ZXTape! 0Created with Ramsoft MakeTZX2w9O Level Maths Revision: Equations & Inequalities - Side A Rose Software1983English EducationalNoneOriginal0Linear Equations 1le1 D2D*F2@32767:1;11 ,9 ;"PLEASE WAIT":"le1 A" le1 A p! r!%502:58:: A.Cowley 1983 %6:6::"sc":59; 2&0:6:6:2: 698b,126~:60<,-60<:98b,66B:60<,60<:30,-30,-:-30,-30,-:-30,-30,-:-30,30,-:-30,30,-:30,30,-:30,30,-:30,-30,-: :89 ,14;"ROSE";10 ,12 ;"SOFTWARE" ;'o$=" " 0);("+"b<0);" y= 1";8,5;("-"b>0);9 ,0;a;" ";b;" ";b:0,103g:8,0:16,103g:16,0:40(,103g:16,0 621,0;"Need help?  Press h":h=0 8050r:w$="y"224 h=1g=0224 q$="n"300, 200 g=1:7010b:14,0;"Rearrange the equation to:","y=";m;"x+1":w$="y"17,0;" SO  correct answer is: ";m:8090:221 218 O8,0;"y";("+"m<0);("-"m>0);m;"x-1=0 ?":215 ,g=0:h=2 /Eh1h3m=(*13 )-6:m<2303/ 0 8000@ 20,0;"TO ";0,3-3*(h=0)+-3*(h=5);"FIND THE";2,0;"EQUATION of";4,0;"a straight";6,0;"line ";:h3345Y 5t"with";8,0;"gradient ";m;10 ,0;"passing";12 ,0;"through(1,";m+1;")" 6h=0381} 8 h07010b:14,0;" PUT  the known values of x,y,m into the equation: y=mx+c";17,0;"GIVING: ";m+1;"=(";m;"x1)+c SO:c=1":h=1g=09000(#:7010b:0,0;" FIND THE  ":381} >H19,0;" THEN  the equation is: y=";m;"x+1":9000(# A4g=1w$="y"g=0:8090:387 Ph=4375w S!h=2h=4:302. Y"passing";8,0;"through ";:1:"(1,";m+1;")";10 ,4;"(0,1)":0:10 ,0;"and" Zh=5381} \7010b:13 ,0;"NOW the gradient=difference in y";14,17;"difference in x":138,63?:117u,0 _16,0;"=";:1:"(";m+1;"-1)";:0:"=";m;" (here)":1:17,1+(m<-1);"(1-0)":0:17,7+2*(m<-1);"1" e12 ,40(:32 +8*(m<-1),0:568+8*(m<-1),40(:8+8*(m<-1),0 hR16,18;" SO  m=";m:h=39000(#:7010b:381} k[19,0;" AND  one value of (x,y)=(0,1)":9000(#:7010b:3128 wJw$="":a$=""::k=(*2)+1:h=5*(k=2):303/ }Sp$="y="+m+"x+1":8100:g=1h=2+2*(k=2):3062 ~>w$="y"h=2+2*(k=2):7010b:3062 "h=17010b:3128 "h=37010b:348\ q$="y"375w ?502:0,14;" END ":9000(#:58: X(i=013 :i,0;c$:i: b)i=13 21:i,0;o$:i: @J:i=104h2488:j=72H1688:i,j:j:i C103g,119w:144,0:-3,3:3,-3:-3,-3:177,71G:0,97a:-3,-3:3,3:3,-3:0,21;"y";7,31;"x" J'i=1:j=-112 M,(j*9 *m+1)>68020T P6x(i)=j*9 :y(i)=j*9 *m+1:8030^ T5y(i)=j*6:m=0x(i)=0:8027[ Xx(i)=(j*6-1)/m ^i=i+1:j:x(1)*8+176,y(1)*8+120x:(x(2)-x(1))*8,(y(2)-y(1))*8: r2a$="":18,0;" Your answer  ?" uD0:q$=:q$="-"18,16;"-";:a$="-":8051s vq$="h"h=18050r wq$="h"h=0h=1: xq$<"0"q$>"9"8050r {]a$=a$+q$:21,0;o$;18,16;a$;19,0;"CORRECT ANSWER: ";m ~a$=m8087 6.5,-10 :1.5@,-20:v=v+1 !h=1h=38090 E21,0;" Like to see why?  y or n":=""8068 !w$=:w$"y"w$"n"8069 ""8071 )w$="y"h=1+2*(k=2): :8093 g.2~L,2:.2~L,2:.2~L,4:.2~L,4:.5,9 :u=u+1 9000(#: t3,7;"TOTAL CORRECT: ";u;5,5;"TOTAL INCORRECT: ";v;16,8;" More?  y or n" !q$=:q$"y"q$"n"8096 h=0:g=0:w$="": `i=1520:h1h321,0;" NEED help? ENTER h " `14,0;" Enter  your working? y or n ":i1514,8;"more" q$= q$="h"8160 q$="n"8130 q$"y"8106 714,20;" ":q$:q$="h"8160 i,0;q$:i:8100 s21,0;o$;14,0;" ENTER  your answer  NOW  ":a$:a$>12 a$="RUBBISH" 7010b:15,1;"Your answer: ";a$:0,60<:128+8*a$,0:0,-16:-128-8*a$,0:0,16:17,0;"CORRECT ANSWER ";p$;19,0;"(same spaces please)":a$=p$8087: 8065:q$="n" h=2*k: "h=1h=3g=1: !h=1+2*(k=2): #(""9000(# #)A21,0;o$;21,9 ;"Press any key":0 #*=""9002*# #+""9003+# #. kh uvC   dO Dsc @AG%#idU#1LS@mSsge[@ '_V%&L=+`e2JPB@d1iD̓1*Tc̙gH-d IIT)HB8@88)<H< 3l;nʯd<ڐC< RfwY@J3$~0xD D0xJcij)"?bU`)o##[L *̔RBDx xLJ T;L<9Ll3TO_$L`1V2@%&sRRTBD@ @@3JfQE+`0TۀI68t@%)I3II)TB8 D< <gm0LXx;*j8sg2`mGO*RH`bw % JJRMyff/%%)TdҐ£@lÌ[@<>m >3(ĒJTdR)J$cz|_JJ JeR'RUJUUURҵiKUUUUUU@JJS3s%IRYTJRRL33O%))TRhg#04% ymGO*l8sg2`)J*IA_*JJ UR)JUM2UZeU.USRT@M*IHЅQTUTJII3yNIJRTI?Ķ6I@0T߀xjQpE3`)TRg_|dJUJUURR|%*UUUP*U>>U*jU*UE$?yUJUT%%&g1RR&NF0[ْ@TOoLl5)U)T풕JUTUTJT*VUPU,JT*VUPU)T좕JUJ*̔T1!b[lJ`)#?"UU*U$6yQU*UT*ʦU>>URҪjUUUJRt%JUU2)U)R7}_$JJ fsi@M3$(dڐqC ;oʷҘf̪U*EIЅIRYTjZeUnUSRT@ YURIRUJ)R*H`_*JJ JITIH3L .da̘[F?K@K*IRgse)RTUUUUUU)JVUUU@ eR7'SJh)J$1>cJR)&lS`j2RP #OVmSsge[@e!FbU@JJRʩh JRRT%J$)T,ߊwD>} ?`m(Ìኛ`TpÄn |<*cl0Rd @@~| Tn>Ç x@x88@@ 0);c;8,0;"are found";10 ,0;"by putting" yw7010b:14,0;"first";14,0;("PUT "h=1);14,6;"y=0 into the equation" |16,0;" THEN  we get: 0=";m;16,17+(m1);"x";("+"c>0);c;"  SO  x=";-c/m:h=1w$"y"9000(#:7010b:187 }F19,0;" ONE INTERCEPT IS:  (";-c/m;",0)":9000(# 7010b:14,0;"next";14,0;("PUT "h=1);14,4;": x=0 into the equation";16,0;"Giving y=";m;"x0";("+"c>0);c;16,18;" SO  y=";c:h=19000(#:7010b:187 I19,0;" THE OTHER INTERCEPT IS:  (0,";c;")":9000(# w$="y"8090:196 Kw$="":h=0:m=(*5)-2:m=0m=-1163 8c=((*7)-3)*2:c=0166 M:8000@:k=(*2)+1:d$="("+(-c/m)+",0)":e$="(0,"+c+")" 20,0;" For the ";2,0;"line y=";m;2,7+(m<0)+(m1);"x";("+"c>0);c;4,0;"ONE INTERCEPT";6,0;"is ";(d$k=1);(e$k=2);8,0;" What is ";10 ,0;"the other";12 ,0;"intercept?" Yp$=(d$k=2)+(e$k=1):8100:w$="y"7000X:7010b:109m h=1133-6*k q$="y"160 Fw$="":h=0:p$="5":w=3:z=1:x=7:y=4 Τm=.75@:c=-1.25 ::8000@:3*8+176,1*8+120x,2:7*8+176,4*8+120x,2 ԗ14,0;" To find  the distance between",,,"the two points (3,1) and(7,4)",,,"we use  Pythagoras' Theorem ":9000(#:7010b ׶0,0;"Points";1,0;" (7,4)";2,0;" and ";3,0;" (3,1)":3*8+176,128:32 ,0:0,24 7010b:14,0;"DIFFERENCE in x values squared =(";x;"-";w;")x(";x;"-";w;")=";(x-w)^2;17,0;"DIFFERENCE in y values squared =(";y;"-";z;")x(";y;"-";z;")=";(y-z)^2:h=19000(#:7010b:254 9000(#:7010b:14,0;" So  the distance between the two points is the square root of (";(x-w)^2;"+";(y-z)^2;")";18,0;"ANSWER: ";p$;" (cms.)":9000(#:w$="y"8090:260 k=(*3)+1:y=4:x=((*(6+(k^2)-(k=2)))-5+"860"(k)):m=.75@:k=1m=5/12 c=y-m*x:8000@:x*8+176,y*8+120x,2:w=x-16+4*k:z=y-"563"(k):w*8+176,z*8+120x,2 0,0;" What is ";2,0;"the distance";4,0;"between the";6,0;"points";8,0;"(";x;",";y;") and";10 ,0;"(";w;",";z;") ?" ap$=(14-(k^2)):f$="(omit cms.)":8100:260-42**(w$="y"h=1) q$="y"230 /Y350^:0,0;" TO FIND ":360h:360h:370r:380| JOh=0:w$="":350^:0,0;" WHAT IS ":360h:"?" M~f$="in the form: y=mx+c":p$="y="+m+"x"+("+"d>0)+d:8100:w$="y"370r:380|:8090:342V SCh=1370r:9000(#:21,0;o$:333M Vq$="y"330J Y?502:0,14;" END ":9000(#:58: ^0m=(*13 )-6:m<2350^ aMc=(*11 )-5:d=(*11 )-5:(c-d)<2353a b c=0d=0353a d9x=(*17)-8:y=m*x+d:y>6350^ fA:8000@:x*8+176,y*8+120x,2: h2,0;"the equation";4,0;"of the line";6,0;"parallel to";8,0;m;"x=";-c;"+y";10 ,0;"passing thro'";12 ,0;"(";x;",";y;")";: rF7010b:14,0;"THE gradient of the line is:";m: |16,0;" So  putting the values of x,y,minto y=mx+c we get:";19,5-(y<0);y;"=";m;"X";x;"+c";19,15;"SO c=";d:9000(#:7010b:16,0;"ANSWER IS: y=";m;"x";("+"d>0);d:9000(#: X(i=013 :i,0;c$:i: b)i=13 21:i,0;o$:i: @J:i=104h2488:j=72H1688:i,j:j:i C103g,119w:144,0:-3,3:3,-3:-3,-3:177,71G:0,97a:-3,-3:3,3:3,-3:0,21;"y";7,31;"x" J'i=1:j=-112 M&(j*9 *m+c)>68020T P0x(i)=j*9 :y(i)=j*9 *m+c:8030^ T5y(i)=j*6:m=0x(i)=0:8027[ Xx(i)=(j*6-c)/m ^i=i+1:j:x(1)*8+176,y(1)*8+120x:(x(2)-x(1))*8,(y(2)-y(1))*8: M.5,-10 :1.5@,-20:v=v+1:h=18090 E21,0;" Like to see why?  y or n":=""8068 !w$=:w$"y"w$"n"8069 ""8071  w$="y" :8093 g.2~L,2:.2~L,2:.2~L,4:.2~L,4:.5,9 :u=u+1  9000(# :3,5;" TOTAL CORRECT : ";u;5,5;"TOTAL INCORRECT: ";v;16,8;" More?  y or n" !q$=:q$"y"q$"n"8096 h=0:w$="": Vi=1620:h121,0;" NEED help? ENTER h " `15,0;" Enter  your working? y or n ":i1615,8;"more" q$=:q$="h"8160 q$="n"8130 q$"y"8106 715,20;" ":q$:q$="h"8160 i,0;q$:i:8100 ‡21,0;o$;14,0;o$;o$;14,0;" ENTER  your answer  NOW ",f$:a$:a$>12 a$="RUBBISH" 7010b:15,1;"Your answer: ";a$:0,60<:128+8*a$,0:0,-16:-128-8*a$,0:0,16:17,0;"CORRECT ANSWER ";p$;19,0;"(same spaces please)":a$=p$8087: 8065:q$="n" h=2*k: h=1a$="h":8133  h=1: #(""9000(# #)A21,0;o$;21,9 ;"Press any key":0 #*=""9002*# #+""9003+# #. khuvC  @WFin the form eg:(3,2)mcJO \sc @A~)#idU#1LS@mSsge[@ '_V%&L=+`e2JPB@d1iD̓1*Tc̙gH-d IIT)HB8@88)<H< 3l;nʯd<ڐC< RfwY@J3$~0xD D0xJcij)"?bU`)o##[L *̔RBDx xLJ T;L<9Ll3TO_$L`1V2@%&sRRTBD@ @@3JfQE+`0TۀI68t@%)I3II)TB8 D< <gm0LXx;*j8sg2`mGO*RH`bw % JJRMyff/%%)TdҐ£@lÌ[@<>m >3(ĒJTdR)J$cz|_JJ JeR'RUJUUURҵiKUUUUUU@JJS3s%IRYTJRRL33O%))TRhg#04% ymGO*l8sg2`)J*IA_*JJ UR)JUM2UZeU.USRT@M*IHЅQTUTJII3yNIJRTI?Ķ6I@0T߀xjQpE3`)TRg_|dJUJUURR|%*UUUP*U>>U*jU*UE$?yUJUT%%&g1RR&NF0[ْ@TOoLl5)U)T풕JUTUTJT*VUPU,JT*VUPU)T좕JUJ*̔T1!b[lJ`)#?"UU*U$6yQU*UT*ʦU>>URҪjUUUJRt%JUU2)U)R7}_$JJ fsi@M3$(dڐqC ;oʷҘf̪U*EIЅIRYTjZeUnUSRT@ YURIRUJ)R*H`_*JJ JITIH3L .da̘[F?K@K*IRgse)RTUUUUUU)JVUUU@ eR7'SJh)J$1>cJR)&lS`j2RP #OVmSsge[@e!FbU@JJRʩh JRRT%J$)T,ߊwD>} ?`m(Ìኛ`TpÄn |<*cl0Rd @@~<| Tn>Ç x@x88@9 );a*(a-1);"-";(a-1)^2;"y";15,27;"=";a*(a-1)*x-(a-1)^2*y:9000(# 17,0;" Multiply  the",,"2nd equation by ";a;":";18,21-(a*a>9 );a*(a-1);"-";a*a;"y";18,27;"=";a*(a-1)*x-a*a*y:9000(# 159,24:96`,0:19,9 ;"SUBTRACT:";19,24;a*a-(a-1)^2;"y =";(a*a-(a-1)^2)*y;20,0;" SO  y=";y:9000(#:7010b: 14,0;" NOW  substitute the value y=";y;16,0;"into the 1st equation";18,0;" giving  ";a;"-(";a-1;" X ";y;")=";a*x-(a-1)*y;18,26;a;"=";a*x;20,0;" SO  =";x:9000(# 7010b:14,0;" CHECK  that =";x;" and y=";y;16,0;"satisfy the 2nd equation:";18,0;"(";a-1;" X ";x;")-(";a;" X ";y;")=";(a-1)*x-a*y;" ":9000(#: ~h=0:w$="":160:0,0;" SOLVE ":f$="in the form eg:=2":r$="x="+x:s$="y="+y:k=(*2) p400*k+170:8100:w$="y"400*k+180:400*k+200:8090:260 Rh=1400*k+180:f$="in the form eg:=2":p$="x="+x:236 700-470*(q$="y") L570::8100:w$="y"180:200:8090:260 :2,0;"the";4,0;"simultaneous";6,0;"equations:";8,0;a-1;"+";a;"y=";(a-1)*x+a*y;10 ,0;"and";12 ,0;a;"=";2*a;"y";("+"(a*(x-2*y)>0));a*(x-2*y): D7010b:14,0;" Multiply  the",,"1st equation by 2:";15,20-(2*a>9 );2*(a-1);"+";2*a;"y=";2*((a-1)*x+a*y):9000(# N17,0;" Re-arrange  the","2nd equation";18,20-(2*a>9 );a;"-";2*a;"y=";a*(x-2*y):9000(# S*159,24:96`,0:19,12 ;" ADD:";19,20-(2*a>9 )-((3*a-2)>9 );((3*a-2)(3*a-2)1);"";19,25;"=";x*(3*a-2);20,0;" SO  =";x:9000(#:7010b: X14,0;" NOW  substitute the value =";x;16,0;"into the 1st equation";18,0;" giving  (";a-1;" X ";x;")+";a;"y=";(a-1)*x+a*y;18,26;a;"y=";a*y;20,0;" SO  y=";y:9000(# [7010b:14,0;" CHECK  that =";x;" and y=";y;16,0;"satisfy the 2nd equation:";18,0;"(";a;" X ";x;")=(";2*a;" X ";y;")";("+"a*(x-2*y)>0);a*(x-2*y);" ":9000(#: :" TO";:tch=1 +h=0:w$="":x=(*11 )+5 xt=(*3)+3:a=(*4)+2:770:tch=1800 :8204:tch=0::706 ˦7010b:f$="as: y=mx+c ":r$="y="+t+"x+"+(a*(t-1)):s$="y=x+"+((x+a)*(t-1)):8100:w$="y"800 :8204:8090:730 !h=1800 :715  :900-194*(q$="y") " FIND THE TWO EQUATIONS ","given by:-";4,0;"In ";a;" years time,"," Peter  will be ";t;" times","older than  Karen ";8,0;" Peter  is ";(x+a)*(t-1);" years","older than  Karen " 11 ,0;"LET years =  Karen's  age","LET y years =  Peter's  age":r$="y="+t+"x+"+(a*t-a):s$="y=x+"+((x+a)*(t-1)-x):  7010b:14,0;" Write  the 1st equation as:","(y+";a;")=";t;" X (+";a;")  So  y=";t;"+";a*(t-1):9000(#: 417,0;" Write  the 2nd equation as:","y-=";(x+a)*(t-1);18,19;" So  y=+";(x+a)*(t-1):9000(#: _:502:0,14;" END ";20,2;"Press RUN & ENTER to re-start": X(i=013 :i,0;c$:i: b)i=13 21:i,0;o$:i: @J:i=104h2488:j=72H1688:i,j:j:i C103g,119w:144,0:-3,3:3,-3:-3,-3:177,71G:0,97a:-3,-3:3,3:3,-3:0,21;"y";7,31;"" J'i=1:j=-112 M&(j*9 *m+c)>68020T P0x(i)=j*9 :y(i)=j*9 *m+c:8030^ T5y(i)=j*6:m=0x(i)=0:8027[ Xx(i)=(j*6-c)/m ^i=i+1:j:x(1)*8+176,y(1)*8+120x:(x(2)-x(1))*8,(y(2)-y(1))*8: M.5,-10 :1.5@,-20:v=v+1:h=18090 E21,0;" Like to see why?  y or n":=""8068 !w$=:w$"y"w$"n"8069 ""8071  w$="y"  8093 g.2~L,2:.2~L,2:.2~L,4:.2~L,4:.5,9 :u=u+1  9000(# x:3,6;" TOTAL CORRECT: ";u;5,6;"TOTAL INCORRECT: ";v;16,8;" More?  y or n" !q$=:q$"y"q$"n"8096 h=0:w$="": Vi=1620:h121,0;" NEED help? ENTER h " `15,0;" Enter  your working? y or n ":i1615,8;"more" q$=:q$="h"8160 q$="n"8130 q$"y"8106 715,20;" ":q$:q$="h"8160 i,0;q$:i:8100 –i=12:21,0;o$;14,0;o$;o$;14,0;" ENTER  no.";i;" answer  NOW ",f$:a$:a$>8a$="" i=1b$=a$ $f$(16)=""f$(16)="y" Yi:7010b:15,1;"Your answer:";18,0;"CORRECT ANSWER " ׷15,15;b$;15,24;a$;18,15;r$;18,24;s$:0,60<:255,0:0,-16:-255,0:0,16 'r$=b$s$=a$r$=a$s$=b$8087: 8065: h=1a$="h":8142  h=1: #(""9000(# #)A21,0;o$;21,9 ;"Press any key":0 #*=""9002*# #+""9003+# #.+.05|L,4:21,0;o$: BWh  C uvbxyam*c@JO Ugr ffHP`@sc @r#idU#1LS@mSsge[@ '_V%&L=+`e2JPB@d1iD̓1*Tc̙gH-d IIT)HB8@88)<H< 3l;nʯd<ڐC< RfwY@J3$~0xD D0xJcij)"?bU`)o##[L *̔RBDx xLJ T;L<9Ll3TO_$L`1V2@%&sRRTBD@ @@3JfQE+`0TۀI68t@%)I3II)TB8 D< <gm0LXx;*j8sg2`mGO*RH`bw % JJRMyff/%%)TdҐ£@lÌ[@<>m >3(ĒJTdR)J$cz|_JJ JeR'RUJUUURҵiKUUUUUU@JJS3s%IRYTJRRL33O%))TRhg#04% ymGO*l8sg2`)J*IA_*JJ UR)JUM2UZeU.USRT@M*IHЅQTUTJII3yNIJRTI?Ķ6I@0T߀xjQpE3`)TRg_|dJUJUURR|%*UUUP*U>>U*jU*UE$?yUJUT%%&g1RR&NF0[ْ@TOoLl5)U)T풕JUTUTJT*VUPU,JT*VUPU)T좕JUJ*̔T1!b[lJ`)#?"UU*U$6yQU*UT*ʦU>>URҪjUUUJRt%JUU2)U)R7}_$JJ fsi@M3$(dڐqC ;oʷҘf̪U*EIЅIRYTjZeUnUSRT@ YURIRUJ)R*H`_*JJ JITIH3L .da̘[F?K@K*IRgse)RTUUUUUU)JVUUU@ eR7'SJh)J$1>cJR)&lS`j2RP #OVmSsge[@e!FbU@JJRʩh JRRT%J$)T,ߊwD>} ?`m(Ìኛ`TpÄn |<*cl0Rd @<~| Tn>Ç x@hD88x88D8@