ZXTape! 0Created with Ramsoft MakeTZXMODULESC > >P@ :1:1::"":20,31;:"MODULESC" C @ <Bf8B 8xB8x?B8 B<<8<<8D @ -!!! > !!!!  <!!!!  B~<B| x<<!!"! !!@Bb888xB8<8hh8 D8xD8x88D8h88B8hxD88B8x8D88x88!!"! !!|@RD DDB DD TTD<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 ;"MATHEMATICS";2;7;0,0;"Module ";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;" Do you wish to work through thenotes before you attempt the questions? Press Y/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;"QUESTIONS";12 ,16;"HINTS" 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 Q3hint120,1;"TRY AGAIN" Se0,9 ;"enter answer: ";h$:v$="":u$""1,0;"enter units of answer: ";v$ V<a$=h$:h$>g$Ʊh$>(16-x)a$=h$(116-x) X20,1;" ";y,x;5;b$(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$1180 m 1165 r20,1;2;6;1;1;"CORRECT";:" ":l=14:.1}L,34":.1}L,30:l:20:8990#:1150~ t 1160 ~hh=0r=r+1  1195 h$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;" In this module you got:- answers correct without a hint. ";9 ,0;" If you need more help, work through the following sections in the PAN STUDY AID. " "a=0r=1:a=12 ҳ9 ;6,10 ;r;" out of ";a:r/a.8L3,11 ;"WELL DONE":j=15:.1}L,16:.1}L,24:.1}L,20:j 2000+10 *qu: "13 ,0;" Pages 63,65" 'r<7''"Then the module again."  5,0;" There is no score for this module. ";13 ,0;" Pages 68,69. ": 813 ,0;" Exercise 7b,qu 1 and 2,page 71.": ,13 ,0;" Exercise 8a,page75.": )13 ,0;" Pages 98 to 101.":  "13 ,0;" Page 101.": 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 S1,5;6;"STRAIGHT LINE GRAPHS":.1}L,35#:8521I!: 65001,22:65000:8720":1,35#:3,0;"2.Draw the graph"'"of y=2+x.";5,8;"2";7,3;"x0 2 4";8,3;"y";9 ,0;" Plot your points"'"on graph paper"'"before checking.":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.Draw the graph"'"of y=3-x.";5,8;"2";7,3;"x0 2 4";8,3;"y";9 ,0;" Plot your points"'"on graph paper"'"before checking.":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: T1,4;6;"DRAWING CURVED GRAPHS":.1}L,35#:8541]!: ^1,1;6;"USING GRAPHS TO SOLVE EQUATIONS":.1}L,35#:8561q!: %t1,6;6;"REGIONS DESCRIBED BY";2,10 ;"INEQUALITIES":.1}L,35#:8581!: &65001,21:65000:1,35#:5,0;"2. How can we"'"describe the"'"region NOT"'"shaded?"''"ENTER < or >"'"and an integer.":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. How can we"'"describe the"'"region NOT"'"shaded?"''"ENTER < or >"'"and an integer.":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. How can we"'"describe the"'"region NOT shaded?"''"ENTER < or >"'"and an integer.":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. How can we"'"describe the"'"region NOT"'"shaded?"''"ENTER < or >"'"and an integer." *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;"MEAN, MODE and MEDIAN":.1}L,35#:8601!: MK1,10 ;6;"FREQUENCIES":.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#: wc1,"2","",11 ,14,2,"a.","When x=1,y=",1,3,"y=x+1"," =1+1"," =2" xc1,"3","",11 ,14,2,"b.","When x=2,y=",1,3,"y=x+1"," =2+1"," =3" yc1,"4","",11 ,14,2,"c.","When x=3,y=",1,3,"y=x+1"," =3+1"," =4" zk1,"2","",11 ,14,2,"a.","When x=0,y=",1,4,"y=2+"," 2"," =2+0"," =2" {k1,"3","",11 ,14,2,"b.","When x=2,y=",1,4,"y=2+"," 2"," =2+1"," =3" |k1,"4","",11 ,14,2,"c.","When x=4,y=",1,4,"y=2+"," 2"," =2+2"," =4" }k1,"3","",11 ,14,2,"a.","When x=0,y=",1,4,"y=3-"," 2"," =3-0"," =3" ~k1,"2","",11 ,14,2,"b.","When x=2,y=",1,4,"y=3-"," 2"," =3-1"," =2" k1,"1","",11 ,14,2,"c.","When x=4,y=",1,4,"y=3-"," 2"," =3-2"," =1" 0,"x+3","",5,17,5,"a. Having the","graph of y=x to","solve x=x+3,","draw the graph","of y=",1,1,"Draw y=x+3" 0,"4-2x","",5,17,5,"b. Having the","graph of y=x to","solve x=4-2x,","draw the graph","of y=",1,1,"Draw y=4-2x" 0,"0.5x+0.5","",5,17,5,"c. Having the","graph of y=x to","solve 2x=x+1,","draw the graph","of y=",2,3,"If 2x=x+1","then x=x+"," 2 2",4,"Draw y=x+"," 2 2","(Enter as"," y=0.5x+0.5)" 0,"3","",5,19,7,"d. Having the","graph of"," y=(x+1)(x-2) to","solve"," (x+1)(x-2)=3","draw the graph","of y=",1,1,"Draw y=3" 0,"1.5","",5,19,7,"e. Having the","graph of"," y=(x+1)(x-2) to","solve","2(x+1)(x-2)=3","draw the graph","of y=",2,3,"If 2(x+1)(x-2)=3","then:-"," (x+1)(x-2)=1.5",2,"Draw"," y=1.5 (or 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" X0,"<3","",3,15,3,""," y>x and"," y",1,1," y<3" 1,"2.8","",6,14,2,"a. 1 4 2 3 4"," Mean=",2,2,"Check definition","of mean. p98.",3,"1+4+2+3+4=14","Mean=145"," =2.8" 0,"4","",6,15,3,"a. 1 4 2 3 4 "," Mean=2.8"," Mode=",2,2,"Check definition","of mode. p98.",1,"Mode=4" 0,"3","",8,16,4,"a. 1 4 2 3 4"," Mean=2.8"," Mode=4"," Median=",2,2,"Check definition","of median. p98.",2," 1 2 3 4 4","Median=3" y1,"2.6","",6,14,2,"b. 0 4 2 3 4"," Mean=",1,3,"0+4+2+3+4=13","Mean=135"," =2.6" g0,"4","",6,15,3,"b. 0 4 2 3 4 "," Mean=2.6"," Mode=",1,1,"Mode=4" 0,"3","",8,16,4,"b. 0 4 2 3 4"," Mean=2.6"," Mode=4"," Median=",1,2," 0 2 3 4 4","Median=3" o1,"2","",6,14,2,"c. 0 4 2 2"," Mean=",1,3,"0+4+2+2=8","Mean=84"," =2" c0,"2","",6,15,3,"c. 0 4 2 2 "," Mean=2"," Mode=",1,1,"Mode=2" 1,"2","",8,16,4,"c. 0 4 2 2"," Mean=2"," Mode=2"," Median=",1,2," 0 2 2 4","Median=(2+2)2=2" u1,"1.25","",6,14,2,"d. 0 1 2 2"," Mean=",1,3,"0+1+2+2=5","Mean=54"," =1.25" f0,"2","",6,15,3,"d. 0 1 2 2 "," Mean=1.25"," Mode=",1,1,"Mode=2" 1,"1.5","",8,16,4,"d. 0 1 2 2"," Mean=1.25"," Mode=2"," Median=",1,3," 0 1 2 2","Median=(1+2)2"," =1.5" y1,"2","",6,14,2,"e. 0 1 4 2 2 3"," Mean=",1,3,"0+1+4+2+2+3=12","Mean=126"," =2" f0,"2","",6,15,3,"e. 0 1 4 2 2 3"," Mean=2"," Mode=",1,1,"Mode=2" 1,"2","",8,16,4,"e. 0 1 4 2 2 3"," Mean=2"," Mode=2"," Median=",1,2," 0 1 2 2 3 4","Median=2"  s0,"10","",1,16,4,"a. 0 1 1 2 2"," 3 3 4 4 4","Total frequency","=",1,1,"10" 0,"24","",1,18,6,"a. 0 1 1 2 2"," 3 3 4 4 4","Total frequency","=10","Total score","=",1,1,"24" 1,"2.4","",5,18,6,"a. 0 1 1 2 2"," 3 3 4 4 4","Total frequency","=10","Total score=24","Mean=",1,2,"Mean=24/10"," =2.4" w0,"12","",1,16,4,"b. 0 1 2 0 2 2"," 7 5 7 4 4 2","Total frequency","=",1,1,"12" 0,"36","",1,18,6,"b. 0 1 2 0 2 2"," 7 5 7 4 4 2","Total frequency","=12","Total score","=",1,1,"36" 1,"3","",5,18,6,"b. 0 1 2 0 2 2"," 7 5 7 4 4 2","Total frequency","=12","Total score=36","Mean=",1,2,"Mean=36/12"," =3" x0,"8","",1,16,4,"c.0 2.5 2.5 -2"," 3.6 4.4 -1 0","Total frequency","=",1,1,"8" 0,"10","",1,18,6,"c.0 2.5 2.5 -2"," 3.6 4.4 -1 0","Total frequency","=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","Total frequency","=8","Total score=10","Mean=",1,2,"Mean=10/8"," =1.25" !I""8521I! !J+5:0:="N"Ŧ="n"8540\! !K"Y"Ʀ"y"8521I! !L7.1}L,35#:65001,22:65000 !M2,0;" Equations like"'"y=3x+2 and"'"3x+2y=1, which"'"contain only"'"terms in x,y and"'"constants,are"'"represented by"'"STRAIGHT LINE"'"GRAPHS.We need"'"only choose 3"'"values of x to"'"give 3 points"'"through which"'"to draw these"'"graphs.To avoid"'"error,use small"'"positive"'"integers (or"'"zero) for the values of x.":8700!:8990# !NA2,0;"eg.1 Draw the "'"graph of "'" y=3x+2 "'" "'"x=1 y=3X1+2=5 "'" Plot (1,5) ":i=719:" ":i:20,0;" ":8990#:8,14;1;"1";0;13 ,21;"X":8990# !Ok9 ,0;"x=2 y=3X2+2=8"'" Plot (2,8)":8990#:10 ,26;"X":8990# !Pm12 ,0;"x=3 y=3X3+2=11"'" Plot (3,11)":8990#:7,31;"X":8990# !QP252,116t:-120x,-72H:0,1:120x,72H !R08990#:65001,22:65000 !S"2,0;"eg.2 Draw the "'"graph of"'" y=3-x"'""'"x=1 y=3-1=2"'" Plot (1,2)":8700!:8,14;" ";3,14;" ";1;13 ,15;"1";8,15;"2";3,15;"3":8990#:8,21;"X":8990# !Ti9 ,0;"x=2 y=3-2=1"'" Plot (2,1)":8990#:13 ,26;"X":8990# !Ul12 ,0;"x=3 y=3X3-3=0"'" Plot (3,0)":8990#:18,31;"X":8990# !VR252,28:-120x,120x:0,-1:120x,-120x !W8990#:8995## !Y""8537Y! !Z+5:0:="Y"Ŧ="y"8524L! !["N"Ʀ"n"8537Y! !\.1}L,35#:65001,22:65000:8720":1,35#:3,0;"1.Draw the graph"'"of y=x+1.";7,3;"x1 2 3";8,3;"y";9 ,0;" Plot your points"'"on graph paper"'"before checking.":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! !_"Y"Ʀ"y"8541]! !`$65001,22:65000 !at8740$":8990#:3,0;"Eg. Draw the"'"graph of y=2-"'" x"'"for the given"'"range of values"'"of x."''" Complete the"'"table and plot"'"the points on the graph.":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# !c171,93]:2,-2:187,125}:2,-2:203,136:2,-2:219,141:2,-2:235,144:2,-2:251,146:2,-2:20,0;"Draw a smooth curve.":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:="Y"Ŧ="y"8544`! !i"N"Ʀ"n"8551g! !j65001,22:65000:1,35#:2,0;"1. Draw the"'"graph of y=__"'" 2+x"'"for the values"'"given below."''" Copy and"'"complete the"'"table and plot"'"the graph"'"before checking"'"each stage.":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. Now draw the"'"graph of"'" y=(x+2)(3-x)"'"for the given"'"range of values"'"of x."'" Complete each"'"stage before"'"pressing key to"'"check your work.":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"Y"Ʀ"y"8561q! !t7.1}L,35#:65001,22:65000 !u13 ,0;"If we have the graph of y=x and the graph of y=2-x, the x-coordinates of the points in which they intersect are the solutions of 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;"ie. The"'"solutions are:-"'" x=-2 or x=1";11 ,15;"-2";11 ,27;"1":8990# !x$65001,22:65000 !y13 ,0;"If we have the graph of y=x "''"and we want to solve 2x=1-x "''"we write the equation x=-x 2 2 and draw the straight line y=-x. 2 2" !zT8770B":124|,156:32 ,-480,/10 :16,-12 ,/8:16,-4,/6:16,4,/6:16,12 ,/8:32 ,480,/10 :124|,116t:96`,-24:3,27;"y=x";8,12 ;"y=-x";9 ,14;"2 2" !{a8990#:8,19;"X";10 ,25;"^";11 ,19;"-1";4,0;"The solutions"'"are x=-1, x=0.5":8990#:8,19;"X";10 ,25;"^";11 ,19;"-1";5,6;"-1";5,12 ;"0.5":65001,12 :65000:8995## !|""8572|! !}+5:0:="Y"Ŧ="y"8564t! !~"N"Ʀ"n"8572|! !I9 ,0;"ENTER decimals"'"if necessary"'"not fractions.": !""8581! !+5:0:="N"Ŧ="n"8599! !"Y"Ʀ"y"8581! !65001,21:65000:.1}L,35#:3,0;"eg.1"''" The region NOT"'"shaded shows all"'"points whose x"'"coordinates are"'"less than 2,"'" ie. x<2.":136,100d:116t,0:-4,3:3,-3:-3,-3:4,3:140,97a:0,513:-3,-4:3,3:3,-3:-3,4:204,84T:0,64@ !1:i=03:10 ,17+4*i;i:i:0:10 ,30;"x";3,16;"y";6,20;"x<2":i=84T1284:205,i:40(,20:i:205,132:32 ,16:205,136:24,12 :205,140:16,8:205,144:8,4:213,84T:16,8:221,84T:8,4:8990# !12 ,0;"eg.2"''" The region NOT"'"shaded shows all"'"points whose y"'"coordinates are"'"greater than 1,"'" ie. y>1.":140,28:112p,0:-4,3:3,-3:-3,-3:4,3:188,24:0,513:-3,-4:3,3:3,-3:-3,4:140,44,:112p,0 !d1:i=02:18-2*i,22;i:i:0:19,29;"x";13 ,22;"y";14,25;"y>1":i=1482444:i,43+:-12 ,-24:i:144,43+:-6,-12 :248,43+:-9 ,-18:252,43+:-10 ,-20:8990# !65001,21:65000:3,0;"eg.3"''" The region NOT"'"shaded shows all"'"points whose y"'"coordinates are"'"less than twice"'"their x"'"coordinates,"'" ie. y<2x.":120x,36$: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;"eg.4"''" The region NOT"'"shaded shows all"'"points whose y"'"coordinates are"'"less than the"'"square of their"'"x coordinates,"'" ie. y"'"and an integer.":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! !"Y"Ʀ"y"8601! !&65001,22:65000:2,0;" Mean,mode and median are all AVERAGES that tell us something about a set of numbers.":8990#:2,0;" Suppose that five pupils have week-end jobs and their earningsone week-end were:- "'" `5 `8 `6 `8 `7" !8990#:6,0;" The average we want may be:-"'"the mean; (`5+`8+`6+`8+`7)5= `345=`6.80":8990#:9 ,0;"or the mode,the commonest,ie.`8";5,9 ;"`8";5,19;"`8":8990# !&5,9 ;"`8";5,19;"`8";10 ,0;"or the median,the middle one when arranged in order of size.":60<:.1}L,35#:12 ,4;"`5 `6 `7 `8 `8":60<:12 ,14;"`7";13 ,14;"ie. `7":8990# !#14,0;" If we have an even number of scores,the median is halfway between the middle two.":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:="Y"Ŧ="y"8604! !"N"Ʀ"n"8610! !.1}L,35#:65001,22:65000:5,0;"Find the MEAN,MODE and MEDIAN ofthe following sets of numbers:-"''"(Enter any fractions as decimals.)":60<: !""8621! !+5:0:="N"Ŧ="n"8634! !"Y"Ʀ"y"8621! !.1}L,35#:65001,22:65000:2,0;" Look at these scores:-";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;" The scores will first be sortedinto order.":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 !q8,0;" You can now see that there are, ";16,0;" These are the FREQUENCIES of the scores.";9 ,11 ;"seven 1's";10 ,11 ;"two 2's";11 ,11 ;"one 3";12 ,11 ;"two 4's";13 ,11 ;"four 5's";14,11 ;"two 6's";15,11 ;"two 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;" To calculate the mean score:-";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;"Mean of the 20 scores =6820=3.4":0:8990# ! 8995## !""8631! !+5:0:="Y"Ŧ="y"8624! !"N"Ʀ"n"8631! !.1}L,35#:65001,22:65000:5,0;" Complete frequency tables to calculate the means of the following sets of scores:-";8,0;" (Enter any fractions as decimals.)":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$1:i=14:10 ,23+2*i;i:i:i=-3-1:10 ,22+2*i;i:i:i=262:9 -i,22;i:i:i=-6-22:9 -i,21;i:i:0:10 ,30;"x";3,21;"y": "Bi=124|2528:i,89Y:0,67C:i:i=92\1568:124|,i:128,0:i:124|,91[:128,0:187,89Y:0,66B "C1:i=-22:11 ,23+4*i;i:i:i=242:10 -2*i,22;i:i:0:11 ,29;"x";2,21;"y": #""8990# #d30:21,0;"press key when ready":2:0:="@"900 # H.1}L,35#:9 ;21,0;" ": #! 1005 ##17,0;" Do you wish to work through thenotes again before you attempt the questions? Press Y/N. ": #':.1}L,35#:7,0;" To use Module again, press R Pree S to STOP ":9100# #("MODULESC"2 #)#"mathcode3"65000,600X # #""9100# #*5:0:="R"Ŧ="r"900 #"="S"Ŧ="s".5,20: # 9100# mathcode3 X+GZ D!X6(#!Y6(#!Y6(#!Z6(#!Y60#!Y60#!Y60#!Y60#!Z60#!0Z60#!PZ60#!pZ60#!Z60#!Z60#!Z60#!Z60# P P P 88 MMbXaXL8Wq !v>D((DDDD<8>>000 q #$RR| P pd<*]\"_\C*]\~}t[3*a\Þ*x\#"x MODULESD > > @ :1:1::"":20,31;:"MODULESD" D @t <Bf8B 8xB8x?B8 B<<8<<8D @!-!!! >!!!!! !<!!!! !B~<B| x<<!!"! !"@Bb888xB8<8hh8 D8xD8x88D8h88B8hxD88B8x8D88x88!!"! !"|@RD DDB DD TTD<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 ;"MATHEMATICS";2;7;0,0;"Module ";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;" Do you wish to work through thenotes before you attempt the questions? Press Y/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;"QUESTIONS";12 ,16;"HINTS" 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 `3hint120,1;"TRY AGAIN" be0,9 ;"enter answer: ";h$:v$="":u$""1,0;"enter units of answer: ";v$ 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$1180 m 1165 r20,1;2;6;1;1;"CORRECT";:" ":l=14:.1}L,34":.1}L,30:l:20:8990#:1150~ t 1160 ~hh=0r=r+1  1195 h$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;" In this module you got:- answers correct without a hint. ";9 ,0;" If you need more help, work through the following sections in the PAN STUDY AID. " "a=0r=1:a=12 ҳ9 ;6,10 ;r;" out of ";a:r/a.8L3,11 ;"WELL DONE":j=15:.1}L,16:.1}L,24:.1}L,20:j 2000+10 *qu: U2,13 ;"DATA";13 ,0;" Exercise 12b,Q.1(a),Q.2(a)p104.": <1,0;" ";13 ,0;"Page 106,108.": 013 ,0;" Exercise 12b, page 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 u1,1;6;"FINDING THE MEAN FROM GROUPED";2,13 ;"DATA":.1}L,35#:8521I!: 65001,21:65000:1,35#:2,0;"2."''" On another holiday the friends again recorded how long it took for their postcards to arrive and the results were:-"'"7 took 1 or 2 days"'"8 took 3 or 4 days"'"9 took 5 or 6 days"'"20 took 7 or 8 days"'"6 took 9 but not more than 12 days"'"Note this information carefully,in order to complete the frequency table which follows.":8990#:8720": J1,10 ;6;"HISTOGRAMS":.1}L,35#:8541]!: a65001,22:65000:1,35#:1,0;"2."'" This time they travelled:-"'"20 less than 200km"'"10 between 200 and 250km"'" 8 between 250 and 300km"'" 5 between 300 and 350km"'" 7 between 350 and 400km"'"16 between 400 and 500km"'"14 between 500 and 600km"'"20 between 600 and 1000km."'"(Let 1 unit = 50km)": Z1,2;6;"CUMULATIVE FREQUENCY CURVES":.1}L,35#:8561q!: 8593!:65001,22:65000:1,35#:2,0;"2. The distance travelled on holiday last year by 1000 students are shown below:-"'" 20 less than 100km,"'" 40 between 100 and 200km,"'" 40 between 200 and 300km,"'"200 between 300 and 400km,"'"320 between 400 and 500km,"'"120 between 500 and 600km,"'"180 between 600 and 800km,"'" 80 between 800 and 1000km."''" Complete the cumulative frequency table,then press key to check.":8990# >65000:3,0;" 20 travelled less than 100km 60 200km 100 300km 300 400km 620 500km 740 600km 920 800km 1000 1000km." ''" Draw your cumulative frequency curve. This time it will not be displayed until after you have answered the questions.":8990#  x65000:3,0;" Select your answers from the following numbers:-"''"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#: Y65001,22:65000:5,0;" Press any key when you have drawn your cumulative frequency curve.":8990#:65000:8750.":87608":8990#:65000:3,0;" Now select one of these numbersas the nearest answer to the following questions."''"21, 57, 180, 190, 360, 550": %65001,22:65000:8750.":87608":8990#:6,0;"The median"'" =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;"The lower"'"quartile=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;"The upper"'"quartile=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;"The median"'" =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;"The lower"'"quartile=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;"The upper"'"quartile=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. The total","frequency,f=",1,3,"Total number of","postcards"," =40" xv1,"7.5","",3,15,3,"b. The 3rd mid-","interval value,"," x=",1,2,"(7+8)2","=7.5" yw1,"9.5","",3,15,3,"c. The 4th mid-","interval value,"," x=",1,2,"(9+10)2","=9.5" zz1,"11.5","",3,15,3,"d. The 5th mid-","interval value,"," x=",1,2,"(11+12)2","=11.5" {z1,"14.5","",3,15,3,"e. The 6th mid-","interval value,"," x=",1,2,"(13+16)2","=14.5" |k1,"17.5","",4,15,3,"f.","The 1st product,"," fx=",1,2,"7X2.5","=17.5" }g1,"44","",4,15,3,"g.","The 2nd product,"," fx=",1,2,"8X5.5","=44" ~g1,"45","",4,15,3,"h.","The 3rd product,"," fx=",1,2,"6X7.5","=45" g1,"57","",4,15,3,"i.","The 4th product,"," fx=",1,2,"6X9.5","=57" h1,"92","",4,15,3,"j.","The 5th product,"," fx=",1,2,"8X11.5","=92" l1,"72.5","",4,15,3,"k.","The 6th product,"," fx=",1,2,"5X14.5","=72.5" _1,"328","",11 ,14,2,"l. The total","product,fx=",1,1,"328" 1,"8.2","",7,17,5,"m. The mean","number of days","it took for the","postcards to","arrive=",1,2,"32840","=8.2" {0,"50","",13 ,14,2,"a. The total","frequency,f,=",1,2,"Total number of","postcards=50" v0,"1.5","",3,15,3,"b. The 1st mid-","interval value,"," x=",1,2,"(1+2)2","=1.5" v0,"3.5","",3,15,3,"c. The 2nd mid-","interval value,"," x=",1,2,"(3+4)2","=3.5" v0,"5.5","",3,15,3,"d. The 3rd mid-","interval value,"," x=",1,2,"(5+6)2","=5.5" v0,"7.5","",3,15,3,"e. The 4th mid-","interval value,"," x=",1,2,"(7+8)2","=7.5" y0,"10.5","",3,15,3,"f. The 5th mid-","interval value,"," x=",1,2,"(9+12)2","=10.5" k1,"10.5","",4,15,3,"g.","The 1st product,"," fx=",1,2,"7X1.5","=10.5" g1,"28","",4,15,3,"h.","The 2nd product,"," fx=",1,2,"8X3.5","=28" k1,"49.5","",4,15,3,"i.","The 3rd product,"," fx=",1,2,"9X5.5","=49.5" j1,"150","",4,15,3,"j.","The 4th product,"," fx=",1,2,"20X7.5","=150" h1,"63","",4,15,3,"k.","The 5th product,"," fx=",1,2,"6X10.5","=63" _1,"301","",11 ,14,2,"l. The total","product,fx=",1,1,"301" 1,"6.02","",7,17,5,"m. The mean","number of days","it took for the","postcards to","arrive=",1,2,"30150","=6.02" f1,"4","",8,15,3,"a. Area=4"," Width=1"," Length=",1,1,"4 units" f1,"6","",8,15,3,"b. Area=6"," Width=1"," Length=",1,1,"6 units" s1,"2","",8,14,3,"c. Area=16"," Width="," Length=",1,2,"100 to 200","2 units" g1,"8","",8,15,3,"c. Area=16"," Width=2"," Length=",1,1,"8 units" s1,"2","",8,14,3,"d. Area=12"," Width="," Length=",1,2,"200 to 300","2 units" g1,"6","",8,15,3,"d. Area=12"," Width=2"," Length=",1,1,"6 units" s1,"4","",8,14,3,"e. Area=32"," Width="," Length=",1,2,"300 to 500","4 units" g1,"8","",8,15,3,"e. Area=32"," Width=4"," Length=",1,1,"8 units" v1,"10","",8,14,3,"f. Area=30"," Width="," Length=",1,2,"500 to 1000","10 units" h1,"3","",8,15,3,"f. Area=30"," Width=10"," Length=",1,1,"3 units" q1,"4","",8,14,3,"a. Area=20"," Width="," Length=",1,2,"0 to 200","4 units" g1,"5","",8,15,3,"a. Area=20"," Width=4"," Length=",1,1,"5 units" i1,"10","",8,15,3,"b. Area=10"," Width=1"," Length=",1,1,"10 units" f1,"8","",8,15,3,"c. Area=8"," Width=1"," Length=",1,1,"8 units" f1,"5","",8,15,3,"d. Area=5"," Width=1"," Length=",1,1,"5 units" f1,"7","",8,15,3,"e. Area=7"," Width=1"," Length=",1,1,"7 units" s1,"2","",8,14,3,"f. Area=16"," Width="," Length=",1,2,"400 to 500","2 units" g1,"8","",8,15,3,"f. Area=16"," Width=2"," Length=",1,1,"8 units" s1,"2","",8,14,3,"g. Area=14"," Width="," Length=",1,2,"500 to 600","2 units" g1,"7","",8,15,3,"g. Area=14"," Width=2"," Length=",1,1,"7 units" t1,"8","",8,14,3,"h. Area=20"," Width="," Length=",1,2,"600 to 1000","8 units" k1,"2.5","",8,15,3,"h. Area=20"," Width=8"," Length=",1,1,"2.5 units" g1,"10","",2,13 ,2,"a. travelled","less than 100km.",1,1,"4+6=10" j1,"26","",2,13 ,2,"b. travelled","less than 200km.",1,1,"4+6+16=26" m1,"38","",2,13 ,2,"c. travelled","less than 300km.",1,1,"4+6+16+12=38" p1,"70","",2,13 ,2,"d. travelled","less than 500km.",1,1,"4+6+16+12+32=70" 1,"100","",2,13 ,2,"e. travelled","less than 1000km.",1,2,"4+6+16+12+32+30"," =100" 1,"360","",1,14,2,"f. The median","= km",2,2,"Check definition","of median.p98.",1,"The median=360km" 1,"190","",9 ,14,2,"g.The lower","quartile= km",2,4," One quarter of","scores are less","than lower","quartile.",1,"190km" 1,"550","",9 ,14,2,"h.The upper","quartile= km",2,4," One quarter of","scores are","greater than","upper quartile.",1,"550km" 1,"180","",1,15,3,"i.The semi-inter","quartile range","= km",2,1,"Semi-iqr=Q2-Q1.",3,"=(550-190)2","=3602","=180km." 1,"57","",11 ,16,4,"j.The number of","students who","travelled less","than 400km=",1,1," 57" 1,"21","",11 ,16,4,"k.The number of","students who","travelled more","than 600km=",1,2,"100-79","=21 students" \1,"460","",1,14,2,"a.The median","= km",1,1,"460km" c1,"380","",9 ,14,2,"b.The lower","quartile= km",1,1,"380km" c1,"610","",9 ,14,2,"c.The upper","quartile= km",1,1,"610km" 1,"115","",1,15,3,"d.The semi-inter","quartile range","= km",1,4,"The semi-iqr","=(610-380)2","=2302","=115km." Œ1,"180","",11 ,16,4,"e.The number of","students who","travelled less","than 350km=",1,1," 180 students" ×1,"170","",11 ,16,4,"f.The number of","students who","travelled more","than 700km=",1,2,"1000-830","=170 students" !I""8521I! !J+5:0:="N"Ŧ="n"8537Y! !K"Y"Ʀ"y"8521I! !L$65001,21:65000 !M .1}L,35#:7,0;" How would you find the mean (average) mass of a class of pupils?"'" If there were 25 of them and their masses were 74kg,60.4kg, 67.5kg etc,you could add their masses to find the total and divide by 25.":8990# !NC65001,21:65000:3,0;" But we may not know the exact mass of each.":8990#:5,0;"Perhaps,"'"2 are between 50 and 55kg"'"4 are between 55 and 60kg"'"7 are between 60 and 65kg"'"5 are between 65 and 70kg"'"6 are between 70 and 75kg"'"1 is between 75 and 80kg":8990# !O12 ,0;" We have to estimate that, the first 2 are 'about' 52.5kg, the next 4 are 'about' 57.5kg, the next 7 are 'about' 62.5kg, and so on.":8990# !Pi17,0;" These values,52.5,57.5,62.5,...are called the MID-INTERVAL values.":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;"The mean mass of a class of 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:1:5,1;"FREQUENCY MID-INTERVAL PRODUCT";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;" The mean mass=1622.525=64.9kg.":8990# !S 8995## !T""8532T! !U+5:0:="Y"Ŧ="y"8524L! !V"N"Ʀ"n"8532T! !Y65001,21:65000:1,35#:2,0;"1."''" Some friends recorded how long their holiday postcards took to arrive."'"7 took between 1 and 4 days"'"8 took 5 or 6 days"'"6 took 7 or 8 days"'"6 took 9 or 10 days"'"8 took 11 or 12 days"'"5 took 13,14,15 or 16 days."''"Note this information carefully,especially the numbers of days, in order to complete the frequency table which follows.":8990# !ZH65001,21:65000:4,151:248,0:0,-71G:-248,0:0,71G:4,136:248,0:4,88X:248,0:84T,80P:0,71G:188,80P:0,71G:1;3,1;"FREQUENCY MID-INTERVAL PRODUCT";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! !_"Y"Ʀ"y"8541]! !`7.1}L,35#:65001,22:65000 !a;2,0;" How far did you travel on your holidays last summer?":8990#:4,0;" A survey of 50 students found how far they travelled:-"'" 6 less than 100km,"'"12 between 100 and 200km,"'"14 between 200 and 300km,"'"10 between 300 and 400km,"'"and"'" 8 between 400 and 500km.":8990# !b12 ,0;" We can represent this data by aHISTOGRAM,in which the AREA of each rectangle is proportional to the frequency.":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" !dK12 ,0;"Distances travelled:-"'" 6 less than 100km,"'"12 between 100 and 200km,"'"14 between 200 and 300km,"'"10 between 300 and 400km,"'"and"'" 8 between 400 and 500km.";9 ,8;"6";6,13 ;"12";5,18;"14";7,23;"10";8,28;"8":8990# !e+12 ,0;" "'" As the widths of the rectanglesare the same,the height of each rectangle is also proportional to the frequency.It is,however, the essential property of the histogram,that it is the area that must be proportional to thefrequency.":8990# !fH65001,22:65000:11 ,0;"Suppose the distances travelled were:-"'" 2 less than 50km,"'" 4 between 50 and 100km,"'" 5 between 100 and 150km,"'" 7 between 150 and 200km,"'"14 between 200 and 300km"'"10 between 300 and 400km"'"and"'" 8 between 400 and 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# !kP13 ,0;" The class intervals are different and so the rectangles are of different widths. "'" Taking 1 unit to represent 50km,the area of each rectangle equals the number of students who travelled each distance.":8990#:65001,8:65000:8995## !l""8556l! !m+5:0:="Y"Ŧ="y"8544`! !n"N"Ʀ"n"8556l! !o.1}L,35#:65001,22:65000:5,0;" Construct histograms to represent the following data."''" You will be asked for the widthand length of each rectangle."''" You should then draw your own histogram before checking.":8990# !pD65000:1,35#:1,0;"1."'" The distances travelled on holiday last year by 100 students were:-"'" 4 less than 50km"'" 6 between 50 and 100km"'"16 between 100 and 200km"'"12 between 200 and 300km"'"32 between 300 and 500km"'"30 between 500 and 1000km"'"(Let 1 unit = 50km)": !q""8561q! !r+5:0:="N"Ŧ="n"8594! !s"Y"Ʀ"y"8561q! !t$65001,22:65000 !u.1}L,35#:2,0;" A survey of 50 students found how far they travelled:-"'" 6 less than 100km,"'"12 between 100 and 200km,"'"14 between 200 and 300km,"'"10 between 300 and 400km,"'"and 8 between 400 and 500km.":8990# !v 10 ,0;"We see that:-"'" 6 students"'" travelled less than 100km,"'"18 (6+12) less than 200km,"'"32 (6+12+14) less than 300km,"'"42 (6+12+14+10) less than 400km,"'"50 (6+12+14+10+8) less than 500km.":8990# !ww18,0;"These cumulative frequencies canbe represented on a CUMULATIVE FREQUENCY CURVE.":8990#: !x65001,22:65000:8750.":87542":.1}L,35#:6,0;" You should be"'"able to draw a"'"much more"'"accurate graph"'"on graph paper.":8990#:6,0;" The median "'"distance "'"travelled is "'"measured "'"against 25.5 on"'"the cumulative"'"frequency axis"'"and is about"'"255km.":80P:1:i=1481984:.1}L,35#:i,103g:i+1,103g:i !y60<:i=102f546-4:.1}L,35#:199,i:199,i-1:i:0:16,25;"2";17,25;"5";18,25;"5" !z8990#:i=514:i,0;b$: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;"We can estimate"'"from the graph"'"that 20 students"'"travelled less"'"than 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$:i:1:i=53592\4:191,i:191,i+1:i:i=192148-4:i,93]:i-1,93]:i:0:.1}L,35#::6,0;"We can estimate"'"from the graph"'"that 20 students"'"(50-30) students"'"travelled more"'"than 290km.":80P !~_1:i=524112p4:.1}L,35#:205,i:205,i+1:i !60<:i=205148-4:.1}L,35#:i,113q:i-1,113q:i:0:7,16;"30";3,16;"50":8990# !|i=611 :i,0;b$: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;"We can estimate"'"from the graph"'"that 32 students"'"travelled less"'"than 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# !li=610 :i,0;b$:i:7,16;"30":1:i=535114r4:207,i:207,i+1:i:i=207148-4:i,115s:i-1,115s:i:0:6,0;"We can estimate"'"from the graph"'"that 15 students"'"(50-35) students"'"travelled more"'"than 330km.":80P !_1:i=524123{4:.1}L,35#:214,i:214,i+1:i !60<:i=214148-4:.1}L,35#:i,123{:i-1,123{:i:0:6,16;"35";3,16;"50":8990# !i=611 :i,0;b$: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;" The lower"'"quartile,Q1,is"'"such that one"'"quarter of the"'"scores are less"'"than Q1 and is"'"read against"'"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;" The upper"'"quartile,Q2,is"'"such that one"'"quarter of the"'"scores are more "'"than Q2 and is read"'"against 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# !G6,0;" The difference"'"between the two"'"quartiles is "'"called the"'"interquartile "'"range. "'" "'" In this case "'"the iqr=365-160"'" =205km."'" "'" The iqr and the"'"semi-iqr are often "'"used as measures of"'"spread or dispersion. ":8990# !/65001,7:65000:8995## !""8590! !+5:0:="Y"Ŧ="y"8564t! !"N"Ʀ"n"8590! !.1}L,35#:65001,22:65000:5,0;" Draw your cumulative frequency curves as accurately as the following data permits,and use them to answer the questions."''" You will need to note the data on paper first.":8990#: !o8593!:65001,22:65000:1,35#:2,0;"1. The distances travelled on holiday last year by 100 students are shown below:-"'" 4 less than 50km,"'" 6 less between 50 and 100km,"'"16 between 100 and 200km,"'"12 between 200 and 300km,"'"32 between 300 and 500km,"'"and 30 between 500 and 1000km.":8990# !}12 ,0;" Complete a cumulative frequencytable and check your answers before drawing the curve.":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@:1;3,1;"FREQUENCY MID-INTERVAL PRODUCT";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": "$65001,22:65000:i=12 11 -1:i,6;"        ":i:10 ,6;"       ":i=9 8-1:i,6;"       ":i:i=76-1:i,10 ;"      ":i:5,10 ;"    ":4,10 ;" ";3,10 ;" " "%8;9 ,7;"20";4,10 ;"1";5,10 ;"0";6,11 ;"8";9 ,12 ;"5";7,13 ;"7";6,14;"16";7,16;"14";11 ,21;"20" "&J480,152:0,-80P:160,0:491,152:0,-79O:159,0:47/,152:-1,0:47/,136:-1,0:47/,120x:-1,0:47/,104h:-1,0:47/,88X:-1,0:13 ,5;"0 2 4 6 1";14,9 ;"0 0 0 0";15,9 ;"0 0 0 0 km";16,25;"0";10 ,4;"2";8,4;"4";6,4;"6";4,4;"8";2,3;"10";5,2;"f" "': ".Ri=14824810 :i,524:0,100d:i:i=14824820:i,480:0,4:i:147,524:0,100d:i=52415210 :148,i:100d,0:i:i=52415220:144,i:4,0:i:148,513:100d,0 "/F3,4;"Cumulative";4,5;"frequency": "216,17;"0 1 2 3 4 5";17,20;"0 0 0 0 0";18,20;"0 0 0 0 0";19,30;"km";12 ,16;"10";10 ,16;"20";7,16;"30";5,16;"40";3,16;"50" "4148,524:20,12 ,/6:20,24,/8:20,28:20,20,-/24:20,16 "5148,535:20,12 ,/6:20,24,/8:20,28:20,20,-/24:20,16: "816,17;"0 2 4 6 8 1";17,20;"0 0 0 0 0";18,20;"0 0 0 0 0";19,28;"km0";12 ,16;"20";10 ,16;"40";7,16;"60";5,16;"80";3,15;"100" "9148,524:5,4,/6:5,6,/6:10 ,16,/12 :10 ,12 :20,32 ,-/24:502,30,-/6 ":148,535:5,4,/6:5,6,/6:10 ,16,/12 :10 ,12 :20,32 ,-/24:502,30,-/6: "B16,17;"0 2 4 6 8 1";17,20;"0 0 0 0 0";18,20;"0 0 0 0 0";19,28;"km0";12 ,15;"200";10 ,15;"400";7,15;"600";5,15;"800";3,14;"1000" "C148,524:10 ,2:10 ,4:10 ,4:10 ,20,/12 :10 ,32 :10 ,12 ,-/6:20,18,-/12 :20,8,-/8 "D148,535:10 ,2:10 ,4:10 ,4:10 ,20,/12 :10 ,32 :10 ,12 ,-/6:20,18,-/12 :20,8,-/8: #""8990# #d30:21,0;"press key when ready":2:0:="@"900 # H.1}L,35#:9 ;21,0;" ": ##17,0;" Do you wish to work through thenotes again before you attempt the questions? Press Y/N. ": #':.1}L,35#:7,0;" To use Module again, press R Press S to STOP ":9100# #("MODULESD"2 #)#"mathcode4"65000,600X # #""9100# #*2:0:="R"Ŧ="r"900 #"="S"Ŧ="s".5,20: # 9100# mathcode4 XZ D!X6(#!Y6(#!Y6(#!Z6(#!Y60#!Y60#!Y60#!Y60#!Z60#!0Z60#!PZ60#!pZ60#!Z60#!Z60#!Z60#!Z60# P P P 88 MMbXaXL8Wq !v>D((DDDD<8>>000 q #$RR| P pd<*]\"_\C*]\~}t[3*a\Þ*x\#"x