ZXTape! 2 %Maths Tutor for the Spectrum - Side BCentury Communications Ltd Robert Carter1984English Educational7.95 ROM LoaderOriginal1TZXed by Andrew Barker Provided by Darren Farrell61 PROGRAM 61 POWERS OF j !0,11 ;"POWERS OF j" "ENTER power (pos int) ";n n-n020 *(n/4)-(n/4)0a$="1" -(n/4)-(n/4)0.25~a$="j" -(n/4)-(n/4)0.5a$="-1" !.(n/4)-(n/4)0.75@a$="-j" (#10 ,12 ;"j^";n;" =";a$ 20::20 nA-j62 .PROGRAM 62 COMPLEX ADDITION "FIRST NUMBER?" "Real Part? ";R1 10 ,2;R1 ("Imaginary Part? ";I1 2%10 ,2;R1;" + j(";I1;")" <#0,0;"SECOND NUMBER?" F"Real Part? ";R2 P110 ,2;R1;" + j(";I1;") PLUS ";R2 Z"Imaginary Part? ";I2: d@10 ,2;R1;" + j(";I1;") PLUS ";R2;" + j(";I2;")" n14,13 ;"EQUALS" x,18,12 ;R1+R2;" + j(";I1+I2;")" $62a 7q9.PROGRAM 62a COMPLEX DIVISION "FIRST NUMBER?" "Real Part? ";R1 10 ,2;R1 ("Imaginary Part? ";I1 2%10 ,2;R1;" + j(";I1;")" <#0,0;"SECOND NUMBER?" F"Real Part? ";R2 P110 ,2;R1;" + j(";I1;") OVER ";R2 Z"Imaginary Part? ";I2: d@10 ,2;R1;" + j(";I1;") OVER ";R2;" + j(";I2;")" n14,13 ;"EQUALS" xh18,12 ;((R1*R2)+(I1*I2))/((R2*R2)+(I2*I2));" + j(";((R2*I1)-(R1*I2))/((R2*R2)+(I2*I2));")" >63 Y 7PROGRAM 63 COMPLEX NUMBER CONVERSION "Real Coefficient? ";a "Imaginary Coefficient? ";b r=((a*a)+(b*b)) ( Thr=(b/a) 2Thd=(Thr*180/) <a;" + j(";b;")" Fz5,0;(r*100d)/100d;" (Cos ";(Thd*100d)/100d;" + j Sin ";(Thd*100d)/100d;")" PU10 ,0;(r*100d)/100d;" exp(j ";(Thr*100d)/100d;")" abrfZ$hVh¡64 dZ-PROGRAM 64 GRAPH OF SINH X K0,88X:255,0:128,0:0,175 x=-33.1}L sinhx=((x)-(-x))/2 (1(x*30)+128,(sinhx*5)+88X 2x Fffa}Linh I7+65 eh-PROGRAM 65 GRAPH OF COSH X K0,88X:255,0:128,0:0,175 x=-33.1}L coshx=((x)+(-x))/2 (1(x*30)+128,(coshx*5)+88X 2x Fffa}Losh!$f66  "-PROGRAM 66 GRAPH OF TANH X K0,88X:255,0:128,0:0,175 x=-33.1}L !tanhx=((x)-(-x))/((x)+(-x)) (2(x*30)+128,(tanhx*502)+88X 2x Fffa}Lanh~b67 ) 2PROGRAM 67 HYPERBOLIC FUNCTIONS "ENTER x ";x "If x equals ";x %"Sinh x is ";((x)-(-x))/2 (%"Cosh x is ";((x)+(-x))/2 2*"Tanh x is ";((x)-(-x))/((x)+(-x)) <:0::10 x68 ]W- _0PROGRAM 68 INVERSE HYPERBOLIC "ENTER x ";x "The number x is ";x &"arcsinh x = ";(x+((x*x)+1)) ( n"ENTER x ";x x"The number x is ";x &"arccosh x = ";(x+((x*x)-1))  "ENTER x ";x "The number x is ";x 5"arctanh x = ";0.5*((1+x)/(1-x))  x69 md'PROGRAM 69 FACTORIAL F=1 x=133! F=F*x (x,F 2x f/.!70 &LT (0PROGRAM 70 APPROXIMATION TO e  tot=1 a=110  10 tot=tot+(1/F) a,tot a :"e",1: F=1:"n?";n  x=1n F=F*x (x 2 o-T= f]|n 71  PROGRAM 71 PROGRESSIONS ;5:"Do you want Arithmetic or Geometric? ";a$ ,a$(1)="g"a$(1)="G"150 "ARITHMETIC PROGRESSION" ("ENTER first term ";a 2"First Term is ";a <"ENTER common difference ";d F"Common Difference is ";d P:"Progression is:" Z:"Term No.";"Term" d,x=110 :x,a+((x-1)*d):x n"ENTER Any Term No. ";n x1nth=a+(n-1)*d::"Term No. ";n;" is ";nth MSn=(n/2)*((2*a)+((n-1)*d))::"Sum to ";n;" terms is ";Sn  "GEOMETRIC PROGRESSION" "ENTER first term ";a "First Term is ";a "ENTER common ratio ";r "Common Ratio is ";r :"Progression is:" :"Term No.";"Term" ,x=110 :x,a*(r^(x-1)):x "ENTER Any Term No. ";n 3nth=a*(r^(n-1))::"Term No. ";n;" is ";nth ASn=a*(1-(r^n))/(1-r)::"Sum to ";n;" terms is ";Sn Aaad dntb@72 )0PROGRAM 72 D'ALEMBERT'S RATIO n=010 .5 &uD=(2^(n-1))/(1+n) uN=(2^n)/(2+n) ( n,uN/uD 2n (  :.*b73  /PROGRAM 73 PASCAL'S TRIANGLE ""x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 " n=010  r=0n !100d:200:300, ("n+1,r*3;Fn/(Fnr*Fr) 2r <n FDx=025524:x,175:0,-100d:x: d'Fn=1:x=1n:Fn=Fn*x:x: ,Fnr=1:x=1n-r:Fnr=Fnr*x:x: ,'Fr=1:x=1r:Fr=Fr*x:x:   ]|Fn]|74  .PROGRAM 74 FIBONACCI SERIES 5"Term No.","Term":1,1:2,1 a=1:b=1 n=321 (f=a+b 2n,f < a=b:b=f Fn amb*f*75 zE~ |,PROGRAM 75 RANDOM VECTORS #6:"Various Random vectors" $n=020:A=(*2) 3x1=30+*195:y1=30+*115s: (x2=*30:y2=*30 2.A=0x1,y1:x2,y2:x1+x2,y1+y2,1 <0A=1x1-x2,y1-y2,1:x1,y1:-x2,-y2 Fn aJ!ư4J@#76 s ,PROGRAM 76 RADIUS VECTORS MAG=502  A=02*ͧ/20  x=MAG*A ( y=MAG*A 2x+128,y+88X <-x,-y F 20: PA a2IڦIڢ~ {xEyK76a  9PROGRAM 76a RADIUS VECTOR OF AN ELLIPSE M1=30:M2=60<  A=02*ͧ/20  x=M1*A ( y=M2*A 2x+128,y+88X <-x,-y F 20: PA <IڦIڢ~ {xm [y-U#X77 lP n1PROGRAM 77 ADDITION OF VECTORS "VECTOR A" X1=*127:Y1=*87W X2=*127:Y2=*87W (1,1:X1,Y1 2 100d <"0,9 ;"PLUS VECTOR B" FX2,Y2 P 100d Z$1,0;"EQUALS VECTOR C" d-(X1+X2),-(Y1+Y2) n200::10 T1y|k877a  3PROGRAM 77a ADDITION OF VECTORS 2 "VECTOR A" X1=*127:Y1=*87W X2=*127:Y2=*87W (1,1:X1,Y1 )1,1:X2,Y2 2 100d <"0,9 ;"PLUS VECTOR B" FX1,Y1:X2,Y2 GX2,Y2:X1,Y1 P 100d Z$1,0;"EQUALS VECTOR C" d!1-(X1+X2),1-(Y1+Y2) n200::10 M`,{K78 V 0PROGRAM 78 RESOLVING A VECTOR o0:6:0,0:71G,71G:100d,0:71G,71G:0,100d t18,2;"x":12 ,20;"y":3,7;"z":0,10 ;"3D COORDINATES":100d /2:71G,71G:502,30 (@10 ,11 ;"A":1,10 ;"VECTOR A":502 2j4:71G,71G:-30,-30:15,4;"Ax":2,10 ;"X COMPONENT" рTՋSf>QUPxNـMuL/K J\|HG/'E.CMlBF@>=/sC;s-9ʣ7O6#74TC2S0*.1@,'̀+)ٟ'-߀%;:#DM!IJGƀ@5x&{6@R\] }'T5\'Nĥ&zyv.b,q%m'hCh)d%_oZщV-aQLH" BCiW>995 90TW+&g!%f#q0R G Z+i~~_~t ~k a~a~W~M :~B(~8;~.ْ~$o~~anghz# =edPsco~=@z# =(y~re<93 \,PROGRAM 93 SIMPSON'S RULE "Upper Limit? ";U "Lower Limit? ";L ,A(101e):RANGE=U-L:h=RANGE/100d (n=1:x=LUh 2y=x <A(n)=y Fn=n+1:x PEVEN=0:ODD=0 Zn=2100d2 dEVEN=EVEN+A(n) nODD=ODD+A(n+1) xn IAREA=(h/3)*(A(1)+A(101e)+(4*EVEN)+(2*ODD)) AREA ~94 pq *PROGRAM 94 PERMUTATIONS ^" PERMUTATION IS THE NUMBER OF WAYS OF CHOOSING R OBJECTS FROM A TOTAL OF N." "TOTAL NUMBER OF OBJECTS? ";T !" NUMBER OF CHOSEN OBJECTS? ";R (N=T:100d 2FT=f:N=T-R:100d 5,16;n;8,8;D1;8,24;D2 P 200 Zn d 100d ? %0JPN8-sh98 j 4PROGRAM 98 BINOMIAL DISTRIBUTION "NUMBER OF TRIALS? ";N "NUMBER OF SUCCESSES? ";X ""PROBABILITY OF ONE SUCCESS? ";P (M=N:100d 2FT=f:M=N-X:100d <RT=f:M=X:100d Fs14,1;"PROBABILITY OF ";X;" SUCCESSES"," IN ";N;" TRIALS IS ";(FT/(RT*f))*(P^X)*((1-P)^(N-X)): d1f=M:Y=M2-1:f=f*(Y-1):Y: nxp~*mfdxy99 s>$ 7PROGRAM 99 MEAN & STANDARD DEVIATION )"NUMBER OF VALUES? ";N:A(N):S=0 +X=1N:"NEXT VALUE? ";A(X):A(X):X CX=1N:S=S+A(X):X:0,10 ;"SUM OF VALUES IS ";S ("1,10 ;"MEAN IS ";S/N 2kSD=0:X=1N:D=((S/N)-A(X))*((S/N)-A(X)):SD=SD+D:X:2,10 ;"ST.DEV. IS ";(SD/N) n+  sL 2>d"100 + PROGRAM 100 GRAPH W0:1:7::0,175:0,-175:255,0 "HOW MANY DATA POINTS?";N s=(255/N):x(N) (;i=1N:0,0;"Value no ";i;"? ":x(i):i 2i0,0;" ":imax=x(1):i=1N:x(i)>imaximax=x(i) <i:sc=imax/170 F$y(N):i=1N:y(i)=x(i)/sc:i Poi=1N:(i*s)-(s-3),y(i)+3,1:(i*s)-(s-3),y(i)+3:i,84T,20,36$,34",0 G0,12 ,18,18,44,,32 ,64@,0 E0,0,0,62>,72H,72H,480,0 E0,0,62>,72H,8,16,16,0 F0,0,100d,36$,36$,24,0,0 D8,8,28,42*,28,8,8,0 F0,34",84T,8,20,37%,66B,0 E8,8,106j,42*,28,8,8,0 E0,0,32 ,66B,82R,44,,0,0  rpAPPENDIX 2Di.PROGRAM APPENDIX 2 UPPER CASE GREEK #n=07:r:"a"+n,r:n "":0::10 H0,24,36$,36$,60<,36$,110n,0 (J120x,36$,36$,568,36$,36$,124|,0 2J126~,34",32 ,32 ,32 ,32 ,112p,0 ,34",34",119wl0 dH62>,65A,85U,93],85U,65A,62>,0 nH568,16,16,16,16,16,568,0 xJ110n,36$,40(,480,40(,36$,118v,0 G8,8,20,20,34",34",119w,0 I99c,546,62>,42*,42*,34",119w,0 J103g,34",502,42*,38&,34",115s,0 I66B,126~,0,126~,0,126~,66B,0 H568,68D,68D,68D,68D,68D,568,0 J119w,34",34",34",34",34",119w,0 J120x,36$,36$,568,32 ,32 ,112p,0 I126~,34",16,8,16,34",126~,0 E127,73I,8,8,8,8,28,0 E99c,34",20,8,8,8,28,0 F28,8,v2>,42*,62>,8,28,0 I119w,34",20,8,20,34",119w,0 H28,73I,107k,42*,62>,8,28,0 I28,34",65A,65A,546,85U,119w,0  rXAPPENDIX 3D $PROGRAM APPENDIX 3 HEXDEC s23658j\,8::5:"ENTER 1 for DEC to HEX 2 for HEX to DEC: ";a:a=270F 8A$="0000":X=4:"ENTER DECIMAL NO.(65535) ";DEC NN=(DEC/16):Q=DEC-16*N:A$(X)=(Q+480+7*(Q>9 )) (+DEC=N:X=X-1:DEC>030 2'10 ,5;"HEX NUMBER IS ";A$ "9"):X d610 ,5;"DECIMAL NUMBER IS ";DEC:60< aA04D2xenqAPPENDIX 4 D! 'PROGRAM APPENDIX 4 PI SERIES A1,0;:s=0:n=010000':k=1 $n/2ɺ(n/2)k=-1 q=k/((2*n)+1) (#s=s+q:0,0;s*4 2n sJʕ$' kqz`p8