ZXTape! 2p$CURSOS EDUCATIVOS. MATEMATICAS (3/4)MONSERGAME (EDUCATIONAL)+D.L. M-41231-1985. TZXed by johnny farragutMATEMATICA? ?A ;1:1::"":20,31;:"MODULO C" 7 @R    @! @`d&$ $$$   @! d&$ $$d$@   @!   @! d&$ $$d$@   @!    @ %# $$d$@   @!    @ %# ##   @!    @ ##%# ##   @! @`##$$$##   @! @`##$$$0 0 000 0 000 00 ??0?<0?0?????00 00 0?00 00 000BBB0 0 000 0 000 00 ??0?BBFB@DBBBB0 0 000 0 000 00 ??0?BB<<<0 0 000 0 000 00 ??0?<999999999999999999999999999999999::::::::::::::::::::::::::::::99:::::999999999999999999999::::99:::::999999999999999999999::::99::::::::::::::::::::::::::::::9999999999999999999999999999999999::::::::::::::::::::::::::::::99:::::<<<<<<<<<<<<<<<<<<<::::::99:::::<<<<<<<<<<<<<<<<<<<::::::99:::::<<<<<<<<<<<<<<<<<<<::::::99:::::<<<<<<<<<<<<<<<<<<<::::::99:::::::::::<<<<<<<::::::::::::99:::::::::::<<<<<<<::::::::::::99:::::::::::<<<<<<<::::::::::::99:::::::::::<<<<<<<::::::::::::99::::::::::::::::::::::::::::::99::::::::::::::::::::::::::::::99::::::::::::::::::::::::::::::99::::::::::::::::::::::::::::::99::::::::::::::::::::::::::::::99::::::::::::::::::::::::::::::9999999999999999999999999999999998888888888888888888888888888888888888888888888888888888888888888MODULO C $$qH &7:0::100d ]1:1:64999:6,5;"MODULO C CASI LISTO":"":1 Z.:6;2,2;"MODULO APRENDIZAJE MATEMATICAS";3,13 ;"13-18";7;'''"13. Graficas de Rectas"'"14. Graficas de Curvas"'"15. Utilizacion de graficas para resolver ecuaciones"'"16. Regiones descritas por desi gualdades"'"17. Media, Moda y Mediana"'"18. Frecuencias": dq90Z:18,0;" Cuando vea el mensaje inferior,pulse @ para salir del modulo. ":8990 # ab$=" ":4:d$(7,16):k$(7,16):qu=0:8 ٲ90Z:.1}L,35#:16,0;" Entra el numero del modulo con el que deseas trabajar:- (0 para finalizar) ":q$=" ":n=0 ""986 /0:i$=:=480q$=" "8999'# @i$480Ưi$579ůi$=12 ůi$=13 990 ;.1}L,-5:2:.4L,-20:984 i$=12 984 Si$=13 n=0.1}L,-5:2:.4L,-20:984 *i$=13 qu=q$-13 :998 `n=n+1:q$=q$+i$:q$>18.1}L,-5:2:.4L,-20:984 P.1}L,35#:17,27;8;1;7;q$:986 Iq$<13 .1}L,-5:2:.4L,-20:984 qu=qu+1 r=0::.1}L,35#:6;0,10 ;"MATEMATICAS";2;7;0,0;"Modulo ";qu+12 :6000p+qu:a,qi1,qi2,qi3,qi4,qi5,qi6,qi7,qi8,qi9,qi10,qi11,qi12,qi13,qi14,qi15,qi16,qi17,qi18,qi19:20:.1}L,35#:17,0;3;7;1;" Deseas repasar antes de respon-der las preguntas? Pulsa S/N. ":6100+20*qu:20 E.1}L,35#:65001,11 :65000:65040 ^n=1a:n=qi1n=qi2n=qi3n=qi4n=qi5n=qi6n=qi7n=qi8n=qi96100+n+20*qu .1}L,35#:65001,12 :65000:65040:12 ,0;"PREGUNTAS";12 ,16;"AYUDAS" 7000X+30*qu+n:vval,g$,u$,x,y,nlsq:l=1nlsq:d$(l):12 +l,0;d$(l):l::l=1(g$+u$+*2):y,x+l-1;"*";:l:1100L an=qi10n=qi11n=qi12n=qi13n=qi14n=qi15n=qi16n=qi17n=qi18n=qi196500d+n+20*qu Jn:2000:8990#:65001,22:65000:984  1000 L5ph=0:hh=0:bb=0:hint=0:i Q:hint120,0;"PRUEBA DE NUEVO " Sf0,5;"escribe la respuesta: ";h$:v$="":u$""1,0;"entra unidades: ";v$ V<a$=h$:h$>g$Ʊh$>(16-x)a$=h$(116-x) X20,0;" ";y,x;5;b$(1̱g$+u$+1);1;7;y,x;a$;v$:h$+v$=g$+u$1138r Zvval=01160 \&vct=0:h$=01180 ^1l=1̱h$:h$(l)=46.vct=vct+1 `]h$(l)<480Ưh$(l)46.Ưh$(l)43+Ưh$(l)45-ůh$(l)>5791180 b=h$(l)43+Ưh$(l)45-Ưh$(l)46.1130j dl=h$1180 e=h$(l+1)>47/Ưh$(l+1)<58:1130j gl=h$-11180 h=h$(l+2)=43+ůh$(l+2)=45-1180 jl:vct>11180 kh$=g$v$=u$1138r lh$ɰg$1180 m 1165 r20,1;2;6;1;1;"CORRECTO";:" ":l=14:.1}L,34":.1}L,30:l:20:8990#:1150~ t 1160 ~hh=0r=r+1  1195 h$g$1180 8v$u$20,1;0;7;1;"UNIDADES!":.1}L,-5:2:.4L,-20:hint=hint+1:8990#::l=1nlsq:5;0;12 +l,0;d$(l):l:l=1(g$+u$+(*2)):y,x+l-1;"*":l:hint=2hh=hh+1:1200  hint=1:hh8ph=0 il=120:.01z# =,35#:.01z# =,25:l:m=1j:k$(m):hh=im=jbb=1 &bb;12 +ph+m,16;k$(m):m  ph=ph+j *20,7;5;" ": 65001,22:65000:5,0;" En este modulo conseguiste:- respuestas correctas sin ayuda. ";9 ,0;" Si necesitas mas ayuda, trabajacon las siguientes secciones de AYUDA AL ESTUDIO MONSER. " "a=0r=1:a=12 ұ9 ;6,10 ;r;" sobre ";a:r/a.8L3,11 ;"MUY BIEN":j=15:.1}L,16:.1}L,24:.1}L,20:j 2000+10 *qu: $13 ,0;" Paginas 60,62" (r<7''"Luego vuelve al modulo."  5,0;" No hay puntuacion en este modulo. ";13 ,0;" Paginas 64,68. ": 813 ,0;" Ejercicio 7b,(1 y 2),pagina 68.": .13 ,0;" Ejercicio 8a,pag. 72.": )13 ,0;" Paginas 95 a 98.":  #13 ,0;" Pagina 98.": q9 ,4,7,.5,.5,.5,.5,.5,.5,.5,1,2,3,4,5,6,7,8,9 ,.5 r0,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5 s5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5 t5,2,3,4,5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5 u15,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5 v9 ,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5 Q1,5;6;"GRAFICAS DE RECTAS":.1}L,35#:8521I!: 65001,22:65000:8720":1,35#:3,0;"2.Dibuja la grafica"'"de y=2+x.";5,8;"2";7,3;"x0 2 4";8,3;"y";9 ,0;" Traza tus puntos"'"en el papel de grafica"'"antes de comprobar.":23,103g:58:,0:0,18:-58:,0:0,-18:32 ,103g:0,18:480,103g:0,18:64@,103g:0,18:24,112p:568,0: 65001,22:65000:8720":1,35#:3,0;"3.Dibuja la grafica"'"de y=3-x.";5,8;"2";7,3;"x0 2 4";8,3;"y";9 ,0;" Traza tus puntos"'"en el papel de grafica"'"antes de comprobar.":23,103g:58:,0:0,18:-58:,0:0,-18:32 ,103g:0,18:480,103g:0,18:64@,103g:0,18:24,112p:568,0: Q1,4;6;"GRAFICAS DE CURVAS":.1}L,35#:8541]!: p1,1;6;"UTILIZACION DE GRAFICAS PARA RE SOLVER ECUACIONES":.1}L,35#:8561q!: %w1,6;6;"REGIONES DESCRITAS POR";2,10 ;"DESIGUALDADES":.1}L,35#:8581!: &65001,21:65000:1,35#:5,0;"2. Como podemos"'"describir la"'"region NO"'"sombreada?"''"ENTRA < o >"'"un n. entero.":140,124|:112p,0:-4,3:3,-3:-3,-3:4,3:188,84T:0,72H:-3,-4:3,3:3,-3:-3,4:140,108l:112p,0:i=1482524:i,107k:-12 ,-24:i:144,107k:-8,-16:252,99c:-8,-16:3,22;"y";7,29;"x";1;4,22;"1";6,22;"0";8,21;"-1": '!65001,21:65000:1,35#:5,0;"3. Como podemos"'"describir la"'"region NO"'"sombreada?"''"ENTRA < o >"'"y un n. entero.":140,100d:112p,0:-4,3:3,-4:-3,-3:4,3:140,99c:112p,0:189,84T:0,72H:188,84T:0,72H:-3,-4:4,3:3,-3:-3,4:164,76L:80P,80P:i=1642444:i,i-88X:244-i,0:i:2,22;"y";10 ,30;"x";1;10 ,23;"0";10 ,25;"1";10 ,27;"2";10 ,29;"3";7,22;"2";5,22;"4";3,22;"6": (65001,21:65000:1,35#:2,22;" ";2,29;" ";5,0;"4. Como podemos"'"describir la"'"region NO sombreada?"''"ENTER < o >"'"y un n. entero.":140,100d:112p,0:-4,3:3,-3:-3,-3:4,3:188,84T:0,72H:-3,-4:3,3:3,-3:-3,4:172,148:80P,-80P:i=1722364:i,320@-i:244-i,0:i:3,22;"y";10 ,29;"x";1;10 ,23;"0";10 ,25;"1";10 ,27;"2";7,22;"1";5,22;"2": )65001,21:65000:1,35#:2,22;" ";5,0;"5. Como podemos"'"describir la"'"region NO"'"sombreada?"''"ENTRA < o >"'"y un n. entero." *124|,92\:128,0:124|,91[:128,0:124|,91[:128,0:188,80P:0,76L:187,80P:0,76L:124|,156:32 ,-480,/10 :16,-12 ,/8:16,-4,/6:16,4,/6:16,12 ,/6:32 ,480,/10 +124|,140:128,0:i=-88.5:188+8*i,80P:0,i*i+10 :188+8*i,140:0,10 :i ,i=-22:1;11 ,23+4*i;i:i:i=14:1;10 -2*i,22;i:i:11 ,29;"x";3,22;"y": 9T1,5;6;"MEDIA, MODA y MEDIANA":.1}L,35#:8601!: MK1,10 ;6;"FRECUENCIAS":.1}L,35#:8621!: yS1;8,4;g$;0;6,23;"X":8990#: zS1;8,6;g$;0;4,25;"X":8990#: {1;8,8;g$:2,27;"X":20:.1}L,35#:220,156:-480,-480:1,0:480,480:8990#: |S1;8,4;g$;0;6,21;"X":8990#: }S1;8,6;g$;0;4,25;"X":8990#: ~1;8,8;g$:2,29;"X":20:.1}L,35#:172,124|:64@,32 :1,0:-64@,-32 :8990#: S1;8,4;g$;0;4,21;"X":8990#: S1;8,6;g$;0;6,25;"X":8990#: 1;8,8;g$:8,29;"X":20:.1}L,35#:172,140:80P,-40(:1,0:-80P,40(:8990#: we1,"2","",11 ,14,2,"a.","Cuando x=1,y=",1,3,"y=x+1"," =1+1"," =2" xe1,"3","",11 ,14,2,"b.","Cuando x=2,y=",1,3,"y=x+1"," =2+1"," =3" ye1,"4","",11 ,14,2,"c.","Cuando x=3,y=",1,3,"y=x+1"," =3+1"," =4" zm1,"2","",11 ,14,2,"a.","Cuando x=0,y=",1,4,"y=2+"," 2"," =2+0"," =2" {m1,"3","",11 ,14,2,"b.","Cuando x=2,y=",1,4,"y=2+"," 2"," =2+1"," =3" |m1,"4","",11 ,14,2,"c.","Cuando x=4,y=",1,4,"y=2+"," 2"," =2+2"," =4" }m1,"3","",11 ,14,2,"a.","Cuando x=0,y=",1,4,"y=3-"," 2"," =3-0"," =3" ~m1,"2","",11 ,14,2,"b.","Cuando x=2,y=",1,4,"y=3-"," 2"," =3-1"," =2" m1,"1","",11 ,14,2,"c.","Cuando x=4,y=",1,4,"y=3-"," 2"," =3-2"," =1" 0,"x+3","",5,17,5,"a. Teniendo la","grafica de y=x para","resolver x=x+3,","traza la grafica","de y=",1,1,"Traza y=x+3" 0,"4-2x","",5,17,5,"b. Teniendo la","grafica de y=x para","resolver x=4-2x,","traza la grafica","de y=",1,1,"Traza y=4-2x"  0,"0.5x+0.5","",5,17,5,"c. Teniendo la","grafica de y=x para","resolver 2x=x+1,","traza la grafica","de y=",2,3,"Si 2x=x+1","entonces x=x+"," 2 2",4,"Traza y=x+"," 2 2","(Entra como"," y=0.5x+0.5)" 0,"3","",5,19,7,"d. Teniendo la","grafica de"," y=(x+1)(x-2) para","resolver"," (x+1)(x-2)=3","traza la grafica","de y=",1,1,"Traza y=3" 0,"1.5","",5,19,7,"e. Teniendo la","grafica de"," y=(x+1)(x-2) para","resolver","2(x+1)(x-2)=3","traza la grafica","de y=",2,3,"Si 2(x+1)(x-2)=3","entonces:-"," (x+1)(x-2)=1.5",2,"Traza"," y=1.5 (o 3/2)" K0,"<3","",3,14,2,""," x",1,1," x<3" M0,">-1","",3,14,2,""," y",1,1," y>-1" P0,">2","",3,14,2,""," y x",1,1," y>2x" O0,"<2","",5,14,2,""," x+y",1,1," x+y<2" V0,"<3","",3,15,3,""," y>x y"," y",1,1," y<3" 1,"2.8","",6,14,2,"a. 1 4 2 3 4"," Media=",2,2,"Comprueba la definicion","de media. p98.",3,"1+4+2+3+4=14","Media=145"," =2.8" 0,"4","",6,15,3,"a. 1 4 2 3 4 "," Media=2.8"," Modo=",2,2,"Comprueba la definicion","de modo. p98.",1,"Modo=4" 0,"3","",8,16,4,"a. 1 4 2 3 4"," Media=2.8"," Modo=4"," Mediana=",2,2,"Comprueba la definicion","de mediana. p98.",2," 1 2 3 4 4","Mediana=3" {1,"2.6","",6,14,2,"b. 0 4 2 3 4"," Media=",1,3,"0+4+2+3+4=13","Media=135"," =2.6" h0,"4","",6,15,3,"b. 0 4 2 3 4 "," Media=2.6"," Modo=",1,1,"Modo=4" 0,"3","",8,16,4,"b. 0 4 2 3 4"," Media=2.6"," Modo=4"," Mediana=",1,2," 0 2 3 4 4","Mediana=3" q1,"2","",6,14,2,"c. 0 4 2 2"," Media=",1,3,"0+4+2+2=8","Media=84"," =2" d0,"2","",6,15,3,"c. 0 4 2 2 "," Media=2"," Modo=",1,1,"Modo=2" 1,"2","",8,16,4,"c. 0 4 2 2"," Media=2"," Modo=2"," Mediana=",1,2," 0 2 2 4","Mediana=(2+2)2=2" w1,"1.25","",6,14,2,"d. 0 1 2 2"," Media=",1,3,"0+1+2+2=5","Media=54"," =1.25" g0,"2","",6,15,3,"d. 0 1 2 2 "," Media=1.25"," Modo=",1,1,"ModO=2" 1,"1.5","",8,16,4,"d. 0 1 2 2"," Media=1.25"," Modo=2"," Mediana=",1,3," 0 1 2 2","Mediana=(1+2)2"," =1.5" {1,"2","",6,14,2,"e. 0 1 4 2 2 3"," Media=",1,3,"0+1+4+2+2+3=12","Media=126"," =2" g0,"2","",6,15,3,"e. 0 1 4 2 2 3"," Media=2"," Modo=",1,1,"Modo=2" 1,"2","",8,16,4,"e. 0 1 4 2 2 3"," Media=2"," Modo=2"," Mediana=",1,2," 0 1 2 2 3 4","Mediana=2"  t0,"10","",1,16,4,"a. 0 1 1 2 2"," 3 3 4 4 4","Frecuencia Total","=",1,1,"10" 0,"24","",1,18,6,"a. 0 1 1 2 2"," 3 3 4 4 4","Frecuencia Total","=10","Puntuacion total","=",1,1,"24" 1,"2.4","",5,18,6,"a. 0 1 1 2 2"," 3 3 4 4 4","Frecuencia Total","=10","Puntuacion total=24","Media=",1,2,"Media=24/10"," =2.4" x0,"12","",1,16,4,"b. 0 1 2 0 2 2"," 7 5 7 4 4 2","Frecuencia Total","=",1,1,"12" 0,"36","",1,18,6,"b. 0 1 2 0 2 2"," 7 5 7 4 4 2","Frecuencia Total","=12","Puntuacion total","=",1,1,"36" 1,"3","",5,18,6,"b. 0 1 2 0 2 2"," 7 5 7 4 4 2","Frecuencia Total","=12","Puntuacion total=36","Media=",1,2,"Media=36/12"," =3" y0,"8","",1,16,4,"c.0 2.5 2.5 -2"," 3.6 4.4 -1 0","Frecuencia Total","=",1,1,"8" 0,"10","",1,18,6,"c.0 2.5 2.5 -2"," 3.6 4.4 -1 0","Frecuencia Total","=8","Total score","=",1,1,"10" 1,"1.25","",5,18,6,"c.0 2.5 2.5 -2"," 3.6 4.4 -1 0","Frecuencia Total","=8","Puntuacion total=10","Media=",1,2,"Media=10/8"," =1.25" !I""8521I! !J+5:0:="N"Ŧ="n"8540\! !K"S"Ʀ"s"8521I! !L7.1}L,35#:65001,22:65000 !M2,0;" Ecuaciones como"'"y=3x+2 y"'"3x+2y=1, que"'"contienen solo"'"terminos en x,e"'"y constantes,son"'"representadas"'"por GRAFICAS DE"'"LINEA RECTA.Nece"'"sitamos solo, e"'"legir 3 valores"'"de x para dar 3"'"puntos por los"'"que dibujar es"'"tas graficas.Pa"'"ra evitar erro"'"res, use n posi"'"tivos pequenos"'"(o cero) para"'"los valores de x.":8700!:8990# !NE2,0;"ej.1 Dibuje la "'"grafica de "'" y=3x+2 "'" "'"x=1 y=3X1+2=5 "'" Trace (1,5) ":i=719:" ":i:20,0;" ":8990#:8,14;1;"1";0;13 ,21;"X":8990# !Ol9 ,0;"x=2 y=3X2+2=8"'" Trace (2,8)":8990#:10 ,26;"X":8990# !Pn12 ,0;"x=3 y=3X3+2=11"'" Trace (3,11)":8990#:7,31;"X":8990# !QP252,116t:-120x,-72H:0,1:120x,72H !R08990#:65001,22:65000 !S&2,0;"ej.2 Dibuje la "'"grafica de"'" y=3-x"'""'"x=1 y=3-1=2"'" Trace (1,2)":8700!:8,14;" ";3,14;" ";1;13 ,15;"1";8,15;"2";3,15;"3":8990#:8,21;"X":8990# !Tj9 ,0;"x=2 y=3-2=1"'" Trace (2,1)":8990#:13 ,26;"X":8990# !Um12 ,0;"x=3 y=3X3-3=0"'" Trace (3,0)":8990#:18,31;"X":8990# !VR252,28:-120x,120x:0,-1:120x,-120x !W8990#:8995## !Y""8537Y! !Z+5:0:="S"Ŧ="s"8524L! !["N"Ʀ"n"8537Y! !\.1}L,35#:65001,22:65000:8720":1,35#:3,0;"1.Dibuje la grafica"'"de y=x+1.";7,3;"x1 2 3";8,3;"y";9 ,0;" Trace sus puntos"'"en papel de grafica"'"antes de repasar.":23,103g:58:,0:0,18:-58:,0:0,-18:32 ,103g:0,18:480,103g:0,18:64@,103g:0,18:24,112p:568,0: !]""8541]! !^+5:0:="N"Ŧ="n"8554j! !_"S"Ʀ"s"8541]! !`$65001,22:65000 !aw8740$":8990#:3,0;"Ej. Dibuje la"'"grafica de y=2-"'" x"'"para la serie"'"de valores de x"'"dados."''" Complete la"'"tabla y trace"'"los puntos en la grafica.":8990#:14,4;"x0.5 1 1.5 2 2.5 2";15,4;"2";16,3;"-";17,4;"x";18,0;"y=2-";19,4;"x" !b30,568:232,0:0,32 :232,0:40(,64@:0,-480:8990#:15,6;"2 2 2 2 2 2":8990#:16,5;1;"-2 -1 -0.67-0.5-0.4-0.33":8990#:18,6;"0 1 1.33 1.5 1.6 1.67":8990# !c"171,93]:2,-2:187,125}:2,-2:203,136:2,-2:219,141:2,-2:235,144:2,-2:251,146:2,-2:20,0;"Dibuje una curva suave.":8990# !d 172,92\:16,32 ,-/10 :16,11 ,-/8:16,5,-/8:16,3:16,2:6,26;"y=2-";7,30;"x":8990#:65001,10 :65000:8995## !g""8551g! !h+5:0:="S"Ŧ="s"8544`! !i"N"Ʀ"n"8551g! !j65001,22:65000:1,35#:2,0;"1.Dibuje la gra"'"fica de y=__"'" 2+x"'"para los valo-"'"res dados abajo"'" Copie y com"'"plete la tabla"'"y trace la"'"grafica antes"'"de comprobar"'"cada paso.":8750.":502 !kL16,3;"x -1.5 -1 -0.5 0 0.5 1 2";17,3;"3 3";18,2;"2+x 0.5";19,0;"y=__ 6";20,2;"2+x":0,24:254,0:0,40(:254,0:47/,47/:0,-40(:8990#:17,12 ;"3 3 3 3 3 3":8990# !lt1;18,12 ;"1 1.5 2 2.5 3 4":8990#:19,12 ;"3 2 1.5 1.2 1 0.75":8990# !m140,156:16,-480,/10 :16,-16,/8:16,-8,/8:16,-5,/8:16,-3,/8:32 ,-4:8990#:65001,22:65000:1,35#:2,0;"2.Ahora dibuje la"'"grafica de"'" y=(x+2)(3-x)"'"para la serie de"'"valores de x da"'"dos.Complete cada"'"paso antes,pulsar"'"tecla para com"'"probar su trabajo.":87608":8990# !n16,4;"x-3 -2 -1 0 1 2 3 4";17,2;"x+2";18,2;"3-x";19,0;"y=";20,0;"(2+x)(3-x)":16,24:208,0:16,40(:208,0:40(,16:0,32 :8990#:1;17,5;"-1 0 1 2 3 4 5 6":8990#:1;18,6;"6 5 4 3 2 1 0 -1":8990#:1;19,5;"-6 0 4 6 6 4 0 -6":8990# !o140,524:16,480:16,32 ,-/10 :16,16,-/6:8,2:8,-2:16,-16,-/6:16,-32 ,-/10 :16,-480:8990# !p !q""8561q! !r+5:0:="N"Ŧ="n"8575! !s"S"Ʀ"s"8561q! !t7.1}L,35#:65001,22:65000 !u13 ,0;"Si tenemos la grafica y=x y la grafica y=2-x, las coordenadas-xde los puntos en que se cruzan son las soluciones de x=2-x.":8770B" !vE124|,156:32 ,-480,/10 :16,-12 ,/8:16,-4,/6:16,4,/6:16,12 ,/8:32 ,480,/10 :124|,156:128,-64@:3,27;"y=x";2,17;"y";3,18;"=2-x" !w8990#:8,27;"X";2,15;"X";5,0;"ej. Las"'"soluciones son:-"'" x=-2 o x=1";11 ,15;"-2";11 ,27;"1":8990# !x$65001,22:65000 !y 13 ,0;"Si tenemos la grafica y=x y queremos resolver 2x=1-x escribi-mos la ecuacion x=-x 2 2 y dibujamos la linea recta y=-x. 2 2" !zT8770B":124|,156:32 ,-480,/10 :16,-12 ,/8:16,-4,/6:16,4,/6:16,12 ,/8:32 ,480,/10 :124|,116t:96`,-24:3,27;"y=x";8,12 ;"y=-x";9 ,14;"2 2" !{c8990#:8,19;"X";10 ,25;"^";11 ,19;"-1";4,0;"Las soluciones "'"son x=-1, x=0.5":8990#:8,19;"X";10 ,25;"^";11 ,19;"-1";5,6;"-1";5,12 ;"0.5":65001,12 :65000:8995## !|""8572|! !}+5:0:="S"Ŧ="s"8564t! !~"N"Ʀ"n"8572|! !M9 ,0;"Entra decimales"'"si es necesario"'"no fracciones.": !""8581! !+5:0:="N"Ŧ="n"8599! !"S"Ʀ"s"8581! !65001,21:65000:.1}L,35#:3,0;"ej.1"''" La region NO som"'"breada muestra to"'"dos los puntos"'"cuyas coordenadas"'"x son menores que"'"2, ej. x<2.":136,100d:116t,0:-4,3:3,-3:-3,-3:4,3:140,97a:0,513:-3,-4:3,3:3,-3:-3,4:204,84T:0,64@ !1:i=03:10 ,17+4*i;i:i:0:10 ,30;"x";3,16;"y";6,20;"x<2":i=84T1284:205,i:40(,20:i:205,132:32 ,16:205,136:24,12 :205,140:16,8:205,144:8,4:213,84T:16,8:221,84T:8,4:8990# !12 ,0;"ej.2"''" La region NO"'"sombreada muestra todos"'"los puntos cuyas"'"coordenadas y son"'"mayores que 1,"'" ie. y>1.":140,28:112p,0:-4,3:3,-3:-3,-3:4,3:188,24:0,513:-3,-4:3,3:3,-3:-3,4:140,44,:112p,0 !d1:i=02:18-2*i,22;i:i:0:19,29;"x";13 ,22;"y";14,25;"y>1":i=1482444:i,43+:-12 ,-24:i:144,43+:-6,-12 :248,43+:-9 ,-18:252,43+:-10 ,-20:8990# !65001,21:65000:3,0;"ej.3"''" La region NO som"'"breada muestra"'"todos los puntos"'"cuyas coordenadas"'"y son menores"'"dos veces sus"'"coordenadas x,"'" ej. y<2x.":120x,36$:132,0:-4,3:3,-3:-3,-3:4,3:140,17:0,131:-3,-4:3,3:3,-3:-3,4:124|,4:70F,140 !e1:i=03:18,17+4*i;i;17-4*i,16;i:i:0:19,30;"x";3,16;"y";12 ,24;"y<2x":i=41444:120x+i/2,i:-(24+i/4),0:i:1:i=03:17-4*i,16;i:i:0:8990# !65001,21:65000:3,0;"ej.4"''" La region NO"'"sombreada muestra todos los"'"puntos cuyas"'"coordenadas y son"'"menores que el"'"cuadrado de sus"'"coordenadas x,"'" ie. y"'"y un n. entero.":136,100d:116t,0:-4,3:3,-3:-3,-3:4,3:140,97a:0,513:-3,-4:3,3:3,-3:-3,4:212,84T:0,64@ !ni=04:1;10 ,3*i+17;i:i:10 ,30;"x";3,16;"y":i=84T1324:213,i:32 ,16:i:213,136:24,12 :213,140:16,8:213,144:8,4:221,84T:6,3:10 ,26;"3": !""8601! !+5:0:="N"Ŧ="n"8613! !"S"Ʀ"s"8601! !965001,22:65000:2,0;" Media, moda y mediana son todosPROMEDIOS que nos dicen algo so-bre un grupo de numeros.":8990#:2,0;" Suponga que cinco estudiantes trabajan los fines de semana y su salario cada fin de semana fuera:- "'" 5 8 6 8 7" !8990#:6,0;" El promedio que queremos puede ser:-"'"la media; (5+8+6+8+7)5= 345=6.80":8990#:9 ,0;"o el modo,lo mas comun,ej.8";5,9 ;"8";5,19;"8":8990# ! 5,9 ;"8";5,19;"8";10 ,0;"o la mediana,el intermedio cuan-do se ordenan de menos a mas.":60<:.1}L,35#:12 ,4;" 5 6 7 8 8":60<:12 ,14;"7";13 ,14;"ej. 7":8990# !$14,0;" Si tenemos una serie uniforme de cantidades la mediana esta entre las dos del centro.":60<:.1}L,35#:17,7;" 3 5 2 4":60<:.1}L,35#:18,7;" 2 3 4 5":60<:19,13 ;"3.50" !8990#:8995## !""8610! !+5:0:="S"Ŧ="s"8604! !"N"Ʀ"n"8610! !.1}L,35#:65001,22:65000:5,0;" Encontrar la MEDIA,MODA y MEDIANA de los siguientes grupos de numeros:-"''"(Entra cualquier fraccion como decimales.)":60<: !""8621! !+5:0:="N"Ŧ="n"8634! !"S"Ʀ"s"8621! !.1}L,35#:65001,22:65000:2,0;" Mire estos numeros:-";3,11 ;"5 4 1 5 1";4,11 ;"2 1 6 6 7";5,11 ;"1 7 2 5 1";6,11 ;"1 3 4 1 5":8990#:8,0;" Los numeros primero se clasiicaran por orden.":8990#:8626!:i=36:j=11 192:num:1;i,j;num:.1}L,35#:20:i,j;num:j:i:8627! !1,1,1,1,1,1,1,2,2,3,4,4,5,5,5,5,6,6,7,7 !m8,0;" Ahora puede ver que hay, ";16,0;" Estas son las FRECUENCIAS de los numeros.";9 ,11 ;"siete 1's";10 ,11 ;"dos 2's";11 ,11 ;"uno 3";12 ,11 ;"dos 4's";13 ,11 ;"cuatro 5's";14,11 ;"dos 6's";15,11 ;"dos 7's":8990# !q65001,16:65000:40(,88X:185,0:225,32 :-186,0:0,73I:186,0:0,-81Q:-140,0:0,81Q:164,104h:0,-80P:1:9 ,5;"SCORE FREQUENCY TOTALS";10 ,7;"x";10 ,15;"f";10 ,25;"fx" !7,0;" Para calcular la media de lo:-";11 ,7;"1 7 1X7= 7";12 ,7;"2 2 2X2= 4";13 ,7;"3 1 3X1= 3";14,7;"4 2 4X2= 8";15,7;"5 4 5X4=20";16,7;"6 2 6X2=12";17,7;"7 2 7X2=14";18,14;"20";18,25;"68";19,0;"Media de los 20 valores =6820=3.4":0:8990# ! 8995## !""8631! !+5:0:="S"Ŧ="s"8624! !"N"Ʀ"n"8631! !.1}L,35#:65001,22:65000:5,0;" Complete las tablas de frecuencia para calcular las medias de los siguientes grupos de valores:-";8,0;" (Entre cualquier fraccion como decimales.)":60<: !128,26:124|,0:130,24:0,135:i=281564:132,i:120x,0:i:i=1322534:i,28:0,131:i !i=2714740(:128,i:124|,0:i:i=13125140(:i,24:0,135:i !1;19,21;"1";19,26;"2";19,31;"3";19,15;"0";13 ,15;"5";8,14;"10";3,14;"15";0;19,29;"x";5,15;"y" " "i=1722528:i,89Y:0,67C:i:i=92\1568:169,i:83S,0:i:169,91[:83S,0:171,89Y:0,67C "1:i=05:11 ,21+2*i;i:i:i=04:10 -2*i,20;i:i:0:11 ,30;"x";2,19;"y": "$i=1562528:i,89Y:0,67C:i:i=92\1568:153,i:99c,0:i:153,91[:99c,0:155,89Y:0,67C "%1:i=03:11 ,19+4*i;i:i:i=02:10 -4*i,18;i:i:0:11 ,29;"x";2,17;"y": ".i=124|2528:i,579:0,99c:i:i=60<1568:124|,i:128,0:i:124|,59;:128,0:187,579:0,99c "/1:i=-22:15,23+4*i;i:i:i=262:14-2*i,22;i:i:0:15,29;"x";3,22;"y": "8i=1402528:i,524:0,104h:i:i=5241568:140,i:112p,0:i:140,99c:112p,0:187,524:0,104h "9$1:i=14:10 ,23+2*i;i:i:i=-3-1:10 ,22+2*i;i:i:i=262:9 -i,22;i:i:i=-6-22:9 -i,21;i:i:0:10 ,30;"x";3,21;"y": "Bi=124|2528:i,89Y:0,67C:i:i=92\1568:124|,i:128,0:i:124|,91[:128,0:187,89Y:0,66B "C1:i=-22:11 ,23+4*i;i:i:i=242:10 -2*i,22;i:i:0:11 ,29;"x";2,21;"y": #""8990# #p30:21,0;" Pulsa ENTER para continuar. ":2:0:="@"900 # T.1}L,35#:9 ;21,0;" ": #! 1005 ##17,0;" Deseas repasar antes de respon der las preguntas? Pulsa S/N. ": #':.1}L,35#:7,0;" Para usar el modulo de nuevo, pulsa R Pulsa S para STOP ":9100# #("MODULO C"2 #)$"mat code 3"65000,600X # #""9100# #*5:0:="R"Ŧ="r"900 #"="S"Ŧ="s".5,20: # 9100# Cmat code 3X$ZD!X6(#!Y6(#!Y6(#!Z6(#!Y60#!Y60#!Y60#!Y60#!Z60#!0Z60#!PZ60#!pZ60#!Z60#!Z60#!Z60#!Z60# P P P 88 MMbXaXL8Wq !v>D((DDDD<8>>000 q #$RR| P pd<*]\"_\C*]\~}t[3*a\Þ*x\#"xMODULO D 55v77:0::100d g1:1:64999:6,5;"MODULO D CASI LISTO":"mat code 4":1 Z:6;2,2;"MODULO APRENDIZAJE MATEMATICA";3,13 ;"19-21";7;''''"19. Hallar la Media de un grupo de datos"''"20. Histogramas"''"21. Curvas de frecuencia acumulativa": dq90Z:18,0;" Cuando veas el mensaje inferior pulsa @ para dejar el modulo. ":8990 # ab$=" ":4:d$(7,16):k$(7,16):qu=0:8 ٲ90Z:.1}L,35#:16,0;" ENTRA el numero del modulo con el que deseas trabajar:- (0 para finalizar) ":q$=" ":n=0 ""986 /0:i$=:=480q$=" "8999'# @i$480Ưi$579ůi$=12 ůi$=13 990 ;.1}L,-5:2:.4L,-20:984 i$=12 984 Si$=13 n=0.1}L,-5:2:.4L,-20:984 *i$=13 qu=q$-19:998 `n=n+1:q$=q$+i$:q$>21.1}L,-5:2:.4L,-20:984 P.1}L,35#:17,27;8;1;7;q$:986 Iq$<19.1}L,-5:2:.4L,-20:984 qu=qu+1 r=0::.1}L,35#:6;0,10 ;"MATEMATICAS";2;7;0,0;"Modulo ";qu+18:6000p+qu:a,qi1,qi2,qi3,qi4,qi5,qi6,qi7,qi8,qi9,qi10,qi11,qi12,qi13,qi14,qi15,qi16,qi17,qi18,qi19:20:.1}L,35#:17,0;3;7;1;" Deseas repasar antes de respon-der las preguntas ? Pulsa S/N. ":6100+20*qu:20 E.1}L,35#:65001,11 :65000:65040 ^n=1a:n=qi1n=qi2n=qi3n=qi4n=qi5n=qi6n=qi7n=qi8n=qi96100+n+20*qu .1}L,35#:65001,12 :65000:65040:12 ,0;"PREGUNTAS";12 ,16;"AYUDAS" c=0:7000X+30*qu+n:vval,g$,u$,x,y,nlsq:l=1nlsq:d$(l):12 +l,0;d$(l):l::l=1(g$+u$+*2):y,x+l-1;"*";:l:1100L an=qi10n=qi11n=qi12n=qi13n=qi14n=qi15n=qi16n=qi17n=qi18n=qi196500d+n+30*qu Jn:2000:8990#:65001,22:65000:984  1000 L5ph=0:hh=0:bb=0:hint=0:i `0hint120,1;"REPITA" bq0,9 ;"entra la respuesta: ";h$:v$="":u$""1,0;"entra unidades de respuesta: ";v$ c<a$=h$:h$>g$Ʊh$>(16-x)a$=h$(116-x) e20,1;" ";y,x;5;b$(1̱g$+u$+1);1;7;y,x;a$;v$:h$+v$=g$+u$1138r fvval=01160 g&vct=0:h$=01180 h1l=1̱h$:h$(l)=46.vct=vct+1 i=h$(l)<480Ưh$(l)46.ůh$(l)>5791180 jl:vct>11180 kh$=g$v$=u$1138r lh$ɰg$1180 m 1165 r20,1;2;6;1;1;"CORRECTO";:" ":l=14:.1}L,34":.1}L,30:l:20:8990#:1150~ t 1160 ~hh=0r=r+1  1195 h$g$1180 5v$u$20,1;0;7;1;"UNITS!":.1}L,-5:2:.4L,-20:hint=hint+1:8990#::l=1nlsq:5;0;12 +l,0;d$(l):l:l=1(g$+u$+(*2)):y,x+l-1;"*":l:hint=2hh=hh+1:1200  hint=1:hh8ph=0 il=120:.01z# =,35#:.01z# =,25:l:m=1j:k$(m):hh=im=jbb=1 &bb;12 +ph+m,16;k$(m):m  ph=ph+j *20,7;5;" ": 65001,22:65000:5,0;" En este modulo consiguio:- respuestas correctas sin ayuda. ";9 ,0;" Si necesita mas ayuda ,trabaje con las siguientes secciones de AYUDA AL ESTUDIO PAN. " "a=0r=1:a=12 Ҳ9 ;6,10 ;r;" out of ";a:r/a.8L3,11 ;"MUY BIEN":j=15:.1}L,16:.1}L,24:.1}L,20:j 2000+10 *qu: V2,13 ;"DATA";13 ,0;" Ejercicio 12b,Q.1(a),Q.2(a)p104.": >1,0;" ";13 ,0;"Pagina 106,108.": 313 ,0;" Ejercicio 12b, pagina 104.": q26,14,.8L,.9ffff,.1}L,1.1 ,1.2,.5,.5,.5,1,5,11 ,12 ,14,19,24,25,.9ffff,.10}L r22,11 ,.9ffff,.1}L,1.1 ,1.2,1.3&fff,.5,.5,.5,10 ,22,.3,.4L,.5,.6,.73333,.8L,.9ffff,.10}L s17,12 ,.5,.5,.5,.5,.5,.5,.5,.5,5,11 ,17,.5,.5,.5,.5,.5,.5,.5 _1,0;6;"HALLAR MEDIA DE GRUPOS DE DATOS ":.1}L,35#:8521I!: 65001,21:65000:1,35#:2,0;"2."''" Unas vacaciones un grupo de amigos anoto cuanto tiempo tardaronsus postales en llegar, y los resultados fueon:-"'"7 tardaron 1 o 2 dias"'"8 tardaron 3 o 4 dias"'"9 tardaron 5 o 6 dias"'"20 tardaron 7 o 8 dias"'"6 tardaron 9, pero ninguna mas de 12 dias."'"Anote esta informacion cuidadosamente, para completar la tabla de frecuencias que sigue.":8990#:8720": K1,10 ;6;"HISTOGRAMAS":.1}L,35#:8541]!: 965001,22:65000:1,35#:1,0;"2."'" Esta vez viajaron:-"'"20 menos de 200km"'"10 entre 200 y 250km"'" 8 entre 250 y 300km"'" 5 entre 300 y 350km"'" 7 entre 350 y 400km"'"16 entre 400 y 500km"'"14 entre 500 y 600km"'"20 entre 600 y 1000km."'"(1 unidad = 50km)": _1,2;6;"CURVAS DE FRECUENCIA ACUMULATIVA":.1}L,35#:8561q!: 8593!:65001,22:65000:1,35#:2,0;"2. La distancia recorrida duran-te las vacaciones pasadas por 1000 estudiantes son las siguientes:-"'" 20 menos de 100km,"'" 40 entre 100 y 200km,"'" 40 entre 200 y 300km,"'"200 entre 300 y 400km,"'"320 entre 400 y 500km,"'"120 entre 500 y 600km,"'"180 entre 600 y 800km,"'" 80 entre 800 y 1000km."''" Complete la tabla de frecuencia acumulativa, luego pulse una tecla para comprobar.":8990# ?65000:3,0;" 20 recorrieron menos de 100km 60 200km 100 300km 300 400km 620 500km 740 600km 920 800km 1000 1000km." ''" Dibuja tu curva de frecuencia acumulativa. Esta vez no aparece-ra hasta despues de responder las preguntas.":8990#  y65000:3,0;" Elige tus respuestas entre los siguientes numeros:-"''"115, 170, 180, 380, 460, 610": D.1}L,35#:1;11 ,4;"40":60<: .1}L,35#:1;7,15;"7.5";8,15;"9.5";9 ,14;"11.5";10 ,14;"14.5":60<: .1}L,35#:1;5,26;"17.5";6,26;"44";7,26;"45";8,26;"57";9 ,26;"92";10 ,26;"72.5":60<: F.1}L,35#:1;11 ,25;"328":60<: D.1}L,35#:1;10 ,4;"50":60<: .1}L,35#:1;5,15;"1.5";6,15;"3.5";7,15;"5.5";8,15;"7.5";9 ,14;"10.5":60<: .1}L,35#:1;5,26;"10.5";6,26;"28";7,26;"49.5";8,25;"150";9 ,26;"63":60<: F.1}L,35#:1;10 ,25;"301":60<: 8730":8990#: 8740$":8990#: ]65001,22:65000:5,0;" Pulsa una tecla cuando hayas dibujado tu curva de frecuencia a-cumulativa.":8990#:65000:8750.":87608":8990#:65000:3,0;" Elige uno de estos numeros comorespuesta mas proxima a las si -guientes preguntas."''"21, 57, 180, 190, 360, 550": %65001,22:65000:8750.":87608":8990#:6,0;"La mediana"'" =360km.":i=1481844:i,103g:i+1,103g:.1}L,35#:i:i=101e502-4:184,i:184,i-1:.1}L,35#:i 8990#:9 ,0;"El primer "'"cuartil=190km.":i=1481674:i,77M:i+1,77M:.1}L,35#:i:i=76L513-4:167,i:167,i-1:.1}L,35#:i 8990#:12 ,0;"El tercer"'"cuartil=550km.":i=1482034:i,127:i+1,127:.1}L,35#:i:i=125}502-4:203,i:203,i-1:.1}L,35#:i:8990#: %65001,22:65000:8750.":8770B":8990#:6,0;"La mediana"'" =460km.":i=1481924:i,103g:i+1,103g:.1}L,35#:i:i=104h502-4:194,i:194,i-1:.1}L,35#:i 8990#:9 ,0;"El primer"'"cuartil=380km.":i=1481844:i,76L:i+1,76L:.1}L,35#:i:i=76L513-4:185,i:185,i-1:.1}L,35#:i 8990#:12 ,0;"El tercer"'"cuartil=610km.":i=1482104:i,127:i+1,127:.1}L,35#:i:i=125}502-4:210,i:210,i-1:.1}L,35#:i:8990#: w1,"40","",12 ,14,2,"a. Frecuencia","total,f=",1,3,"Numero total de","postales"," =40" xw1,"7.5","",3,15,3,"b. 3er valor de","intervalo medio,"," x=",1,2,"(7+8)2","=7.5" yx1,"9.5","",3,15,3,"c. 4to valor de","intervalo medio,"," x=",1,2,"(9+10)2","=9.5" z{1,"11.5","",3,15,3,"d. 5to valor de","intervalo medio,"," x=",1,2,"(11+12)2","=11.5" {{1,"14.5","",3,15,3,"e. 6to valor de","intervalo medio,"," x=",1,2,"(13+16)2","=14.5" |h1,"17.5","",4,15,3,"f.","1er producto,"," fx=",1,2,"7X2.5","=17.5" }d1,"44","",4,15,3,"g.","2do producto,"," fx=",1,2,"8X5.5","=44" ~d1,"45","",4,15,3,"h.","3er producto,"," fx=",1,2,"6X7.5","=45" d1,"57","",4,15,3,"i.","4to producto,"," fx=",1,2,"6X9.5","=57" e1,"92","",4,15,3,"j.","5to producto,"," fx=",1,2,"8X11.5","=92" i1,"72.5","",4,15,3,"k.","6to producto,"," fx=",1,2,"5X14.5","=72.5" \1,"328","",11 ,14,2,"l. Producto","total,fx=",1,1,"328" 1,"8.2","",7,17,5,"m. Numero","medio de dias","que tardaron las","postales en","llegar=",1,2,"32840","=8.2" w0,"50","",13 ,14,2,"a. Frecuencia","total,f,=",1,2,"Numero total de","postales=50" w0,"1.5","",3,15,3,"b. 1er valor de","intervalo medio,"," x=",1,2,"(1+2)2","=1.5" w0,"3.5","",3,15,3,"c. 2do valor de","intervalo medio,"," x=",1,2,"(3+4)2","=3.5" w0,"5.5","",3,15,3,"d. 3er valor de","intervalo medio,"," x=",1,2,"(5+6)2","=5.5" w0,"7.5","",3,15,3,"e. 4to valor de","intervalo medio,"," x=",1,2,"(7+8)2","=7.5" z0,"10.5","",3,15,3,"f. 5to valor de","intervalo medio,"," x=",1,2,"(9+12)2","=10.5" h1,"10.5","",4,15,3,"g.","1er producto,"," fx=",1,2,"7X1.5","=10.5" d1,"28","",4,15,3,"h.","2do producto,"," fx=",1,2,"8X3.5","=28" h1,"49.5","",4,15,3,"i.","3er producto,"," fx=",1,2,"9X5.5","=49.5" g1,"150","",4,15,3,"j.","4to producto,"," fx=",1,2,"20X7.5","=150" e1,"63","",4,15,3,"k.","5to producto,"," fx=",1,2,"6X10.5","=63" \1,"301","",11 ,14,2,"l. Producto","total,fx=",1,1,"301" 1,"6.02","",7,17,5,"m. Numero ","medio de dias","que tardaron las","postales en","llegar=",1,2,"30150","=6.02" h1,"4","",8,15,3,"a. Area=4"," Base=1"," Altura=",1,1,"4 unidades" h1,"6","",8,15,3,"b. Area=6"," Base=1"," Altura=",1,1,"6 unidades" t1,"2","",8,14,3,"c. Area=16"," Base="," Altura=",1,2,"100 a 200","2 unidades" i1,"8","",8,15,3,"c. Area=16"," Base=2"," Altura=",1,1,"8 unidades" t1,"2","",8,14,3,"d. Area=12"," Base="," Altura=",1,2,"200 a 300","2 unidades" i1,"6","",8,15,3,"d. Area=12"," Base=2"," Altura=",1,1,"6 unidades" t1,"4","",8,14,3,"e. Area=32"," Base="," ALtura=",1,2,"300 a 500","4 unidades" i1,"8","",8,15,3,"e. Area=32"," Base=4"," Altura=",1,1,"8 unidades" w1,"10","",8,14,3,"f. Area=30"," Base="," Altura=",1,2,"500 a 1000","10 unidades" j1,"3","",8,15,3,"f. Area=30"," Base=10"," Altura=",1,1,"3 unidades" r1,"4","",8,14,3,"a. Area=20"," Base="," Altura=",1,2,"0 a 200","4 unidades" i1,"5","",8,15,3,"a. Area=20"," Base=4"," Altura=",1,1,"5 unidades" k1,"10","",8,15,3,"b. Area=10"," Base=1"," Altura=",1,1,"10 unidades" h1,"8","",8,15,3,"c. Area=8"," Base=1"," Altura=",1,1,"8 unidades" h1,"5","",8,15,3,"d. Area=5"," Base=1"," Altura=",1,1,"5 unidades" h1,"7","",8,15,3,"e. Area=7"," Base=1"," Altura=",1,1,"7 unidades" t1,"2","",8,14,3,"f. Area=16"," Base="," Altura=",1,2,"400 a 500","2 unidades" i1,"8","",8,15,3,"f. Area=16"," Base=2"," Altura=",1,1,"8 unidades" t1,"2","",8,14,3,"g. Area=14"," Base="," Altura=",1,2,"500 a 600","2 unidades" i1,"7","",8,15,3,"g. Area=14"," Base=2"," Altura=",1,1,"7 unidades" u1,"8","",8,14,3,"h. Area=20"," Base="," ALtura=",1,2,"600 a 1000","8 unidades" m1,"2.5","",8,15,3,"h. Area=20"," Base=8"," Altura=",1,1,"2.5 unidades" f1,"10","",2,13 ,2,"a. viajaron","menos de 100km.",1,1,"4+6=10" h1,"26","",2,13 ,2,"b. viajaron","menos de 200km.",1,1,"4+6+16=26" k1,"38","",2,13 ,2,"c. viajaron","menos de 300km.",1,1,"4+6+16+12=38" n1,"70","",2,13 ,2,"d. viajaron","menos de 500km.",1,1,"4+6+16+12+32=70" ~1,"100","",2,13 ,2,"e. viajaron","menos de 1000km.",1,2,"4+6+16+12+32+30"," =100" 1,"360","",1,14,2,"f. Mediana","= km",2,2,"Comprueba la definicion","de mediana.p98.",1,"Mediana=360km" 1,"190","",9 ,14,2,"g. El primer","cuartil= km",2,4,"Hay un cuarto de","datos por debajo","del primer","cuartil.",1,"190km" 1,"550","",9 ,14,2,"h. El tercer","cuartil= km",2,4,"Hay un cuarto de","datos por debajo","del tercer","cuartil.",1,"550km" 1,"180","",1,15,3,"i.El semi-inter-","cuartil","= km",2,1,"Semi-iqr=Q2-Q1.",3,"=(550-190)2","=3602","=180km." 1,"57","",11 ,16,4,"j. TNumero de","estudiantes que","viajaron menos","de 400km=",1,1," 57" 1,"21","",11 ,16,4,"k. Numero de","estudiantes que","viajaron mas","de 600km=",1,2,"100-79","=21 estudiantes" Z1,"460","",1,14,2,"a. Mediana","= km",1,1,"460km" c1,"380","",9 ,14,2,"b. El primer","cuartil= km",1,1,"380km" c1,"610","",9 ,14,2,"c. El tercer","cuartil= km",1,1,"610km" 1,"115","",1,15,3,"d.El semi-inter-","cuartil","= km",1,4,"El semi-iqr","=(610-380)2","=2302","=115km." 1,"180","",11 ,16,4,"e. Numero de","estudiantes que","viajaron menos","de 350km=",1,1," 180 estudiantes" Ö1,"170","",11 ,16,4,"f. Numero de","estudiantes que","viajaron mas","de 700km=",1,2,"1000-830","=170 estudiantes" !I""8521I! !J+5:0:="N"Ŧ="n"8537Y! !K"S"Ʀ"s"8521I! !L$65001,21:65000 !M.1}L,35#:7,0;" Como hallarias el peso medio deuna clase de alumnos ?"'" Si hubiese 25, y sus masas fue-ran de 74kg,60.4kg,67.5kg, etc, podrias sumar sus pesos para en-contrar el total y dividir por 25.":8990# !NB65001,21:65000:3,0;" Pero puede que no conozcamos el peso exacto de cada uno.":8990#:5,0;"Quizas,"'"2 estan entre 50 y 55kg"'"4 estan entre 55 y 60kg"'"7 estan entre 60 y 65kg"'"5 estan entre 65 y 70kg"'"6 estan entre 70 y 75kg"'"1 esta entre 75 y 80kg":8990# !O12 ,0;" Tenemos que calcular que, los 2primeros son 'alrededor de' 52.5kg, los 4 siguientes 'alrededor de' 57.5kg, los 7 siguientes 'alrededor de' 62.5kg, y asi sucesivamente.":8990# !P_17,0;" Estos valores,52.5,57.5,62.5,..se llaman de INTERVALO MEDIO.":8990# !Q1;6,26;"52.5kg";7,26;"57.5kg";8,26;"62.5kg";9 ,26;"67.5kg";10 ,26;"72.5kg";11 ,26;"77.5kg":8990# !R(65001,21:65000:3,0;"El peso medio de una clase de 25":4,137:248,0:0,-73I:-248,0:0,73I:4,120x:248,0:4,72H:248,0:84T,136:0,-72H:188,136:0,-72H:1:6,5;"f";6,16;"x";6,26;"fx";7,5;"2 52.5 105";8,5;"4 57.5 230";9 ,5;"7 62.5 437.5";10 ,5;"5 67.5 337.5";11 ,5;"6 72.5 435";12 ,5;"1 77.5 77.5";13 ,4;"25";13 ,24;"1622.5":0:15,0;" Peso medio=1622.525=64.9kg.":8990# !S 8995## !T""8532T! !U+5:0:="S"Ŧ="s"8524L! !V"N"Ʀ"n"8532T! !Y65001,21:65000:1,35#:2,0;"1."''" Unos amigos apuntaron cuanto tardaron en llegar sus postales de vacaciones."'"7 tardaron entre 1 y 4 dias"'"8 tardaron 5 o 6 dias"'"6 tardaron 7 o 8 dias"'"6 tardaron 9 o 10 dias"'"8 tardaron 11 o 12 dias"'"5 tardaron 13,14,15 o 16 dias."''"Anote esta informacion, especialmente el numero de dias, para completar la tabla de frecuen- cias que sigue.":8990# !Z 65001,21:65000:4,151:248,0:0,-71G:-248,0:0,71G:4,136:248,0:4,88X:248,0:84T,80P:0,71G:188,80P:0,71G:4,5;"f";4,16;"x";4,27;"fx";5,5;"7";6,5;"8";7,5;"6";8,5;"6";9 ,5;"8";10 ,5;"5";5,15;"2.5";6,15;"5.5": !]""8541]! !^+5:0:="N"Ŧ="n"8559o! !_"S"Ʀ"s"8541]! !`7.1}L,35#:65001,22:65000 !a-2,0;" Que distancia viajo sus ultimasvacaciones de verano?":8990#:4,0;" Una encuesta entre 50 estudian-tes muestra cuanto viajaron:-"'" 6 menos de 100km,"'"12 entre 100 y 200km,"'"14 entre 200 y 300km,"'"10 entre 300 y 400km,"'"y"'" 8 entre 400 y 500km.":8990# !b12 ,0;" Podemos representar estos datoscon un HISTOGRAMA, en el que el AREA de cada rectangulo es pro-porcional a la frecuencia.":8990#:65001,22:65000:i=10 8-1:i,6;"":i:i=10 5-1:i,11 ;"":i:47/,108l:-1,0:47/,128:-1,0:47/,148:-1,0 !ci=10 4-1:i,16;"":i:i=10 6-1:i,21;"":i:i=10 7-1:i,26;"":i:480,152:0,-64@:200,0:491,152:0,-63?:199,0:11 ,5;"0 100 200 300 400 500";12 ,27;"km";6,2;"f";8,4;"5";5,3;"10";3,3;"15" !d:12 ,0;"Distancias recorridas:-"'" 6 menos de 100km,"'"12 entre 100 y 200km,"'"14 entre 200 y 300km,"'"10 entre 300 y 400km,"'"y"'" 8 entre 400 y 500km.";9 ,8;"6";6,13 ;"12";5,18;"14";7,23;"10";8,28;"8":8990# !e!12 ,0;" "'" Como las bases de los rectangu-los son iguales,la altura de ca-da rectangulo es tambien propor-cional a la frecuencia.Sin embargo, la propiedad fundamental delhistograma, es que el area debe ser proporcional a la frecuencia":8990# !f665001,22:65000:11 ,0;" Suponga que las distancias recorridas fueron:-"'" 2 menos de 50km,"'" 4 entre 50 y 100km,"'" 5 entre 100 y 150km,"'" 7 entre 150 y 200km,"'"14 entre 200 y 300km"'"10 entre 300 y 400km"'"y"'" 8 entre 400 y 500km.":8990# !gX11 ,0;" ":i=10 9 -1:i,6;"":i:i=87-1:i,8;"":i:6,11 ;"":i=54-1:i,13 ;"":i !i480,152:0,-65A:200,0:491,152:0,-63?:1;11 ,5;"0 50 150 300 400 500";12 ,10 ;"100 200 km";8,4;"2";6,4;"4";4,4;"6";2,4;"8";5,2;"f":47/,104h:-1,0:47/,120x:-1,0:47/,136:-1,0:47/,152:-1,0 !j10 ,7;"2";8,9 ;"4";7,12 ;;"5";5,14;"7";5,18;"14";7,23;"10";8,28;"8":8990# !k=13 ,0;" Los intervalos de clase son di-ferentes y por tanto los rectan-gulos son de bases diferentes."'" Tomando 1 unidad para represen-tar 50km, el area de cada rectangulo iguala el numero de estu- diantes que recorrieron esa dis-tancia.":8990#:65001,8:65000:8995## !l""8556l! !m+5:0:="S"Ŧ="s"8544`! !n"N"Ʀ"n"8556l! !o .1}L,35#:65001,22:65000:5,0;" Construye histogramas para re- presentar los siguientes datos."''" Se te pedira la base y altura de cada rectangulo."''" Luego dibujaras tu propio histograma antes de comprobarlo.":8990# !p265000:1,35#:1,0;"1."'" Las distancias recorridas en las pasadas vacaciones por 100 estudiantes fueron:-"'" 4 menos de 50km"'" 6 entre 50 y 100km"'"16 entre 100 Y 200km"'"12 entre 200 y 300km"'"32 entre 300 y 500km"'"30 entre 500 Y 1000km"'"(1 unidad = 50km)": !q""8561q! !r+5:0:="N"Ŧ="n"8594! !s"S"Ʀ"s"8561q! !t$65001,22:65000 !u.1}L,35#:2,0;" Una encuesta entre 50 estudian-tes muestra la distancia que viajaron:-"'" 6 menos de 100km,"'"12 entre 100 y 200km,"'"14 entre 200 y 300km,"'"10 entre 300 y 400km,"'"y 8 entre 400 y 500km.":8990# !v10 ,0;"Vemos que:-"'" 6 estudiantes"'" viajaron menos de 100km,"'"18 (6+12) menos de 200km,"'"32 (6+12+14) menos de 300km,"'"42 (6+12+14+10) menos de 400km,"'"50 (6+12+14+10+8) menos de 500km.":8990# !w18,0;" Estas frecuencias acumulativas se pueden representar en una CURVA DE FRECUENCIA ACUMULATIVA.":8990#: !x65001,22:65000:8750.":87542":.1}L,35#:6,0;" Deberias ser"'"capaz de dibujar"'"una grafica"'"mucho mas exacta"'"en papel milim.":8990#:6,0;" La distancia"'"media recorrida "'"se mide "'"sobre 25.5 en "'"el eje de fre-"'"cuencia acumulativa"'"y es alrededor de"'"255km.":80P:1:i=1481984:.1}L,35#:i,103g:i+1,103g:i !y60<:i=102f546-4:.1}L,35#:199,i:199,i-1:i:0:16,25;"2";17,25;"5";18,25;"5" !z8990#:i=514:i,0;b$:i:16,25;"3";17,25;"0";18,25;"0":1:i=1481984:i,103g:i+1,103g:i:i=102f546-4:199,i:199,i-1:i:0:.1}L,35#:6,0;"Podemos calcular"'"por la grafica"'"que 20 estudiantes"'"viajaron menos"'"de 215km.":80P !{^1:i=53592\4:.1}L,35#:191,i:191,i+1:i !|60<:i=192148-4:.1}L,35#:i,93]:i-1,93]:i:0:10 ,16;"20":8990# !}10 ,16;"20":i=610 :i,0;b$:i:1:i=53592\4:191,i:191,i+1:i:i=192148-4:i,93]:i-1,93]:i:0:.1}L,35#::6,0;"Podemos calcular"'"por la grafica"'"que 20 estudiantes"'"(50-30) estudiantes"'"viajaron mas"'"de 290km.":80P !~_1:i=524112p4:.1}L,35#:205,i:205,i+1:i !60<:i=205148-4:.1}L,35#:i,113q:i-1,113q:i:0:7,16;"30";3,16;"50":8990# !}i=611 :i,0;b$:i:7,16;"30";3,16;"50":1:i=524112p4:205,i:205,i+1:i:i=205148-4:i,113q:i-1,113q:i:0:.1}L,35#::6,0;"Podemos calcular"'"por la grafica"'"que 32 estudiantes"'"viajaron menos"'"de 300km.":80P !_1:i=535114r4:.1}L,35#:207,i:207,i+1:i !60<:i=207148-4:.1}L,35#:i,115s:i-1,115s:i:0:7,16;"32":8990# !ni=610 :i,0;b$:i:7,16;"30":1:i=535114r4:207,i:207,i+1:i:i=207148-4:i,115s:i-1,115s:i:0:6,0;"Podemos calcular"'"por la grafica"'"que 15 estudiantes"'"(50-35) estudiantes"'"viajaron mas"'"de 330km.":80P !_1:i=524123{4:.1}L,35#:214,i:214,i+1:i !60<:i=214148-4:.1}L,35#:i,123{:i-1,123{:i:0:6,16;"35";3,16;"50":8990# !i=611 :i,0;b$:i:3,16;"50";6,16;" ":1:i=524123{4:214,i:214,i+1:i:i=214148-4:i,123{:i-1,123{:i:0:.1}L,35#:6,0;" El primer"'"cuartil,Q1,es"'"tal que deja"'"1 cuarto de los"'"datos por debajo"'"aqui Q1 es"'"correspondido"'"por 12.75. Q1=160km.":80P:i=1481804:.1}L,35#:i,77M:i+1,77M:i !60<:i=76L546-4:.1}L,35#:180,i:180,i-1:i:16,22;"1";17,22;"6";18,22;"0" !8990#:14,0;" El tercer"'"cuartil,Q2,es"'"tal que deja"'"1 cuarto de los"'"datos por encima"'"de Q2 aqui le co"'"rresponde 38.25. Q2=365km." !b 80P:i=1482184:.1}L,35#:i,127:i+1,127:i !60<:i=129546-4:.1}L,35#:220,i:220,i-1:i:16,27;"3";17,27;"6";18,27;"5":8990# ! 6,0;" La diferencia"'"entre los dos"'"cuartiles se "'"llama intervalo"'"intercuartil"'" En este caso "'"el iqr=365-160"'" =205km."'" "'" El iqr y el"'"semi-iqr son usa-"'"das como medidas"'"de dispersion. ":8990# !/65001,7:65000:8995## !""8590! !+5:0:="S"Ŧ="s"8564t! !"N"Ʀ"n"8590! !.1}L,35#:65001,22:65000:5,0;" Dibuja tus curvas de frecuenciaacumulativa tan exactamente comote permitan los siguientes datosy usalos para responder las preguntas."''" Necesitaras anotar primero los datos en un papel.":8990#: !U8593!:65001,22:65000:1,35#:2,0;"1. Las distanciasque recorrieronlas vacaciones pasadas 100 estu-diantes son las siguientes:-"'" 4 menos de 50km,"'" 6 entre 50 y 100km,"'"16 entre 100 y 200km,"'"12 entre 200 y 300km,"'"32 entre 300 y 500km,"'"y 30 entre 500 y 1000km.":8990# !12 ,0;" Completa una tabla de frecuen- cia acumulativa y comprueba tus respuestas antes de dibujar la curva.":8990#: !128,26:124|,0:130,24:0,135:i=281564:132,i:120x,0:i:i=1322534:i,28:0,131:i !i=2714740(:128,i:124|,0:i:i=13125140(:i,24:0,135:i !1;19,21;"1";19,26;"2";19,31;"3";19,15;"0";13 ,15;"5";8,14;"10";3,14;"15";0;19,29;"x";5,15;"y" " "65001,21:65000:4,152:248,0:0,-64@:-248,0:0,64@:4,136:248,0:4,96`:248,0:84T,88X:0,64@:188,88X:0,64@:4,5;"f";4,16;"x";4,27;"fx";5,5;"7";6,5;"8";7,5;"9";8,4;"20";9 ,5;"6": ",65001,22:65000:i=10 8-1:i,6;"      ":i:7,6;"     ":i=65-1:i,7;"    ":i:i=43-1:i,8;" ";i,12 ;" ":i "480,152:0,-64@:200,0:491,152:0,-63?:199,0:47/,152:-1,0:47/,136:-1,0:47/,120x:-1,0:47/,104h:-1,0:11 ,5;"0 1 2 3 5 1";12 ,7;"0 0 0 0 0";13 ,7;"0 0 0 0 0 km";14,25;"0";8,4;"2";6,4;"4";4,4;"6";2,4;"8";5,2;"f" "8,6;"4";6,7;"6";4,8;"16";6,10 ;"12";4,13 ;"32";9 ,20;"30": "$65001,22:65000:i=12 11 -1:i,6;"        ":i:10 ,6;"       ":i=9 8-1:i,6;"       ":i:i=76-1:i,10 ;"      ":i:5,10 ;"    ":4,10 ;" ";3,10 ;" " "%8;9 ,7;"20";4,10 ;"1";5,10 ;"0";6,11 ;"8";9 ,12 ;"5";7,13 ;"7";6,14;"16";7,16;"14";11 ,21;"20" "&J480,152:0,-80P:160,0:491,152:0,-79O:159,0:47/,152:-1,0:47/,136:-1,0:47/,120x:-1,0:47/,104h:-1,0:47/,88X:-1,0:13 ,5;"0 2 4 6 1";14,9 ;"0 0 0 0";15,9 ;"0 0 0 0 km";16,25;"0";10 ,4;"2";8,4;"4";6,4;"6";4,4;"8";2,3;"10";5,2;"f" "': ".Ri=14824810 :i,524:0,100d:i:i=14824820:i,480:0,4:i:147,524:0,100d:i=52415210 :148,i:100d,0:i:i=52415220:144,i:4,0:i:148,513:100d,0 "/H3,4;"Frecuencia";4,4;"acumulativa": "216,17;"0 1 2 3 4 5";17,20;"0 0 0 0 0";18,20;"0 0 0 0 0";19,30;"km";12 ,16;"10";10 ,16;"20";7,16;"30";5,16;"40";3,16;"50" "4148,524:20,12 ,/6:20,24,/8:20,28:20,20,-/24:20,16 "5148,535:20,12 ,/6:20,24,/8:20,28:20,20,-/24:20,16: "816,17;"0 2 4 6 8 1";17,20;"0 0 0 0 0";18,20;"0 0 0 0 0";19,28;"km0";12 ,16;"20";10 ,16;"40";7,16;"60";5,16;"80";3,15;"100" "9148,524:5,4,/6:5,6,/6:10 ,16,/12 :10 ,12 :20,32 ,-/24:502,30,-/6 ":148,535:5,4,/6:5,6,/6:10 ,16,/12 :10 ,12 :20,32 ,-/24:502,30,-/6: "B16,17;"0 2 4 6 8 1";17,20;"0 0 0 0 0";18,20;"0 0 0 0 0";19,28;"km0";12 ,15;"200";10 ,15;"400";7,15;"600";5,15;"800";3,14;"1000" "C148,524:10 ,2:10 ,4:10 ,4:10 ,20,/12 :10 ,32 :10 ,12 ,-/6:20,18,-/12 :20,8,-/8 "D148,535:10 ,2:10 ,4:10 ,4:10 ,20,/12 :10 ,32 :10 ,12 ,-/6:20,18,-/12 :20,8,-/8: #""8990# #p30:21,0;" Pulsa ENTER para continuar. ":2:0:="@"900 # T.1}L,35#:9 ;21,0;" ": ##17,0;" Deseas repasar otra vez antes de responder las preguntas? Pulsa S/N. ": #':.1}L,35#:7,0;" Para usar el modulo de nuevo, pulsa R Pulsa S para PARAR ":9100# #("MODULO D"2 #)$"mat code 4"65000,600X # #""9100# #*2:0:="R"Ŧ="r"900 #"="S"Ŧ="s".5,20: # 9100# &mat code 4X5Z D!X6(#!Y6(#!Y6(#!Z6(#!Y60#!Y60#!Y60#!Y60#!Z60#!0Z60#!PZ60#!pZ60#!Z60#!Z60#!Z60#!Z60# P P P 88 MMbXaXL8Wq !v>D((DDDD<8>>000 q #$RR| P pd<*]\"_\C*]\~}t[3*a\Þ*x\#"x