ZXTape! 2 %Maths Tutor for the Spectrum - Side ACentury Communications Ltd Robert Carter1984English Educational7.95 ROM LoaderOriginal1TZXed by Andrew Barker Provided by Darren Farrell1 hhj 0  1  2 ( 3 2 4 < 5 F 6 P 7 1a U 0  502  1  502  2 # 502 ( 3 - 502 2 4 7 502 < 5 A 502 F 6 K 502 P 7 &2 kk m PROGRAM 2 0,0 255,0 0,175 (255,175 |2a `` b PROGRAM 2a L0,0:255,0:0,175:255,175 G3 ** , PROGRAM 3 0,0 502,0 0,502 (28,15 2-502,0 <0,-502 "3" 3 3 c] ] k4  )PROGRAM 4 GREEN CROSS 10:4:7::128,88X N=380P3 128+N,88X+N (128+N,88X-N 2128-N,88X+N <128-N,88X-N FN QP5 5 +PROGRAM 5 SCREEN BORDER 0,0 255,0  0,175  (-255,0 20,-175 6 <M /PROGRAM 6 CHARACTER SQUARES X=82558 X,0:0,175 X (Y=81758 20,Y:255,0 <Y  (6a bO d PROGRAM 6a F4N=010 :(*21),(*31);"X" PN FL7 F #PROGRAM 7 ONION 0 N=-̧0.5 *80P,40(:100d,100d,N (N V%^Iڢ8 n )PROGRAM 8 CONCENTRICS N=180P5 128,88X,N N 8P 9 --PROGRAM 9 PI APPROXIMATIONS n=41000 d=(n/4)n/3 p=n/d (0p>-0.0001sQXp<+0.0001sQXn;"/";d,n/d 2d <n F10 ,15  N&p@13j10 \V ^*PROGRAM 10 CIRCLES & PI "Radius in cm? (1 to 87)";R D128,88X:R,0:"Radius ";R;" cm":1,20 O128,88X:-R,0:"Diameter ";R*2;" cm":1,20 (L128,88X,R:"Circumference ";R*2*;" cm":1,20 2"Area ";*R*R;" sq.cm" r/10a  /PROGRAM 10a CIRCLE STATISTICS "Radius? ";R  "Diameter ";R*2;" units" '"Circumference ";R*2*;" units" ("Area ";R*R*;" square units" r11  %PROGRAM 11 MASSAGE "Enter diameter ";d C=*d "Circumference is ";C ("Enter circumference ";C 2d=C/ <"Diameter is ";d dcUE12 yfV {-PROGRAM 12 SIMPLE FOR LOOP N=110 "Loop number ";n n  13  +PROGRAM 13 RANK AND FILE x=82488 y=81688 x,y (y 2x  }14 p]r+PROGRAM 14 POWERS OF TWO p=010  2^p p  14a @ 4PROGRAM 14a GRAPH OF POWERS OF TWO p=08 "2^";p;" is ";2^p n=040( ((n+128,0:0,2^p 2n <p  (%15 %PROGRAM 15 SQUARES "Enter length of side ";s "Enter unit of length ";s$ s;" ";s$;" square" ( A=s^2 2"has area ";A;" square ";s$ <300,:10 sda@Scm16  #PROGRAM 16 CUBES "Enter length of side ";s "Enter unit of length ";s$ s;" ";s$;" cube" ( V=s^3 2"has volume ";V;" cubic ";s$ <300,:10 sda@Scmz17 ne 3PROGRAM 17 INVALID ARGUMENT DEMO N=5-5-1  N^2 N  sHr H18 A #PROGRAM 18 ROOTS n=110  s=n^2 r=s^(1/2) (n;10 ;s;20;r 2n  sHr 19  0PROGRAM 19 FRACTIONAL INDICES "Enter X ";X "Enter a ";a "Enter b ";b (Y=a/b 2R=X^Y <(X;" to the power (";a;"/";b;") is ",R xaby@rWD>20  .PROGRAM 20 NEGATIVE INDICES "Enter X ";X "Enter Y ";y  L=x^(-y) (R=1/(x^y) 2L,R xylXrX20a i2PROGRAM 20a AUTONEGATIVE INDICES x=*100d y=*10  L=x^(-y) (R=1/(x^y) 2L,R < 10 xKzyEl})IrN)21 mk6PROGRAM 21 POWERS OF TEN (COMPLETE) p=-10 10 10 ^p,p p xKzyEl})IrN\22 xr *PROGRAM 22 SQUARE ROOTS X=(*100d) Y=X^.5  Z=X (Y,Z 2 10 xGyтkz&Fq%23  (PROGRAM 23 ROOT GRAPH _0,0:255,0:0,175:-255,0:0,-175 N=0255 "N,0:0,(N)*10 (N 24 c9 ,PROGRAM 24 ASSORTED ROOTS _0,0:255,0:0,175:-255,0:0,-175 Y=26 -1,1;"Graph of ";Y;"th root " (-Y=21,9 ;" square root" 2+Y=31,9 ;" cube root" <x=0175  Fx,(x^(1/y))*13 P=3,6;" ":4,6;" " Z43,6;x:4,6;x^(1/Y) dX:Y <.25  &PROGRAM 25 SORT OUT n=021 x=-.5 x>0x,"POSITIVE" (x<0x,"NEGATIVE" 2x=0x,"ZERO" <n  x~26 .PROGRAM 26 LOGICAL SORT OUT n=021 x=(*20) x10 n,0;"*",x (n  xE27 g $PROGRAM 27 SIGNUM "Number","Signum" n=121 x=((-0.5)*10 ) (n,0;x,x 2n x>28 y` {*PROGRAM 28 EXPONENTIALS x=121 y=x x,y (x  y728a 0PROGRAM 28a EXP INVESTIGATIONS x=121 y=x  z=2^x (x;5;y;19;z 2x  y7z29 )2+-PROGRAM 29 POPULATIONS 1-D %0,88X:200,0 n=112 x (x/4,89Y 2n ,61=,59;,568 x829a  U -PROGRAM 29a POPULATIONS 2-D n=112 x n*20,x/5 (n 2t782,584H,252,214,128,108l,100d,74J,62>,61=,59;,568  x830 .PROGRAM 30 AXES WITH CURVES H0,0:255,0:0,0:0,175 .0,1;"Y":20,31;"X" n=013 ( n,n^2 2n  30a  /PROGRAM 30a EXPONENTIAL CURVE H0,0:255,0:0,0:0,175 .0,1;"Y":20,31;"X" n=050.02{# = (n*502,n 2n {# =30b   6PROGRAM 30b THE HUMBLE STRAIGHT LINE H0,0:255,0:0,0:0,175 .0,1;"Y":20,31;"X" x=0255 ( y=88X 2x,y <x yXf31 |W)~/PROGRAM 31 THE STRAIGHT LINE K128,0:0,175:0,88X:255,0 /0,15;"Y":10 ,31;"X" "Enter Slope ";m ("Enter Intercept ";c 2x=-128127 < y=m*x+c F0y<88Xy>-87Wx+128,y+88X Px Z 30 mc\2yiUDCL g $USER DEFINED CHARACTER LOADER N=07 row:"a"+n,row n (I66B,68D,72H,87W,33!,71G,132,7  o32 jSl2PROGRAM 32 HEX TO DEC CONVERTER "4-DIGIT HEX NUMBER? ";a$  d=0 a$410 (5,13 ;a$ 2&x$=a$(4):n=1:100d <'x$=a$(3):n=16:100d F(x$=a$(2):n=256:100d P)x$=a$(1):n=4096:100d Z 15,10 ;"IS: ";d: d*x$480Ưx$579d=d+((x$)*n) nx$="A"d=d+(10 *n) xx$="B"d=d+(11 *n) x$="C"d=d+(12 *n) x$="D"d=d+(13 *n) x$="E"d=d+(14*n) x$="F"d=d+(15*n)  AFFFFdnXF33 {b},PROGRAM 33 NAPIER'S BONES x=120 y=x x,y (x  y-P 33a +,PROGRAM 33a NAPERIAN GRAPH T4:128,0:0,175:0,88X:255,0 /128+32 ,0:0,175 10 ,31;"4":10 ,0;"-4":10 ,15;"0":10 ,19;"1":21,15;"-1.75":0,15;"1.75" ("x=0.2~L3.95|.01z# = 2y=x <,(x*32 )+128,y*502+88X F(0,0;x:1,0;y Px \(|z# =(y ßm34 M;r O(PROGRAM 34 ANGLE DRAW D:4:167,88X,87W:2;-87W,0 "ANGLE IN DEGREES?";A 0,0;A;" DEGREES" ()A<90Z1,0;"IS ACUTE" 21A=90Z1,0;"IS A RIGHT ANGLE" <6A>90ZA<1801,0;"IS OBTUSE" F5A=1801,0;"IS A STRAIGHT ANGLE" P+A>1801,0;"IS REFLEX" ZX=87W*(A*/180) dY=87W*(A*/180) nX,Y x621,0;"PRESS ANY KEY":0:10 ax-V$yr?35 2 ?PROGRAM 35 OPPOSITE, ADJACENT AND HYPOTENUSE <4:21,1;"A":"ADJACENT SIDE? (<255) ";c A0,0:c,0:0,0;"ADJACENT SIDE ";c "OPPOSITE SIDE? (<175) ";a (00,a:1,0;"OPPOSITE SIDE ";a 2100d:-c,-a < AA=(a/c) F83,0;"ANGLE IS ";AA*180/;" DEGREES" P@1;4,0;"PRESS ANY KEY":0::10 ca6'@36  8PROGRAM 36 DEGREES, RADIANS AND TANGENTS x=090Z 5x;4;x*/180;16;(x*/180) x Z !36a lS n4PROGRAM 36a GRAPH OF TAN & RADIAN 4:0:7: x=090Z.5 y=(x*/180) (n0,1;"x=";x:1,0;"X(r)=";x*/180:2,0;"TAN x=";(x*/180) 2D2*x,y*10 :(2*x)-1,(x*/180)*10 <x .Zy*36b  -PROGRAM 36b SUPER TAN & RAD I4:1,5;" ":2,6;" " x=090Z.5  1,6;" " !2,7;" " y=(x*/180) (n0,1;"x=";x:1,0;"X(r)=";x*/180:2,0;"TAN x=";(x*/180) 2D2*x,y*10 :(2*x)-1,(x*/180)*10 7 10 <x .Zy*37  'PROGRAM 37 SIN & COS x=0360h5 y1=(x*/180) y2=(x*/180) (x;4;y1;16;y2 2x mh 38 c (PROGRAM 38 SINE GRAPH .5:0,88X:255,0 $0,0:0,175 x=012755 (y=(x*/180) 2!x/5,(y*87W)+88X <x y39 3 (PROGRAM 39 PYTHAGORAS 4:"SIDE No.1 ";a 0,0:a,0 "SIDE 1 = ";a ("SIDE No.2 ";b 2 0,b <"SIDE 2 = ";b F100d:-a,-b Pc=((a^2)+(b^2)) Z"HYPOTENUSE = ";c ab(cHW40 Ae 5PROGRAM 40 TRIGONOMETRIC FUNCTIONS "ANGLE IN DEGREES? ";x "ANGLE IN DEGREES ";x r=x*/180 ("ANGLE IN RADIANS ";r 2sin=r <"Sine of Angle ";sin Fcos=r P"Cosine of Angle ";cos Ztan=r d"Tangent of Angle ";tan nsec=1/r x"Secant of Angle ";sec cosec=1/r "Cosecant of Angle ";cosec cot=1/r "Cotangent of Angle ";cot ::10 xHr~_fi~]Xoya~ceSoseܣoW\41 kZ -PROGRAM 41 SIX TRIG GRAPHS 5:0,88X:255,0:64@,0:0,175:128,0:0,175:192,0:0,175 x=0360h x<15100d (#x>75Kx<105i100d 2$x>165x<195100d <$x>255x<285100d Fx>345Y100d Pr=x*/180 Z.x*255/360h,88X+(r)*20 [.x*255/360h,88X+(r)*20 \.x*255/360h,88X+(r)*20 ]6x*255/360h,88X+(1/r)*20 ^6x*255/360h,88X+(1/r)*20 _6x*255/360h,88X+(1/r)*20 dx .hrMI41a  )PROGRAM 41a SELECT TRIG B23658j\,8:"Select SIN, COS, TAN, SEC, COSEC or COT" a$: 5:0,88X:255,0:64@,0:0,175:128,0:0,175:192,0:0,175 x=0360h x<15100d (#x>75Kx<105i100d 2$x>165x<195100d <$x>255x<285100d Fx>345Y100d Pr=x*/180 Z8a$="SIN"x*255/360h,88X+(r)*20 [8a$="COS"x*255/360h,88X+(r)*20 \8a$="TAN"x*255/360h,88X+(r)*20 ]Ba$="COSEC"x*255/360h,88X+(1/r)*20 ^@a$="SEC"x*255/360h,88X+(1/r)*20 _@a$="COT"x*255/360h,88X+(1/r)*20 dx A15hrhV>42 x 3PROGRAM 42 QUADRATIC REAL ROOTS u5:n=07:r:"a"+n,r:n:112p,16,112p,64@,112p,0,0,0 (2,7;"ROOTS OF QUADRATICS" 8"ENTER coefficient a: ";a:6,6;a;"*x + " (8"ENTER coefficient b: ";b:6,14;b;"*x + " 29"ENTER coefficient c: ";c:6,22;c;" = 0" -87W2;(x*12 )+128,88X+y Zx d0::10 X43a  *PROGRAM 43a A FAMILY OF PARABOLAS T4:0,88X:255,0:128,0:0,175 a=0:c=0 b=-662 2)0,1;"a=";a;" b=";b;" c=";c <" x=-10 +10 .05|L Fy=(a*x*x)+(b*x)+c PDy<87Wy>-87W2;(x*12 )+128,88X+y Zx db ac33 |L<y$ffT44 "PROGRAM 44 CIRCLE ONE ROOT T5:0,88X:255,0:128,0:0,175 x=-10 10 y=-(100d-(x*x)) (x+128,y+88X 2x y44a cB e#PROGRAM 44a CIRCLE BOTH ROOTS T5:0,88X:255,0:128,0:0,175 x=-10 10 .1}L y1=(100d-(x*x)) (y2=-(100d-(x*x)) 2-(x*8)+128,(y1*8)+88X <-(x*8)+128,(y2*8)+88X Fx  }L4̹45 ftPROGRAM 45 ELLIPSE T5:0,88X:255,0:128,0:0,175 a=10 :b=5 x=-10 10 .5 (#y1=((b*b)*(1-(x*x)/(a*a))) 2$y2=-((b*b)*(1-(x*x)/(a*a))) <-(x*8)+128,(y1*8)+88X F-(x*8)+128,(y2*8)+88X Px a b( k46  PROGRAM 46 PARABOLA T5:0,88X:255,0:128,0:0,175  p=3 x=-10 10 (y=x*x/(4*p) 2,(x*8)+128,(y*8)+88X <x p yUUU47  PROGRAM 47 HYPERBOLA T5:0,88X:255,0:128,0:0,175 a=5:b=5 x=-10 10 .1}L #!((x*x)/(a*a))<180P (y1=b*(((x*x)/(a*a))-1) 2 y2=-b*(((x*x)/(a*a))-1) <-(x*8)+128,(y1*8)+88X F-(x*8)+128,(y2*8)+88X Px abffd }L~">sډ48  PROGRAM 48 POLAR CIRCLE R=502 A=02* x=R*A (y=R*A 2x+128,y+88X <A r2Iڢx@y߈K;49  %PROGRAM 49 POLAR ELLIPSE aa=127:bb=87W  A=02*ͧ/20  x=aa*A ( y=bb*A 2x+128,y+88X <A WIڦIڢ~ {xzr\ys50 PROGRAM 50 CARDIOID aa=30  A=02*ͧ/502 R=2*aa*(1-A) (x=R*A 2y=R*A <x+128,y+88X FA KIڢ}rxy51 v $PROGRAM 51 ARCHIMEDEAN SPIRAL aa=15  A=02*ͧ/502 R=aa*A (x=R*A 2y=R*A <x+128,y+88X FA KIڢ}rIڡxIڡyhN52  $PROGRAM 52 LOGARITHMIC SPIRAL aa=20:k=.2~L  A=02*ͧ/502  R=aa*(k*A) (x=R*A 2y=R*A <x+128,y+88X FA k~LKIڢ}r x yjM53 V%X&PROGRAM 53 CURVE SKETCHER 55:a=1:b=0:c=1:d=1 K0,88X:255,0:128,0:0,175 !x=-1616.125} (y=x 2:y>-88Xy<87W(x*8)+128,y+88X <x abcd}y54  PROGRAM 54 COSINE RULE "Side a?";aa  "Side b?";b  "Side c?";c (;R=(((b^2)+(c^2)-(aa^2))/(2*b*c)) 2A=R*180/ <1"Angle opposite side a is ";A;" degrees" bcr ap55 ] #PROGRAM 55 COSINE RULE AGAIN "Side a?";a  "Side c?";c "ANGLE B (degrees)?";B (R=B*/180 20bb=((a^2)+(c^2)-(2*a*c*R)) <"Last side is ";bb acb<r Q56 **/ ,PROGRAM 56 SINE RULE "Angle A? ";A "Angle B? ";B "Side c? ";cc (C=180-(A+B) 2)aa=cc*(A*/180)/(C*/180) <)bb=aa*(B*/180)/(A*/180) F"Side a is ";aa P"Side b is ";bb Z"Angle C is ";C a-b-4cZqqs57  &PROGRAM 57 AREA OF TRIANGLE "Side a?";a  "Side b?";b  "Side c?";c (s=(a+b+c)/2 2area=(s*(s-a)*(s-b)*(s-c)) <""Area is ";area;" square units." abcs@re]Eq58  +PROGRAM 58 TRIG IDENTITY !x=02*ͧ/180 20,0;((x*x)+(x*x)),x*180/ x IÃIڢ{5 y59  &PROGRAM 59 IDENTITY VERIFIER !x=02*ͧ/180 &(2*x),(2*x*x)-1 x DIڢ{5 60 g6Xi1PROGRAM 60 QUADRATIC ALL ROOTS u5:n=07:r:"a"+n,r:n:112p,16,112p,64@,112p,0,0,0 (2,7;"ROOTS OF QUADRATICS" 8"ENTER coefficient a: ";a:6,6;a;"*x + " (8"ENTER coefficient b: ";b:6,14;b;"*x + " 29"ENTER coefficient c: ";c:6,22;c;" = 0"