ZXTape! 0Created with Ramsoft MakeTZXMODULESA > > @ :1:1::"":20,31;:"MODULESA" A @<Bf8B 8xB8x?B8 B<<8<<8D @!-!!! >!!!!! ?<!!!! ?B~<B| x<<!!"! !!@Bb888xB8<8hh8 D8xD8x88D8h88B8hxD88B8x8D88x88!!"! !!|@RD DDB DD TTD<6.1}L,-5:2:.4L,-20:984 P.1}L,35#:17,27;8;1;7;q$:986 Hq$<1.1}L,-5:2:.4L,-20:984 qu=qu+1 r=0::.1}L,35#:6;0,10 ;"MATHEMATICS";2;7;0,0;"Module ";qu: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+20*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=qi196101+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:hh6ph=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: 813 ,0;"Examples 1.9(a),(b),(c),page 16.": 413 ,0;"Examples 1.9(d),(e),page 16.": *13 ,0;"Standard Form p20.": 713 ,0;"Standard Form Exercise 1c, p21.": 015,0;"Significant figures p27.":  215,0;"P28 and exercise 2b, qu.2.":  q 5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5 r 5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5 s 5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5 t 10 ,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5 u 15,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5 v10 ,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5 Y1,3;6;"MULTIPLICATION OF DECIMALS":.1}L,35#:85015!: S1,5;6;"DIVISION OF DECIMALS":.1}L,35#:8521I!: L1,9 ;6;"STANDARD FORM":.1}L,35#:8541]!: %]1,1;6;"USING NUMBERS IN STANDARD FORM":.1}L,35#:8581!: 9R1,6;6;"SIGNIFICANT FIGURES":.1}L,35#:8561q!: MM1,9 ;6;"DECIMAL PLACES":.1}L,35#:8601!: m1,"0.28","",10 ,14,2,"a. 0.4X0.7=","",2,5,"0.4X0.7="," (4X7=28)","Count the digits","after decimal","point.",1," =0.28" n1,"0.048","",10 ,14,2,"b.0.4X0.12=","",2,5,"0.4X0.12="," (4X12=48)","Count the digits","after decimal","point.",1," =0.048" o1,"0.036","",10 ,14,2,"c.0.4X0.09=","",2,5,"0.4X0.09="," (4X9=36)","Count the digits","after decimal","point.",1," =0.036" p1,"0.06","",10 ,14,2,"d.0.4X0.15=","",3,5,"0.4X0.15="," (4X15=60)","Count the digits","after decimal","point.",5," 0.4X0.15=0.060","Count the last","digit but do not","write it down.","",1," =0.06" q1,"0.036","",10 ,15,3,"e."," 0.45X0.08=","",3,5,"0.45X0.08="," (45X8=360)","Count the digits","after decimal","point.",5,"0.45X0.08=0.0360","Count the last","digit but do not","write it down.","",1," =0.036" w1,"1.75","",8,13 ,2,"a. ="," 0.4",2,2," ="," 0.4 4",1," =1.75" 1,"144","",10 ,13 ,2,"b. _="," 0.005",2,2," _="," 0.005 5",1," =144" 1,"32.8","",9 ,13 ,2,"c. ="," 0.025",2,2," _="," 0.025 25",1," =32.8" |1,"40","",9 ,13 ,2,"d. _="," 0.03",2,2," _="," 0.03 3",1," =40" 1,"0.035","",10 ,13 ,2,"e. ="," 0.7",2,2," ="," 0.7 7",1," =0.035" 0,"5","",14,13 ,2,"a.","123000=1.23X10",3,4," 1","123000=12300X10"," 2"," =1230X10",4," 3","123000=123X10"," 4"," =12.3X10",4," 5"," =1.23X10",""," Ans= 5" 0,"7","",10 ,14,3,"b. 45000000",""," =4.5X10",2,5," The decimal","point moves 7","places to the","left from","45000000 to 4.5",5,"","So:-"," 7","45000000=4.5X10"," Ans= 7" 0,"-6","",9 ,14,3,"c. 0.0000067",""," =6.7X10",2,5," The decimal","point moves 6","places to the","right from","0.0000067 to 6.7",5,"","So:-","0.0000067 -6"," =6.7X10"," Ans= -6" 0,"-3","",10 ,14,3,"d. 0.00809",""," =8.09X10",2,5," The decimal","point moves 3","places to the","right from","0.00809 to 8.09",5,"","So:-","0.00809 -3"," =8.09X10"," Ans= -3" 0,"-5","",9 ,14,3,"e. 0.0000102",""," =1.02X10",2,6," The decimal","point moves 5","places to the","right from","0.0000102"," to 1.02",6,"","So:-","0.0000102 -5"," =1.02X10",""," Ans= -5" 0,"3.5","",2,16,5,"a. 3 -5","(5X10 )X(7X10 )"," *"," = X10"," ^^^ 1st answer",2,4,"5X7=35 Is your","decimal point in","the correct","place?",1," Ans= 3.5" 0,"-1","",8,15,4,"a. 3 -5","(5X10 )X(7X10 )",""," =3.5X10",1,5," 3 -5","(5X10 )X(7X10 )"," -2 -1","=35X10 =3.5X10"," Ans= -1" 0,"4.8","",2,16,5,"b. 5 2","(6X10 )X(8X10 )"," *"," = X10"," ^^^ 1st answer",2,4,"6X8=48 Is your","decimal point in","the correct","place?",1," Ans= 4.8" 0,"8","",8,15,4,"b. 5 2","(6X10 )X(8X10 )",""," =4.8X10",1,5," 5 2","(6X10 )X(8X10 )"," 7 8","=48X10 =4.8X10"," Ans= 8" 0,"1.2","",2,16,4,"c. 3 -1","(4X10 )X(3X10 )"," *"," = X10",2,4,"3X4=12 Is your","decimal point in","the correct","place?",1," Ans= 1.2" 0,"3","",8,15,4,"c. 3 -1","(4X10 )X(3X10 )",""," =1.2X10",1,5," 3 -1","(4X10 )X(3X10 )"," 2 3","=12X10 =1.2X10"," Ans= 3" 0,"7.5","",2,16,4,"d. 2 5","(3X10 )(4X10 )"," *"," = X10",2,4,"34=0.75 Is your","decimal point in","the correct","place?",1," Ans= 7.5" 0,"-4","",8,15,4,"d. 2 5","(3X10 )(4X10 )",""," =7.5X10",1,6," 2 5","(3X10 )(4X10 )"," -3","=0.75X10 -4"," =7.5X10"," Ans= -4" 0,"3.75","",2,16,4,"e. -3 -7","(3X10 )(8X10 )"," *"," = X10",2,4,"38=0.375","Is your decimal","point in the","correct place?",1," Ans= 3.75" 0,"3","",9 ,15,4,"e. -3 -7","(3X10 )(8X10 )",""," =3.75X10",1,6," -3 -7","(3X10 )(8X10 )"," 4","=0.375X10 3"," =3.75X10"," Ans= 3" 0,"1360","",5,14,2,"a.","1357= to 3sf",2,1,"Examine 4th sf.",2,"1357"," =1360 to 3sf" 0,"1400","",5,14,2,"b.","1357= to 2sf",2,1,"Examine 3rd sf.",2,"1357"," =1400 to 2sf" 0,"1000","",5,14,2,"c.","1357= to 1sf",2,1,"Examine 2nd sf.",2,"1357"," =1000 to 1sf" 1,"0.0975","",3,15,3,"d.","0.09753"," = to 3sf",2,2,"Examine 4th sf.","ie. 3",2,"0.09753"," =0.0975 to 3sf" 1,"0.098","",3,15,3,"e.","0.09753"," = to 2sf",2,2,"Examine 3rd sf.","ie. 5",2,"0.09753"," =0.098 to 2sf" ™1,"0.1","",3,15,3,"f.","0.09753"," = to 1sf",2,2,"Examine 2nd sf.","ie. 7",2,"0.09753"," =0.1 to 1sf" Ò0,"10310","",3,15,3,"g.","10305"," = to 4sf",2,1,"The 5th sf is 5.",2,"10305"," =10310 to 4sf" w0,"10300","",3,15,3,"h.","10305"," = to 3sf",1,2,"10305"," =10300 to 3sf" w0,"10000","",3,15,3,"i.","10305"," = to 2sf",1,2,"10305"," =10000 to 2sf" ƀ1,"0.02041","",2,15,3,"j.","0.020406"," = to 4sf",1,2,"0.020406"," =0.02041to 4sf" 1,"0.0204","",3,15,3,"k.","0.020406"," = to 3sf",1,2,"0.020406"," =0.0204 to 3sf" }1,"0.020","",3,15,3,"l.","0.020406"," = to 2sf",1,2,"0.020406"," =0.020 to 2sf" {1,"0.02","",3,15,3,"m.","0.020406"," = to 1sf",1,2,"0.020406"," =0.02 to 1sf" {0,"901000","",3,15,3,"n.","900705"," = to 3sf",1,2,"900705"," =901000 to 3sf" }1,"0.010","",3,15,3,"o.","0.010203"," = to 2sf",1,2,"0.010203"," =0.010 to 2sf" Ѭ0,"1.358","",9 ,14,3,"a."," 1.3579="," to 3 dp",2,3,"The digit in the","4th dp. is 9.","1.3579",1," =1.358 to 3 dp" Ҫ0,"1.36","",9 ,14,3,"b."," 1.3579="," to 2 dp",2,3,"The digit in the","3rd dp. is 7.","1.3579",1," =1.36 to 2 dp" Ө0,"1.4","",9 ,14,3,"c."," 1.3579="," to 1 dp",2,3,"The digit in the","2nd dp. is 5.","1.3579",1," =1.4 to 1 dp" Ԯ1,"0.0247","",9 ,14,3,"d."," 0.02468="," to 4 dp",2,3,"The digit in the","5th dp. is 8.","0.02468",1," =0.0247 to 4 dp" խ1,"0.025","",9 ,14,3,"e."," 0.02468="," to 3 dp",2,3,"The digit in the","4th dp. is 6.","0.02468",1," =0.025 to 3 dp" ֫1,"0.02","",9 ,14,3,"f."," 0.02468="," to 2 dp",2,3,"The digit in the","3rd dp. is 4.","0.02468",1," =0.02 to 2 dp" ׄ0,"5.432","",9 ,14,3,"g."," 5.4321="," to 3 dp",1,3,"","5.4321"," =5.432 to 3 dp" ؂0,"5.43","",9 ,14,3,"h."," 5.4321="," to 2 dp",1,3,"","5.4321"," =5.43 to 2 dp" ـ0,"5.4","",9 ,14,3,"i."," 5.4321="," to 1 dp",1,3,"","5.4321"," =5.4 to 1 dp" ڀ0,"0.0","",9 ,14,3,"j."," 0.0499="," to 1 dp",1,3,"","0.0499"," =0.0 to 1 dp" !5""85015! !6!5:0:="N"Ŧ="n" !7"Y"Ʀ"y"85015! !8D65001,22:65000:30:.5,35#:2,0;"eg.1":502:.1}L,35#:3,4;"0.4X0.06=":8990#:3,13 ;"_X__=";4,13 ;"10 100":8990#:3,20;"__=";4,20;"1000":8990#:3,25;"0.024" !98990#:3,6;"4";3,10 ;"06":5,0;"There are 1 + 2 digits after thedecimal point in the question.":8990#:8,0;"So, there must be 3 digits afterthe decimal point in the answer.":3,27;"024":8990# !:A12 ,0;"eg.2";12 ,6;"0.4X0.03=":8990#:12 ,19;"12":8990#:12 ,8;"4";12 ,12 ;"03":8990#:12 ,20;"2":8990#:12 ,19;"1":8990#:12 ,18;"0":8990#:12 ,16;"0." !;M8990#:13 ,0;"eg.3";13 ,6;"0.7X0.05=":8990#:13 ,19;"35":8990#:13 ,8;"7";13 ,12 ;"05":8990#:13 ,20;"5":8990#:13 ,19;"3":8990#:13 ,18;"0":8990#:13 ,16;"0." !<14,0;"eg.4";14,6;"0.07X0.005=":8990#:14,22;"35":8990#:14,8;"07";14,13 ;"005":8990#:14,23;"5":8990#:14,22;"3":8990#:14,21;"0":8990#:14,20;"0":8990#:14,19;"0":8990#:14,17;"0." !=M8990#:15,0;"eg.5";15,6;"0.4X0.05=":8990#:15,19;"20":8990#:15,8;"4";15,12 ;"05":8990#:15,20;"0":8990#:15,19;"2":8990#:15,18;"0":8990#:15,16;"0." !>8990#:16,20;"^"'"NOTE! You must count this final zero but it is not usually written down.":200:i=120:15,20;" ":.05|L,10 :15,20;"0":i:15,20;" ";16,20;" " !?8990#:8995## !@""8512@! !A+5:0:="Y"Ŧ="y"85048! !B"N"Ʀ"n"8512@! !FT65001,13 :65000:11 ,0;" DO NOT USE A CALCULATOR": !I""8521I! !J!5:0:="N"Ŧ="n" !K"Y"Ʀ"y"8521I! !M65001,22:65000:30:.5,35#:2,0;"eg.1":502:.1}L,35#:3,4;"0.040.008=":8990#:3,15;"_=";4,15;"0.008" !NW8990#:3,21;"_X";4,21;"0.008X1000":8990# !O5,0;" choosing 1000 so that the denominator becomes a whole number.":8990#:65001,19:65000 !P?5,0;"=_X";6,1;"0.008X1000":8990#:5,1;" _X ";6,1;" 0.08X100 ":8990#:5,2;" _X ";6,2;" 0.8X10 ":8990#:5,4;"= ";6,3;" 8 ":8990#:5,8;"5":8990# !QR7,0;"eg.2";7,8;"_=";8,8;"0.05":8990#:7,13 ;"_X";8,13 ;"0.05X100":8990#:7,13 ;" _X ";8,13 ;" 0.5X10 ":8990#:7,14;" = ";8,14;" 5 ":8990#:7,19;"4":8990# !RL9 ,0;"eg.3";9 ,8;"=";10 ,8;"0.07":8990#:9 ,13 ;"";10 ,13 ;"0.07":8990#:9 ,13 ;" ";10 ,13 ;" 0.7":8990#:9 ,14;" =";10 ,14;" 7":8990#:9 ,19;"0.429 to 3sf":8990# !S11 ,0;"eg.4";11 ,8;"=";12 ,8;"0.3":8990#:11 ,13 ;"";12 ,13 ;"0.3":8990#:11 ,13 ;" =";12 ,13 ;" 3":8990#::11 ,19;"0.233 to 3sf":8990#:8995## !T""8532T! !U+5:0:="Y"Ŧ="y"8525M! !V"N"Ʀ"n"8532T! !XT65001,13 :65000:11 ,0;" DO NOT USE A CALCULATOR": !]""8541]! !^!5:0:="N"Ŧ="n" !_"Y"Ʀ"y"8541]! !a65001,22:65000:30:.1}L,35#:3,0;" 5X10 means 5X10X10=500";5,0;" This will be displayed as 5X10";4,31;2:8990# !b65001,20:65000:3,0;" Large numbers like 5000000";4,18;"(five million";5,0;"and small numbers like 0.000005";6,15;"(five millionths)";7,0;"are conveniently written as a product of a power of 10 and a number between 1 and 10.":8990#:11 ,2;"eg. 5000000=5X10";10 ,18;6;13 ,2;"and 0.000005=5X10";12 ,18;"-6":8990# !c15,0;" To write a number in STANDARD FORM put the decimal point after the first NON-ZERO digit.";19,2;"eg. 5.76 or 1.05":8990# !dp65001,22:65000:3,0;"eg.1 57600=":8990#:3,11 ;"57600":8990#:3,11 ;"5760.0X10":8990#:3,11 ;"576.0X100":8990#:3,11 ;"57.6X1000":8990#:3,11 ;"5.76X10000":8990#:3,21;"=5.76X10";2,29;"4":8990# !eJ5,0;" Notice, the decimal point moved4 places to the LEFT." !f48990#:8,0;"eg.2 0.00675=":8990#:8,13 ;"0.00675":8990#:8,13 ;"0.0675X0.1":8990#:8,13 ;"0.675X0.01":8990#:8,13 ;"6.75X0.001":8990#:8,23;"=6.75X10";7,30;"-3":8990# !gR10 ,0;" This time the decimal point moved 3 places to the RIGHT." !h8990#:14,0;"eg.3 2350=":8990#:14,11 ;"2350":8990#:14,11 ;"235.0X10":8990#:14,11 ;"23.5 X10";13 ,19;2:8990#:14,11 ;"2.35 X10";13 ,19;"3":8990# !i$16,0;"eg.4 0.0381=":8990#:16,12 ;"0.0381":8990#:16,12 ;"0.381 X10";15,20;"-1":8990#:16,20;" ";15,21;" ";16,12 ;"3.81 X10";15,19;"-2":8990#:8995## !j""8554j! !k+5:0:="Y"Ŧ="y"8545a! !l"N"Ʀ"n"8554j! !n !q""8561q! !r!5:0:="N"Ŧ="n" !s"Y"Ʀ"y"8561q! !u65001,22:65000:30:.1}L,35#:3,0;" There is not much difference between a bill of `12345.67 for a new car and `12345.70.":8990#:6,0;" The difference may be describedas NOT SIGNIFICANT.":8990# !v65001,19:65000:3,0;" For SIGNIFICANT FIGURES, start counting at the first NON-ZERO digit;":8990#:5,7;"after the required numberof figures, if the next digit isless than 5, ignore it;":8990# !w7,24;"if it is5 or more, round the previous digit up.":8990#:10 ,0;" So, to 3 significant figures (3sf); 12345=":8990#:11 ,14;"12345":100d:.1}L,35#:11 ,14;"1":502:.1}L,35#:11 ,15;"2":502:.1}L,35#:11 ,16;"3":502:j=130:11 ,17;" ":.05|L,10 :11 ,17;"4":j:11 ,17;"00":8990# !x12 ,0;"and 0.012345=":8990#:12 ,17;"0.012345":1:100d:.1}L,35#:12 ,20;1:502:.1}L,35#:12 ,21;2:502:.1}L,35#:12 ,22;3:502:0:j=130:12 ,23;" ":.05|L,10 :12 ,23;"4":j:20:12 ,23;" ":8990# !y65001,14:65000:10 ,0;"eg.1 to 3sf 3456=":8990#:10 ,18;"3456":502:10 ,18;"3":.1}L,35#:502:10 ,19;"4":.1}L,35#:502:10 ,20;"5":.1}L,35#:502:j=130:10 ,21;" ":.05|L,10 :10 ,21;6:j:20:10 ,18;"3460":8990# !zc11 ,0;"eg.2 to 2sf 3456=":8990#:11 ,18;"3456":502:11 ,18;"3":.1}L,35#:502:11 ,19;"4":.1}L,35#:502:j=130:11 ,20;" ":.05|L,10 :11 ,20;5:j:20:11 ,18;"3500":8990# !{*12 ,0;"eg.3 to 1sf 3456=":8990#:12 ,18;"3456":502:12 ,18;"3":.1}L,35#:502:j=130:12 ,19;" ":.05|L,10 :12 ,19;4:j:20:12 ,18;"3000":8990# !|13 ,0;"eg.4 to 3sf 0.07654=":8990#:13 ,21;"0.07654":502:13 ,24;"7":.1}L,35#:502:13 ,25;"6":.1}L,35#:502:13 ,26;"5":.1}L,35#:502:j=130:13 ,27;" ":.05|L,10 :13 ,27;4:j:20:13 ,21;"0.0765";13 ,27;" ":8990# !}14,0;"eg.5 to 2sf 0.07654=":8990#:14,21;"0.07654":502:14,24;"7":.1}L,35#:502:14,25;"6":.1}L,35#:502:j=130:14,26;" ":.05|L,10 :14,26;5:j:20:14,21;"0.077";14,26;" ":8990# !~U15,0;"eg.6 to 1sf 0.07654=":8990#:15,21;"0.07654":502:15,24;"7":.1}L,35#:502:j=130:15,25;" ":.05|L,10 :15,25;6:j:20:15,21;"0.08";15,25;" ":8990#:8995## !""8575! !+5:0:="Y"Ŧ="y"8565u! !"N"Ʀ"n"8575! !&65001,14:65000: !""8581! !!5:0:="N"Ŧ="n" !"Y"Ʀ"y"8581! !65001,22:65000:30:.1}L,35#:3,0;"(6X10 )X(9X10 )=";2,5;4;2,13 ;5:8990# !L3,16;"54X10 =54X10";2,21;"5+4";2,30;9 ;2,22;"+":8990#:4,0;"But, 54 is not between 1 and 10. So,":8990#:6,11 ;"=5.4X10 X10 =";"5.4X10";5,18;1;5,22;9 ;5,29;"10":8990# !0,119w:255,0:1;7,0;"Also,";0;9 ,0;"(2X10 )(5X10 )=0.4X10 =0.4X10";8,5;6;8,13 ;2;8,21;"6-2";8,31;4;8,22;"-":8990#:10 ,0;"But 0.4 is not between 1 and 10. So,":8990#:12 ,6;"=(4X10 )X10 =4X10 =";"4X10";11 ,11 ;"-1";11 ,17;4;11 ,22;"-1+4";11 ,31;"3":8990# !0,68D:255,0:14,0;"Whereas,";15,5;"(2X10 )X(3X10 )=";"6X10";14,10 ;3;14,18;5;14,25;"8":8990# !0,44,:255,0:17,0;"and,";18,5;"(3X10 )(2X10 )=";"1.5X10";17,10 ;2;17,18;5;17,26;"-3":8990# !65001,22:65000:3,0;"eg.1 (4X10 )X(9X10 )=36X10";2,10 ;3;2,18;7;2,26;10 ;5,20;"=3.6X10";4,27;11 :8990# !8,0;"eg.2 (9X10 )(4X10 )=2.25X10";7,10 ;3;7,18;7;7,27;"-4":8990# !11 ,0;"eg.3 (1.2X10 )(4X10 )=0.3X10";10 ,12 ;3;10 ,20;7;10 ,28;"-4";13 ,22;"=3X10";12 ,26;"-5":8990# !16,0;"eg.4 (3.5X10 )X(4X10 )=14X10";15,11 ;"-4";15,19;"-3";15,27;"-7";18,22;"=1.4X10";17,28;"-6":8990#:8995## !""8594! !+5:0:="Y"Ŧ="y"8585! !"N"Ʀ"n"8594! ! !""8601! !!5:0:="N"Ŧ="n" !"Y"Ʀ"y"8601! !65001,22:65000:30:.1}L,35#:2,0;"All numbers are referred to the decimal point.":8990#:4,0;" Start counting at the decimal point and examine the digit in the next position to see if it is 5 or more.":8990# !8,0;"eg.1 to 3dp 0.0163=":8990#:8,20;"0.0163":502:8,22;"0":.1}L,35#:502:8,23;"1":.1}L,35#:502:8,24;"6":.1}L,35#:502 !|j=130:8,25;" ":.05|L,10 :8,25;"3":j:8,25;" ":8990# !10 ,0;"But,";11 ,0;"eg.2 to 2dp 0.0163=":8990#:11 ,20;"0.0163":502::11 ,22;"0":.1}L,35#:502::11 ,23;"1":.1}L,35#:502 !j=130:11 ,24;" ":.05|L,10 :11 ,24;"6":j:11 ,23;"2";11 ,24;" ":8990# !13 ,0;"eg.3 to 1dp 0.0163=":8990#:13 ,20;"0.0163":502:13 ,22;"0":.1}L,35#:502 !j=130:13 ,23;" ":.05|L,10 :13 ,23;"1":j:13 ,23;" ":8990# !15,0;"eg.4 to 3dp 12.3456=":8990#:15,20;"12.3456":502:15,23;"3":.1}L,35#:502:15,24;"4":.1}L,35#:502::15,25;"5":.1}L,35#:502 !j=130:15,26;" ":.05|L,10 :15,26;"6":j:15,25;"6";15,26;" ":8990# !17,0;"eg.5 to 2dp 12.3456=":8990#:17,20;"12.3456":502:17,23;"3":.1}L,35#:502:17,24;"4":.1}L,35#:502 !j=130:17,25;" ":.05|L,10 :17,25;"5":j:17,24;"5";17,25;" ":8990# !19,0;"eg.6 to 1dp 12.3456=":8990#:19,20;"12.3456":502:19,23;"3":.1}L,35#:502 !j=130:19,24;" ":.05|L,10 :19,24;"4":j:19,23;"3";19,24;" ":8990#:8995## !""8618! !+5:0:="Y"Ŧ="y"8605! !"N"Ʀ"n"8618! ! #""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# #("MODULESA"2 #)#"mathcode1"65000,600X # #""9100# #21:0:i$=:i$="R"i$="r"900 #$i$="S"i$="s".5,20: # 9100# mathcode1 X:GBZ D!X6(#!Y6(#!Y6(#!Z6(#!Y60#!Y60#!Y60#!Y60#!Z60#!0Z60#!PZ60#!pZ60#!Z60#!Z60#!Z60#!Z60# P P P 88 MMbXaXL8Wq !v>pPp8A8y9BBB9PLB q #$RR| P pd<*]\"_\C*]\~}t[3*a\Þ*x\#"x MODULESB > > @ :1:1::"":20,31;:"MODULESB" B @ <Bf8B 8xB8x?B8 B<<8<<8D @!3!"! !3!"! !-!!! >>-!!! >>!!!! !<!!!! !B~<B| x<<!!"! !!@Bb888xB8<8hh8 D8xD8x88D8h88B8hxD88B8x8D88x88!!"! !!|@RD DDB DD TTD<@NJD DD| DD @BFD DD@ D< DTT@D"<DD<DxDDTD DBDTxD@ BDDDDDB@<B8 8D@ 8 12 .1}L,-5:2:.4L,-20:984 P.1}L,35#:17,27;8;1;7;q$:986 Hq$<7.1}L,-5:2:.4L,-20:984 qu=qu+1 r=0::.1}L,35#:6;0,10 ;"MATHEMATICS";2;7;0,0;"Module ";qu+6:6000p+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 .01z# =,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=qi196110+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: 013 ,0;"Percentages pp33,34, Ex 3b" (r<13 ''"Then the module again."  A13 ,0;" Simple Interest, Ex 3c, p36 Q 1-7": *13 ,0;" Exercise 5b, p47,": s13 ,0;"Inequalities p47."'"Remember that > becomes < if youmultiply or divide by a negativenumber.": M15,0;" Examples 5.6 and 5.7 on p48 andp49 then Exercise 5d.":  (15,0;" Exercise 6d, p59." 'r<4''"Then the module again."  q15,11 ,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5 r5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5 s17,4,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5 t 14,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5 u 12 ,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5 v5,2,3,4,5,.5,.5,.5,.5,.5,1,2,3,4,5,.5,.5,.5,.5,.5 K1,10 ;6;"PERCENTAGES":.1}L,35#:8521I!: 65001,22:65000:2,0;" In question a. the length was"'"stretched by 6%, so the new"'"length was 106% of old length.":8990#:5,0;" Similarly,in b. the length was"'"increased by 2%, so the new"'"length was 102% of old length.":8990#:65001,22:65000:3,0;"Finding the Original Price"'"If a price has been increased by"'"6%,the new price is 106%= of";6,25;"100"'"the old price.":8990# ]8,0;"So, the old price is of the";9 ,21;"106 new.":8990#:12 ,0;"If a price is reduced by 6%, the"'"new price is 94%=_ of the old.";14,17;"100":8990#:15,0;"So,the old price is  of the";16,21;"94 new.":8990#: N1,8;6;"SIMPLE INTEREST":.1}L,35#:8541]!: O1,7;6;"LINEAR EQUATIONS":.1}L,35#:8561q!: 65001,22:65000:.1}L,35#:2,0;" If there is a minus sign in front of a bracket, that minus sign applies to every term in the bracket,":8990# 6,0;"eg.1 if 3x-4(x+1)=5":8990#:7,10 ;"3x-4x-4 =5";6,12 ;"-";7,15;"-":8990# >9 ,0;"eg.2 if 2x-3(x-2)=5":8990#:10 ,10 ;"2x-3x+6 =5";9 ,12 ;"-";10 ,15;"+":8990#:12 ,0;" When you have removed any fractions and brackets,gather together like terms and solve the equation.":8990#: %R1,6;6;"LINEAR INEQUALITIES":.1}L,35#:8581!: 9y1,4;6;"SIMULTANEOUS EQUATIONS":.1}L,35#:8601!:65001,22:65000: MI1,11 ;6;"VARIATION":.1}L,35#:8621!: N 65001,19:65000:5,0;"b. Under some conditions,the distance,s metres,required to stop a car travelling at x metres per second is proportional to the square of the speed and is written:-";11 ,13 ;"s=***": O65001,19:65000:5,0;"c. The cost,`C,of carpeting a square room is proportional to the square of the length, x metres, of a side of the room and is written:-";11 ,13 ;"C=***": P/65001,19:65000:5,0;"d. The time,T years,in which a sum of money invested at simple interest doubles itself is inversely proportional to the rate per cent,x,at which the money is invested and is written:-";11 ,13 ;"T=***": Q65001,19:65000:5,0;"e. The height,h metres,of a balloonist is proportional to the square of the distance, x metres,of his horizon and is written:-";11 ,13 ;"h=***": W,11 ,15;"kx":8990#: X,11 ,15;"kx":8990#: Y,11 ,15;"kx":8990#: Z,11 ,15;"k/x":8990#: [,11 ,15;"kx":8990#: w1,"6","",2,17,5,"a. If a rod of","length 100cm is","stretched by 6%,","the extension","= cm.",2,2,"6%=__X100cm"," 100",1," =6cm." x1,"106","",6,19,7,"a. If a rod of","length 100cm is","stretched by 6%,","the extension","= 6cm."," New length"," = cm.",2,1,"New length=106%",2," =100+6"," =106cm." y1,"8","",2,17,5,"b. If a rod of","length 400cm is","stretched by 2%,","the extension","= cm.",2,2,"2%=__X400cm"," 100",1," =8cm." z1,"408","",6,19,7,"b. If a rod of","length 400cm is","stretched by 2%,","the extension","= 8cm."," New length"," = cm.",2,1,"New length=102%",2," =400+8"," =408cm." {1,"35","",2,17,5,"c. If a rod of","length 700cm is","stretched by 5%","the extension","= cm.",2,2,"5%=__X700cm"," 100",1," =35cm." |1,"735","",6,19,7,"c. If a rod of","length 700cm is","stretched by 5%,","the extension","= 35cm."," New length"," = cm.",2,1,"New length=105%",2," =700+35"," =735cm." }1,"36","",2,17,5,"d. If a rod of","length 900cm is","stretched by 4%,","the extension","= cm.",2,2,"4%=__X900cm"," 100",1," =36cm." ~1,"936","",6,19,7,"d. If a rod of","length 900cm is","stretched by 4%,","the extension","= 36cm."," New length"," = cm.",2,1,"New length=104%",2," =900+36"," =936cm." 1,"84","",2,17,5,"e. If a rod of","length 1200cm is","stretched by 7%,","the extension","= cm.",2,2,"7%=__X1200cm"," 100",1," =84cm." 1,"1284","",6,19,7,"e. If a rod of","length 1200cm is","stretched by 7%,","the extension","= 84cm."," New length"," = cm.",2,1,"New length=107%",2," =1200+84"," =1284cm." 1,"108","",12 ,18,7,"f. After an 8%","increase,the new","price= of the"," 100 old.","Old price = ","","of the new.",1,1,"108" 1,"126","",12 ,18,7,"g. After a 26%","increase,the new","price= of the"," 100 old.","Old price = ","","of the new.",1,1,"126" 1,"90","",12 ,18,7,"h. After a 10%","reduction, new","price=_ of the"," 100 old.","Old price = ","","of the new.",1,1," 90" 1,"75","",12 ,18,7,"i. After a 25%","reduction, new","price=_ of the"," 100 old.","Old price = ","","of the new.",1,1," 75" 1,"225","",12 ,18,7,"j. After a 125%","increase,the new","price= of the"," 100 old.","Old price = ","","of the new.",1,1,"225" 1,"60","",2,16,4,"a. The interest","on `300 at 10%","for 2 years.","=`",2,2,"I=`XX"," 100",1," =`60 interest" 1,"30","",2,16,4,"b. The interest","on `200 at 3%","for 5 years.","=`",2,2,"I=`XX"," 100",1," =`30 interest" 1,"1200","",2,16,4,"c. The interest","on `2000 at 20%","for 3 years.","=`",2,2,"I=`XX"," 100",1," =`1200 interest" 1,"1400","",2,16,4,"d. The interest","on `8000 at 5%","for 3.5 years.","=`",2,2,"I=`XX"," 100",1," =`1400 interest" 1,"150","",2,16,4,"e. The interest","on `250 at 10%","for 6 years.","=`",2,2,"I=`XX"," 100",1," =`150 interest" 0,"12","",9 ,16,4,"a. -=1"," 3 4"," Multiply both","sides by",1,2,"lcm of 3 and 4"," =12" 0,"20","",9 ,16,4,"b. +="," 5 4 2"," Multiply both","sides by",1,2,"lcm of 2,4 and 5"," =20" 0,"15","",9 ,16,4,"c. -=0"," 3 5"," Multiply both","sides by",1,2,"lcm of 3 and 5"," =15" 0,"6","",9 ,17,5,"d. Solve for x:-"," -=1"," 2 3"," Multiply both","sides by",1,2,"lcm of 2 and 3"," =6" 0,"1","",1,19,7,"d. Solve for x:-"," -=1"," 2 3"," Multiply both","sides by 6 and","simplify."," x=",3,4,"Multiply both","sides by 6:-"," 6-6=6"," 2 3",2,"Simplify:-"," 3x-2x=6",1," 1x= (1x=x)" k1,"6","",5,16,4,"d. Solve for x:-"," -=1"," 2 3"," x=",1,1," x=6" 0,"30","",9 ,17,5,"e. Solve for x:-"," -="," 2 3 5"," Multiply both","sides by",1,2,"lcm of 2,3 and 5"," =30" 0,"9","",1,19,7,"e. Solve for x:-"," -="," 2 3 5"," Multiply both","sides by 30 and","simplify."," x=",3,4,"Multiply both","sides by 30:-"," 30-=30"," 2 3 5",3,"Simplify:-"," 15x-10=6x"," 15x-6x=10",1," 9x=" p0,"10","",5,16,4,"e. Solve for x:-"," -="," 2 3 5"," 9x=",1,1," 9x=10" 1,"1.11","",5,17,6,"e. Solve for x:-"," -="," 2 3 5"," 9x=10"," x="," (to 3 sf)",1,2," x=10/9"," =1.11 (to 3 sf)" 0,"3x+9-2x+8=7","",0,16,7,"f. Solve for x:-","3(x+3)-2(x-4)=7","Remove brackets:-","","Enter next line","exactly - no"," spaces.",1,1,"3x+9-2x+8=7" 1,"-10","",4,16,4,"f. Solve for x:-","3(x+3)-2(x-4)=7","3x+9-2x+8=7"," x=",2,1,"3x-2x=7-9-8",1," x=-10" 0,"5x+5-6+3x=7","",0,16,7,"g. Solve for x:-","5(x+1)-3(2-x)=7","Remove brackets:-","","Enter next line","exactly - no"," spaces.",1,1,"5x+5-6+3x=7" 1,"1","",4,16,4,"g. Solve for x:-","5(x+1)-3(2-x)=7","5x+5-6+3x=7"," x=",2,1,"5x+3x=7-5+6",2," 8x=8"," x=1" 1,"12","",9 ,17,5,"h. Solve for x:-","-=2"," 4 3","Multiply both","sides by",1,2,"lcm of 3 and 4","=12" ¸0,"15-3x-4x-12=24","",0,17,7,"h. Solve for x:-","-=2"," 4 3","3(5-x)-4(x+3)=24","","Enter next line -"," (no spaces)",1,1,"15-3x-4x-12=24" 1,"-3","",4,18,6,"h. Solve for x:-","-=2"," 4 3","3(5-x)-4(x+3)=24","15-3x-4x-12=24"," x=",3,1,"-3x-4x=24-15+12",1," -7x=21",1," x=-3" {0,">3","",5,14,4,"a. 4x>12"," x","Enter the answer"," (no spaces)",1,1," x>3" }0,"<-2","",5,14,4,"b. 3x<-6"," x","Enter the answer"," (no spaces)",1,1," x<-2" ӂ0,"<-3","",6,14,4,"c. -3x>9"," x","Enter the answer"," (no spaces)",1,1," x<-3" [0,">4","",6,14,2,"d. -2x<-8"," x",1,1," x>4" Y0,">6","",4,15,3,"e. >3"," 2"," x",1,1," x>6" b0,">-6","",5,15,3,"f. -<2"," 3"," x",1,1," x>-6" Y0,">8","",7,14,2,"g. 4x-3>5"," 4x",1,1," 4x>8" f0,">2","",7,15,3,"g. 4x-3>5"," 4x>8"," x>2",1,1," x>2" Z0,"<4","",7,14,2,"h. 3-4x<7"," -4x",1,1," -4x<4" j0,">-1","",7,15,3,"h. 3-4x<7"," -4x<4"," x",1,1," x>-1" Z0,">6","",7,14,2,"i. 2-3x>8"," -3x",1,1," -3x>6" j0,"<-2","",7,15,3,"i. 2-3x>8"," -3x>6"," x",1,1," x<-2" \0,"<-6","",7,14,2,"j. 8-3x<2"," -3x",1,1," -3x<-6" i0,">2","",7,15,3,"j. 8-3x<2"," -3x<-6"," x",1,1," x>2" 1,"1","",6,18,6,"a. Eliminate y","between these","equations:-","5x+ y=4 (1)","3x+2y=1 (2)"," x=",2,2,"10x+2y=8 (1)X2"," 3x+2y=1 (2)",2," 7x =7 (1)-(2)"," x=1" 1,"-1","",3,19,7,"a. 5x+ y=4 (1)"," 3x+2y=1 (2)"," x=1","Substitute x in","(1) and solve","for y."," y= (check)",1,2," 5+ y=4 (1)"," y=-1" 1,"3","",6,18,6,"b. Eliminate y","between these","equations:-","3x-4y=1 (1)","5x+ y=17 (2)"," x=",2,2," 3x-4y=1 (1)","20x+4y=68(2)X4",2,"23x =69(1)+(2)"," x=3" 1,"2","",3,19,7,"b. 3x-4y=1 (1)"," 5x+ y=17 (2)"," x=3","Substitute x in","(1) and solve","for y."," y= (check)",1,2," 9-4y=1 (1)"," y=2" 1,"-1","",6,18,6,"c. Eliminate y","between these","equations:-","5x+3y=1 (1)","7x-2y=-11 (2)"," x=",2,2,"10x+6y=2 (1)X2","21x-6y=-33 (2)X3",2,"31x =-31 (1)+(2)"," x=-1" 1,"2","",3,19,7,"c. 5x+3y=1 (1)"," 7x-2y=-11 (2)"," x=-1","Substitute x in","(1) and solve","for y."," y= (check)",1,2," -5+3y=1 (1)"," y=2" 1,"1","",6,18,6,"d. Eliminate x","between these","equations:-"," x+5y=8 (1)","3x-2y=7 (2)"," y=",2,2," 3x+15y=24 (1)X3"," 3x -2y=7 (2)",2," 17y=17 (1)-(2)"," y=1" 1,"3","",3,19,7,"d. x+5y=8 (1)"," 3x-2y=7 (2)"," y=1","Substitute y in","(1) and solve","for x."," x= (check)",1,2," x+ 5=8 (1)"," x=3" 1,"-2","",6,18,6,"e. Eliminate x","between these","equations:-","3x-5y=25 (1)","4x+7y=6 (2)"," y=",2,2,"12x-20y=100(1)X4","12x+21y= 18(2)X3",2," -41y=82 (1)-(2)"," y=-2" 1,"5","",3,19,7,"e. 3x-5y=25 (1)"," 4x+7y=6 (2)"," y=-2","Substitute y in","(1) and solve","for x."," x= (check)",1,2," 3x+10=25 (1)"," x=5" 1,"1","",6,18,6,"f. Eliminate x","between these","equations:-","4y-3x=7 (1)","5y+2x=3 (2)"," y=",2,2," 8y-6x=14 (1)X2","15y+6x=9 (2)X3",2,"23y =23(1)+(2)"," y=1" 1,"-1","",3,19,7,"f. 4y-3x=7 (1)"," 5x+2y=3 (2)"," y=1","Substitute y in","(1) and solve","for x."," x= (check)",1,2," 4-3x=7 (1)"," x=-1"  p0,"3","",11 ,14,2,"a.","Enter 1-5.",2,1,"Note:cube",1,"3 V=kx" r0,"2","",11 ,14,2,"b.","Enter 1-5.",2,1,"Note:square",1,"2 s=kx" r0,"2","",11 ,14,2,"c.","Enter 1-5.",2,1,"Note:square",1,"2 C=kx" p0,"4","",11 ,14,2,"d.","Enter 1-5.",2,1,"inversely",1,"4 T=k/x" r0,"2","",11 ,14,2,"e.","Enter 1-5.",2,1,"Note:square",1,"2 h=kx" !I""8521I! !J!5:0:="N"Ŧ="n" !K"Y"Ʀ"y"8521I! !M$65001,22:65000 !Nr30:.1}L,35#:2,0;" Percentages are fractions"'"'out of one hundred'.":8990#:4,0;" So:- 10% of `50=_X`50=`5";5,17;"100":8990#:6,6;"20% of `50=_X`50=`10";7,17;"100":8990#:8,6;"35% of `50=_X`50=`17.50";9 ,17;"100":8990# !O10 ,0;" If the price of an item was `20and is increased by 6%,"'"the increase is __X`20=`1.20";13 ,16;"100":8990#:14,0;" So,new price=`20+`1.20=`21.20"''"or, new price=X`20 =`21.20";17,14;"100":8990# !PJ65001,22:65000:4,156:126~,0:0,-72H:-126~,0:0,71G:125},0:0,-70F:-124|,0:0,70F:1;3,6;"SALE"'" Price Reduction"''" 6% off!!!"''" Radio-was `20"''" Now  ":8990# !Q5,17;"New price=94%";6,17;"=_X`20=";7,18;"100":8990#:6,26;"`18.80";10 ,9 ;"`18.80":8990#:10 ,9 ;"`18.80" !R :8995## !S""8531S! !T+5:0:="Y"Ŧ="y"8524L! !U"N"Ʀ"n"8531S! !\ !]""8541]! !^!5:0:="N"Ŧ="n" !_"Y"Ʀ"y"8541]! !a.1}L,35#:65001,22:65000:2,0;"If a sum of money,the principal,say `P,is lent at R% interest a year (per annum,pa.),"'"` PR = the interest for 1 year 100":8,128:24,0:8990# !b7,0;"`PRx2 = the interest for 2 years 100":8,112p:32 ,0:8990#:9 ,0;"`PRx3 = the interest for 3 years 100":8,96`:32 ,0:8990# !cx11 ,0;"and"'"`PRT = the interest for T years 100":8,72H:24,0:8990# !d.14,0;" This is SIMPLE INTEREST, in which we pay interest when it isdue.":8990#:65001,22:65000:2,0;" For example,suppose that we areborrowing money to buy a car.";5,0;"The price of the car";6,12 ;"is `3000"' !fx184,124|:47/,0:0,4:-8,12 :-18,0:-8,-8:-5,0:-8,-3,/8:0,-5:188,124|:7,0,:222,124|:7,0,:198,132:31,0:212,140:1,-16:200,124|:-2,8 !h=7,0;"and we need to borrow"'"all that at 18% pa. for 2 years.":8990#:9 ,0;" We shall have to pay"'" `PRT=`3000X18X2";11 ,6;"100";11 ,14;"100";12 ,9 ;"=`1080 interest":480,88X:24,0:88X,88X:72H,0 !i502:224,91[,10 :228,94^:228,93]:220,94^:220,93]:224,94^:-1,-4:2,0:220,86V:8,0,-/1.5@:8990# !js13 ,0;" But,if we have saved `1800,so that we only need to borrow `1200 and if we can find someoneto lend at 8% pa. for 2 years,weshall only have to pay:-";18,5;"`PRT=`1200X8X2";19,6;"100";19,13 ;"100";20,9 ;"=`192 interest":480,24:24,0:88X,24:64@,0 !k502:224,25,10 :228,28:229,28:220,28:219,28:224,28:-1,-4:2,0:220,22:8,0,/1.3&fff:8990#:65001,11 :65000:8995## !l""8556l! !m+5:0:="Y"Ŧ="y"8545a! !n"N"Ʀ"n"8556l! !o !q""8561q! !r!5:0:="N"Ŧ="n" !s"Y"Ʀ"y"8561q! !u.1}L,35#:65001,22:65000:2,0;" If there are fractions in a linear equation, multiply both sides of the equation by the lcmof the denominators of these fractions.":8990# !v7,0;"eg.1";8,4;"If +=1";9 ,8;"2";9 ,11 ;"3":8990#:9 ,8;"2";9 ,11 ;"3";9 ,18;"multiply by 6,";10 ,18;"lcm of 2 and 3":8990# !wO12 ,0;"eg.2";13 ,4;"if +=";14,8;"2";14,11 ;"3";14,15;"5":8990#:14,8;"2";14,11 ;"3";14,15;"5";14,17;"multiply by 30,";15,16;"lcm of 2,3 and 5":8990#:8995## !""8576! !+5:0:="Y"Ŧ="y"8565u! !"N"Ʀ"n"8576! ! !""8581! !!5:0:="N"Ŧ="n" !"Y"Ʀ"y"8581! !65001,22:65000:.1}L,35#:2,0;"If x>3, then 2x>6";3,14;"3x>9";4,14;"5x>15, etc,";5,0;"whatever POSITIVE multiplier we use.":8990# !8,0;" But, when we multiply by a NEGATIVE number,"'"if x>3, then -2x<-6";11 ,14;"-3x<-9";12 ,14;"-5x<-15, etc.":8990# !14,0;" So,";14,16;"4>3":8990#:15,0;"Multiply by 5,say";16,14;"5X4>5X3";17,15;"20>15":8990# !65001,9 :65000:14,0;" But,";14,16;"4>3":8990#:15,0;"Multiply by -5,say";16,13 ;"-5X4<-5X3";17,14;"-20<-15":8990# !65001,22:65000:2,0;" To solve inequalities, we may need to divide both sides by a positive or a negative number.":8990#:6,0;"eg.1";6,21;"2x>6":8990#:7,3;"divide by 2,then, x>3":8990# !9 ,0;"eg.2 But,";9 ,20;"-3x>6":8990#:10 ,3;"divide by -3,then, x<-2":8990#:;12 ,0;"eg.3";12 ,21;"5x>20":8990#:13 ,3;"divide by 5,then, x>4":8990# !15,0;"eg.4 But,";15,20;"-5x>30":8990#:16,3;"divide by -5,then, x<-6":8990#:8995## !""8592! !+5:0:="Y"Ŧ="y"8585! !"N"Ʀ"n"8594! ! !""8601! !!5:0:="N"Ŧ="n" !"Y"Ʀ"y"8601! !K.1}L,35#:65001,22:65000:2,0;" To solve these simultaneous equations,";4,11 ;"3x+y=4";5,11 ;"2x-y=6"'"we add the two equations so thatthe terms in y vanish,":8990#:8,11 ;"5x =10":8990#:9 ,14;"x=2":8990# !/10 ,0;" We then substitute x=2 into thefirst equation,";12 ,11 ;"3x+y=4":8990#:j=115:12 ,11 ;"3x":.05|L,10 :5:12 ,11 ;" 6":.05|L,10 :5:j:8990#:13 ,14;"y=-2":8990# !14,0;"and finally,check by substituting into the second equation,";17,11 ;"2x-y=2X2-(-2)=6":8990#:18,0;"so that we know x=2 and y=-2 arethe solutions of the equations.":8990# !65001,22:65000:2,0;" If we do not have terms with the same coefficients, we make them the same by multiplying oneor both equations by suitable numbers,";7,11 ;"4x-3y=2 (1)";8,11 ;"2x+ y=1 (2)":8990# !9 ,0;"we could multiply (2) by 3 and then add to (1),":8990#:11 ,11 ;"6x+3y=3 (2)X3":8990#:12 ,0;"adding, 4x-3y=2"'"we have 10x =5";14,15;"x=0.5":8990# !65001,15:65000:9 ,0;"we could have multiplied (2) by 2 and then subtracted,":8990#:11 ,11 ;"4x+2y=2 (2)X2":8990#:12 ,0;"subtracting,";13 ,11 ;"4x-3y=2 (1)"'"we have 5y=0";15,15;"y=0":8990#:17,0;" Having found one unknown, we usually find the other one bysubstitution.":8990#:8995## !""8611! !+5:0:="Y"Ŧ="y"8605! !"N"Ʀ"n"8611! ! !""8621! !-5:0:="N"Ŧ="n"8645!: !"Y"Ʀ"y"8621! !.1}L,35#:65001,22:65000:3,0;" Walking at a"'"CONSTANT speed,"'"our distance,"'"s km is propor-"'"tional to the"'"time, t,"'" s=kt,"'"the constant"'"of proportion,"'"k, being our"'"speed." !8700!:8990#:132,28:120x,72H:133,28:119w,71G:12 ,28;"s=3t" !z8990#:132,28:120x,96`:133,28:119w,95_:8,28;"s=4t" !|8990#:132,28:120x,120x:133,28:119w,119w:4,26;"s=5t" !8990#:65001,22:65000:3,0;" If we have a"'"fixed distance,"'"s km,to walk,"'"the faster we"'"walk the sooner"'"we shall reach"'"our"'"destination."'"The time,t hours"'"is INVERSELY"'"proportional"'"to the speed,"'"v kmh."'" t=s/v" !8710":8990#:139,152:13 ,-84T,/10 :20,-20,/6:20,-10 ,/8:60<,-3,/12 :16,24;"t=2/v" !138,152:13 ,-84T,/10 :20,-20,/6:20,-10 ,/8:60<,-4,/10 :8990# !152,148:20,-60<,/8:20,-20,/6:60<,-20,/8:12 ,21;"t";13 ,22;"=";14,22;"6/v" !{153,148:20,-60<,/8:20,-20,/6:60<,-20,/8:8990# !165,152:7,-24,/10 :40(,-502,/4:20,-10 ,/10 :20,-7,/10 :6,22;"t=10/v" !164,152:7,-24,/10 :40(,-502,/4:20,-10 ,/10 :20,-7,/10 :8990# !65001,22:65000:3,0;" The surface"'"AREA,A, of a"'"spherical ball"'"is proportional"'"to the"'"SQUARE of the"'"diameter,d,"'" A=kd,"'"the VOLUME,V,"'"is proportional"'"to the CUBE of"'"the diameter,"'" V=kd":8720":8990# !132,28:40(,16,/5:40(,480,/6:10 ,27;"y=";11 ,29;"2":133,28:40(,16,/6:40(,480,/6:8990# !132,28:40(,32 ,/6:40(,96`,/6:6,26;"y=x":133,28:40(,32 ,/6:40(,96`,/6:8990# !132,28:40(,64@,/12 :16,64@,/12 :2,18;"y=2x":133,28:40(,64@,/12 :16,64@,/12 :8990#:8995## !""8644! !+5:0:="Y"Ŧ="y"8625! !"N"Ʀ"n"8644! !ɭ65001,22:65000:2,0;" To answer the questions, enter,1 for kx 2 for kx 3 for kx 4 for k/x 5 for k/x":8990# !5,0;"a. The volumes,V cubic metres,ofliquid in glasses of similar shape are proportional to the cubes of the heights,x metres, of the glasses and are written:-";11 ,13 ;"V=***": !128,26:124|,0:130,24:0,135:i=281568:132,i:120x,0:i:i=1322538: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";18,15;"0";13 ,15;"5";8,14;"10";3,14;"15";0;20,18;"Time t (hours)";2,13 ;"Distance(km)";5,15;"s" " "128,26:124|,0:130,24:0,135:i=2815610 :132,i:120x,0:i:i=13225310 :i,28:0,131:i "i=2714720:128,i:124|,0:i:i=13125120:i,24:0,135:i "1;19,18;"1";19,21;"2";19,24;"3";19,26;"4";19,29;"5";19,31;"6";18,15;"0";16,15;"1";13 ,15;"2";10 ,15;"3";8,15;"4";5,15;"5";3,15;"6";0;20,19;"Speed(v kmh)";2,14;"Time(t hours)": "128,26:124|,0:130,24:0,135:i=281568:132,i:120x,0:i:i=1322538:i,28:0,131:i "i=2715716:128,i:124|,0:i:i=13125140(:i,24:0,135:i "1;19,21;"1";19,26;"2";19,31;"3";19,15;"0";14,15;"1";10 ,15;"2";6,15;"3";2,15;"4";0;2,14;"y";20,29;"d": #""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. ": #'o:7,0;" To use Module again, press R Press S to STOP. ":9100# #("MODULESB"2 #)#"mathcode2"65000,600X # #""9100# #*5:0:="R"Ŧ="r"900 #"="S"Ŧ="s".5,20: # 9100# 5mathcode2 X% Z 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