)W$(3):H$(3)W$(7IS IN" A$(4)U2$(C(1))". WHAT ARE THE":A$(5)"UNITS OF "U3$(I8)"?":I65:U5$(1)"/":U5$(2)"*":C(1)3F$U5$(1):U5$(1)U5$(2):U5$(2)F$ C(1)3C(1)63500 C(1)1C(1)5A9$W$(6):W$(6)W$(5):W$(5)A9$ H$(1)W$(6)U5$(2)W$(2)U5$(1)W$12:530:A$(1)" A KEY FORMULA IN PHYSICS IS ":I8C(1):L21:L13:530:I83120,32200 A$(2)U$(I8)", WHERE M(MASS) IS IN ":A$(3)U1$(C(1))" AND V(VELOCITY) IS IN":3300 C(1)C(1)3:A$(2)U$(I8)", WHERE F (FORCE) IS IN ":A$(3)U1$(C(1))" AND AREA 15:C(K)C(K)1:A(K)(T1$(I2))3C(K)::3040n L25:L119:530:K15:C(K)C(K)1:A(K)(T1$(I2))2C(K): A$(1)"CONVERT "(C(1))" "V$(I1)" TO "T$(I3)" "T$(I2):I11A$(2)"(1 LITER = 1 CUBIC DECIMETER)":I62:3970 I61:3970S L21:L601.09::A$(1)" CONVERT "(C(1))" METERS/SECOND TO":A$(2)"MILES/HOUR (1 METER = 1.09 YARDS)":I62:3970 L21:L13:530:I1C(1):L21:L12:530:C(1)3010,3100 L21:L12:530:I2C(1):I11I2C(1)2:I12I35:3030. I36:L25:L119:530:KITER = 1.06 QUARTS)":I63:3970 L25:L119:530:K15:C(K)C(K)1:A(K)C(K)176036000.914::A$(1)" CONVERT "(C(1))" MILES/HOUR TO":A$(2)"METERS/SECOND (1 YARD = 0.914 METERS)":I62:3970mT L25:L119:530:K15:C(K)C(K)1:A(K)C(K)360017TO":A$(2)"POUNDS/QUART (1 GRAM = 0.0353 OUNCES;":A$(3)"1 QUART = 0.946 LITERS)":I63:3970 L25:L119:530:K15:C(K)C(K)1:A(K)C(K)1.0628.316::A$(1)" CONVERT "(C(1))" POUNDS/QUART TO":A$(2)"GRAMS/LITER (1 OUNCE = 28.3 GRAMS;":A$(3)"1 LMANY "Z2$(I3)"S ARE THERE IN":A$(2)(C(1))" "D$(I4)"LITERS? (1 LITER = 1.06 QUARTS)":I62:3970 L21:L14:530:C(1)2600,2700,2800,2900:\( L25:L119:530:K15:C(K)C(K)1:A(K)C(K)0.9460.035316::A$(1)" CONVERT "(C(1))" GRAMS/LITER 0:I212090"K15:C(K)C(K)1:A(K)(Y3$(3))C(K)I7(W2$(I4))::A$(1)"HOW MANY "D$(I4)"LITERS ARE THERE IN":A$(2)(C(1))" "Z2$(I2)"S? (1 QUART = 0.946 LITERS)":I62:3970e*K15:C(K)C(K)1:A(K)(Y2$(3))C(K)I7(W2$(I4))::A$(1)"HOW )"S? (1 OUNCE = 28.3 GRAMS)":I62:3970 K15:C(K)C(K)1:A(K)(Y2$(2))C(K)I7(W2$(I4))::A$(1)"HOW MANY "Z1$(I3)"S ARE THERE IN":A$(2)(C(1))" "D$(I4)"GRAMS? (1 GRAM = 0.0353 OUNCES)":I62:3970 I71:I23I33I74 !L25:L119:53:A$(2)(C(1))" "D$(I4)"METERS? (1 METER = 1.09 YARDS)":I62:3970_ I71:I22I32I716~ L25:L119:530:I212070( K15:C(K)C(K)1:A(K)(Y3$(2))C(K)I7(W2$(I4))::A$(1)"HOW MANY "D$(I4)"GRAMS ARE THERE IN":A$(2)(C(1))" "Z1$(I2 THERE IN":R$Z$(I2)"S?":Z$(I2)"FEET"R$Z$(I2)"?"u A$(2)(C(1))" "R$" (1 YARD = 0.914 METERS)":I62:3970 K15:C(K)C(K)1:A(K)(Y2$(1))C(K)I7(W2$(I4))::R$Z$(I3)"S":Z$(I3)"FEET"R$Z$(I3)E A$(1)"HOW MANY "R$" ARE THERE IN":I2C(1):I21I31:20306 L21:L12:530:I3C(1)1d L21:L17:530:I4C(1):I12040,2060,2080} I71:I23I33I73 L25:L119:530:I2120506 K15:C(K)C(K)1:A(K)(Y3$(1))C(K)1I71(W2$(I4))::A$(1)"HOW MANY "D$(I4)"METERS ARE::K13:Y$(K),Y1$(K),Y2$(K),Y3$(K)::K17:D$(K),W2$(K)::K13:V$(K),U$(K)::K16:T$(K)::K14:T1$(K): 8K16:U1$(K),U2$(K)::K19:W$(K)::K12:U3$(K)::L21:L13:530:C(1)2000,2500,3000 L21:L13:530:I1C(1):L21:L13:530  ALG14Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.}103,1:104,8:750:700::I90A$:(A$)999051011L21:L16:530:C(1)6C9$"E":I95:W11:1040C9$"":I91:W10u K13:Z$(K),Z1$(K),Z2$(K)        ::3995@ X6X:Y6Y:Z(1)2:Z(2)3:Z(3)5:Z(4)7:K14:JZ(K)u X6J(X6J)Y6J(Y6J)X6X6J:Y6Y6J:3320 :P2X6Y6:X$"("(X6)"/"(Y6)")":Y61X$(X6) A$(3)" "X$" HRS. EARLIER THAN THE PLANE."(13):L21:L13:530:W4C(1):W4"THE TRAIN TRAVELS AT "(Y)" MPH AND IS":A$(4)(X)" MILES AHEAD OF THE PLANE AT THE":A$(5)" START OF THE TRAVELING."(13):A$(6)"HOW MUCH TIME DOES THE PLANE HAVE TO"z A$(7)" TRAVEL BEFORE IT CATCHES THE TRAIN?(IN HRS.)":K77:K14:A(K)T(KW1)W MANY MORE MILES DID THE PLANE HAVE TO TRAVEL?":K76:K14:A(K)D(K)::3995^b P22:3150f A$(5)"IF THE PLANE TRAVELED "(X)" MORE MILES":A$(6)" THAN THE TRAIN, WHAT WAS THE TRAIN'S RATE? (IN MPH)":K76:K14:A(K)B(KW1)::3995v A$(3)A$(2)A$(2)"."(13))0 C(1)3125,3300V5 L21:L13:530:P20:C(1)3150,3170,3190N A$(3)"AFTER "O$"THE PLANE AND THE TRAIN":A$(4)" ARRIVE AT POINT C SIMULTANEOUSLY."(13):P223174OQ A$(5)"IF THE TRAIN TRAVELED AT "(Y)" MPH,":A$(6)" HO0:K15:T(K)C(K)::WT(1):YB(1) R$(W):XW(AY):ZWA:K14:D(K)W(AB(KW1)):P(K)T(KW1)A::L21:L12:530:O$R$" HRS. ":W1O$R$" HR. " ' C(1)1Q4:P2:3114 ) Q3:P2 * A$(2)"A TRAIN LEAVES FROM POINT "C$(Q)C$(P)+ C(1)177,2488' K14:A(K)B(KW1)::3995G K14:A(K)T(KW1)::3995d K14:A(K)D(K)::3995" L21:L121:530:AC(1)10190:L25:L17:530:K15:B(K)C(K)1020::A$(1)"PLANE A LEAVES FROM POINT A DUE EAST AT "(A)" MPH."(13):L25:L19:53W1))W::X(AY)W:Q3:P2:S1:T2:4910:2050 ` L21:L140:530:EC(1)10011000:K14:F(K)(B(KW1)A)W:D(K)EF(K)::XE(YA)W:S2:T1:U2:V2:Q4:P1:4910:K7K71:A$(K7)"NOTE:THE PLANES ARE "(E)" MILES APART AT THE START." C(1)2467,24 L21:L13:530:C(1)2040,2200,2400j K14:D(K)(B(KW1)A)W::X(YA)W:Q3:P1:S2:T3:L2:4910 C(1)2108,2118,2138 <K14:A(K)B(KW1)::3995 FK14:A(K)T(KW1)::3995 ZK14:A(K)D(K)::3995/ Y11:L1:K14:D(K)(AB(KC(1)2000,2000,2000,3000,3000 L26:L115:530:AC(1)10530:K15:B(K)C(K1)10280::A$(1)"PLANE A TRAVELS FROM POINT A DUE EAST AT "(A)" MPH."(13):L25:L19:530:K15:T(K)C(K)::WT(1):YB(1):R$(W) O$(W)" HRS. ":W1O$"1 HR. "&  ALG15Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.x103,1:104,8:700::I90A$:(A$)999061009L21:L16:530:C(1)6C9$"E":I95:W11:1030C9$"":I91:W10 K14:C$(K)::L21:L15:530:      )(13)" (1 FOOT) = (12 INCHES)":D$(9)" = 144 SQUARE INCHES.":715:3::"THE EXAMPLES BELOW MAY HELP YOU SEE":3:"HOW TO SOLVE THE PREVIOUS PROBLEM: "::L89:721YLCONVERT 4 FEET TO INCHES: "(13)D$(6)D$(6)" (4 FT.)*(12 INCHES/1 FT.) = 48 INCHES"(13)" NOTE: FT. UNIT IN NUMERATOR CANCELS":D$(7)" OUT WITH FT. UNIT IN DENOMINATOR. ":D$(8)"EXAMPLE: CONVERT 1 SQUARE FOOT TO INCHES"D$(8)D$(8PROPRIATECONVERSION FACTOR. FOR EXAMPLE:":D$(2)"":D$(3)"TO CONVERT FROM MULTIPLY BY THIS ---------------- -------- -------------"&D$(4)"FEET TO INCHES FEET 12 IN./1 FOOT POUNDS TO OUNCES POUNDS 16 OZ./1 LB.":D$(5)"":D$(6)"EXAMPLE: 3974)W$(K)((W$(K)).00000001)/XK25:J1K1:W$(J)W$(K)J8:K8j::K91000A91:R110:K1I6:A$(K)::580:R91215,3980,1000,4000,46,6D$(1)"TO CONVERT FROM ONE UNIT TO ANOTHER, MULTIPLY THE QUANTITY BY THE AP)U5$(2)W$(9)U5$(1)W$(4):H$(4)W$(7)U5$(2)W$(8)U5$(1)W$(4):H$(5)W$(6)U5$(2)W$(9)U5$(1)W$(3)C(1)3A1$H$(1):H$(1)H$(2):H$(2)A1$K14:W$(K)H$(KW1)::3980K14:W$(K)((A(KW1)100000000)100000000):(W$(K),3)"999"3973530:DC(1)1:A(D)A(5)%A90:D92`R112:P$:S$:Q$::580:R91215,4000,1000,4600,46,6@D$(1)"TO SOLVE PROBLEMS OF THIS TYPE, YOU SHOULD SET UP AN EQUATION WHICH EXPRESSES THE RELATIONSHIP DESCRIBED.":D$(2)"":D$(3)"HERE ARE EXAMOSITIVE":S$"INTEGERS IS "(Y)". THEIR SUM IS "(V(3))". WHAT":Q$"IS THE SMALLER OF THE TWO?" L22:L1Y1:530:A(1)X:A(2)XY:A(3)XY:Z13035 A(4)XC(1):A(5)XYC(2):3041 A(4)XC(1):A(5)XYC(2) I95I91:3995 L21:L13:UM":Y$(2)"DIFFERENCE":Z1L21:L12:530:HC(1):LH:3004G H3:L1 P$"ONE POSITIVE NUMBER IS "(Y)" "Z$(Z):S$"THAN ANOTHER NUMBER. THEIR "Y$(L):Q$"IS "(V(H))". WHAT IS THE SMALLER OF THE TWO?":3030b P$" THE DIFFERENCE BETWEEN TWO P, ":Q$"WHAT IS SUE'S AGE?"* .A95:4000 T L21:L110:530:XC(1)6:L21:L14:530:YC(1)2:V(1)X(Y1):V(2)X(Y1):V(3)2XY:L21:L12:530:GC(1):G3000,3015; L21:L13:530:ZC(1):Z$(1)"TIMES GREATER ":Z$(2)"GREATER ":Z$(3)"LESS ":Y$(1)"S+"(A):W$(5)(AB)"X":I95W$(I8)W$(5):C9$"E"Q I9I8W$(D)W$(5):C9$"" L$(1)"TIMES YOUNGER":L$(2)"YEARS YOUNGER":L$(3)"TIMES OLDER":L$(4)"YEARS OLDER":P$" SUE IS "(A)" "L$(I8)" THAN "(B):S$"TIMES MARK'S AGE. IF MARK'S AGE IS XC(1):DC(2):I95I9I8R C$"("(B)"/"(A)")":BABA(BA)C$((BA))} BAAB(AB)C$"(1/"((AB))")" (AB10)(BA)C$"(2/3)" (AB10)(BA)C$"(3/2)"3 W$(1)C$"X":W$(2)(B)"X-"(A):W$(3)(AB)"X":W$(4)(B)"X}  ALG16Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.103,1:104,8:700:C9$"":Z0:I91:L21:L16:530:C(1)4I95:C9$"E"L21:L12:530:C(1)1010,2900 L22:L15:530:AC(1)1:BC(2)1:L22:L14:530:I8 75:LA$(3)"PLANE B TRAVELS AT "(Y)" MPH."(13):A$(4)"AFTER "O$"THE PLANES WILL BE HOW":A$(5)" MANY MILES APART?":K75:UOW FAST IS PLANE B TRAVELING? (IN MPH)":K75:~;A$(5)"HOW FAST IS PLANE B, WHICH IS SLOWER, TRAVELING? (IN MPH)":K75:BA$(3)"PLANE B TRAVELS AT "(Y)" MPH."(13):A$(4)"HOW SOON WILL BE THE PLANES BE "(X):A$(5)" MILES APART? (IN HRS.)":KT D = (360)(9), WHICH MEANS D = 3240 MILES.";L87:721.A$(2)"PLANE B LEAVES FROM POINT "C$(Q)C$(P)"."(13):L21:L13:530:C(1)4920,4930,49408A$(3)"AFTER "O$"THE PLANES WILL BE":A$(4)(X)" MILES APART."(13):Y114923.:A$(5)"H= (PR)(PT) AND (TR)(TT) = (PR)(PT). IN THIS PROBLEM,"-D$(6)"PR = 360 AND TR = 90 AND SINCE THE TRAINLEFT 27 HRS. EARLIER, TT=PT+27. SUBSTITUTING, (90)(PT+27) = (360)(PT). SOLVING, WE FIND PT=9. SINCE":D$(7)"D = (PR)(PT) WE SEE THAD THE PLANE GO BEFORE CATCHING THE TRAIN?"(13):D$(3)" LET D = DISTANCE TRAVELED AND LET PT=PLANE'S TIME PR=PLANE'S RATE"? D$(4)" TT=TRAIN'S TIME TR=TRAIN'S RATE ":D$(5)" FROM THE FORMULA D=RT WE GET D = (TR)(TT), D A$(K)::R117:580:R91215,3995,1000,4100,46,6715:734:D$(1)"PLANE A LEAVES FROM POINT A DUE EAST AT 360 MPH. A TRAIN LEAVES FROM POINT A DUEEAST 27 HOURS EARLIER THAN THE PLANE."D$(2)"IF THE TRAIN TRAVELS AT 90 MPH., HOW MANY MILES WOULTHE TRAIN, WHAT WAS THE RATE OF THE TRAIN?(IN MPH)":K75:K14:A(K)B(KW1)::3995 A$(4)"IF THE TRAIN TRAVELED AT "(Y)" MPH,":A$(5)" HOW LONG DID THE PLANE TAKE TO CATCH THE TRAIN? (IN HRS.)":K75:K14:A(K)T(KW1):1700:A90:K1K7:1W43  C(1)3510,3530,3550 A$(4)"IF THE TRAIN TRAVELED AT "(Y)" MPH,":A$(5)" HOW MANY MILES WOULD THE PLANE GO":A$(6)" BEFOR CATCHING THE TRAIN?":K76:K14:A(K)P(K)::3995U A$(4)"IF THE PLANE, AFTER "O$"OF TRAVEL,":A$(5)" CAUGHT SUM OF THE AREAS OF THE TWO RECTANGLES IS LX+LY, WHICH CAN BE":D$(5)"FACTORED TO GIVE L(X+Y).":D$(6)(13)"THE DIFFERENCE OF THE AREAS OF THE TWO RECTANGLES IS LX-LY, WHICH CAN BE "D$(6)D$(6)"FACTORED TO GIVE L(X-Y).":D$(7)(13)"E SUM OF THE SIDES TIMES THE DIFFERENCE OF THE SIDES."(13):L88:D$(1)"CONSIDER TWO RECTANGLES. THE LARGER HAS LENGTH L AND WIDTH X. ITS AREA IS LX. THE SMALLER RECTANGLE HAS LENGTH L AND":D$(2)"WIDTH Y. ITS AREA IS LY.":D$(3)""D$(4)"THENG, WE GET:":D$(4)(13)" A - B = (A+B)(A-B)":D$(5)(13)"SINCE THE SUM OF THE SIDES IS (A+B) AND THE DIFFERENCE OF THE SIDES IS (A-B),":D$(6)"WE CAN SEE DIRECTLY THAT THE DIFFERENCE"CkD$(7)"IN THE AREAS OF THE TWO SQUARES IS":D$(8)"EQUAL TO TH732  721\D$(1)(13)"CONSIDER TWO SQUARES. THE LARGER HAS A SIDE OF LENGTH A, AND THEREFORE HAS AREA OF A. THE SMALLER HAS A SIDE OF":D$(2)"LENGTH B, AND THEREFORE HAS AREA B. THE DIFFERENCE IN THEIR AREAS"aD$(3)"IS A-B. FACTORI HOW MANY SQ. INCHES WILL ITS":A$(3)"AREA BE IF EACH SIDE OF THE SQUARE IS" A$(4)T$(C(1))" BY "A$"?":I84:S$("+-*/",C(1),1):C(1)4900,4900,4850,4850K1I8:A$(K):::R112:580:R91215,3990,1000,4100,46,6L89İ731:4109715:L14:530:Z7$"/"(I7):I71Z7$""X A$(I6)Z7$:4800:C(1)1C(1)2A$A$" FEET"L C2(1)I6:C1(1)12:E(1)I7:H(1)4I7:T$(1)"INCREASED":T$(2)"DECREASED":T$(3)"MULTIPLIED":T$(4)"DIVIDED":A$(1)" IF THE PERIMETER OF A SQUARE IS":A$(2)"X FEET,TWO":A$(6)"RECTANGLES?":A$(7)"":I87\ >L24:L1I7:530:K25:B(K)C(K1):B(K)B(1)K8l H:K92110 RK14:A(K)B(KW1)::3990 A91:L22:L18:530:I6C(1)1:I7C(2)1:K23 I6K(I6K)I7K(I7K)I6I6K:I7I7K:3003$ :L21:AS OF TWO":D$(8)" L(X"(412C(1))"Y) = "T$(C(1))" OF AREAS.":A$(2)"RECTANGLES IS "(D(1))". IF BOTH RECTANGLES":A$(3)"HAVE A SIDE OF LENGTH "(I1)", WHAT"& A$(4)"IS THE "T$(C(1))" OF THE LENGTHS OF":A$(5)"THE TWO DIFFERING SIDES IN THE K)B(KW1)::3990 A90:L23:L19:530:I4C(1):I6C(2):I1C(3):I2I1I4:I3I1I6:4750:L22:L12:530:T$(1)"SUM":T$(2)"DIFFERENCE":C(1)1D(1)I2I3:I717:B(1)I4I6:2040 D(1)(I2I3):I78:B(1)(I4I6) A$(1)" THE "T$(C(1))" OF THE ARE(3)"IF THE "T$(C(1))" OF LENGTHS OF A SIDE":A$(4)"FROM EACH SQUARE IS "(D(1))", WHAT IS THE":A$(5)T$(C(2))" OF THOSE TWO SIDES?" yA$(6)"(HINT: USE A-B)":I86 ~L24:L1I7:530:K25:B(K)C(K1):B(K)B(1)K8 :K91150 K14:A(:I1I4I4:I2I6I6:4700:L22:L12:530:T$(1)"SUM":T$(2)"DIFFERENCE":I3(I1I2):C(1)1D(1)I4I6:I78:B(1)(I4I6):1105 ND(1)(I4I6):I717:B(1)I4I6 QA$(1)"THE DIFFERENCE BETWEEN THE AREAS OF":A$(2)"TWO SQUARES IS "(I3)" SQ. UNITS.":A$  ALG17Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.103,1:104,8:750:700:I91:L21:L16:530:C9$"":W10:C(1)6C9$"E":I95:W11L21:L13:530:C(1)1050,2000,3000~ A90:L22:L19:530:I4C(1):I6C(2)        HAN 'OLDER' AND 'MORE' GENERALLY MEAN 'GREATER'. ALSO, 'YOUNGER' GENERALLY MEANS 'LESS'."|715:732:L89:721ES GREATER THAN"X/D$(6)D$(6)" 4 TIMES B: A=5(4B)"D$(7)"A IS 5 GREATER THAN 4 TIMES B: A=4B+5":D$(8)"A IS 5 LESS THAN 4 TIMES B: A=4B-5"(13)dD$(9)"WHEN SETTING UP EQUATIONS OF THIS KIND, KEEP IN MIND TPLES OF HOW TO EXPRESS RELATIONSHIPS USING EQUATIONS:"(13)*D$(4)"A IS 4 TIMES GREATER THAN B: A=4B A IS 4 GREATER THAN B: A=B+4":D$(5)"A IS 4 TIMES SMALLER THAN B: A=(1/4)B A IS 4 LESS THAN B: A=B-4":D$(6)"A IS 5 TIMD(3)):D$(I52)"AND Q DIVIDES "(D(5))". EVENTUALLY YOU WILL":1150 I62D$(2)"FACTOR OUT -1: "W$(0):D$(3)" = (-1)("W$(5)")."d D$(I5)"LOOK FOR FACTORS OF "W$(5)" OF":I82:D(1)A(1):D(2)B(1):1150:D(1)A(7):D(2)B(7):I83:1150:D$(IS A FACTOR OF:"::" "W$(0)" ?":580:R91215,1030,1000,1036,46,6 D$(1)"SINCE THE FIRST TERM IS NEGATIVE,":I51:I62I54E I85:D(3)A(7)A(1):D(4)A(7)B(1)A(1)B(7):D(5)B(7)B(1):D$(I51)"THE FORM P"T$(1)"+Q"T$(2)", WHERE P DIVIDES "(:D(5)B(1)B(2):I80:I62D(3)D(3):D(4)D(4):D(5)D(5) 1150:A(7)A(2):B(7)B(2):A(2)A(6):B(2)B(6):I815:D(1)A(I8):D(2)B(I8):1150::R17:A91:C9$"":I91:L21:L19:500:I7((C(1)3)2):W$(I7)W$(5):I71I95C "WHICH OF THE FOLLOWING I)C9$""T T$(3)A9$"":I10:1100:1100:A(1)A(2)B(1)B(2)İ1100:1100:1015 A(3)A(1):B(3)B(1):A(4)A(2):B(4)B(2):I14:1100:1100:L22:L16:500:I6C(2):C(1)0A(2)A(1):B(2)B(1); D(1)0:D(2)0:D(3)A(2)A(1):D(4)A(2)B(1)B(2)A(1)O ALG18 INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.m103,1:104,8:750:700:A$:(A$)999101003L21:L15:500:I102C(1):A9$::C9$:T$(1)A9$:T$(2)C9$:C9$""T$(4)A9$:T$(5)"":1010 T$(4)A9$C9$:T$(5 K94900T3990N4900%T39902T39901)1A9$"">FO$"("(E(KW1))"X"S$:E(KW1)1O$"(X"S$xHP$(Y3(KW1))")":Q$"/"(H(KW1)):H(KW1)1Q$""JR$"(":A1$")":C1(KW1)1H(KW1)1R$"":A1$""LW$(K)R$A9$O$P$Q$A1$""::K25:M1K1:W$(K)W$(M)M8:K8 R::K(E(J)K)Y3(J)K(Y3(J)K)4923-94924o;H(J)K(H(J)K)E(J)E(J)K:Y3(J)Y3(J)K:H(J)H(J)K:4920|<:K27=C1(J)K(C1(J)K)H(J)K(H(J)K)C1(J)C1(J)K:4927>4928?H(J)H(J)K:4925 @::K14:A9$(C1(KW1)):C1(KWR$"":A1$""O W$(K)R$A9$O$A1$""::K25:M1K1:W$(K)W$(M)M8:K8a::K94850k3990$C2(1)I6:C1(1)12:E(1)I7:H(1)4I7:Y3(1)4C2(1):J25:L24:L19:530:E(J)C(1):C1(J)C(2):Y3(J)2C(3):H(J)2C(4)::J15:K27#8E(J)C1(K)C2(K)::J15:K29VE(J)K(E(J)K)C1(J)K(C1(J)K)E(J)E(J)K:4866`4868xC1(J)C1(J)K:4862::K14:A9$(C1(KW1))"X":C1(KW1)1A9$"X"O$"/"(E(KW1)):E(KW1)1O$""  R$"(":A1$")":C1(KW1)1E(KW1)1 INCHES. THEREFORE THE AREA IS":D$(9)"(SIDE) = (3X-12Y)."(13):J25:L23:L19:530:C1(J)C(1):C2(J)C(2):E(J)C(3)::C2(1)I6:C1(1)12:E(1)I7:H(1)4I7:S$"/"48564858K15:WE(K):E(K)C2(K):C2(K)W:K15:E(K)4E(K):C1(K) INCHES, SO THE SIDE LENGTH IS":D$(5)"3X+12Y INCHES. THEREFORE THE AREA IS":D$(6)"(SIDE) = (3X+12Y).":L89DD$(7)(13)"IF THE LENGTH OF EACH SIDE IS DECREASED BY Y FEET, THEN IT IS BEING DECREASED BY12Y INCHES, SO THE SIDE LENGTH IS":D$(8)"3X-12YOF EACH SIDE IS DIVIDED BY A FACTOR OF F, THEN THE NEW SIDE LENGTH WILL BE (3X)/F INCHES. THEREFORE,THE AREA WILL BE (SIDE)=((3X)/F)."(13):L86:nD$(4)(13)"IF THE LENGTH OF EACH SIDE IS INCREASED BY Y FEET, THEN IS IS BEING INCREASED BY12YT, OR 12*(X/4) = 3X INCHES.":C(1)34830D$(4)(13)"IF THE LENGTH OF EACH SIDE IS MULTIPLIEDBY A FACTOR OF F, THEN THE NEW SIDE LENGTH WILL BE (3X)F INCHES. THEREFORE,":D$(5)"THE AREA WILL BE (SIDE) = ((3X)F)."D$(6)(13)"IF THE LENGTH TO SOLVE THE PREVIOUS PROBLEM, SET UP THE EQUATION:":D$(9)(13)"THEN, TO SOLVE, DIVIDE BOTH SIDES OF THEEQUATION BY L."(13):L89:)D$(1)(13)"CONSIDER A SQUARE. IF THE PERIMETER IS":D$(2)"X FEET, THEN THE LENGTH OF EACH SIDE IS":D$(3)"X/4 FEE""C9$"0":530:C(3)6C(1)C(2):C9$"":T$(1)"X":T$(2)"X":T$(3)"":I213:I3C(I2):I4B(I3):I401160R$"-":I40R$"+":C9$""R$""(I41T$(I3)"")(I41)R$R$((I4),2)(I41T$(I3)"")(I41)R$R$(I4)C9$C9$R$T$(I3) :C9$6)" -B+"R$" -B-"R$(13)C9$" OR"C9$(13)" 2A 2A":D$(7)"SO HERE WE HAVE B-4AC="(I7)".":D$(9)D$(9)(13):L89:720LB(I1)(A(2)(D(I1)))(2A(1)):C(I1)(A(2)(D(I1)))(2A(1)):I1I11:`~L22:L13(1)"THE QUADRATIC FORMULA CAN BE USED TO":D$(2)"FIND THE ROOTS OF EQUATIONS OF THE FORM":D$(3)"AX+BX+C=0. IN THIS PROBLEM,":D$(4)"A="(A(1))", B="(A(2))", AND C="(A(3))".":D$(5)"THE FORMULA IS:"GR$"(B-4AC)":C9$" X = ------------":D$(0@4D$(8)"SINCE B-4AC < 0, THERE ARE NO REAL":D$(9)"ROOTS."8:"YOU ARE GIVEN THIS EQUATION:"::" "A9$:I110I2I3I4::R110:I61ĺ"FIND";:C9$"ALL":1086<"DESCRIBE";:C9$"">" THE ROOTS":580:R91215,1080,1000,1090,46,6B715:D$W$(I1)(B(I1))","(C(I1))R,:W$(5)"NO REAL ROOTS":R91:A95:I91:I70I95.L23:L14:530:I4C(1):I2C(2):I3C(3):I55:I9510760D(1)I7:I11:1100:D$(8)"THEREFORE, ONE ROOT IS "(B(1))",":D$(9)"AND THE OTHER ROOT IS "(C(1))".":108(A(2)A(2)A(1)A(3)):I11:1100:1100:1100:A(2)A(2):1100:A(2)A(2) I113:I2I114:(B(I1)B(I2)).02(C(I1)C(I2)).021062 $B(I2)B(I2).5:C(I2)C(I2).5:I18:I28 &::I291056 (I114:B(I1)C(I1)W$(I1)(B(I1)):1068*ONALROOTS.":1080w D$(8)"SINCE B-4AC>0 BUT IS NOT A PERFECT":D$(9)"SQUARE, THERE ARE TWO IRRATIONAL ROOTS.":1080 D$(8)"SINCE B-4AC = 0, THERE ARE TWO EQUAL":D$(9)"ROOTS.":1080J I80:D(1)(I7):D(2)(A(2)A(2)4A(1)A(3)):D(4)(I7):D(3)4:W$(1)"TWO DIFFERENT RATIONAL ROOTS":I11:I22:W$(2)"TWO IRRATIONAL ROOTS":I33:I44:W$(3)"TWO EQUAL (RATIONAL) ROOTS":W$(4)"NO REAL ROOTS":I91040,1044,1048,1076 D$(8)"SINCE B-4AC>0 AND IS A PERFECT":D$(9)"SQUARE, THERE ARE TWO DIFFERENT RATI0:C(1)1A(1)A(1):A(3)A(3) L23:L119:500:I113:B(I1)C(I1)9::1150:A9$C9$:I113:B(I1)B(I1)A(I1)::1150:A9$C9$"="A9$:L21:L12:500:I6C(1):L88:I611050 I94:I70I93 I70I1((I7.1)):I92:I1I1I7I91 R91:A9ЭI84C(3)C(1):C(4)C(2)Z A(1)C(1)C(3):A(2)C(1)C(4)C(2)C(3):A(3)C(2)C(4):1018 L23:L110:500:A(1)C(1)1:A(2)C(2):I21A(2)A(2) A(3)C(3)1:I21I23A(3)A(3) I7A(2)A(2)4A(1)A(3):I70I81I82:1014 L21:L12:50  ALG19Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.103,1:104,8:750:700:L21:L14:500:I2C(1):L15:500:I8C(1):I831014L24:500:C(1)C(1)1:C(3)C(3)1:I21C(2)C(2)I21I23C(4)C(4)    -":A90R$"+":A9$""R$""[D(I2)0:(A91T$(I2)"")(A91)R$R$((A9),2):1158(A91T$(I2)"")(A91)R$R$(A9)A9$A9$R$T$(I2):W$(I8)A9$:::4C(1)1:C(2)80RC(1)C(2)18C(1)3:C(2)8PTC(1)C(2)24C(1)5:C(2)8gVC(3)4C(2)C(2)XA(I1)C(1):B(I1)C(2):I11ıZI21I11:A(I2)A(I1)B(I2)B(I1)I28\:I291102^~A9$"":I215:D(I2)01160A9D(I2):R$"53)"GUESS THE FACTORS "W$(2)" AND "W$(3)".":D$(I54)"YOU CAN THEN CHECK THESE BY MULTIPLYING" D$(I55)"THEM, WHICH GIVES "W$(5)"."(13):L8I55:715:720 LI1I11 NL23:L17:530:C(1)C(2)8C(1)1:C(2)1PC(1)C(2)8(C(1)C(2))?  ALG21Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.s103,1:104,8:700:A$:(A$)999111004L21:L15:500:I102C(1):C9$::W$(8),W$(9)L22:L14:530:C(1)C(2)41008 D(7)C(1)1:D(8)C(2 !!! ! ! ! ! !!!!!R$:A$""C9$A$R$;R$"-":I60R$"+":A1$""R$""h(I61C9$"")(I61)R$R$((I6),2)(I61C9$"")(I61)R$R$(I6)A1$A1$R$C9$:T7A(I8):I70ıZvC(2)C(1)D(I7):C(1)C(1)B(I7)C(0)D(I7):C(0)C(0)B(I7):I78KK1`z~A1$"":K1K01:I6C(K1):I601168C9$"":K10C9$W$(8):K12C9$C9$""R$"":K1KR$W$(9):KK12R$""R$R$""R$""A$C9$:C9$=[T$(I8)(B$,((I1I2)2))A1$(B$,((I1I21)2)):1118\((I2I1)2)0T$(I82)T$(I82)(B$,((I2I11)2)):I1I2:1118]T$(I82)(B$,((I2I1)2))T$(I82)(B$,((I2I11)2)):I1I2^T$(I81)("------------------",I1):tI8I81:I0:1140:1150:T$(I8)A1$:I1(A1$):K0:C(0)1:C(1)0:1140:1140:1150:A1$"1"1112RT$(I81)T$(I82):T$(I8)(B$B$,I1):T$(I82)T$(I8):XT$(I8)A1$:I2(A1$):I2I11118YI2I11116Z((I1I2)2)0T$(I8)A1$(B$,((I1I21)2)):1118 (-8X+6)-(-3X+31) = ------------, SO S-R=---------------- "<D$(4)D$(4)"(4X-3)*(X+5) "B$:D$(5)" -5X-25 -5*(X+5) -5 =------------ = ------------ = ---- . (4X-3)*(X+5) (4X-3)*(X+5) 4X-3":720VLC(0)1:C(1)0:K4X+17X-15":D$(2)" -2 "B$B$"S = ---. THEN FACTOR R'S DENOMINATOR TO X+5"E6D$(3)"1 (-2)*(4X-3) GET R=------------, SO S=------------ ":B$" (4X-3)*(X+5)":D$(3)" -3X+3"D$(3)B$B$:L85:D$(4)" -8X+6 :" "R$R$R$T$(I72)R$R$R$R$" "T$(7I7):*"WHICH OF THE FOLLOWING IS THE SAME AS"::" "T$(7):" "T$(8)" ?":" "T$(9):580:R91215,1056,1000,1071,46,6Z/715:734:D$(1)B$B$" -3X+31 SUPPOSE YOU ARE GIVEN R= -----------, "B$B$""R+S":W$(4)"-R-S":L21:L12:500:C(1)0I23:I32u W$(I2)"R-S":W$(I3)"S-R":R$" ":(T$(1))(T$(4))27R$""+"R115:I73I25:"SUPPOSE YOU ARE GIVEN THAT:"::" "R$R$R$T$(I7)R$R$R$R$" "T$(5I7):R$"R"R$"="R$T$(I71)R$","R$"S"R$"="R$T$(6I7)B(I2)D(7)B(7)D(I2)1000] I52B(I3)B(I3):D(I3)D(I3):A(4)7:A(6)I1:A(7)I4:A(9)0 I92I7A(1):B(I7)B(I7):D(I7)D(I7) I92I94I7A(4):B(I7)B(I7):D(I7)D(I7)4 I80:1100:1100:1100:R91:C9$"":A94:I11:I22:I33:I44:W$(1)(I3)- I70I72B(I4)B(I4):D(I4)D(I4)I I51038,1040,1038,1040u B(7)B(I3)B(I4):D(7)D(I3)D(I4):1042 B(7)B(I3)B(9)B(I1):D(7)D(I3)B(9)D(I1):1042 B(7)B(8)B(I2)B(9)B(I1):D(7)B(8)D(I2)B(9)D(I1) B(I1)D(7)B(7)D(I1)I1:L22:L14:500:I9C(1)1:I7C(2):L24:L16:530:I1C(1):I2C(2):I3C(3):I4C(4):L21:L15:500:I5C(1):A(2)I1:A(5)I2:A(7)7:A(3)I2:A(8)I2:I52I54I38:A(3)0 A(1)I3:A(6)I1:A(9)I1:I50I49:A(6)0 A(4)I4:I72B(I3)B(I3):D(I3)DB(9)C(2)1:B(8)C(1)1:B(5)0:D(6)0:B(6)1:D(5)1:D(8)0:I114p L22:L15:530:C(1)C(2)8C(1)1:C(2)1 D(I1)C(1):B(I1)C(2):L21:L12:500:C(1)0B(I1)B(I1) I111022 I21I11:D(I1)D(I2)B(I1)B(I2)I28 I2:I291012 O ALG20 INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.m103,1:104,8:750:700:A$:(A$)999111003L21:L15:500:I102C(1):C9$::W$(8),W$(9):L22:L14:D(9)0:B$" "530:C(1)C(2)41008B         1025 I7$(B$,I7)a T$(9)" \/ "I7$W$(2):R110:A95:I7((I4I2)2):I70I7$"":1027r I7$(B$,I7) T$(7)B$" /"I7$W$(1):A1$" __________":T$(6)B$(A1$,I42):T$(8)B$("/ ----------",I42):B$B$B$:W$(2)"1"T$(7)" \/"W$(1):530:I114:A(I1)C(I1):0 I8$(13)" "k L16:500:K1:I114:B(I1)C(I1):D(I1)0:B(I1)1K0 :K1018:D(1)B(1):D(2)B(2):I10:1100:D(3)B(3):D(4)B(4):1100:I2(W$(1)):I3(W$(2)):I4I2:I3I2I4I3 I7((I4I3)2):I70I7$"":  ALG22Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.s103,1:104,8:700:A$:(A$)999131004 L21:L13:500:I103C(1):R$::B$" ":I70:A20:A2$"":I7$"":A30:A3$"":T$(1),T$(4),T$(5):L24:L15!!!""" " " " " $"1"ıHA1$"1"A1$A9$:>JA1$"("A1$")*("A9$")":")(I61)R$R$((I6),2)A(I61C9$"")(I61)R$R$(I6)TA9$A9$R$C9$\:1090:I7I1:1300:A1$A9$:I7I2:1300:1350:T$(I8)A1$I7I3:1300:A1$A9$:I7I4:1300:1350:T$(I82)A1$:1120C(0)1:C(1)0:K0:1150:1200:FA9C(0)D(I6):7A9$"":K1K01:I6C(K1):I601218eC9$"":K10C9$W$(8):K12C9$C9$"^2"R$"":K1KR$W$(9):KK12R$""R$R$"^2"R$""A$C9$:C9$R$:A$""C9$A$"*"R$R$"-":I60R$"+":A9$""R$""(I61C9$"(I81)("------------------",I3):I8I83:f~I6A(I7):I61152,1152,1152,1152,1156,1158,1160,1160:C(2)C(1)D(I6):C(1)C(1)B(I6)C(0)D(I6):C(0)C(0)B(I6):KK1:C(2)C(1):C(1)C(0):C(0)0:KK1:KK1:C(K)0: C(1)C(1)D(I6):C(0)2)0T$(I8)T$(I8)(B$,((I3I11)2)):1128ndT$(I8)(B$,((I3I1)2))T$(I8)(B$,((I3I11)2)):1128e((I1I3)2)0T$(I82)T$(I82)(B$,((I1I31)2)):I3I1:1128fT$(I82)(B$,((I1I3)2))T$(I82)(B$,((I1I31)2)):I3I1+hT$:K0:C(0)1:C(1)0:I7I3:1150:I7I4:1150:1200PZT$(I82)A9$:A9$"1"1120w\T$(I81)T$(I8):T$(I8)"1"I90:^I2(T$(I8)):T$(I8)(B$B$,I2):T$(I82)T$(I8):I8I83:`I1(T$(I8)):I3(T$(I82)):I1I31128aI1I31125.b((I3I1)E, "W$(I9)" = "T$(8):D$(8)""B$T$(9)(13)(13)(13):L88:721`BA(I1)A(I3)I10:I30{DA(I2)A(I3)I20:I30FA(I1)A(I4)I10:I40HA(I2)A(I4)I20:I40JL1090:K0:C(0)1:C(1)0:I7I1:1150:I7I2:1150:12000XT$(I8)A9$1:I26:I32:I45:I91I93I12:I25:I31:I46 ,1250:D$(3)(13)" "T$(1)" "T$(4):D$(4)" R="T$(2)" , S="T$(5) .D$(5)" "T$(3)" "T$(6) 0I13:I25:I34:I46:1250:B$B$(B$,(W$(I9))):D$(6)(13)B$T$(7)E2D$(7)"THEREFORING IS THE SAME AS"::" "T$(1):" "T$(2)" ?"i " "T$(3)::580:R91215,1040,1000,1056,46,6 715:D$(1)(13)"FIRST, YOU SHOULD TOTALLY FACTOR BOTH":D$(2)(13)"FRACTIONS:":I81:I12:I24:I31:I43:I93I11:I23:I32:I44/ (1250:I1":R91:A94:C9$"":R115u " SUPPOSE YOU ARE GIVEN THAT:"::I11:I22:I33:I44:R$" ":(T$(4))(T$(7))27R$""3 " "R$R$R$T$(4)" "R$R$R$R$T$(7):R$"R"R$"="R$T$(5)R$","R$"S"R$"="R$T$(8):" "R$R$R$T$(6)" "R$R$R$R$T$(9)::"WHICH OF THE FOLLOW1)C(I1)::L21:L14:500:A(0)0:I9C(1)1:I13:I25:I34:I46:I81:1100:I12:I24:I31:I43:I93I13:I21:I34:I42 1100:I11:I26:I32:I45:I91I93I12:I25:I31:I46 1100:I901024 W$(1)"R*S":W$(2)"R/S":W$(3)"S/R":W$(4)"1/(R*S))1:I1149 L22:L15:530:C(1)C(2)8C(1)1:C(2)1v D(I1)C(1):L21:L12:B(I1)C(2):500:C(1)0B(I1)C(2) I111022 I21I11:D(I1)D(I2)B(I1)B(I2)I28 I2:I291012 I1:B$" "w L26:L19:500:I116:A(I5):B(2)D(2)D(3):A(2)A(1)D(1):I12:I60:1100:I61*D$(3)"FIRST, MULTIPLY THE TERMS OUTSIDE THE RADICAL AND THEN MULTIPLY THE TERMS":A9$""A9$A9$"":A9$"AB"A9$"(AB)"J.D$(4)"INSIDE THE RADICAL.":B(1)B(2)D(1)D(1):I11:1100:D$(5)MPLIFY BOTH RADICALS:":D$(5)"THEN, YOU CAN "R$" THEM:":I113:B(I1)I7:1100::A2$A1$:A1$"=":A6:B1:1200:D$(4)W$(0):A7:B2:1200:D$(4)D$(4)W$(0)$A1$A2$:A1:B2:1200:D$(6)(W$(0),(W$(0))1)" ="I8$W$(3)(13):L86:7215(A(1)D(4)D(E SAME AS:":4:W$(0)< 580:R91215,1047,1000,1050,46,6u 715::D$(1)"WE ARE ASKED TO SIMPLIFY:":D$(2)W$(0) I81064:A(1)D(1)D(2):A(2)D(3)D(4):A(3)A(1)A(2):A1$"+":R$"ADD":I92A(3)A(1)A(2):R$"SUBTRACT":A1$"-" D$(3)"FIRST, SII28:I18 ::I191030; I115:1100::I81I61 1100:I17:1100:A91:C9$"":K15:W$(K)W$(K)(13)::L22:L15:R17:500:I5C(1)1:I5I9C(2)2I53I9 W$(I5)W$(5):I5I9C9$"E" A6:B7:1200 "WHICH OF THE FOLLOWING IS TH:B(5)I7D(2):L21:L12:500:I9C(1)1:I5I1D(1):A1$"+":I92I5I5:A1$"-" A(3)I1I5:A(4)A(I9):A(5)A(I9):A(6)D(1):B(6)D(2)D(2)I7:A(7)D(3):B(7)D(4)D(4)I7 I125:I3A(I1)A(I1)B(I1):I21I11 A(I2)A(I2)B(I2)I3A(I1)A(I1)2:B(1):A(4)2D(4)D(5):B(2)1B(2)2` B(4)B(1):A(5)A(1):B(5)B(2)2:I60:A1$"*":I91:1030 L21:L14:500:I7C(1):I72I75I7N L24:L14:500:K14:D(K)C(K)1::I1D(1)D(2):I2D(3)D(4):A(1)I1I2:A(2)I1I2:B(1)I7:B(2)I7:B(3)I7:B(4)22:500:I6C(1):I8C(2):I801018U L23:L14:530:K13:D(K)C(K):C(K)4D(K)5$ :L22:L14:500:D(4)C(1)1:D(5)C(2)1:A(6)D(4):B(6)D(1)D(2):A(7)D(5):B(7)D(1)D(3):A(1)D(1)D(4)D(5):B(1)D(2)D(3):A(2)A(1):B(2)D(2):A(3)D(4)D(5):B(3)Ь  ALG23Z INTELLIGENT TUTOR / ALGEBRA 1 (C) 1983 INTELLIGENT SOFTWARE, INC.s103,1:104,8:700:A$:(A$)999141004I8$(13)" ":A2$"":L21:L19:500:K0C(1):A9$::L22:L12:500:I6C(1):I8C(2):I801018" L22:L1"""""""" "\/"W$(8)>B(3)0B(4)0A(3)A(4)6W$(7)"("W$(7)")"`W$(7)"1"C9$C9$"/"W$(7)A3(C9$):A30A3$"":1165K1A3:A3$A3$" ":W$(I2)A2$R$I8$C9$(13):I2I21A20:A2$"":A30:A3$"":3$"":AB$B$:I2I21I4)B(I4)2D(I4)::1100:I434:D(I4)((B(I4)1)2):C(I4)2D(I4)B(I4)::1100:I414:D(I4)C(I4)::1100:C9$W$(6):W$(8)"1"R$"":1160C9$"1"C9$""A2(C9$):A20A2$"":1159K1A2:A2$A2$" ": R$(A1$,(W$(8))2):C9$C9$ȁI414:I5D(I4):I501108MND(I4)0:I6A(I4):I62I63A9A9I6I5:1108fPC9$""C9$C9$"*"RC9$C9$T$(I6):I51C9$C9$(" ",I5,1)T:A91C9$""C9$((A9.1))C9$VI1I11:W$(I1)C9$:~I15:I412:D(I4)(B(I4)2):C(TIPLY THROUGH BY \/3/3 TO GET:"D$(8)B$" ___ __ __"(13)" X*Y /3*X X*Y\/3X X*Y\/3X"(13)"= ------ / --- = -------- = --------"D$(9)" 2*3 \/ 3*3 2*3 108"(13):L89:715:734:721LA91:C9$"":DENOMINATOR TO GET / X*Y"Y D$(4)B$B$B$"/ ------- "B$B$" \/"" 2*3" D$(5)B$B$B$" _ BRING OUT ALL EVEN POWERS: X*Y /X "B$B$" ------- / -":D$(6)B$B$" 2*3 \/ 3"D$(7)B$B$" ___"(13)"MULICH OF THE FOLLOWING IS THE SAME AS:":I669:T$(I6)::580:R91215,1040,1000,1044,46,6 D$(1)"SUPPOSE YOU ARE ASKED TO SIMPLIFY:"B$" _______":D$(2)" / X*Y"(13)" / -------"(13)" \/ 3888":D$(3)B$B$B$" _______"" FACTOR THE :T$(8)I8$:T$(9)I8$:R18 I21:1150:I3B(1):B(1)(I31):1150:B(1)I3:B(4)B(4)2:1150:B(4)B(4)2:I3B(3):B(3)2I3:I30B(3)1 1150:B(3)I3:B(2)B(2)1:1150:B(2)B(2)1:I91:L21:L19:500:I6((C(1)1)2)1:W$(I6)W$(5):I61I95Z "WH