ZXTape! 0Created with Ramsoft MakeTZX2w9O Level Maths Revision: Equations & Inequalities - Side B Rose Software1983English EducationalNoneOriginal0Quadratic Equations%qe SM(502:58::A.Cowley Mar.1983 06:6::"gr""a":"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$=" " 0);q;"=";p+q:9000(#:h=17010b:7000X:121y N7000X:7010b:2,0;" Now  ";:n=3:160 6n=14:180:w$="y"8090:260 r=3:85004! 7010b:0,0;" By a process ";2,0;"of trial and";4,0;"error, we";6,0;"can ";:n=7:160:h=17010b:200 Cn=15:180:tch=0:w$="y"8090:260 100d t"re-write ";n,31;"":170:"=0 ";n+3,0;"as";n+5,0;"(";:r=3"3"; 7"";("+"p>0);p;")(";("+"q>0);q;")=0": @("3"r=3);"";:p+q*r=0("+"p*q>0);p*q;: 0("+"p+q*r>0);:(p+r*q)1p+r*q; p+r*q=-1"-"; "";("+"p*q>0);p*q;: n,0;" So either:  (";r;n,15-(r3);"";("+"p>0);p;")=0";n+2,7;" or:  (";("+"q>0);q;")=0" tn+4,0;" SOLUTION:-  =";-p*((((p/r)*100d+.5))/100d);" or =";-q:9000(#: 58100:(w$="y"h=1)r=1130 )(w$="y"h=1)r=3154 q$="y"100d ,rn=8::" If a quadratic equation ",,,"cannot be factorised",,," then  use the formula:":370r /n=6:15,0;" where  a+b+c=0",,,"is the equation to be solved":9000(#::" For example:  5+2-1=0":370r Gz3,0;" here  a=5,b=2,c=-1";11 ,0;" So  =-2+(2-4 X 5 X -1)";13 ,12 ;"2 X 5" J74J,78N:4,0:568,74J:152,0:15,0;"=-2+24";17,4;"10";16,15;"OR";15,22;"=-2-24";17,26;"10" M16,44,:480,0:192,44,:480,0:19,0;" Solution:  =0.29 or =-0.69":9000(#:900 rn,0;"=-b+b-4ac";n+2,5;"2a":34",166-8*n:4,0:480,177-8*n:-1,-2:1,2:480,0:16,162-8*n:80P,0: ?502:0,14;" END ":9000(#:58: X(i=013 :i,0;c$:i: b)i=13 21:i,0;o$:i: 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(# v:3,7;"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$:i:8100 i=12:21,0;o$;14,0;o$;o$;14,0;" ENTER  no.";i;" answer  NOW ","=? (no more than 2 dec.pl.)":a$:a$>6űa$=0a$=" " i=1b$=a$ Ίi:7010b:15,1;"Your answer:";18,0;" CORRECT ANS: ":x=-p*((((p/r)*100d+.5))/100d) 15,14;"=";b$;15,22;"or =";a$;18,14;"=";x;18,22;"or =";-q:0,60<:255,0:0,-16:-255,0:0,16 <i=1̱a$:a$(i)<45-ůa$(i)>5798154 ?i:i=1̱b$:b$(i)<45-ůb$(i)>5798154 ,i:x=b$-q=a$x=a$-q=b$8087: 8065: &h=1a$="h":b$="":8142  h=1: !4J:i=1442488:j=72H1688:i,j:j:i !7143,121y:104h,0:-3,3:3,-3:-3,-3:193,71G:0,97a:-3,-3:3,3:3,-3:0,23;"y";7,31;"" !@iy(14)=0:i=113 :x(i)=i-7:y(i)=f$:y(i)>y(14)y(14)=y(i) !B/:i:y(14)6y(14)=1 !C8y(14)>6y(14)=y(14)/6 !Fx(1)*8+192,(y(1)*8/y(14)+120x):i=112 :(x(i+1)-x(i))*8,(y(i+1)-y(i))*8/y(14):i: #(""9000(# #)A21,0;o$;21,9 ;"Press any key":0 #*=""9002*# #+""9003+# #.+.05|L,4:21,0;o$: cuv4!hpqrh4!nxB A QnD IC WFr*x(i)*x(i)+(p+r*q)*x(i)+p*qO gr X)ff$pp@psc @r)#idU#1LS@mSsge[@ '_V%&L=+`e2JPB@d1iD̓1*Tc̙gH-d IIT)HB8@88)<H< 3l;nʯd<ڐC< RfwY@J3$~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 xBD888@4+5 Inequalities  6-1>4+5 ":i Sji=110 :.1}L,3:.1}L,4:.2~L,6:i:0:6:6: dNz=6:w$="":h=0:qu=0:tch=1:f$="(key in eg: x>2 )" gHa=(*7)+3:b=(*7)+2:a"+x:8000@:1,0;" INEQUALITIES ";1,0;(" SOLVE:  "tch=0) lx0,168:63?+480*(tch0),0:0,159:63?+480*(tch0),0 mn=3:n,0;c$;n,1;("IF:"(tch=1h=1w$="y")):180+20*qu:tch=0h=0w$"y"133 n-190+20*qu:h=1133 p199+20*qu:9 +5*qu,2;"SO ";a-b;">";(a-b)*x;16,0;" GIVING: >";x;18,0;"(the shaded part on the diagram)":0,480:63?,0:0,39':63?,0:w$="y"8090:139 v$9000(#:tch=0130 y" SO we can treat inequalities much like equations ";4,0;" EXCEPT THAT  when you change",,,"the  sign  throughout an",,,"inequality";11 ,0;"you must also change",,,"the  direction  of the arrow" |L0,144:103g,0:0,135:103g,0 X16,0;"FOR EXAMPLE: if -2>4";18,11 ;"then 2<-4":9000(# ;tch=0:qu=(*2):h=0:w$="":103g 58100:w$="y"h=17010b:109m q$="y"130 300, Vn,0+6*(tch=1h=1w$="y");a;"-1>";b;"";("+"k>0);k: @n+3,0;"THEN ";a;"-";b;">1";("+"k>0);k:  Ln,0+6*(tch=1h=1w$="y");k;"-";a;"<";b;"(1-)": jn+3,0;"THEN ";k;"-";a;"<";b;"-";b;"";n+6,2;"SO ";-a;"+";b;"<";-k;"+";b: n+8,6;b-a;"<";(b-a)*x;n+10 ,0;" Change signs and reverse arrow:":0,175-(n+10 )*8:255,0:0,168-(n+10 )*8:255,0: Rn,0+6*(tch=1h=1w$="y");a*x-b;"<";a;"-";b;"<";a*z-b: ,)tch=1:f$="(key in eg: {-2,-1} )" /<w$="":h=0:qu=(*2):tch=1qu=0 5Op$="":a=(*7)+3:b=(*7)+2:a";x;11 ,6;z;">":h=1369q \0,568:176,0:0,47/:176,0:15,0;" The solution set is: ";17,0;p$:w$="y"8090:372t _;9000(#:tch=1qu=0qu=1:3095 htch=0:303/ q58100:w$="y"h=17010b:339S tq$="y"303/ d:502:0,14;" END ";21,9 ;" Press any key ":0:58: *7,0;"AND: is a -ve no.": >7,1;"SO: ";a*x-b;"+";b;"<";a;"<";a*z-b;"+";b:  0,0,102f,24,24,24,102f,0,1,1,2,2,4,36$,24,8,112p,16,112p,64@,112p,0,0,0 25000:i=023:a:"a"+i,a:i: p"ineq"3:"sc": X(i=013 :i,0;c$:i: b)i=13 21:i,0;o$:i: @J:i=1522488:j=72H1688:i,j:j:i C151,119w:96`,0:-3,3:3,-3:-3,-3:201,71G:0,97a:-3,-3:3,3:3,-3:0,24;"y";7,31;"" Gi=112 :x*8+200,64@+i*8:0,5:0,-3:(25+z)*8-1-x*8-200,8:i: M.5,-10 :1.5@,-20:v=v+1:h=18090 E21,0;" Like to see why?  y or n":=""8068 !w$=:w$"y"w$"n"8069 ""8071  w$="y"  8093 g.2~L,2:.2~L,2:.2~L,4:.2~L,4:.5,9 :u=u+1  9000(# y:3,6;" TOTAL CORRECT: ";u;5,6;"TOTAL INCORRECT: ";v;16,8;" More? y or n" @480,136:143+8*(v>9 )+8*(v>99c),0:480,127:143+8*(v>9 )+8*(v>99c),0:480,152:143+8*(u>9 )+8*(u>99c),0:480,143:143+8*(u>9 )+8*(u>99c),0 L64@,480:103g,0:64@,39':103g,0 !q$=:q$"y"q$"n"8096 h=0:w$="": Vi=1620:h121,0;" NEED help? ENTER h " 0,568:568,0:0,47/:568,0:15,0;" Enter  your working? y or n ":i1615,8;"more" q$=:q$="h"8160 q$="n"8130 q$"y"8106 715,20;" ":q$:q$="h"8160 i,0;q$:i:8100 66:0,47/:568,0:9 Ç21,0;o$;14,0;o$;o$;14,0;" ENTER  your answer  NOW ",f$:a$:a$>15a$="RUBBISH" ]7010b:15,1;"Your answer: ";a$:0,60<:128+8*a$,0:0,-16:-128-8*a$,0:0,16:17,0;"CORRECT ANSWER ";p$;19,0;"(same spaces please)":0,40(:111o,0:0,31:111o,0:a$=p$8087: 8065: h=1a$="h":8133 ""8163  h=1: #(""9000(# #)A21,0;o$;21,9 ;"Press any key":0 #*=""9002*# #+""9003+# #.: O 9sc @ .)#idU#1LS@mSsge[@ '_V%&L=+`e2JPB@d1iD̓1*Tc̙gH-d IIT)HB8@88)<H< 3l;nʯd<ڐC< RfwY@J3$~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 xx8D<8< 8 8"s$="<");("<"s$=">");-p;" and ";s$;-q;19,5;"Let's calculate that:-":9000(# J7000X:7010b:n=3:160:h=1w$=""200 6180:9000(#:w$="y"8093:260 tch=0:100d 0,176-(n-1)*8:79O,0:0,167-(n-1)*8:79O,0:n-1,0;" Re-write ";n,31;"":170:s$;"0 ";n+3,0;"as";n+5,0;"(";:r=3"3"; <"";("+"p>0);p;")(";("+"q>0);q;")";s$;"0": @("3"r=3);"";:p+q*r=0("+"p*q>0);p*q;: 0("+"p+q*r>0);:(p+r*q)1p+r*q; p+r*q=-1"-"; "";("+"p*q>0);p*q;: 0,96`:103g,0:0,71G:103g,0:10 ,0;" ALWAYS DRAW ";11 ,0;" A SKETCH OF ";12 ,0;" THE CURVE ";15,0;"It cuts -axis at =";-p*((((p/r)*100d+.5))/100d);",=";-q m0,40(:72H,0:0,31:72H,0:17,0;"SOLUTION: "; m198:t$;" ";u$;19,0;"(function";s$;"0 ";("above"s$=">");("below"s$="<");" -axis)": Ɖt$=""+(">"s$="<")+("<"s$=">"):v$=(-p*((((p/r)*100d+.5))/100d)):u$=""+s$+-q:v$(1)="0"v$=v$(2) t$=t$+v$: )8100:w$="y"h=1145 q$="y"100d ?502:0,14;" END ":9000(#:58: 0,0,102f,24,24,24,102f,0,1,1,2,2,4,36$,24,8,112p,16,112p,64@,112p,0,0,0 25000:i=023:a:"a"+i,a:i: p"quad ineq":"quad ineq": X(i=013 :i,0;c$:i: b)i=13 21:i,0;o$:i: 6.5,-10 :1.5@,-20:v=v+1 E21,0;" Like to see why?  y or n":=""8068 !w$=:w$"y"w$"n"8069 ""8071  w$="y"  8093 g.2~L,2:.2~L,2:.2~L,4:.2~L,4:.5,9 :u=u+1  9000(# }:3,6;" TOTAL CORRECT: ";u;5,6;"TOTAL INCORRECT: ";v;16,7;" More?  y or n " @480,136:143+8*(v>9 )+8*(v>99c),0:480,127:143+8*(v>9 )+8*(v>99c),0:480,152:143+8*(u>9 )+8*(u>99c),0:480,143:143+8*(u>9 )+8*(u>99c),0 L568,480:119w,0:568,39':119w,0 !q$=:q$"y"q$"n"8096 h=0:w$="": Vi=1620:h121,0;" NEED help? ENTER h " 0,568:557,0:0,47/:557,0:15,0;" Enter  your working? y or n ":i1615,8;"more" q$=:q$="h"8160 q$="n"8130 q$"y"8106 715,20;" ":q$:q$="h"8160 i,0;q$:i:8100 66:0,47/:568,0:9 i=12:21,0;o$;14,0;o$;o$;14,0;" ENTER  no.";i;" answer  NOW  as eg: x>-2 (no more than 2 dec.pl.)":a$:a$>8űa$=0a$=" " i=1b$=a$ i .7010b:14,1;"Your answer:" ~14,15;b$;" ";a$:0,68D:255,0:0,-16:-255,0:0,16 0,40(:111o,0:0,31:111o,0:17,0;"CORRECT ANSWER ";:194 Ut$="x"+t$(2):u$="x"+u$(2):(t$=b$u$=a$)(t$=a$u$=b$)8087: 8065: &h=1a$="h":b$="":8142  h=1: !4J:i=1442488:j=72H1688:i,j:j:i !7143,121y:104h,0:-3,3:3,-3:-3,-3:193,71G:0,97a:-3,-3:3,3:3,-3:0,23;"y";7,31;"" !@iy(14)=0:i=113 :x(i)=i-7:y(i)=f$:y(i)>y(14)y(14)=y(i) !B/:i:y(14)6y(14)=1 !C8y(14)>6y(14)=y(14)/6 !Fx(1)*8+192,(y(1)*8/y(14)+120x):i=112 :(x(i+1)-x(i))*8,(y(i+1)-y(i))*8/y(14):i: #(""9000(# #)A21,0;o$;21,9 ;"Press any key":0 #*=""9002*# #+""9003+# #.+.05|L,4:21,0;o$: acuvhpqrp4!nB A V-4Tx>-4Ux<-1QnD IC WSm >3(ĒJTdR)J$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 xBD888x8D<8< 8 8