ZXTape! 2 Micro Maths - Tape 2LCL G. Ludinski1984English Educational24.00 UndeterminedOriginalrTZXed by Andrew Barker For Karl Brown. 1984 Release, Original in 1981 perhaps only available to Education/Schools0 on 33 topics0 SUITE 14004A) Simplification of bracketed quantities in AlgebraLCL140A =\q6'? 5110 LCL140A COPYRIGHT (C) G.LUDINSKI 1981 LS=13P A$(24@,LS) 'S$=" " 6:6: 2:6:S$; %" LCL140A  G.Ludinski 1981 "; (S$:6:0:6 2 <"What is your name ? " FN$ P Z"Here are some problems ";N$ d C=0 f T=1 h W=1 i P=0 n o P0 p P=P+1 x 500z }  Q$;"="; I$ I$="?"3500 I$ I$=""220\ X=9172, LI=I$ I=1LI ,I$(I)"-"(I$(I)<"0"I$(I)>"9")220\ I (I$-A)X1804 220\ I$T$="Y"+(E) HE<0T$="-"+T$ RA$(1)=E+"Y"+V$ \A$(2)=V+E$+"Y" fA$(3@)=T$+V$ p'A$(4)=V+E$(1)+"Y"+(E) z N=4 L$=A$(1) eS=0N$="AND A MINUS SIGN OUTSIDE THE BRACKETS MEANS CHANGE SIGNS INSIDE THE BRACKETS" AM$="AS YOU MUST MULTIPLY EACH TERM INSIDE THE BRACKETS BY "+E W=-11205 Q$="(Y"+E$+")(Y"+F$+")" H$="(y+A)(y+B) = y^2 + (A+B)y + AB FIRST MULTIPLY THE y TERMS TOGETHER THEN MULTIPLY THE TWO INSIDE TERMS (A AND THE 2ND y) AND THEN THE TWO OUTSIDE TERMS (B AND THE FIRST y),THEN ADD THEM.tHEN MULTIPLY THE CONSTANTS"  T$="Y^2"  U$=D$+"Y" W$=D$(1)+"Y"+(D)  Z$="+Y^2"  X$=D+"Y" D>0C$="Y"+D D<0C$="-Y"+(D) A$(1)=T$+U$+V$ A$(2)=T$+W$+V$ A$(3)=V+Z$+U$ A$(4)=V+Z$+W$ A$(5)=X$+V$+Z$ A$(6)=C$+V$+Z$ $A$(7)=T$+V$+U$ .A$(8)=T$+V$+W$ 8A$(9 )=V+U$+Z$ BA$(10 )=V+W$+Z$ LA$(11 )=X$+Z$+V$ VA$(12 )=C$+Z$+V$ ` N=24@ jL$=A$(1) t%M$="AS "+E$+"y + "+F$+"y = "+D$+"y" ~ N$="AND "+E$+" X "+F$+" = "+V$  1205 Y$=Y Y>0Y$="+"+Y$   LF=B$ LFB1350( I=1̺(LF/B) EL=B*I B$(EL)=" "1340'  B$(EL+1)" "1290!@ B$=B$(EL)+B$(EL+2) LF=LF-1  1340'  K=131x B$(EL-K)" "1335& 'B$=B$(EL-K)+S$(K)+B$(EL-K+1) ( LF=LF+K 2 1340' 7K <I F P#Z=1̺(Z$/32)+1 `BZ=B*Z aBZ>Z$BZ=Z$ bZ$(B*(Z-1)+1BZ); nZ p Z$Q$+"=" s x w VP=22 - 23689\:1;19,0;" Calculator mode ";1;19,0 B$="" #BR=0:B$:B$=""3503 B$="?"B$="AC"3510 I=1̱B$:I$=B$(I):(I$<40(ůI$>579)I$" "I$"^"I$"="I$"/"I$""I$""I$""I$""I$""3503 BR=BR+(I$="(")-(I$=")") I BR03503 B$="?"3530 DB$="AC"20,0;S$;19,0:B$="":3502 "B$(B$)="="B$=B$(̱B$-1) #B$;19,0:3502 A19,0;S$;S$;S$(10 );VP+2,0:I$: I=0̱B$ I=05025  CB=B$(I) CCB<65A(CB91[CB96`)32006},CB:5020 ACB97aCB122z32006},(CB-32 ):5020 32006},(CB+32 ) H=32000} I  D=32000} ?A(D$t,B)=D$(B)-480-7*(D$(B)>579)  4C(D$t)=16*A(D$,1)+A(D$,2) 0D$:D$"**"D,C(D$):D=D+1:5140 3"3E","02","CD","01","16","3E","00","D7","C9","**" ( P d Pctwp@bxP@0efsgvy n@6hS}= 6Y+30 30+6Y Y6+30 30+Y6 S U+10YW+Y10Z+Y^2X10YCY10IBAND +8 X +2 = +16RYNE+6F+5V+30Y+11D+11Q6(Y+5)H2A(y + B) = Ay + AB -A(y + B) = -Ay - AB TY6L 6Y+30 M8AS YOU MUST MULTIPLY EACH TERM INSIDE THE BRACKETS BY 60B) Ratio and ProportionLCL140B a" 5110 LCL140B COPYRIGHT (C) G.LUDINSKI 1981 'S$=" " 6:6: 2:6:S$; %" LCL140B  G.Ludinski 1981 "; (S$:6:0:6 2 <"What is your name ? " FN$ P Z"Here are some problems ";N$ d C=0 f T=1 h W=1 i P=0 n o P0 p P=P+1 x 500z }  B$=Q$:5000:"="; I$ I$="?"3500 I$ I$=""220\ W=1172, LI=I$ I=1LI 6I$(I)"-"I$(I)"/"(I$(I)<"."I$(I)>"9")220\ I &I$=A$Ž(I$-A)0.01z# =1804 220\ I$=A$1804 220\  "Yes,well done" C=C+1  3520 :.5,5:.73333,2:T1270  )"No,";:B$=H$:5000:",try again" T=2  130  "Sorry,the answer = "  ,L$ . @B$=M$:5000: J TB$=N$:5000: ^ cSC=(C/P*100H) h"Your score = ";SC;" %" r |"Do you want more? (Y/N)" R$ .R$"Y"R$"N"R$""R$"y"R$"n"362j R$="N"R$="n"450  T=1  110\  "End of program" H=4535 L$="" M$="" N$=""  X=9 A=0:A$=""  B=32  W=-W &E=(*9+1) 0!G=(*4+1)*10 :F=G*E D!W=1F>59l550 N"W=-1F>99F550 XE$=E bF$=F lW-1680* vR1=G/10  R2=10  R3=1  K=100H  7204 R1=G/10  R2=6@  R3=1  K=60p I=15 *(R1/I)ɺ(R1/I)(R2/I)ɺ(R2/I)770@  R1=R1/I  R2=R2/I  R3=R3*I I  OB$="AS BOTH "+F$+" AND "+(E*K)+" ARE EXACTLY DIVISIBLE BY "+(R3*E*10 )  1210@  N$=B$ *W=1870Y 43Q$="wHAT PROPORTION OF "+E$+" M. IS "+F$+" CM." >H$="PUT BOTH VALUES INTO THE SMALLER UNITS.pUT THE SECOND VALUE OVER THE FIRST VALUE.tHEN CANCEL OUT BY ANY COMMON FACTORS" HA$=R1+"/"+R2 J A=(R1*100d/R2)/100d RL$=A+" or "+A$ \QM$="AS "+E$+" X 100 = "+(E*100H)+" AND "+F$+" / "+(E*100H)+" = "+A$ fW=-11000z pZ$=" MINUTES " zF=1Z$=" MINUTE " Y$=" HOURS " E=1Y$=" HOUR " *B$="wHAT IS RATIO OF "+F$+Z$+"TO "+E$+Y$  1210@ Q$=B$ VH$="PUT BOTH VALUES INTO THE SMALLER UNITS THEN CANCEL OUT BYANY COMMON FACTORS" A$=R1+":"+R2 *L$=A$+" as "+E$+" x 60 = "+(E*60<) +M$="AND "+F$+" : "+(E*60p)+" = "+A$  LF=B$ LFB1350( I=1̺(LF/B) EL=B*I B$(EL)=" "1340'  B$(EL+1)" "1290!@ B$=B$(EL)+B$(EL+2) LF=LF-1  1340'  K=131x B$(EL-K)" "1335& 'B$=B$(EL-K)+S$(K)+B$(EL-K+1) ( LF=LF+K 2 1340' 7K <I F P#Z=1̺(Z$/32)+1 `BZ=B*Z aBZ>Z$BZ=Z$ bZ$(B*(Z-1)+1BZ); nZ p Z$Q$+"=" s x w VP=22 - 23689\:1;19,0;" Calculator mode ";1;19,0 B$="" #BR=0:B$:B$=""3503 B$="?"B$="AC"3510 I=1̱B$:I$=B$(I):(I$<40(ůI$>579)I$" "I$"^"I$"="I$"/"I$""I$""I$""I$""I$""3503 BR=BR+(I$="(")-(I$=")") I BR03503 B$="?"3530 DB$="AC"20,0;S$;19,0:B$="":3502 "B$(B$)="="B$=B$(̱B$-1) #B$;19,0:3502 A19,0;S$;S$;S$(10 );VP+2,0:I$: I=0̱B$ I=05025  CB=B$(I) CCB<65A(CB91[CB96`)32006},CB:5020 ACB97aCB122z32006},(CB-32 ):5020 32006},(CB+32 ) H=32000} I  D=32000} ?A(A$Pp,B)=A$(B)-480-7*(A$(B)>579)  4C(A$Pp)=16*A(A$,1)+A(A$,2) 0A$:A$"**"D,C(A$):D=D+1:5140 3"3E","02","CD","01","16","3E","00","D7","C9","**" ( P d }ctwp@xa~Lbeg f x 9}<DhS}S Z MINUTES Y HOUR RYE4F80N/AS BOTH 80 AND 400 ARE EXACTLY DIVISIBLE BY 80Q#wHAT PROPORTION OF 4 M. IS 80 CM.H}PUT BOTH VALUES INTO THE SMALLER UNITS.pUT THE SECOND VALUE OVER THE FIRST VALUE.tHEN CANCEL OUT BY ANY COMMON FACTORSA1/5L 0.2 or 1/5M#AS 4 X 100 = 400 AND 80 / 400 = 1/5IB}PUT BOTH VALUES INTO THE SMALLER UNITS.pUT THE SECOND VALUE OVER THE FIRST VALUE.tHEN CANCEL OUT BY ANY COMMON FACTORS0C) Polygon PropertiesLCL140C Q0S 5110 LCL140C COPYRIGHT (C) G.LUDINSKI 1981 'S$=" " 6:6: 2:6:S$; %" LCL140C  G.Ludinski 1981 "; (S$:6:0:6 2 <"What is your name ? " FN$ P Z"Here are some problems ";N$ d C=0 f T=1 h W=1 i P=0 n o P0 p P=P+1 x 500z zW-1139 {{::::::ST=8*23689\+8:SK=3:119w,ST-24:6*SK,0:4*SK,4*SK |E40,6*SK }#E5-4*SK,4*SK ~ E6-6*SK,0 $E7-4*SK,-4*SK E80,-6*SK 119w,ST-24 #E=310 *SK,4*SK $E=410 *SK,10 *SK #E=56*SK,14*SK E=60,14*SK $E=7-4*SK,10 *SK #E=8-4*SK,4*SK  B$=Q$:5000:"="; I$ I$="?"3500 I$ I$=""220\ X=9172, LI=I$ I=1LI ,I$(I)"-"(I$(I)<"0"I$(I)>"9")220\ I (I$-A)X1804 220\ I$=A$1804 220\  "Yes,well done" C=C+1  3520 :.5,5:.73333,2:T1270 150: )"No,";:B$=H$:5000:",try again" T=2  122z  "Sorry,the answer = "  ,B$=L$:5000: . @B$=M$:5000: J TB$=N$:5000: ^ cSC=(C/P*100H) h"Your score = ";SC;" %" r |"Do you want more? (Y/N)" R$ .R$"Y"R$"N"R$""R$"y"R$"n"362j R$="N"R$="n"450  T=1  110\  H=4535 L$="" M$="" N$=""  B=32  W=-W & X=1 0E=(*6+3) :E$=E DZ$="THE SUM OF THE INTERIOR ANGLES OF A POLYGON = (2N - 4) X 90 DEGREES WHERE N IS THE NUMBER OF SIDES " N A=(2*E-4)*904 SA1=A XA$=A b'M$="AS ((2 X "+E$+") - 4) X 90 = "+A$ lW=1660% v@Q$="tHE SUM OF THE INTERIOR ANGLES OF A "+E$+" SIDED POLYGON" H$=Z$ L$=A$+" DEGREES" W=-11000z SQ$="tHE SIZE OF EACH OF THE INTERIORANGLES OF A "+E$+" SIDED REGULAR POLYGON" ?H$=Z$+"AND A REGULAR POLYGON HAS ALL INTERIOR ANGLES EQUAL"  A=(A/E) A$=A L$=A$+" DEGREES" ?N$="AND EACH INTERIOR ANGLE = "+(A1)+" / "+E$+" = "+A$  LF=B$ LFB1350( I=1̺(LF/B) EL=B*I B$(EL)=" "1340'  B$(EL+1)" "1290!@ B$=B$(EL)+B$(EL+2) LF=LF-1  1340'  K=131x B$(EL-K)" "1335& 'B$=B$(EL-K)+S$(K)+B$(EL-K+1) ( LF=LF+K 2 1340' 7K <I F P#Z=1̺(Z$/32)+1 `BZ=B*Z aBZ>Z$BZ=Z$ bZ$(B*(Z-1)+1BZ); nZ p Z$Q$+"=" s x w VP=22 - 23689\:1;19,0;" Calculator mode ";1;19,0 B$="" #BR=0:B$:B$=""3503 B$="?"B$="AC"3510 I=1̱B$:I$=B$(I):(I$<40(ůI$>579)I$" "I$"^"I$"="I$"/"I$""I$""I$""I$""I$""3503 BR=BR+(I$="(")-(I$=")") I BR03503 B$="?"3530 DB$="AC"20,0;S$;19,0:B$="":3502 "B$(B$)="="B$=B$(̱B$-1) #B$;19,0:3502 A19,0;S$;S$;S$(10 );VP+2,0:I$: I=0̱B$ I=05025  CB=B$(I) CCB<65A(CB91[CB96`)32006},CB:5020 ACB97aCB122z32006},(CB-32 ):5020 32006},(CB+32 ) H=32000} I  D=32000} ?A(A$p,B)=A$(B)-480-7*(A$(B)>579)  4C(A$p)=16*A(A$,1)+A(A$,2) 0A$:A$"**"D,C(A$):D=D+1:5140 3"3E","02","CD","01","16","3E","00","D7","C9","**" ( P d }ctwp@bxea4454NhS}S IRyNE6Z}THE SUM OF THE INTERIOR ANGLES OF A POLYGON = (2N - 4) X 90 DEGREES WHERE N IS THE NUMBER OF SIDES A720MAS ((2 X 6) - 4) X 90 = 720Q4tHE SUM OF THE INTERIOR ANGLES OF A 6 SIDED POLYGONH}THE SUM OF THE INTERIOR ANGLES OF A POLYGON = (2N - 4) X 90 DEGREES WHERE N IS THE NUMBER OF SIDES L 720 DEGREESB4tHE SUM OF THE INTERIOR ANGLES OF A 6 SIDED POLYGON0+D) Graphs of linear and quadratic functionsLCL140D v<' 5110 LCL140D COPYRIGHT (C) G.LUDINSKI 1981 'S$=" " PI=22/7 6:6: 2:6:S$; %" LCL140D  G.Ludinski 1981 "; (S$:6:0:6 2 <"What is your name ? " FN$ P Z"Here are some problems ";N$ d C=0 f T=1 h W=1 i P=0 n o P0 p P=P+1 x 500z z}ST=8*23689\-16:W2((ST-8-F)/E)+100d,(ST-8):-(E)*502,-502:126~ ~0,ST-33!:255,0:(27-23689\),30;"x":W2XL=502+(1+(E*F))*75K:XL,ST-8:0,-502:134 v108l,ST-8:14,-30,(PI/6):12 ,0,(PI/2):14,30,(PI/6) "E<0F<0XL=78N #E>0F>0XL=188 +(E*F)<0ƺE+F<0XL=124| +(E*F)<0ƺE+F>0XL=132 #(E*F)<0ƺE=FXL=128 "XL,ST-8:0,-502 ?22-(ST-8)/8,(XL/8)+(X2);"y": $30-23689\,0;" " B$=Q$:5000:"="; I$ I$="?"3500 I$ I$=""220\ X=9172, LI=I$ I=1LI ,I$(I)"-"(I$(I)<"0"I$(I)>"9")220\ I (I$-A)X1804 220\ I$=A$I$=C$1804 220\  "Yes,well done" C=C+1  3520 :.5,5:.73333,2:T1270 150  )"No,";:B$=H$:5000:",try again" T=2  122z Z$=S$(B-1)  1360* :"Sorry,the answer = "  ,B$=L$:5000: . @B$=M$:5000: J TB$=N$:5000: ^ cSC=(C/P*100H) h"Your score = ";SC;" %" r |"Do you want more? (Y/N)" R$ .R$"Y"R$"N"R$""R$"y"R$"n"362j R$="N"R$="n"450  T=1  110\  H=4535 L$="" M$="" N$=""  B=32 A$="" X=0:A=0 &C$="" + 0W=(*3@) 5 P=1W=2560 :"E=10 -(*19+1) D"F=10 -(*19+1) N5E=0E=1E=-1F=0570 XG=E+F bJ=E*F l;W=2(G=0G=1G=-1E=F)570 vY=G  1000z G$=Y$ Y=J  1000z J$=Y$ Y=E  1000z E$=Y$ Y=F  1000z F$=Y$ Z$="OF THE STRAIGHT LINE" W$="Y="+E+"X"+F$ W0822M  Q$="tHE GRADIENT "+Z$+" "+W$  X=0  H$="THE GRADIENT OF A STRAIGHT LINE IS THE COEFFICIENT OF X WHEN THE EQUATION IS WRITTEN IN THE FORM Y=MX+C WHERE M AND C ARE NUMBERS" *A=E 4L$=E 5(M$="AS "+E+" IS THE COEFFICIENT OF X" 6W1849T@ 79B$="tHE GRAPH OF "+Z$+" "+W$+" CROSSES THE Y AXIS AT Y" 8 1210@ 9Q$=B$ :.H$="THIS IS FOUND BY FINDING Y WHEN X = 0" < X=0 >A=F @L$=F BM$="AS WHEN X=0 , Y=0"+F$ QW21030 RRB$="tHE GRAPH OF THE PARABOLA Y=X^2"+G$+"X"+J$+" CROSSES THE X AXIS AT X" \ 1210@ fQ$=B$ pH$="THE VALUES OF X WHEN Y IS ZERO ARE FOUND BY FACTORISING THE EQUATION INTO THE FORM (X+A)(X+B)=0. tHEREFORE EITHER (X+A)=0 OR (X+B)=0. iF (X+A)=0 THEN X=-A. iF (X+B)=0 THEN X=-B" z X=9 -E-F970r U$=E$ E$=F$ F$=U$  T$=(-E)  V$=(-F)  990w  V$=(-E)  T$=(-F) A$=V$+" "+T$ C$=T$+" "+V$ L$=A$ 0M$="AS FACTORISING GIVES (X"+E$+")(X"+F$+")=0" 4N$="SO GRAPH CROSSES X AXIS AT X="+V$+" AND X="+T$  1030 Y$=Y Y>0Y$="+"+Y$   LF=B$ LFB1350( I=1̺(LF/B) EL=B*I B$(EL)=" "1340'  B$(EL+1)" "1290!@ B$=B$(EL)+B$(EL+2) LF=LF-1  1340'  K=131x B$(EL-K)" "1335& 'B$=B$(EL-K)+S$(K)+B$(EL-K+1) ( LF=LF+K 2 1340' 7K <I F P#Z=1̺(Z$/32)+1 `BZ=B*Z aBZ>Z$BZ=Z$ bZ$(B*(Z-1)+1BZ); nZ p Z$Q$+"=" s x w VP=22 - 23689\:1;19,0;" Calculator mode ";1;19,0 B$="" #BR=0:B$:B$=""3503 B$="?"B$="AC"3510 I=1̱B$:I$=B$(I):(I$<40(ůI$>579)I$" "I$"^"I$"="I$"/"I$""I$""I$""I$""I$""3503 BR=BR+(I$="(")-(I$=")") I BR03503 B$="?"3530 DB$="AC"20,0;S$;19,0:B$="":3502 "B$(B$)="="B$=B$(̱B$-1) #B$;19,0:3502 A19,0;S$;S$;S$(10 );VP+2,0:I$: I=0̱B$ I=05025  CB=B$(I) CCB<65A(CB91[CB96`)32006},CB:5020 ACB97aCB122z32006},(CB-32 ):5020 32006},(CB+32 ) H=32000} I  D=32000} ?A(A$Xu,B)=A$(B)-480-7*(A$(B)>579)  4C(A$Xu)=16*A(A$,1)+A(A$,2) 0A$:A$"**"D,C(A$):D=D+1:5140 3"3E","02","CD","01","16","3E","00","D7","C9","**" ( P d }I$Ictwp@bxaefg@jyD('x x5hS}RG+3J-40E+8Y-5F-5ZOF THE STRAIGHT LINEWY=8X-5QDtHE GRAPH OF THE PARABOLA Y=X^2+3X-40 CROSSES THE X AXIS AT XHTHE VALUES OF X WHEN Y IS ZERO ARE FOUND BY FACTORISING THE EQUATION INTO THE FORM (X+A)(X+B)=0. tHEREFORE EITHER (X+A)=0 OR (X+B)=0. iF (X+A)=0 THEN X=-A. iF (X+B)=0 THEN X=-BV-8T5C5 -8L-8 5M!AS FACTORISING GIVES (X+8)(X-5)=0N'SO GRAPH CROSSES X AXIS AT X=-8 AND X=5IB'SO GRAPH CROSSES X AXIS AT X=-8 AND X=5A**S 0 SUITE 1500A) Statistics IILCL150A l}9'n 5110 LCL150A COPYRIGHT (C) G.LUDINSKI 1981 F(4)  D(16)  C(5 ) 'S$=" " 6:6: 2:6:S$; %" LCL150A  G.Ludinski 1981 "; (S$:6:0:6 2 <"What is your name ? " FN$ P Z"Here are some problems ";N$ d C=0 f T=1 h W=1 i P=0 n o P0 p P=P+1 x 500z yW2130 z::19;"Men":: {ST=8*23689\+16:128,ST-16,16:144,ST-16:-16,0:16*((E*)/(NR*180)),16*((E*)/(NR*180)) |r128,ST-16:AL=((F*)/(NR*180)):BE=((E*)/(NR*180)):16*(AL+BE),16*(AL+BE)  B$=Q$:5000:"="; I$ I$="?"3500 I$ I$=""220\ X=9172, LI=I$ I=1LI I$(I)<"0"I$(I)>"9"220\ I (I$-A)X1804 220\ I$=A$I$=B$1804 220\  "Yes,well done" C=C+1  3520 :.5,5:.73333,2:T1270 #W=2150::240  )"No,";:B$=H$:5000:",try again" T=2  121y  "Sorry,the answer = "  ,B$=L$:5000: . @B$=M$:5000: J TB$=N$:5000: ^ cSC=(C/P*100H) h"Your score = ";SC;" %" r |"Do you want more? (Y/N)" R$ .R$"Y"R$"N"R$""R$"y"R$"n"362j R$="N"R$="n"450  T=1  110\  H=4535 L$="" M$="" N$=""  B=32  MC=0 & DN=1 0 MO=0 :W=(*3@) DI=15 NC(I)=(*4) XC(I)=MC590 ]C(I)MC630 b MC=C(I) lMO=I vC(I)=0680* J=DN(DN+C(I)-1) D(J)=I J  DN=DN+C(I) I DN=DN-1  DN2=0 'DN/2=(DN/2)DN2=1 DN2=1DN=DN+1 DN2=1D(DN)=6@ D$="" I=1DN D$=D$+(D(I))+"," I D$=D$((DN*2)-1)  T$="TH" MM=(DN/2)+1  MM=1T$="ST" *MM=2T$="ND" 4MM=3@T$="RD" >W0900a C X=0 H3Q$="tHE MODE OF THE FOLLOWING NUMBERS "+D$ R:H$="THE MODE IS THE NUMBER THAT OCCURS MOST FREQUENTLY" \A=MO fA$=A pL$=A$ z*M$="AS THERE ARE MORE OF THE NUMBER "+A$ -N$="IN THE LIST THAN ANY OTHER NUMBER" W1980u  X=0 3Q$="tHE MEDIAN OF THE FOLLOWING NUMBERS "+D$ rH$="THE MEDIAN IS THE MIDDLE NUMBER WHEN THE NUMBERS ARE ARRANGED IN ASCENDING ORDER (AS THEY ARE HERE)" A=D(1+(DN/2)) A$=A L$=A$ #M$="AS THERE ARE "+DN+" NUMBERS" <N$="AND THE "+((DN/2)+1)+T$+" NUMBER IS "+A$ W21200  X=1 NR=(*5 +1) E=(*160 +10 )*NR F=(*160 +10 )*NR G=(3604*NR)-E-F E$=E F$=F G$=G $B$="iF "+E$+" MEN, "+F$+" WOMEN AND "+G$+" CHILDREN ARE WATCHING FOOTBALL.tHE ANGLE AT THE CENTRE OF THE SECTOR REPRESENTING MEN IN A PIE CHART" . 1210@ 8Q$=B$ BmH$="ANGLE = (MEN / TOTAL) * 360 DEGREES WHERE MEN IS THE NUMBER OF MEN AND TOTAL IS THE NUMBER OF PEOPLE" L A=(E/NR) VA$=A `L$=A$+" DEGREES" b5M$="AS "+E+" + "+F+" + "+G+" = "+(360h*NR) j5N$="AND ("+E$+" / "+(360h*NR)+") X 360 = "+A$  LF=B$ LFB1350( I=1̺(LF/B) EL=B*I B$(EL)=" "1340'  B$(EL+1)" "1290!@ B$=B$(EL)+B$(EL+2) LF=LF-1  1340'  K=131x B$(EL-K)" "1335& 'B$=B$(EL-K)+S$(K)+B$(EL-K+1) ( LF=LF+K 2 1340' 7K <I F P#Z=1̺(Z$/32)+1 `BZ=B*Z aBZ>Z$BZ=Z$ bZ$(B*(Z-1)+1BZ); nZ p Z$Q$+"=" s x w VP=22 - 23689\:1;19,0;" Calculator mode ";1;19,0 B$="" #BR=0:B$:B$=""3503 B$="?"B$="AC"3510 I=1̱B$:I$=B$(I):(I$<40(ůI$>579)I$" "I$"^"I$"="I$"/"I$""I$""I$""I$""I$""3503 BR=BR+(I$="(")-(I$=")") I BR03503 B$="?"3530 DB$="AC"20,0;S$;19,0:B$="":3502 "B$(B$)="="B$=B$(̱B$-1) #B$;19,0:3502 A19,0;S$;S$;S$(10 );VP+2,0:I$: I=0̱B$ I=05025  CB=B$(I) CCB<65A(CB91[CB96`)32006},CB:5020 ACB97aCB122z32006},(CB-32 ):5020 32006},(CB+32 ) H=32000} I  D=32000} ?A(A$q,B)=A$(B)-480-7*(A$(B)>579)  4C(A$q)=16*A(A$,1)+A(A$,2) 0A$:A$"**"D,C(A$):D=D+1:5140 3"3E","02","CD","01","16","3E","00","D7","C9","**" ( P d }S@@@ S ctwpb@;: n xa@5hS}IRyD1,1,3,3,3,4,4,5,5TTHQ:tHE MODE OF THE FOLLOWING NUMBERS 1,1,3,3,3,4,4,5,5H3THE MODE IS THE NUMBER THAT OCCURS MOST FREQUENTLYA3L3M!AS THERE ARE MORE OF THE NUMBER 3N&IN THE LIST THAN ANY OTHER NUMBERB:tHE MODE OF THE FOLLOWING NUMBERS 1,1,3,3,3,4,4,5,50"B) Solution of Algebratic EquationLCL150B #o&% 5110 LCL150B COPYQIGHT (C) G.LUDINSKI 1981 'S$=" " 6:6: 2:6:S$; %" LCL150B  G.Ludinski 1981 "; (S$:6:0:6 2 <"What is your name ? " FN$ P Z"Here are some problems ";N$ d C=0 f T=1 h W=1 i P=0 n o P0 p P=P+1 x 500z }  Q$;"="; I$ I$="?"3500 I$ I$=""220\ X=9172, LI=I$ I=1LI ,I$(I)"-"(I$(I)<"0"I$(I)>"9")220\ I (I$-A)X1804 220\ $I$=A$I$=B$I$=C$I$=D$1804 220\  "Yes,well done" C=C+1  3520 :.5,5:.73333,2:T1270  )"No,";:B$=H$:5000:",try again" T=2  130  "Sorry,the answer = "  ,B$=L$:5000: . @B$=M$:5000: J TN$ ^ cSC=(C/P*100H) h"Your score = ";SC;" %" r |"Do you want more? (Y/N)" R$ .R$"Y"R$"N"R$""R$"y"R$"n"362j R$="N"R$="n"450  T=1  110\  H=4535 L$="" M$="" N$=""  B=32  X=0 &E=(*9+1) 0F=(*9+1) :G=(*8+2) DJ=(*9+1)*G NY=E X 1100 bE$=Y$ lF$=F vG$=G J$=J P4680* W=P  690, W=(*3@+1) W1760>  X=0 Q$="If Y"+E$+"="+F$+" then Y" _H$="IF y+C=D THEN TO FIND y, SUBTRACT C FROM BOTH SIDES OF THE EQUATION TO GIVE y=D-C " A=F-E A$=A L$=A$ M$="AS "+F$+" - "+E+" = "+A$ W2830O  X=0 Q$="If "+G$+"Y="+J$+" then Y"  QH$="IF Cy=D THEN TO FIND y,DIVIDEBOTH SIDES OF THE EQUATION BY C TO GIVE y=D/C" A=J/G  A$=A *L$=A$ 4#M$="AS y = "+J$+" / "+G$+" = "+A$ >W31130j HK=(*9+1)*G RY=K \ 1100 fK$=Y$ p'Q$="If "+G$+"Y"+K$+"="+J$+"X then Y" zH$="APPLY BOTH OF THE RULES YOU HAVE JUST LEARNT.tHAT IS, IF Ay+B=Cx THEN FIRST SUBTRACT B FROM BOTH SIDES THEN DIVIDE BOTHSIDES BY A" R1=J/G  R2=-K/G Y=R1  1100  T$=Y$+"X" Y=R2  1100 U$=Y$ O$=R1 R1=1O$=""  R1=1T$=T$(1)+"X"  V$="X"+O$ R1<0V$="-"+V$ A$=O$+"X"+U$  B$=V$+U$  C$=R2+T$ D$=R2+T$(1)+"X"+O$  N=4 L$=A$ $>M$="AS EQUATION BECOMES "+G$+"y = "+J$+"x"+U$(1)+(K) .GN$="so Y = ("+J$+"/"+G$+")X "+U$(1)+" ("+(K)+"/"+G$+") = "+A$ 8 X=9 B 1130j LY$=Y VY>0Y$="+"+Y$ ` j LF=B$ LFB1350( I=1̺(LF/B) EL=B*I B$(EL)=" "1340'  B$(EL+1)" "1290!@ B$=B$(EL)+B$(EL+2) LF=LF-1  1340'  K=131x B$(EL-K)" "1335& 'B$=B$(EL-K)+S$(K)+B$(EL-K+1) ( LF=LF+K 2 1340' 7K <I F P#Z=1̺(Z$/32)+1 `BZ=B*Z aBZ>Z$BZ=Z$ bZ$(B*(Z-1)+1BZ); nZ p Z$Q$+"=" s x w VP=22 - 23689\:1;19,0;" Calculator mode ";1;19,0 B$="" #BR=0:B$:B$=""3503 B$="?"B$="AC"3510 I=1̱B$:I$=B$(I):(I$<40(ůI$>579)I$" "I$"^"I$"="I$"/"I$""I$""I$""I$""I$""3503 BR=BR+(I$="(")-(I$=")") I BR03503 B$="?"3530 DB$="AC"20,0;S$;19,0:B$="":3502 "B$(B$)="="B$=B$(̱B$-1) #B$;19,0:3502 A19,0;S$;S$;S$(10 );VP+2,0:I$: I=0̱B$ I=05025  CB=B$(I) CCB<65A(CB91[CB96`)32006},CB:5020 ACB97aCB122z32006},(CB-32 ):5020 32006},(CB+32 ) H=32000} I  D=32000} ?A(A$o,B)=A$(B)-480-7*(A$(B)>579)  4C(A$o)=16*A(A$,1)+A(A$,2) 0A$:A$"**"D,C(A$):D=D+1:5140 3"3E","02","CD","01","16","3E","00","D7","C9","**" ( P d }ctwpbxefgjya S 0hS}IB AS 1 - 1 = 0RyNY+3E+3F2G3J6QIf 3Y=6 then YHJIF Cy=D THEN TO FIND y,DIVIDEBOTH SIDES OF THE EQUATION BY C TO GIVE y=D/CA2L2MAS y = 6 / 3 = 220 C) VectorsLCL150C S( 5110 LCL150C COPYRIGHT (C) G.LUDINSKI 1981  D(4) 'S$=" " 6:6: 2:6:S$; %" LCL150C  G.Ludinski 1981 "; (S$:6:0:6 2 <"What is your name ? " FN$ P Z"Here are some problems ";N$ d C=0 f T=1 h W=1 i P=0 n o P0 p P=P+1 x 500z yW=1126~ z$W=2I=112 ::I {VW=01:" X":2:" Y":3:" X+Y":I=113 ::I |ST=8*23689\+72H:1:96`,ST-40(:D(1)*3,D(2)*3:W=02:96`,ST-40(:D(3)*3,D(4)*3:0 }0:96`,ST-40(:0,36$:96`,ST-40(:36$,0:W=03:96`,ST-40(:(D(1)+D(3))*3,(D(2)+D(4))*3:0 ~W1130 2::::13 ;"U";26;E$;"U"::::: GST=8*23689\+568:568,ST-40(:0,36$:568,ST-40(:36$,0:568,ST-40(:D(1)/2,D(2)/2:160,ST-40(:0,36$:160,ST-40(:36$,0:160,ST-40(:(E*D(1))/2,(E*D(2))/2  B$=Q$:5000:"="; I$ I$="?"3500 I$ I$=""220\ X=9172, LI=I$ I=1LI ,I$(I)"-"(I$(I)<"0"I$(I)>"9")220\ I (I$-A)X1804 220\ I$=A$1804 220\  "Yes,well done" C=C+1  3520 :.5,5:.73333,2:T1270 150: )"No,";:B$=H$:5000:",try again" T=2  121y  "Sorry,the answer = "  ,B$=L$:5000: . @B$=M$:5000: J TB$=N$:5000: ^ cSC=(C/P*100H) h"Your score = ";SC;" %" r |"Do you want more? (Y/N)" R$ .R$"Y"R$"N"R$""R$"y"R$"n"362j R$="N"R$="n"450  T=1  110\  H=4535 L$="" M$="" N$=""  B=32 A=0:X=0:A$=""   X=1 &I=14 0D(I)=(*9+1) :>0.5D(I)=-D(I) NI PV$=D(1) RW$=D(2) TX$=D(3@) VY$=D(4) XE=(*8+2) bE$=E l L1=(V$) v8Z$="iF u = ("+V$+")"+S$(30-L1)+"("+W$+") THEN " W=(*3@) W0790E  L1=(V$)  L3=(X$)  L2=(W$) Q$="iF x = ("+V$+") AND y = ("+X$+")"+S$(19-L1-L3)+"("+W$+")"+S$(9 +L1-L2)+"("+Y$+") THEN"+S$(7-L1-Y$)+ "x+y " :H$="TO ADD VECTORS,ADD THEIR COMPONENTS SEPARATELY" T$=(D(1)+D(3@))  LR=(T$) U$=(D(2)+D(4)) +A$="("+T$+")"+S$(30p-LR)+"("+U$+")" L$=A$ M$="AS "+V$+" + "+X$+" = "+T$  N$="AND "+W$+" + "+Y$+" = "+U$  X=9 W1900a  Q$=Z$+E$+"u " *H$="WHEN MULTIPLYING A SCALAR QUANTITY (I.E. AN ORDINARY NUMBER) BY A VECTOR,MULTIPLY EACH COMPONENT OF THE VECTOR BY THE SCALAR" 4T$=(E*D(1)) > LR=(T$) H X=9 R8A$="("+T$+")"+S$(30p-LR)+"("+(E*D(2))+")" \ X=9 fL$=A$ pM$="AS "+E$+" X "+V$+" = "+T$ z-N$="AND "+E$+" X "+W$+" = "+(E*D(2)) W2990w Q$=Z$+"THE MODULUS OF u " qH$="THE MODULUS OF A VECTOR IS THE SQUARE ROOT OF (A^2 + B^2) WHERE A AND B ARE THE COMPONENTSOF THE VECTOR" 5A=((D(1)*D(1)+D(2)*D(2))) A$=A L$=A$ ^M$="AS ("+V$+")^2 = "+(D(1)*D(1))+" AND ("+W$+")^2 = "+(D(2)*D(2)) YN$="SO SQUARE ROOT ("+(D(1)*D(1))+" + "+(D(2)*D(2))+") = "+A$  LF=B$ LFB1350( I=1̺(LF/B) EL=B*I B$(EL)=" "1340'  B$(EL+1)" "1290!@ B$=B$(EL)+B$(EL+2) LF=LF-1  1340'  K=131x B$(EL-K)" "1335& 'B$=B$(EL-K)+S$(K)+B$(EL-K+1) ( LF=LF+K 2 1340' 7K <I F P#Z=1̺(Z$/32)+1 `BZ=B*Z aBZ>Z$BZ=Z$ bZ$(B*(Z-1)+1BZ); nZ p Z$Q$+"=" s x w VP=22 - 23689\:1;19,0;" Calculator mode ";1;19,0 B$="" #BR=0:B$:B$=""3503 B$="?"B$="AC"3510 I=1̱B$:I$=B$(I):(I$<40(ůI$>579)I$" "I$"^"I$"="I$"/"I$""I$""I$""I$""I$""3503 BR=BR+(I$="(")-(I$=")") I BR03503 B$="?"3530 DB$="AC"20,0;S$;19,0:B$="":3502 "B$(B$)="="B$=B$(̱B$-1) #B$;19,0:3502 A19,0;S$;S$;S$(10 );VP+2,0:I$: I=0̱B$ I=05025  CB=B$(I) CCB<65A(CB91[CB96`)32006},CB:5020 ACB97aCB122z32006},(CB-32 ):5020 32006},(CB+32 ) H=32000} I  D=32000} ?A(A$'s,B)=A$(B)-480-7*(A$(B)>579)  4C(A$'s)=16*A(A$,1)+A(A$,2) 0A$:A$"**"D,C(A$):D=D+1:5140 3"3E","02","CD","01","16","3E","00","D7","C9","**" ( P d }S ctwpbax5Be hS}IRyV-8W-4X-6Y-8E3Z1iF u = (-8) (-4) THEN QBiF u = (-8) (-4) THEN THE MODULUS OF u HjTHE MODULUS OF A VECTOR IS THE SQUARE ROOT OF (A^2 + B^2) WHERE A AND B ARE THE COMPONENTSOF THE VECTORA8L8MAS (-8)^2 = 64 AND (-4)^2 = 16NSO SQUARE ROOT (64 + 16) = 8BBiF u = (-8) (-4) THEN THE MODULUS OF u +0D) Indicies IILCL150D ! 5110 LCL150D COPYRIGHT (C) G.LUDINSKI 1981  D(4) 'S$=" " 6:6: 2:6:S$; %" LCL150D  G.Ludinski 1981 "; (S$:6:0:6 2 <"What is your name ? " FN$ P Z"Here are some problems ";N$ d C=0 f T=1 h W=1 i P=0 n o P0 p P=P+1 x 500z }  B$=Q$:5000:"="; I$ I$="?"3500 I$ I$=""220\ X=9172, LI=I$ I=1LI ,I$(I)"-"(I$(I)<"0"I$(I)>"9")220\ I (I$-A)X1804 220\ I$=A$1804 220\  "Yes,well done" C=C+1  3520 :.5,5:.73333,2:T1270  )"No,";:B$=H$:5000:",try again" T=2  130  "Sorry,the answer = "  ,B$=L$:5000: . @B$=M$:5000: J TB$=N$:5000: ^ cSC=(C/P*100H) h"Your score = ";SC;" %" r |"Do you want more? (Y/N)" R$ .R$"Y"R$"N"R$""R$"y"R$"n"362j R$="N"R$="n"450  T=1  110\  H=4535 L$="" M$="" N$=""  B=32 X=0:A=0:A$=""  J=(*2*4) &F=J*J 0 G=J*J*J :F$=F DG$=G NJ$=J XW=(*4) bE=(*4+2) lD(W=2(E=2E=4))(W=3@E=3@)610 vE$=E W0700/ >Q$="wRITE THE ANSWER IN THE FORM OF A FRACTION. y^-"+E$+" " H$="y^-P = 1/y^P"  X=9 A$="1/Y^"+E$ L$="1/y^"+E$ W1760>  Q$=E$+"^0 "  A=1  X=0 &H$="ANY NUMBER TO THE POWER OF 0 =1" L$="1" W<2860W !W=2Q$=F$+"^("+E$+"/2) "  !W=3@Q$=G$+"^("+E$+"/3) " hH$="TO CALCULATE y^(P/Q) FIRST TAKE THE QTH ROOT OF y,THEN RAISE THIS RESULT TO THE POWER OF P"  A=(J^E) *A$=A 4N$="AND "+J$+"^"+E$+" = "+A$ >L$=A$ HMW=2M$="AS THE DENOMINATOR = 2 SO THE SQUARE ROOT OF "+F$+" = "+J$ RKW=3@M$="AS THE DENOMINATOR = 3 SO THE CUBE ROOT OF "+G$+" = "+J$ \ LF=B$ LFB1350( I=1̺(LF/B) EL=B*I B$(EL)=" "1340'  B$(EL+1)" "1290!@ B$=B$(EL)+B$(EL+2) LF=LF-1  1340'  K=131x B$(EL-K)" "1335& 'B$=B$(EL-K)+S$(K)+B$(EL-K+1) ( LF=LF+K 2 1340' 7K <I F P#Z=1̺(Z$/32)+1 `BZ=B*Z aBZ>Z$BZ=Z$ bZ$(B*(Z-1)+1BZ); nZ p Z$Q$+"=" s x w VP=22 - 23689\:1;19,0;" Calculator mode ";1;19,0 B$="" #BR=0:B$:B$=""3503 B$="?"B$="AC"3510 I=1̱B$:I$=B$(I):(I$<40(ůI$>579)I$" "I$"^"I$"="I$"/"I$""I$""I$""I$""I$""3503 BR=BR+(I$="(")-(I$=")") I BR03503 B$="?"3530 DB$="AC"20,0;S$;19,0:B$="":3502 "B$(B$)="="B$=B$(̱B$-1) #B$;19,0:3502 A19,0;S$;S$;S$(10 );VP+2,0:I$: I=0̱B$ I=05025  CB=B$(I) CCB<65A(CB91[CB96`)32006},CB:5020 ACB97aCB122z32006},(CB-32 ):5020 32006},(CB+32 ) H=32000} I  D=32000} ?A(A$n,B)=A$(B)-480-7*(A$(B)>579)  4C(A$n)=16*A(A$,1)+A(A$,2) 0A$:A$"**"D,C(A$):D=D+1:5140 3"3E","02","CD","01","16","3E","00","D7","C9","**" ( P d }ctwpbxajfg@eaQhS}S RyF16G64J4E5Q 16^(5/2) HaTO CALCULATE y^(P/Q) FIRST TAKE THE QTH ROOT OF y,THEN RAISE THIS RESULT TO THE POWER OF PA1024NAND 4^5 = 1024L1024M5AS THE DENOMINATOR = 2 SO THE SQUARE ROOT OF 16 = 4I BaTO CALCULATE y^(P/Q) FIRST TAKE THE QTH ROOT OF y,THEN RAISE THIS RESULT TO THE POWER OF P00 SUITE 1600(A) Geometry of the circle and its chordsLCL160A  bsx'  LCL160A COPYRIGHT (C) G.LUDINSKI 1981 'S$=" " 6:6: 2:6:S$ %" LCL160A  G.Ludinski 1981 "; (S$:6:0:6 2 <"What is your name ? " FN$ P Z"Here are some problems ";N$ d C=0 f T=1 h W=1 i P=0 jR$="" n o P0 p P=P+1 x 500z zM17;"A":::16;"O Q"::12 ;"B P D"::17;"C" {ST=8*23689\+480:128,ST-32 ,25:128,ST-32 :20,-16:-39',0:128,ST-32 :0,-16 |Q128,ST-32 :-19,-16:27,-8:12 ,8 }Q-8,37%:-30,-37%:128,ST-32 :16,2  Q$;"="; I$ I$="?"3500 I$ I$=""220\ X=9172, LI=I$ I=1LI ,I$(I)"-"(I$(I)<"0"I$(I)>"9")220\ I (I$-A)X1804 220\ I$=A$1804 220\  "Yes well done" C=C+1  3520 :.5,5:.73333,2:T1262 150   "No,";H$;",try again" T=2  122z  "Sorry the answer = "  &L$ . 8M$ J LN$ ^ cSC=(C/P*100H) h"Your score = ";SC;" percent" r |"Do you want more ?(Y/N)" R$ .R$"Y"R$"N"R$""R$"y"R$"n"362j R$="N"R$="n"450  T=1  110\  H=4535 L$="" M$="" N$=""  B=32   X=0 &L1=(*9+1) 0L2=(*9+1) :AN=(*70 +10 ) DT$=L1 NU$=L2 XV$=AN bZ$="ABCD is a cyclic quadrilateral, O is the centre of the circle and OP is perpendicular to BD meeting BD at P.OQ is perpendicular to AD,meeting AD at Q. " lW=(*4) vW07101 "Q$=Z$+"If BP="+T$+"cm. then BD " _H$="a line drawn from the centre of a circle perpendicular to a chord bisects that chord " A=2*L1 A$=A  L$=A$+"cm." &M$="as BD is a chord bisected by OP" N$="and 2 x "+T$+" = "+A$ W1770@ @Q$=Z$+"If BD="+T$+"cm., OQ="+U$+"cm. and AD="+T$+"cm. then OP" A=L2  L$=U$+"cm." ,M$="as BD and AD are equal chords soOP=OQ" JH$="equal chords are the same distance from the centre of the circle" W2850T  8Q$=Z$+"If angle BAD="+V$+" degrees,then angle BOD " qH$="the angle subtended by the arc of a circle at the centre istwice the angle at the circumference"  A=2*AN *A$=A 4&L$=A$+" degrees as 2 x "+V$+" = "+A$ >-M$="and BOD is the angle at the centre" H4N$="and BAD is the angle at the circumference" RW3@1000z \7Q$=Z$+"If angle BAD="+V$+" degrees then angle BCD" f?H$="opposite angles of a cyclic quadrilateral =180 degrees " pA=1804-AN zA$=A (L$=A$+" degrees as 180 - "+V$+" = "+A$ 4M$="and ABCD is a cyclic quadrilateral" -N$="and BAD and BCD are opposite angles"  LF=B$ LFB1350( I=1̺(LF/B) EL=B*I B$(EL)=" "1340'  B$(EL+1)" "1290!@ B$=B$(EL)+B$(EL+2) LF=LF-1  1340'  K=131x B$(EL-K)" "1335& 'B$=B$(EL-K)+S$(K)+B$(EL-K+1) ( LF=LF+K 2 1340' 7K <I F P#Z=1̺(Z$/32)+1 `BZ=B*Z aBZ>Z$BZ=Z$ bZ$(B*(Z-1)+1BZ); nZ p Z$Q$+"=" s x w VP=22 - 23689\:1;19,0;" Calculator mode ";1;19,0 B$="" #BR=0:B$:B$=""3503 B$="?"B$="AC"3510 I=1̱B$:I$=B$(I):(I$<40(ůI$>579)I$" "I$"^"I$"="I$"/"I$""I$""I$""I$""I$""3503 BR=BR+(I$="(")-(I$=")") I BR03503 B$="?"3530 DB$="AC"20,0;S$;19,0:B$="":3502 "B$(B$)="="B$=B$(̱B$-1) #B$;19,0:3502 A19,0;S$;S$;S$(10 );VP+2,0:I$: S ctwpbxaIRyNT6U4V16ZABCD is a cyclic quadrilateral, O is the centre of the circle and OP is perpendicular to BD meeting BD at P.OQ is perpendicular to AD,meeting AD at Q. QABCD is a cyclic quadrilateral, O is the centre of the circle and OP is perpendicular to BD meeting BD at P.OQ is perpendicular to AD,meeting AD at Q. If BD=6cm., OQ=4cm. and AD=6cm. then OPL4cm.M%as BD and AD are equal chords soOP=OQHCequal chords are the same distance from the centre of the circle0 B) MatricesLCL160B  '&  POPULAR 160B COPYRIGHT (C) G.LUDINSKI 1981 A$(4,1) B$(4,1)  A(4)  B(4)  C(4) 'S$=" " 6:6: 2:6:S$ %" LCL160B  G.Ludinski 1981 "; (S$:6:0:6 2 8L2=(*70F+10 ) <"What is your name?" FN$ P Z"Here are some problems ";N$ d C=0 f T=1 h W=1 i P=0 o P0 p P=P+1 x 500  Q$;"="; I$ I$="?"3500 I$ I$=""220 X=9 172 LI=I$ I=1LI I$(I)<"0"I$(I)>"9"220 I (I$-A)X180 220 I$=C$180 220  "Yes well done" C=C+1  352` :.5,5:.73333,2:T1270 150: "No,";H$;",try again" T=2  130  "Sorry,the answer = " " ,L$ 6 @M$ J TN$ ^ cSC=(C/P*100d) h"Your score = ";SC;" percent" r |"Do you want more? (Y/N)" R$ .R$"N"R$"n"R$""R$"Y"R$"y"362j R$="N"450  T=1  110n  H=4535 L$="" M$="" N$=""  B=32   X=9 &W=(*3) 0I=14 :A(I)=(*9 +1) DB(I)=(*9 +1) NA$(I)=(A(I)) XB$(I)=(B(I)) bI l4R1=(A(1)*A(4))-(A(2)*A(3)) v2W=2(R1>A(4)R1=0)5600 Z$="Matrix P = ("+A$(1)+" "+A$(2)+") Q = ("+B$(1)+" "+B$(2)+") ("+A$(3)+" "+A$(4)+") ("+B$(3)+" "+B$(4)+")" W0770 Q$=Z$+" so P + Q " XH$="to add (or subtract) matricesadd or subtract their appropriate elements" T$=(A(1)+B(1)) U$=(A(2)+B(2)) V$=(A(3)+B(3)) W$=(A(4)+B(4)) @C$="("+T$+" "+U$+")"+S$((29-T$-U$))+"("+V$+" "+W$+")" L$=C$ 1M$="as "+A$(1)+" + "+B$(1)+" = "+T$ 9N$="and "+A$(2)+" + "+B$(2)+" = "+U$+" etc" W1890z  Q$=Z$+" P x Q" H$="P x Q = (ae+bg af+bh) (ce+dg cf+dh) where P = (a b) and Q = (e f) (c d) (g h) that is, if matrix PxQ=S the element S(row r,col. c) is created from P(row r) and Q(col. c)"  3T$=(A(1)*B(1)+A(2)*B(3)) *3U$=(A(1)*B(2)+A(2)*B(4)) 4L1=T$ >L2=U$ H3V$=(A(3)*B(1)+A(4)*B(3)) R3W$=(A(3)*B(2)+A(4)*B(4)) \>C$="("+T$+" "+U$+")"+S$((29-L1-L2))+"("+V$+" "+W$+")" fL$=C$ pdM$="as,for example,("+A$(1)+" x "+B$(1)+") + ("+A$(2)+" x "+B$(3)+")= "+T$ ubN$="and ("+A$(1)+" x "+B$(2)+") + ("+A$(2)+" x "+B$(4)+") = "+U$+" etc." zW21060$ zQ$="Matrix P = ("+A$(1)+" "+A$(2)+")"+S$(27)+"("+A$(3)+" "+A$(4)+") so the inverse of P " H$="inverse of P = (1/(ad-bc)) x ( d -b)"+S$(25)+"(-c a) where matrix P = (a b) (c d) (ad-bc) is called the determinant of P" C(1)=A(4)/R1 C(2)=-A(2)/R1 C(3)=-A(3)/R1 C(4)=A(1)/R1 $T$=((C(1))*(C(1))) $U$=((C(2))*(C(2))) $V$=((C(3))*(C(3))) $W$=((C(4))*(C(4))) L1=T$ L2=U$ >C$="("+T$+" "+U$+")"+S$((29-L1-L2))+"("+V$+" "+W$+")" L$=C$ wM$="as,the determinant = ("+A$(1)+" x "+A$(4)+") - ("+A$(2)+" x "+A$(3)+") = "+R1 nN$="so,for example, as d = "+A$(4)+S$(8)+"so d / determinant = "+A$(4)+" / "+R1+" = "+T$ $ w VP=22 - 23689\:1;19,0;" Calculator mode ";1;19,0 D$="" #BR=0:D$:D$=""3503 D$="?"D$="AC"3510 I=1̱D$:I$=D$(I):(I$<40(ůI$>579)I$" "I$"^"I$"="I$"/"I$""I$""I$""I$""I$""3503 BR=BR+(I$="(")-(I$=")") I BR03503 D$="?"3530 DD$="AC"20,0;S$;19,0:D$="":3502 "D$(D$)="="D$=D$(̱D$-1) #D$;19,0:3502 A19,0;S$;S$;S$(10 );VP+2,0:I$: Izh` ctwpb x 0+IRYZ;Matrix P = (7 3) Q = (4 4) (2 7) (6 8)QIMatrix P = (7 3) Q = (4 4) (2 7) (6 8) so P + Q HQto add (or subtract) matricesadd or subtract their appropriate elementsT11U7V8W15C&(11 7) (8 15)L&(11 7) (8 15)M as 7 + 4 = 11Nand 3 + 4 = 7 etc   S 0+C) Operations on numbers in different basesLCL160C  +$ LCL160C COPYRIGHT (C) G.LUDINSKI 1981 'S$=" " 6:5: 2:6:S$ %" LCL160C  G.Ludinski 1981 "; (S$:6:0:6 2 <"What is your name?" FN$ P Z"Here are some problems ";N$ d C=0 e'S$=" " f T=1 gRC$(5,5):B(3,5):O$(2,5):O(3,5) h W=1 i P=0 jR$="" o P0 p P=P+1 x 500  'T=114,0;Q$;" ="; T=2Q$;" ="; I$ I$="?"3500 I$ I$=""220 X=9 172 LI=I$ LJ=0 I=1LI !I$(I)" "LJ=1165 I$(I)="0" 167 ,I$(I)"-"(I$(I)<"0"I$(I)>"9")220 LJ=1 I (I$-A)X180 220 I$=A$I$=B$180 220  "Yes well done" C=C+1  352` :.5,5:.73333,2:T1262   "No,";H$;",try again" T=2  130  "Sorry, the answer = "  &L$ . 8M$ ; @N$ ^ cSC=(C/P*100d) h"Your score = ";SC;" percent" r |"Do you want more ? (Y/N)" R$ .R$"Y"R$"y"R$"n"R$"N"R$""362j R$="N"R$="n"450  T=1  100d  H=4535 L$="" M$="" N$=""  B=32   X=0 &T$="" 0U$="" :O$(1)="" DO$(2)="" N CA=0 XW=(*3) bC$(2)="" lC$(4)="" vI=14 B(1,I)=(*2) O(1,I)=(*8) B(2,I)=(*2) O(2,I)=(*8)  W1I4710 )O(1,4)=(*4+4) !O(2,4)=(*4) T$=(B(1,I))+T$ U$=(B(2,I))+U$ )O$(1)=(O(1,I))+O$(1) )O$(2)=(O(2,I))+O$(2) W0780   Y=B(1,I)+B(2,I)+CA  21004  W1860\  Y=O(1,I)-O(2,I)-CA  Y0840H * CA=1 4O(3,I)=Y+8 > 860\ HO(3,I)=Y R CA=0 \)C$(2)=(B(3,I))+C$(2) f)C$(4)=(O(3,I))+C$(4) pI zY$=T$  2160p T$=Y$ Y$=U$  2160p U$=Y$ Y$=C$(4)  2160p C$(4)=Y$ Y$=O$(1)  2160p O$(1)=Y$(Y$-3) Y$=O$(2)  2160p O$(2)=Y$(Y$-3) 3W1CA=1C$(2)="1"+C$(2) 3W1CA=0C$(2)="0"+C$(2) $W01220 .U$=U$(U$-3) 8cQ$="Binary numbers "+T$+S$(27)+"+"+U$+S$(28)+""+S$(25) BH$="if the sum of the two digits is greater than or equal to the base (and base=2 for binary numbers) then carry 1 leaving the sum minus the base" LC$(1)="0" V KA=0 `=(B(1,1)+B(2,1))<21150~ jC$(1)="1" t KA=1 ~C$(3)="0" E(B(1,2)+B(2,2)+KA)2C$(3)="1" A=(C$(2)) Y$=C$(2)  2160p  L$=" "+Y$ nM$="as "+(B(1,1))+" + "+(B(2,1))+" = "+(B(3,1))+" carry "+C$(1) N$="and "+(B(1,2))+" + "+(B(2,2))+" + "+C$(1) (̱C$(1))+"(carried) = "+(B(3,2))+" carry "+C$(3) W11360P vQ$="Octal numbers "+O$(1)+S$(26)+"-"+O$(2)+S$(27)+""+S$(25) ؃H$="if the difference is negative then borrow the base (i.e. 8 for octal numbers) leaving the difference plus 8 " C$(1)="0"  KA=0 >(O(1,1)-O(2,1)) 01300 C$(1)="8"  KA=1 C$(5)="0" E(O(1,2)-O(2,2)-KA)<0C$(5)="8" (A=C$(4) 2Y$=C$(4) 4 2160p 6 L$=" "+Y$  CA=0 HY<22150f RB(3,I)=Y-2 \ CA=1 f p L=Y$ z#L<5Y$=S$(5-L)+Y$   8#Z=1̺(Z$/32 )+1 HBZ=B*Z IBZ>Z$BZ=Z$ JZ$(B*(Z-1)+1BZ); VZ X Z$Q$+"=" [ w VP=22 - 23689\:1;19,0;" Calculator mode ";1;19,0 B$="" #BR=0:B$:B$=""3503 B$="?"B$="AC"3510 I=1̱B$:I$=B$(I):(I$<40(ůI$>579)I$" "I$"^"I$"="I$"/"I$""I$""I$""I$""I$""3503 BR=BR+(I$="(")-(I$=")") I BR03503 B$="?"3530 DB$="AC"20,0;S$;19,0:B$="":3502 "B$(B$)="="B$=B$(̱B$-1) #B$;19,0:3502 A19,0;S$;S$;S$(10 );VP+2,0:I$: cS t8 0000 42648 P7160 2674 PwpRb xvylT 1001U 1101QOctal numbers 7160 -2674 H|if the difference is negative then borrow the base (i.e. 8 for octal numbers) leaving the difference plus 8 aY 4264L 4264Mas 0 - 4 = 4 borrow 8 N,and 6 - 7 - 1(borrowed) = 6 borrow 8 I{0D) Simultaneous EquationsLCL160D ` nކb LCL160D COPYRIGHT (C) G.LUDINSKI 1981 C$(2,3) F$(2,2) F$(4,2) G$(2,1)  K(4) K$(8,3) 'S$=" " 6:6: 2:6:S$ %" LCL160D  G.Ludinski 1981 "; (S$:6:0:6 2 <"What is your name?" FN$ P Z"Here are some problems ";N$ d C=0 f T=1 h W=1 i P=0 o P0 p P=P+1 x 500  Q$;" ="; I$ I$="?"3500 I$ T2154 150  Q$;" =";I$ I$=""220 X=9 172 LI=I$ I=1LI ,I$(I)"-"(I$(I)<"0"I$(I)>"9")220 I (I$-A)X180 220 I$=A$180 220  "Yes well done" C=C+1  352` :.5,5:.73333,2:T1270  "No,";H$;",try again" T=2  130  "Sorry,the answer = " " &L$ , :M$ J LN$ T WD$ YJ$ [O$ ]P$ ^ cSC=(C/P*100d) h"Your score = ";SC;" percent" |"Do you want more ? (Y/N)" R$ .R$"Y"R$"y"R$"n"R$"N"R$""362j R$="N"R$="n"450  T=1  110n  H=4535 L$="" M$="" N$=""  B=32   X=9 &XX=(*9 +1) 0Y=(*9 +1) :X$=XX DY$=Y NI=14 XK(I)=(*8+2) b"(*2)=0K(I)=-K(I) lK$(I+4)=K(I) vEK(I)>0(I=2I=4)K$(I+4)="+"+K$(I+4) I #C1=(K(1)*XX)+(K(2)*Y) #C2=(K(3)*XX)+(K(4)*Y) N1=K(1) N2=K(2) N3=C1  1900l F1=FC M1=N1 M2=N2 M3=N3 N1=K(3) N2=K(4) N3=C2  1900l <F11FC1(N1=M1ƽN2=M2ƽN3=M3)590N  C$(1)=C1 *C$(2)=C2 4F1=K(1) >F2=K(3) HJ=27 R*(F1/J)ɺ(F1/J)(F2/J)ɺ(F2/J)890z \ F1=F1/J f F2=F2/J p 850R zJ F$(1)=F1 F$(2)=F2 L1=K$(5) L2=C$(1) L3=K$(7) L4=C$(2) B$=K$(5)(L1) 2500 :E$=B$ FB$=K$(6)(̱K$(6)(2)+1):2500 :J$=B$ (B$=K$(7)(L3):2500 :R$=B$ FB$=K$(8)(̱K$(8)(2)+1):2500 :W$=B$ Q$=E$+"x"+J$+"y="+C$(1)(L2)+S$(16-L1-L2)+"Equation 1 "+R$+"x"+W$+"y="+C$(2)(L4)+S$(16-L3-L4)+"Equation 2 so x and y" H$="to find y, multiply equationsby the numbers that make the coefficients of the x terms equal. Then subtract Eqn. 2 fromEqn. 1.Calculate y. Substitute this value back into Eqn. 1 to get x" E$="" 5F21E$="multiply Eqn.1 by "+F$(2)+"," V$="" 1F11V$="multiply Eqn.2 by "+F$(1) A$=X$+" "+Y$ L$=A$ B$="as to find y,"+E$+V$  2210 $M$=B$ .K$(1)=(K(1)*F2) 8 T$=(C1*F2) BL1=K$(1) GLA=T$ LK$(3)=(K(3)*F1) V U$=(C2*F1) `L3=K$(3) jLB=U$ tK$(2)=(K(2)*F2) ~L2=K$(2) !K$(4)=((K(4)*F1)) L4=K$(4) G$(1)="+" *(K(2)*F2)<0G$(1)="-" G$(2)="+" *(K(4)*F1)<0G$(2)="-" N$=K$(1)(̱K$(1))+"x"+G$(1)+K$(2)(L2)+"y="+T$+S$(18-L1-L2-LA)+"Equation 1"+K$(3)(̱K$(3))+"x"+G$(2)+K$(4)(̱K$(4))+"y="+U$+S$(18-L3-L4-LB)+"Equation 2" !D$="Subtract Eqn.2 from Eqn. 1" JJ$="("+(K(2)*F2)+"-"+(K(4)*F1)+")y="+(C1*F2)+"-"+(C2*F1) GO$="so y="+Y$+" . Substituting for y in Eqn.1" P$=K$(5)(̱K$(5))+"x"+K$(6)(1)+"("+K(2)+"*"+Y$+")="+C$(1)(̱C$(1))+" so x="+X$  2000 l FC=1 vJ=27 ;(N1/J)ɺ(N1/J)(N2/J)ɺ(N2/J)(N3/J) (N3/J)1980  N1=N1/J  N2=N2/J  N3=N3/J  FC=FC*J  1920 J   LF=B$ LFB2350. I=1̺(LF/B) EL=B*I B$(EL)=" "2340$  B$(EL+1)" "2290 B$=B$(EL)+B$(EL+2) LF=LF-1  2340$ K=131 B$(EL-K)" "2335 'B$=B$(EL-K)+S$(K)+B$(EL-K+1)  LF=LF+K  2340$ K $I . "B$=1B$=" +":2510 B$=-1B$=" -"  ( w VP=22 - 23689\:1;19,0;" Calculator mode ";1;19,0 B$="" #BR=0:B$:B$=""3503 B$="?"B$="AC"3510 I=1̱B$:I$=B$(I):(I$<40(ůI$>579)I$" "I$"^"I$"="I$"/"I$""I$""I$""I$""I$""3503 BR=BR+(I$="(")-(I$=")") I BR03503 B$="?"3530 DB$="AC"20,0;S$;19,0:B$="":3502 "B$(B$)="="B$=B$(̱B$-1) #B$;19,0:3502 A19,0;S$;S$;S$(10 );VP+2,0:I$: ctwpb x y2H2#  50 -5 1 -1 -+-7 3 -7 6 7 +3 -7 +6 S X5Y5R-7W+6QJ7x+3y=50 Equation 1 -7x+6y=-5 Equation 2 so x and yHto find y, multiply equationsby the numbers that make the coefficients of the x terms equal. Then subtract Eqn. 2 fromEqn. 1.Calculate y. Substitute this value back into Eqn. 1 to get xEmultiply Eqn.1 by -1,VA5 5L5 5B#as to find y,multiply Eqn.1 by -1,M#as to find y,multiply Eqn.1 by -1,T-50U-5N@-7x-3y=-50 Equation 1-7x+6y=-5 Equation 2DSubtract Eqn.2 from Eqn. 1J(-3-6)y=-50--5O;so y=5 . Substituting for y in Eqn.1P7x+(3*5)=50 so x=5I