directions& (8x=7:y=6:z=0:y:y:z::1200 g64999:x=7:y=6:z=0:y:y:z::5,3;"Please leave tape running" "UDG"65000,536 G:f$=" STOP THE TAPE ":v=12 :m=8:f=980:910 !2,0;"":1000  500 ( 5 B21,0;" ";x;" Press any key to continue ";y;" " ""510 =""520   i$ *k$="":f=i$ 4f=0800  > n=1f Hi$(n)=32 860\ R k$=k$+i$(n) \n f  f=990  v,m;""; 23729\,v n=1̱f$ f 23728\,m:65000 m=m+1:n  1;f$(n);: %1;5;1;f$(n);: 2;f$(n);: 3;6;f$(n);: -2;"MATHEMATICS EXAMINATION PRACTICE"  11 ;2;"AND TESTS"  +v=4:m=10 :f$=" MATHEMATICS "  f=985  910 R8,6;2;"EXAMINATION PRACTICE";6;"" ?11 ,11 ;2;"AND TESTS";11 ;"" @18,8;"SPHERE SOFTWARE";8;"" 82,3;3;"" n=313 2n,3;3;"";n,28;3;""  <n:14,3;3;""  500  (#f$="  CELTIC REVISION SOFTWARE " 2v=3:m=2 < 900 F?:::"Text by E.J. Perkins,B.Sc.(Hons)M.Ed.(Wales),F.B.I.M." P7:"Programme by M.G. Fincher, B.Sc (Hons) Elec. Eng." Zp15,2;"A Software product from the"::9 ;"Publishers of"::6;"CELTIC REVISION AIDS" d 500: xBf$="INSTRUCTIONS":v=0:m=10 :f=995:910 ::"The mathematics revision and test tape is arranged as eightseparately loadable programmes.The first of these programmes (which you are running now) gives all the details relevantto the tape." :"On side one of the tapethe programmes ""directions"" , ""section 1"" , ""section 2"" , ""section 3"" and ""section 4"" are recorded." V:"Side two contains ""section 5"",""section 6"", ""section 7"" and ""tests""."  500: -;3;6;"INSTRUCTIONS CONTINUED" r:"Each programme can be loaded independently in the normal wayby loading the programme names given above." :"Additionally at the end of each programme, the next programme on the index can be loaded automatically if required." z:"An index of the programmes is given on the next display page. Operating instructions follow the programme index."  500: *2;" Programme Index and Content" 9:"Section 1-Fractions, Standard Form, Number Bases." F:"Section 2-Simple Interest,Rates Percentages,Cost & Selling Price" @:"Section 3-Averages, Speed, Ratioand Proportion, Variation." %:"Section 4-Factorisation,LCM,HCF" :"Section 5-Equations" :"Section 6-Graphs" "*:"Section 7-Geometry,Trigonometry,Sets" ,#:"Tests -20 sample questions" 6 500: @M. G. Fincher T 1000 h rx;"OPERATING INSTRUCTIONS": |"Each question contains five possible answers. To select the correct answer press a,b,c,d or e(as appropriate) then ENTER." ?"Errors can be erased by pressingDELETE (caps shift and 0)": "Following the selection of the correct answer you can move to the next question by pressing SPACE, or run the sample answer by pressing ENTER." T:"If the selected answer is wrong the sample answer is displayedautomatically."  500: )x;"OPERATING INSTRUCTIONS CONTINUED": r"After a sample answer display press SPACE for the next question or ENTER to rerun the same question." ̚:"At the end of each programme press ""n"" to load the next programme, press ""r"" to rerun the same programme or press ""b"" to goto BASIC." ֹ:"At all points in the programmes where a user response is needed you will be prompted with the appropriate options. Therefore it is NOT necessary to memorise these instructions."  500 #:h$,l$:"directions","section 1"  9f$="End of "+h$:v=3:m=((32 -f$)/2) & 900 0U10 ,0;x;"Press n then ENTER";y;" to auto-load programme ";2;l$ ::::x;"Press r then ENTER";y;" to rerun thisprogramme" D1::x;"Press b then ENTER";y;" to goto BASIC" N 800  X"k$="n"k$="r"k$="b"2000 b721,0;x;"Undefined key please re-select" l 1870N k$="n"21004 k$="r"5 L:5,2;"RETURNING TO BASIC DESTROYS";8;"THIS PROGRAMME" E::x;"Press y to return to BASIC"''"Press any other key to abort" 0:i$= i$="y"i$="Y"  1800 4/:f$=" START THE TAPE ":v=5:m=8 > 900 H::l$ xyzF STOP THE TAPE v mfUDG ݀'K\y 8x8͞ x<͞  ~%~%|Xg~ wP P 03nMN=MK0 !v>!{\6X#6V+^!w#~!VUw+!~#~+w#w$$$$$<<8$((|< 8$$$,2" P P 88 MGG\GWq !v> ~ (X~H~0H xB$$Bx0H00P@  @@  @|BB|@@|BB|DB0H x~BBBBB<section 1 > q>>8x=7:y=6:z=0:y:y:z::1400x g64999:x=7:y=6:z=0:y:y:z::5,3;"Please leave tape running" "UDG"65000,536 Q:70F:f$=" STOP THE TAPE ":v=10 :m=8:f=980:910  500 ( 5 FE2;"MATHEMATICS EXAMINATION PRACTICE";11 ;"AND TESTS": d n%2;"Q";q;0,12 ;h$  ques n=65195 n=1230  a;"a ";a$ b;"b ";b$ c;"c ";c$ d;"d ";d$ e;"e ";e$  a=y b=y c=y d=y "e=y ' ,""300, 6=""3106 @=32 J?21,0;x;"Undefined key?";y;" please try again " T 300, ^""350^ h=""360h r=32 Ŧ=13 | 350^  q=q+1 ques,a$,b$,c$,d$,e$,w$,s  B21,0;" ";x;" Press any key to continue ";y;" " ""510 =""520  &!a=0:b=0:c=0 0d=0:e=0 : X618,0;" " b619,0;" " l n=0100d:n   600X 18,0;2;f$  )n=65196:n=165136p  )n=65196:n=065136p    i$ *k$="":f=i$ 4f=0800  > n=1f Hi$(n)=32 860\ R k$=k$+i$(n) \n f  f=990  v,m;""; 23729\,v n=1̱f$ f 23728\,m:65000 m=m+1:n  1;f$(n);: %1;5;1;f$(n);: 2;f$(n);: 5;f$(n);:  250  100d ?21,0;x;"Please select your answer";y;" "  800  ~0k$="a"k$="b"k$="c"k$="d"k$="e"1180 ?21,0;x;"Undefined Key ?";y;" Please try again"  1050 k$w$1280 w$="a"a=5 w$="b"b=5 w$="c"c=5 w$="d"d=5 w$="e"e=5  100d =f$="CORRECT":f=995:v=0:m=25:910 B20,0;"Use ";x;"ENTER";y;" for answer explanation" B21,0;"Use ";x;"SPACE";y;" for the next question "  350^ =13 1300 =32 C20,0;x;"Wrong-Correct answer is ";w$;" ";:" "  I21,0;x;"Answer explanation follows";:" ":350^  s (B20,0;"Use ";x;"ENTER";y;" to rerun this question" 2B21,0;"Use ";x;"SPACE";y;" for the next question " Z=32 d=13 1000 n 1320( x:q=0::250  h$,l$,qty  70F :f$=h$:v=3:m=((32 -f$)/2):900 -:::7;2;"Programme Content"  2010 !f$=" CELTIC REVISION SOFTWARE" v=18:m=3  900  500: k=1qty  750:65195,0  400  1000 k  9f$="End of "+h$:v=3:m=((32 -f$)/2) " 900 ,U10 ,0;x;"Press n then ENTER";y;" to auto-load programme ";2;l$ 6:::x;"Press r then ENTER";y;" to rerun thisprogramme" @M. G. Fincher E1::x;"Press b then ENTER";y;" to goto BASIC" J 800  T"k$="n"k$="r"k$="b"1700 ^721,0;x;"Undefined key please re-select" h 1610J k$="n"1800 k$="r"5 L:5,2;"RETURNING TO BASIC DESTROYS";8;"THIS PROGRAMME" E::x;"Press y to return to BASIC"''"Press any other key to abort" 0:i$= i$="y"i$="Y"  1550 /:f$=" START THE TAPE ":v=5:m=8  900 ::l$ !"Section 1","section 2",8 T:10 ,8;"Fractions";8;"Standard Form";8;"Number Bases": (65195,1:"When simplified" :" 1 1 3" " 4 - 2 1" " 2 4 4"  "gives" :" 2",b;" 3 " "a) 1",b;"b) 3" " 7",b;" 14" &:," 5","c) 1","d) 3",," 14" :" 1"'"e) 2"'" 4"    *2020,"","","","","","b",2090*  9 ,0;a;"Brackets" !10 ,0;b;"Multiply" 11 ,0;c;"Divide" 12 ,0;d;"Add" !13 ,0;e;"Subtract"   "12 ,15;"1 1 3" "#13 ,14;"4 - 2 1" %"14,15;"2 4 4" ' *"In this example the division must be worked out first. It ismade easier by putting bracketsaround the part to be worked outfirst. The whole sum must be kept together.": 4 "The order of working out is:" >550&:2070 H 2080  RP500:a=2:2070:2;18,0;"Insert Brackets" \a;12 ,18;"";12 ,26;"";13 ,18;"";13 ,26;"";14,18;"";14,26;"" f"500:550&:2070 p 600X za;12 ,18;"";12 ,26;"";13 ,18;"";13 ,26;"";14,18;"";14,26;"" Ib=2:2070:18,0;2;"Nothing to multiply" "500:550&:2070 c=2:2070 -c;18,0;"Simplify the bracket" "2;"Form vulgar fractions"  500 w12 ,20;"9";12 ,24;"7 ";13 ,19;" ";13 ,24;" ";14,24;"4 " N600X:2;18,0;"Convert bracket into multiply form"  500 F12 ,24;"4";14,24;"7";13 ,22;"" 0600X:18,0;2;"Cancel" h500:12 ,24;"";14,20;"";11 ,25;"1";15,19;"1" E600X:18,0;2;"Simplify and remove bracket" 500:11 ,25;" ";15,19;" ";12 ,18;" 2 ";13 ,18;" 1 ";14,18;" 7 " Z550&:d=2:2070:600X:18,0;2;"Nothing to add" m500:550&:e=2:2070:600X:18,0;2;"Form intermediate step" $b500:12 ,15;" 7-4 ";13 ,14;"3 ";14,15;" 14 " .I600X:18,0;2;"Therefore answer is:":500 8.550&:600X:2070:2080  BL16,16;"3";17,12 ;"= 3 ";18,16;"14" L `(65195,1:"When simplified" j" 2 1 1" t" 1 4 - 2" ~" 5 4 2" " " " 2 1 1 1" " 1 1 + 3 1" " 3 5 2 4" "gives": 0" 6 ";b;" 1";y;" 49" 0"a) ";b;"b) ";y;" c) " 0" 47 ";b;" 6";y;" 96" D:" 7 2","d) e) "," 36 11"  *2400` ,"","","","","","b",2520 ,600X:18,0;2;f$: $7,7;" 2 1 1" $8,7;" 1 4 - 2" $9 ,7;" 5 4 2" %10 ,7;" " '11 ,6;" 2 1 1 1" '12 ,6;"1 1 + 3 1" '13 ,6;" 3 5 2 4"  ֖"Numerator and denominator are simplified in successive steps. In the denominator it is clearerif brackets are added as part ofthe working out.": 2518 +2510 :f$="Add brackets":2505 500 )11 ,5;" 2 1 1 1" )12 ,5;"1 1+3 1" )13 ,5;" 3 5 2 4" Jf$="Form vulgar fractions in the denominator.":2505 :500 *11 ,5;" 5 6 7 5 " (*12 ,5;" + " -*13 ,5;" 3 5 2 4 " 2]f$="Simplify numerator bracket, formmultiply bracket in denominator":2505 :500 <7,14;" 1-2 " F8,14;" 2 " P9 ,14;" 4 " ZF12 ,20;"";11 ,22;"4";13 ,22;"5" dSf$="Simplify numerator Cancel in denominator":2505 :500 ne7,9 ;" 2 3 ";8,8;" 1 1 ";9 ,9 ;" 5 4 " x10 ,7;"1";11 ,8;"";13 ,12 ;"";14,13 ;"1";13 ,18;"";14,17;"1";11 ,22;"";10 ,23;"2" ]f$="Form vulgar fractions in the numerator, simplify denominator":2505 :500 E10 ,7;" ";14,11 ;" " y11 ,6;" 4 ";12 ,6;" 2 + 2 ";13 ,6;" 5 " O7,13 ;"7 7 ";8,12 ;" ";9 ,17;"4 " \f$="Form multiply and cancel in numerator,simplify denominator":2505 :500 t6,12 ;"1";7,13 ;" 4";8,15;"";9 ,17;"";10 ,18;"1" Q11 ,15;"4 ";12 ,13 ;" 4 ";13 ,15;"5 " 0f$="Simplify numerator":2505 :500 6,12 ;" ";7,13 ;" 4 ";8,12 ;" ";9 ,13 ;" 5 ";10 ,18;" " Kf$="Make vulgar fractions in multiply form":2505 :500 a:2518 :9 ,13 ;"4 5";10 ,13 ;" ";11 ,13 ;"5 24" $f$="Cancel":2505 :500 q8,12 ;"1 1";9 ,13 ;" ";11 ,13 ;" ";12 ,12 ;"1 6" 5f$="Therefore the answer is":2505 :500 :2518 :2510 H16,16;"1";17,14;"= ";18,16;"6" " T~"In a school, five-eighths of thestudents are girls and there are96 boys. The total number of students in the school is:" ^ h92900T ,"114","144","160","180","256","e",2930r r"The number of students is divided into 8 parts. 5 of these parts are girls and theremaining 3 parts are boys. Thus" |6,17;"5" " No. of girls= of total" E8,17;"8";10 ,17;"3";12 ,17;"8" 311 ,3;"No. of boys = of total = 96" Zf$="Obtain the value of one eighth of the total no. of students":2505 :500 [14,8;"1 96 ";15,8;" = = 32";16,8;"8 3" ?600X:18,0;"No. of students = 32 8 = 256"  "0.036 0.13 is:": &D3100 ,"46.8","4.68","0.468","0.0468","0.00468","e",31200 +#7,6;"0.036 0.13": 0"When multiplying decimals, it isnecessary to count the total number of digits (including 0's)to the right of the decimal point. In this example," : 3115+ D&:"there are 5 places to the right." Na500:590N:7,8;2;"0";6,8;"1":650:3115+ XK7,9 ;2;"3";6,9 ;"2":650:3115+ bM7,10 ;2;"6";6,10 ;"3":650:3115+ lM7,16;2;"1";6,16;"4":650:3115+ vM7,17;2;"3";6,17;"5":650:3115+ 11 ,5;"0.036":5;"0.13":5;"":7;"108":7;"360":3;"":3;"0.00468":3;"" 12 ,14;"It is necessary to";13 ,14;"enter two 0's to";14,14;"the right of the";15,14;"decimal point in";16,14;"the answer."  "0.0084 0.042 is":: 73500 ,"200","20","2","0.2","0.02","d",3520 \"The decimal point is moved so that the divisor becomes a wholenumber. In this example:" :" 0.0084 0.042" @:"The decimal point is moved on the top and bottom giving:" R11 ,3;"0.0084";12 ,2;" ";13 ,3;"0.042" 500:590N /10 ,4;"";14,4;"" ^11 ,12 ;"0.084";12 ,10 ;"= ";13 ,12 ;"0.42":650 110 ,13 ;"";14,13 ;"" [11 ,20;"0.84";12 ,18;"= ";13 ,20;"4.2":650 110 ,21;"";14,21;"" $M11 ,27;"8.4";12 ,25;"= ";13 ,27;"42" .16,0;"i.e." 8g17,9 ;"0.2";18,6;"42)8.4 Answer = 0.2";17,8;1;"____" B t 770:65195,1 ~""2460000 in standard form is:": I" "'"a 2x10"'" "'"b 20x10"'" "'"c 246x10" d;" " d;"d 2.46x10" " "'"e 24.6x10"  *3700t,"","","","","","d",3730 "Any number can be written as avalue between one and ten multiplied by a power of 10. In this example, the number betweenone and ten is 2.46, therefore:" -:23;"":" 2460000 = 2.46 x 10"  750:  770 "394 to the base 5 is:"  " "  @3800,"3134","3034","3144","1304","1034","b",3840 "The answer cannot contain a number greater than or equal to the base. In this example,the answer can contain 0,1,2,3,or4."  Lf$="Progressively divide the baseinto the number":700:500 5,0;"5394":"5 78 Remainder 4":"5 15 Remainder 3 i.e.":"5 3 Remainder 0 394 = 3034 - Remainder 3 " "f$="Check":700:500 (p600X:11 ,0;"In base 10: ":" 394 = 3x10 + 9x10 + 4x1":" = 300 + 90 + 4" 2W:"In base 5: ":" 3034 = 3x5 + 0 + 3x5 + 4x1 = 375 + 0 + 15 + 4" <618,10 ;"= 394";19,15;"" F U770:"The following numbers are to thebase 2,"''" 10111 1001 11" :"their sum is:"  H4000,"101011","110011","111101","100011","101011","d",4050 ȉ11 ;"10111";12 ;"1001 +";14;"11";10 ;"";10 ;"100011";10 ;"";3;"carry 1111": ""The addition is:"::4040 Of$="This can be checked by changing to denary numbers.":700:500  :700 R0,0;"In the denary system, the place values are "  11 ;"10,10,10,10,1" ="In the binary system, the place values are " 11 ;"2,2,2,2,2" "that is 16,8,4,2,1" "Sf$="Convert each binary number to its decimal equivalent":700:500 ,48,0;"10111 = 16 + 0 + 4 + 2 + 1 = 23" 6" 1001 = 8 + 0 + 0 + 1 = 9" @" 11 = 2 + 1 = 3" J:"Therefore:": TF"10111 + 1001 + 11 = 23 + 9 + 3":18;"= 35":22;"" h8f$="Convert denary 35 to binary":700:500 r |6"To change 35 to binary, divide successively by 2."  " 235" " 217 R1 Therefore:" " 2 8 R1" " 2 4 R0 35 = 100011" " 2 2 R0 " !" 2 1 R0 which checks with" " 0 R1 the answer." 3:"10111+1001+11 = 23+9+3 = 35":27;""  4040  xyzF STOP THE TAPE v mfgUDG qK\y 8x8͞ x<͞  ~%~%|Xg~ w$<<8$((!{\6X#6V+^!w#~!VUw+!~#~+w#w$$$$$<<8$((|< 8$ 8$ P P 2LL2Wq !v> ~ (X~H~B$$B@  @~D|b|>F <`~~"0H x~BBBBB<section 2 q (s8x=7:y=6:z=0:y:y:z::1400x g64999:x=7:y=6:z=0:y:y:z::5,3;"Please leave tape running" "UDG"65000,536 Q:70F:f$=" STOP THE TAPE ":v=10 :m=8:f=980:910  500 ( 5 FE2;"MATHEMATICS EXAMINATION PRACTICE";11 ;"AND TESTS": d n%2;"Q";q;0,12 ;h$  ques n=65195 n=1230  a;"a ";a$ b;"b ";b$ c;"c ";c$ d;"d ";d$ e;"e ";e$  a=y b=y c=y d=y "e=y ' ,""300, 6=""3106 @=32 J?21,0;x;"Undefined key?";y;" please try again " T 300, ^""350^ h=""360h r=32 Ŧ=13 | 350^  q=q+1 ques,a$,b$,c$,d$,e$,w$,s  B21,0;" ";x;" Press any key to continue ";y;" " ""510 =""520  &!a=0:b=0:c=0 0d=0:e=0 : X618,0;" " b619,0;" " l n=0100d:n   600X 18,0;2;f$  )n=65196:n=165136p  )n=65196:n=065136p    i$ *k$="":f=i$ 4f=0800  > n=1f Hi$(n)=32 860\ R k$=k$+i$(n) \n f  f=990  v,m;""; 23729\,v n=1̱f$ f 23728\,m:65000 m=m+1:n  1;f$(n);: %1;5;1;f$(n);: 2;f$(n);: 5;f$(n);:  250  100d ?21,0;x;"Please select your answer";y;" "  800  ~0k$="a"k$="b"k$="c"k$="d"k$="e"1180 ?21,0;x;"Undefined Key ?";y;" Please try again"  1050 k$w$1280 w$="a"a=5 w$="b"b=5 w$="c"c=5 w$="d"d=5 w$="e"e=5  100d =f$="CORRECT":f=995:v=0:m=25:910 B20,0;"Use ";x;"ENTER";y;" for answer explanation" B21,0;"Use ";x;"SPACE";y;" for the next question "  350^ =13 1300 =32 C20,0;x;"Wrong-Correct answer is ";w$;" ";:" "  I21,0;x;"Answer explanation follows";:" ":350^  s (B20,0;"Use ";x;"ENTER";y;" to rerun this question" 2B21,0;"Use ";x;"SPACE";y;" for the next question " Z=32 d=13 1000 n 1320( x:q=0::250  h$,l$,qty  70F :f$=h$:v=3:m=((32 -f$)/2):900 -:::7;2;"Programme Content"  2010 !f$=" CELTIC REVISION SOFTWARE" v=18:m=3  900  500: k=1qty  750:65195,0  400  1000 k  9f$="End of "+h$:v=3:m=((32 -f$)/2) " 900 ,U10 ,0;x;"Press n then ENTER";y;" to auto-load programme ";2;l$ 6:::x;"Press r then ENTER";y;" to rerun thisprogramme" @M.G. Fincher E1::x;"Press b then ENTER";y;" to goto BASIC" J 800  T"k$="n"k$="r"k$="b"1700 ^721,0;x;"Undefined key please re-select" h 1610J k$="n"1800 k$="r"5 L:5,2;"RETURNING TO BASIC DESTROYS";8;"THIS PROGRAMME" E::x;"Press y to return to BASIC"''"Press any other key to abort" 0:i$= i$="y"i$="Y"  1550 /:f$=" START THE TAPE ":v=5:m=8  900 ::l$ !"Section 2","section 3",4 y:8;"Percentages";8;"Cost Price";8;"Selling Price";8;"Simple Interest";8;"Rates": (/"40% of 871, to 2 significant figures is:" - 2<2600( ,"348.40","348","340","341","350","e",2700 B"Percentage is a fraction in which the denominator is 100": 14;"40" #" 40% of 871 = x 871 = 348.4" 14;"100": " A number to two significant figures means that 2 digits are needed together with any noughtsnecessary to show the positionof the decimal point. In 348.4 three places are occupied beforethe decimal point. To two significant figures,this becomestwo numbers and a nought. The number 8 is dropped, but becausethis is greater than 5 the finalanswer is 350 (and not 340)"  V"A man sells a car for `1320making a loss of 12%. The man bought the car for"  B3060 ,"`162","`1320","`1478","`1500","`1584","d",3090 "The ";2;"cost price (CP)";z;" is the moneypaid for goods, and the ";2;"selling price (SP)";z;" is the money obtainedwhen the goods are sold. If theselling price is greater than the cost price a profit is made.If the selling price is less than the cost price, a loss is made. The ";2;"profit percent";z;" is always calculated on the cost price." &13 ;"SP - CP" 0#4;"Profit = x 100" :15;"CP" D:13 ;"CP - SP" N" Loss = x 100" X15;"CP" bDf$="Select and apply the appropriateformula":700:500 l vD"In this example, a loss is made,and the second equation is used." "(SP=`1320, loss=12%)"  13 ;"CP - 1320" !8;"12 = x 100" 15;"CP"  "" 12xCP = 100xCP - 1320x100" $:" 12xCP - 100xCP = -132000" :" -88xCP = -132000"  13 ;"132000" 8;"CP = = `1500" 15;"88" :"Cost price = `1500"  C"The simple interest on `550 invested at 15% for 6 years is:"  ?3500 ,"`330","`495","`825","`880","`1045","b",3550 "Interest is the profit made by investing money";2;"-the principal(P)";z;"Money is invested when it isused to buy shares in a businessor loaned or put in a specialbank account. "; "The ";2;"rate(R)";z;" is the";2;"rate per cent";z;" and is the money obtained by investing `100 for 1 year. An interest rate of 15%means that `100 invested for 1 year earns `15 and becomes `115 The interest for 2 years would be `30." 500: D:"Simple interest (S.I.) is calculated using the equation:" ::18;"PRT";11 ;"S.I. = ";18;"100" :"P = Principal (`550)" $"R = Rate of interest (15%)" .:"T = Number of years money is invested (6 years)" 8f$="Apply the formula" B700:500 L 600X VU13 ,11 ;"550 x 15 x 6";," S.I. = ` = `495";15;"100"  "The rateable value of a city is `169,820,000."'"A rate of 2.5 pence in the `1 isneeded to pay for a hospital."'"The cost of the hospital is:"  X4000,"`212,275","`424,550","`4,245,500","`6,792,800","`8,491,000","c",4030 S"Rates are levied by Local Authorities. The money is used to provide amenities (libraries,roads etc). Rateable value ofproperty (decided by the local District Valuer) depends on locality, size and use, and is not the same as its market value."'"The rate is calculated as so much in the `1 of the rateable value."  500: ,"Rateable value of city " 6 @" = `169,820,000" J;:"Therefore the rates contributionto the hospital is:": T$"Rate = 2.5 x 169,820,000 pence": ^T7;"2.5 x 169,820,000";5;"= pounds";14;"100" h r" = ` 4,245,500" | xyzF STOP THE TAPE v mfuUDG (K\y 8x8͞ x<͞  ~%~%|Xg~ wP P 03nMN=MK0 !v>!{\6X#6V+^!w#~!VUw+!~#~+w#w$$$$$<<8$((|< 8$$$,2" P P 88 MGG\GWq !v> ~ (X~H~0H xB$$Bx0H00P@  @@  @|BB|@@|BB|DB0H x~BBBBB<section 3  8x=7:y=6:z=0:y:y:z::1400x g64999:x=7:y=6:z=0:y:y:z::5,3;"Please leave tape running" "UDG"65000,536 Q:70F:f$=" STOP THE TAPE ":v=10 :m=8:f=980:910  500 ( 5 FE2;"MATHEMATICS EXAMINATION PRACTICE";11 ;"AND TESTS": d n%2;"Q";q;0,12 ;h$  ques n=65195 n=1230  a;"a ";a$ b;"b ";b$ c;"c ";c$ d;"d ";d$ e;"e ";e$  a=y b=y c=y d=y "e=y ' ,""300, 6=""3106 @=32 J?21,0;x;"Undefined key?";y;" please try again " T 300, ^""350^ h=""360h r=32 Ŧ=13 | 350^  q=q+1 ques,a$,b$,c$,d$,e$,w$,s  n=f17 $" " n  B21,0;" ";x;" Press any key to continue ";y;" " ""510 =""520  &!a=0:b=0:c=0 0d=0:e=0 : X618,0;" " b619,0;" " l n=0100d:n   600X 18,0;2;f$  )n=65196:n=165136p  )n=65196:n=065136p    i$ *k$="":f=i$ 4f=0800  > n=1f Hi$(n)=32 860\ R k$=k$+i$(n) \n f  f=990  v,m;""; 23729\,v n=1̱f$ f 23728\,m:65000 m=m+1:n  1;f$(n);: %1;5;1;f$(n);: 2;f$(n);: 5;f$(n);:  250  100d ?21,0;x;"Please select your answer";y;" "  800  ~0k$="a"k$="b"k$="c"k$="d"k$="e"1180 ?21,0;x;"Undefined Key ?";y;" Please try again"  1050 k$w$1280 w$="a"a=5 w$="b"b=5 w$="c"c=5 w$="d"d=5 w$="e"e=5  100d =f$="CORRECT":f=995:v=0:m=25:910 B20,0;"Use ";x;"ENTER";y;" for answer explanation" B21,0;"Use ";x;"SPACE";y;" for the next question "  350^ =13 1300 =32 C20,0;x;"Wrong-Correct answer is ";w$;" ";:" "  I21,0;x;"Answer explanation follows";:" ":350^  s (B20,0;"Use ";x;"ENTER";y;" to rerun this question" 2B21,0;"Use ";x;"SPACE";y;" for the next question " Z=32 d=13 1000 n 1320( x:q=0::250  h$,l$,qty  70F :f$=h$:v=3:m=((32 -f$)/2):900 -:::7;2;"Programme Content"  2010 !f$=" CELTIC REVISION SOFTWARE" v=18:m=3  900  500: k=1qty  750:65195,0  400  1000 k  9f$="End of "+h$:v=3:m=((32 -f$)/2) " 900 ,U10 ,0;x;"Press n then ENTER";y;" to auto-load programme ";2;l$ 6:::x;"Press r then ENTER";y;" to rerun thisprogramme" @M.G. Fincher E1::x;"Press b then ENTER";y;" to goto BASIC" J 800  T"k$="n"k$="r"k$="b"1700 ^721,0;x;"Undefined key please re-select" h 1610J k$="n"1800 k$="r"5 L:5,2;"RETURNING TO BASIC DESTROYS";8;"THIS PROGRAMME" E::x;"Press y to return to BASIC"''"Press any other key to abort" 0:i$= i$="y"i$="Y"  1550 /:f$=" START THE TAPE ":v=5:m=8  900 :: l$ !"Section 3","section 4",5 c8,8;"Averages";8;"Speed";8;"Ratio and Proportion";8;"Variation"  n"A student obtains examination marks of 64%, 80%, 75%, 45%, 50%56%, 85%, and 73%."''"The average mark is:"  92500 ,"64%","85%","45%","66%","50%","d",2560 `13 ;"Sum of the marks";3;"Average = ";14;"Number of marks" i:"The marks are 64%,80%,75%,45%,50%,56%,85% and 73%."''"There are 8 marks and they add up to 528%." ?:19;"528";4;"Average mark = ";20;"8" :17;"= 66%" ( o"A car travels 50km at 25km/h andthen travels 60km at 20km/h. Theaverage speed for the whole journey is:"  K3000 ,"22km/h","22.5km/h","45km/h","55km/h","110km/h","a",3060 k3000 ::17;"Total distance";1;"Average speed = ";18;"Total time" 8f$="Calculate the journey times":700:500  "First part of journey"'"Distance travelled =50km"'"Time to travel 50km at 25km/h":15;"50";13 ;"= = 2h";15;"25" 7,0;"Second part of journey"'"Distance travelled = 60km"'"Time to travel 60km at 20km/h":15;"60";13 ;"= = 3h";15;"20" &$:"Total distance = 50+60 = 110km" 0"Total time = 2+3 = 5h" :A18;"110"'"Average speed = = 22km/h";19;"5" D u"A student buys a red pen for 45pand a blue pen for `1.80. The ratio,"''"cost of red pen:cost of blue pen"''"is:"  G3500 ,"4 :1","1 :4","5 :0.2","2.5:1.0","1 :5","b",3560 "A ratio compares two or more quantities. The quantities mustbe in the same units so that theratio does not have any units."  " Cost of red pen = 45p" $" Cost of blue pen = `1.80 = 180p"  %"Cost of red pen:Cost of blue pen " 18;"= 45p:180p" $18;"= 1:4" . O"`2400 is divided between three people X,Y,Z in the ratio 4:3:1.Y receives:"  =4000,"`3","`150","`300","`900","`1500","d",4060 ^"The money is divided into 8 parts (the sum of 4+3+1) and Y receives 3 of these parts." E:4,18;"3";6;"Y receives `x2400";18;"8" #f$="Cancel":700:500 r600X:4,22;"300";7,17;"1";6,18;"";5,20;1;"" 8,13 ;"= `900" @:13 ;"4":"[X receives `x2400 = `1200";13 ;"8": =13 ;"1":" Z receives `x2400 = `300 ]";13 ;"8" " Y"The weight of a square of fixed thickness varies directly as thesquare of its length." _:"If the square weighs 500g when its length is 5cm, the weight ofa square of length 4cm is"  <4500,"25g","80g","100g","400g","320g","e",4560 +"Weight varies directly as lengthsquared"  12 ;"W" 1770:" W";:750:"l or = k" 12 ;"l" Gf$="Calculate the value of the constant k":700:500  600X 47,0;"When w=500g,l=5cm. Therefore:":  69 ;"500";5;"k = = 20";9 ;"25" B:"When l=4cm,"''11 ;"w = kxl";13 ;"= 20x4 = 320g"   xyzF STOP THE TAPE v mfUDG ̀7K\y 8x8͞ x<͞  ~%~%|Xg~ w$<<8$((!{\6X#6V+^!w#~!VUw+!~#~+w#w$$$$$<<8$((|< 8$ 8$8p2LL28v> ~ (X~H~B$$B@  @~D|b|>F <`~~"0H x>F n=1f Hi$(n)=32 860\ R k$=k$+i$(n) \n f  f=990  v,m;""; 23729\,v n=1̱f$ f 23728\,m:65000 m=m+1:n  1;f$(n);: %1;5;1;f$(n);: 2;f$(n);: 5;f$(n);:  250  100d ?21,0;x;"Please select your answer";y;" "  800  ~0k$="a"k$="b"k$="c"k$="d"k$="e"1180 ?21,0;x;"Undefined Key ?";y;" Please try again"  1050 k$w$1280 w$="a"a=5 w$="b"b=5 w$="c"c=5 w$="d"d=5 w$="e"e=5  100d =f$="CORRECT":f=995:v=0:m=25:910 B20,0;"Use ";x;"ENTER";y;" for answer explanation" B21,0;"Use ";x;"SPACE";y;" for the next question "  350^ =13 1300 =32 C20,0;x;"Wrong-Correct answer is ";w$;" ";:" "  I21,0;x;"Answer explanation follows";:" ":350^  s (B20,0;"Use ";x;"ENTER";y;" to rerun this question" 2B21,0;"Use ";x;"SPACE";y;" for the next question " Z=32 d=13 1000 n 1320( x:q=0::250  h$,l$,qty  70F :f$=h$:v=3:m=((32 -f$)/2):900 -:::7;2;"Programme Content"  2010 !f$=" CELTIC REVISION SOFTWARE" v=18:m=3  900  500: k=1qty  750:65195,0  400  1000 k  9f$="End of "+h$:v=3:m=((32 -f$)/2) " 900 ,U10 ,0;x;"Press n then ENTER";y;" to auto-load programme ";2;l$ 6:::x;"Press r then ENTER";y;" to rerun thisprogramme" @M.G. Fincher E1::x;"Press b then ENTER";y;" to goto BASIC" J 800  T"k$="n"k$="r"k$="b"1700 ^721,0;x;"Undefined key please re-select" h 1610J k$="n"1800 k$="r"5 L:5,2;"RETURNING TO BASIC DESTROYS";8;"THIS PROGRAMME" E::x;"Press y to return to BASIC"''"Press any other key to abort" 0:i$= i$="y"i$="Y"  1550 /:f$=" START THE TAPE ":v=5:m=8  900 5:::2;" At the beginning of SIDE TWO":: l$ !"Section 4","section 5",6 o8,2;"Lowest Common Multiple(LCM)";2;"Highest Common Factor(HCF)";2;"Factorisation"  "The LCM of 18,63 and 99 is:"  72500 ,"9","72","154","462","1386","e",2560 "The Lowest Common Multiple,LCM, of two or more numbers is the smallest number into which each of the numbers will divide exactly.":"Each number is expressed in its prime factors."  +:9 ;"18 = ";4;"3x3";y;"x2" +:9 ;"63 = ";4;"3x3";y;"x7" ,:9 ;"99 = ";4;"3x3";y;"x11" (1:8;"LCM = ";4;"3x3";y;"x2x7x11" 2:12 ;"= 1386" < "The HCF of 24,60 and 112 is"  13000 ,"4","3","105","7","5","a",3060 "The highest common factor(HCF) of a set of numbers is the biggest number which will divideexactly into each of the given numbers." .:10 ;"24 = ";4;"2x2";y;"x2x3" .:10 ;"60 = ";4;"2x2";y;"x3x5" 0:9 ;"112 = ";4;"2x2";y;"x2x2x7" $:9 ;"HCF = ";4;"2x2" &:13 ;"= 4" 0 D"Remove the brackets and simplify"''6;"4m(3m-2) - 4m(2m-3)"  P3500 ,"20m-20m","4m -20m","24m-16m","12m-8m","4m +4m","e",3560 "The first bracket is multiplied by 4m.":"The second bracket is multipliedby -4m.":"Then like terms are collected together."  8;"4m(3m-2) - 4m(2m-3)" ":8;"= 12m-8m - 8m+12m" :8;"= 4m+4m"  5"The factors of "''9 ;"3(p-q) - (q-p)"''"are"  K 4000,"3(p-q)","4(p-q)","2(q-p)","3(q-p)","4(q-p)","b",4060 {"The negative sign in between thetwo brackets changes the sign inthe second bracket,":"i.e.-(q-p)=-q+p or p-q or +(p-q)" :11 ;"3(p-q) -(q-p)" :9 ;"= 3(p-q) + (p-q)" :9 ;"= (3+1)(p-q)" :9 ;"= 4(p-q)"  5"The factors of"'';9 ;"6p -7pq -3q"''"are:"  g4500,"(2p-3q)(3p+q)","(6p-3q)(p+q)","(6p+3q)(p-q)","(2p+3q)(3p-q)","(6p-q)(p+q)","a",4560 W"For 6p-7pq-3q the letters can be placed immediately as:";9 ;"(p q)(p q)" >"The second sign in the given expression is negative." "Therefore the signs in the two brackets are different. i.e. oneis negative and the other positive. (If the second sign inthe expression is positive then the signs in the two bracketsare both negative or both positive.)" q:"The factors of 6 and -3 must be selected so that -7 is obtained in the middle of the given expression." Ff$="Obtain all possible factors of 6 and -3.":700:500 %:"The expression is 6p -7pq -3q"  n:"The factors of 6 are:"'" 6x1, (-6)x(-1), 2x3, (-2)x(-3)"''"The factors of -3 are:";11 ;"-3x1, -1x3" S:"The different combinations have to be tried out"'';8;"( p q)( p q)"  Ff$="Try the factors of 6 as 3x2 and -3 as-3x1":700:500 *Rp$="3":q$="2":r$="":s$="":t$="":250:a=4:c=4:4900$ 4-a=4:d=4:r$="+3pq":4900$ >-b=4:c=4:s$="-6pq":4900$ H-b=4:d=4:t$="-3q":4900$ R 4900$ \=15,6;"= 6p -3pq -3q"'"Incorrect combination" fFf$="Try the factors of 6 as 2x3 and -3 as-3x1":700:500 pf=13 :450 zRp$="2":q$="3":r$="":s$="":t$="":250:a=4:c=4:4900$ -a=4:d=4:r$="+2pq":4900$ -b=4:c=4:s$="-9pq":4900$ -b=4:d=4:t$="-3q":4900$  4900$ ;15,6;"= 6p -7pq -3q"'"Correct combination"  600X  $h11 ,9 ;a;p$;11 ,12 ;b;"-3";11 ,17;c;q$;11 ,20;d;"+1" .250:500 8]13 ,6;"= 6p";13 ,12 ;r$;13 ,17;s$;13 ,22;t$ B 65195,1 ""Factorize and hence simplify":  5080 G8,4;"3p +3p -6"'"a) b) 3"'" p + 1" #c;13 ,0;"c) 3p + 6" `12 ,21;"3p -9p +6";13 ,17;"d) ";14,23;"p + 1" 516,4;"3p - 6"'"e) "'" p + 1"  ]5;"3p +p -2 6p -24";5;" x ";5;"p -p -2 6p -4"  *5000,"","","","","","c",5110 (:"Factorize each expression first:":  5080  l7,4;"(3p-2)(p+1) 6(p-2)(p+2)"'" = x "'" (p-2)(p+1) 2(3p-2)" ,12 ,4;"(3p-2)(p+1)(p-2)(p+2)6" .13 ,2;"= " ('14,7;"(p-2)(p+1)(3p-2)2" 2.f$="Cancel":700:500:770  ~ (X~H~>D|Rb|@  @~D|b|>F <`~~"0H x~BBBBB<section 5 2C B4C8x=7:y=6:z=0:y:y:z::1400x g64999:x=7:y=6:z=0:y:y:z::5,3;"Please leave tape running" "UDG"65000,536 Q:70F:f$=" STOP THE TAPE ":v=10 :m=8:f=980:910  500 ( 5 FE2;"MATHEMATICS EXAMINATION PRACTICE";11 ;"AND TESTS": d n%2;"Q";q;0,12 ;h$  ques n=65195 n=1230  a;"a ";a$ b;"b ";b$ c;"c ";c$ d;"d ";d$ e;"e ";e$  a=y b=y c=y d=y "e=y ' ,""300, 6=""3106 @=32 J?21,0;x;"Undefined key?";y;" please try again " T 300, ^""350^ h=""360h r=32 Ŧ=13 | 350^  q=q+1 ques,a$,b$,c$,d$,e$,w$,s  n=f17 /n,0;" " n  B21,0;" ";x;" Press any key to continue ";y;" " ""510 =""520  &!a=0:b=0:c=0 0d=0:e=0 : N821,0;" ": X618,0;" " b619,0;" " l n=0100d:n   600X 18,0;2;f$  )n=65196:n=165136p  )n=65196:n=065136p    i$ *k$="":f=i$ 4f=0800  > n=1f Hi$(n)=32 860\ R k$=k$+i$(n) \n f  f=990  v,m;""; 23729\,v n=1̱f$ f 23728\,m:65000 m=m+1:n  1;f$(n);: %1;5;1;f$(n);: 2;f$(n);: 5;f$(n);:  250  100d ?21,0;x;"Please select your answer";y;" "  800  ~0k$="a"k$="b"k$="c"k$="d"k$="e"1180 ?21,0;x;"Undefined Key ?";y;" Please try again"  1050 k$w$1280 w$="a"a=5 w$="b"b=5 w$="c"c=5 w$="d"d=5 w$="e"e=5  100d =f$="CORRECT":f=995:v=0:m=25:910 B20,0;"Use ";x;"ENTER";y;" for answer explanation" B21,0;"Use ";x;"SPACE";y;" for the next question "  350^ =13 1300 =32 C20,0;x;"Wrong-Correct answer is ";w$;" ";:" "  I21,0;x;"Answer explanation follows";:" ":350^  s (B20,0;"Use ";x;"ENTER";y;" to rerun this question" 2B21,0;"Use ";x;"SPACE";y;" for the next question " Z=32 d=13 1000 n 1320( x:q=0::250  h$,l$,qty  70F :f$=h$:v=3:m=((32 -f$)/2):900 -:::7;2;"Programme Content"  2010 !f$=" CELTIC REVISION SOFTWARE" v=18:m=3  900  500: k=1qty  750:65195,0  400  1000 k  9f$="End of "+h$:v=3:m=((32 -f$)/2) " 900 ,U10 ,0;x;"Press n then ENTER";y;" to auto-load programme ";2;l$ 6:::x;"Press r then ENTER";y;" to rerun thisprogramme" @M.G. Fincher E1::x;"Press b then ENTER";y;" to goto BASIC" J 800  T"k$="n"k$="r"k$="b"1700 ^721,0;x;"Undefined key please re-select" h 1610J k$="n"1800 k$="r"5 L:5,2;"RETURNING TO BASIC DESTROYS";8;"THIS PROGRAMME" E::x;"Press y to return to BASIC"''"Press any other key to abort" 0:i$= i$="y"i$="Y"  1550 /:f$=" START THE TAPE ":v=5:m=8  900 :: l$ ""Section 5","section 6",11 "10 ,11 ;"Equations": 65195,1 2"In the equation";8;"3p-6 = 4-2p"'"p is:" (5,5;"2"'"a) -"'" 5" (9 ,5;"2"'"b) "'" 5" 13 ,0;c;"c) 2" 15,0;"d) 10" )17,5;"4"'"e) "'" 5"  *2500 ,"","","","","","c",2600( ("In this equation all p's are collected on the left hand side.Remember that it is essential todo the same thing to both sides." 2:7;"3p - 6 = 4 - 2p" <-:"Add 2p to both sides of the":"equation" F" 2p + 3p - 6 = 4 - 2p + 2p" P:7;"5p - 6 = 4" Z-:"Add 6 to both sides of the":"equation" d11 ;"5p = 10" n:12 ;"p = 2" x 65195,1 "In the equation"  6;"3m - 4 2 - 5m 7" 6;" - = " *8;"3";17;"2";24;"6" :"m is" 6;"1";23;"1" 7"a) -6";17;"b) -2";6;"2"," 3" &:c;"c) 1";y;17;"d) 17" ':6;"1"'"e) 24";6;"2" : D*3000 ,"","","","","","c",3150N NL"Do the same thing to both sides of the equation.":"The LCM of 2,3,6 = 6" X"Multiply both sides of the equation by 6.":"Remember that both terms on the left hand side must be multiplied by 6.":"Brackets are added to make the working easier." b:" 6(3m-4) 6(2-5m) 7" l!" - = x 6" v*7;"3";17;"2";24;"6" #f$="Cancel":700:500 E10 ,3;"2";10 ,13 ;"3";10 ,27;"1" E14,6;"1";14,16;"1";14,23;"1" E11 ,4;"";11 ,14;"";12 ,28;"" E13 ,7;"";13 ,17;"";13 ,24;"" +16,4;"2(3m-4) - 3(2-5m) = 7" %f$="Simplify":700:500 ,:0,4;"2(3m-4) - 3(2-5m) = 7" "2,13 ;"21m - 14 = 7" .:"Add 14 to both sides of the equation" +7,8;"21m - 14 + 14 = 7 + 14" 9:"Therefore:"''9 ;"21m = 21"'';11 ;"m = 1"  /"Solve by factorizing, the equation:": !9 ;"p-p-20 = 0"''"p is:"  R3500 ," 0 or 1","-1 or 1"," 2 or -10"," 1 or -20"," 5 or -4","e",3560 9 ;"p-p-20 = 0" &:"The possible factors of -20 are:" ?"(1)(-20), (-1)(20)"'"(2)(-10), (-2)(10)"'"(4)(-5) , (-4)(5)" ?:"The factors must yield -1. Try -5 and +4 as the factors:" $10 ,9 ;"(p-5)(p+4) = 0" E250:a=4:c=4:3800:11 ,5;"p" $;a=4:d=4:3800:11 ,8;"+4p" .<b=4:c=4:3800:11 ,12 ;"-5p" 8@b=4:d=4:3800:11 ,16;"-20 = 0" Bk10 ,10 ;a;"p";10 ,11 ;b;"-5";10 ,15;c;"p";10 ,16;d;"+4" L 590N VJ13 ,0;"Simplifying gives the originalequation. Therefore:" `!:"Either (p-5) = 0 and p = 5" j "or (p+4) = 0 and p = -4" t"i.e. p = 5 or -4" ~ k10 ,10 ;a;"p";10 ,11 ;b;"-5";10 ,15;c;"p";10 ,16;d;"+4" 250:500: 65195,1 7"Use the equation formula to solve the equation:" 4:6;"-3x-2x+5 = 0"''"The values of x are:" B8,27;"2"'"a) -3 or 1","b) -5 or -";27;"3" jd;12 ,16;" 2 ";13 ,16;"d) -1 or 1";14,16;" 3 " 412 ,10 ;"2"'"c) -1 or "'" 3" /16,5;"2"'"e) 1 or -1"'" 3"  *4000,"","","","","","d",4100 x"This equation does not factorizeeasily and it is best to use theformula. For the equation:"'';6;"ax+bx+c = 0" U13 ;"";6;"x = -bb-4ac";10 ;"";14;"2a" /:"For -3x-2x+5=0 a=-3,b=-2,c=5 Therefore" "g10 ;""'" -(-2)(-2)-4(-3)(5)"'"x = ";12 ;"2(-3)" ,%f$="Simplify":700:500 612 ,6;" "'" 24 + 60 264 28"'"x = = = ";7;"-6 -6 -6" @v590N:17,4;"10 -6";25;"2"'"x = or i.e. x = -1 or 1"'" -6 -6";25;"3" h j"A father is three times as old as his son. He is also 20 years older than his son. The son's age is"  R4500," 5 years","10 years","15 years","20 years","25 years","b",4530 "It is important to state the information given, if possible, in the form A=B. It is best to begin with the quantity you haveto find, in this example, the age of the son." :" Let son's age = y years" $3;"Father's age = 3y years" *3;"Father's age = son's age + 20" 13 ;"3y = y+20"  :"Subtract y from both sides" :11 ;"3y-y = y-y+20" 13 ;"2y = 20"  14;"y = 10" #:6;"Son's age = 10 years"   "`480 is shared between three people x,Y,Z, so that X receives3 times as much as Z, and Y receives 4 times as much as Z.":"Therefore Z receives"  ;5000,"`48","`60","`80","`160","`240","b",5030 1"Begin with the quantity you haveto calculate." :5;"Let Z receive `m" S:"State the information given in the form A=B. X receives 3 timesas much as Z." &5;"Money received by X = `3m" &5;"Money received by Y = `4m"  13 ;"Total money = `480" ":13 ;"m + 3m + 4m = 480" 22;"8m = 480"  023;"m = 60"''"Therefore Z receives `60" $9 ;"(X receives `4m = `240)" $9 ;"(Y receives `3m = `180)" ( |"A school sells one thousand tickets for a school play, some at 50p and the remainder at `1. If the total money received is `600, the number of tickets soldat 50p is"  95500|,"400","500","600","800","900","d",5530 ]"Begin with what you have to calculate. Let the number of 50 pence tickets sold = q" 2:"State the information given in the form A=B" C:" Total tickets sold = 1000"'"Total `1 tickets sold = 1000-q" C:"Money received from q tickets at 50 pence each = 50q pence." f:11 ;"50q";20;"q"';7;"= ` ";16;"= ` "';11 ;"100";20;"2" x17,0;2;"Equate the total money received with the sum of money received from each type of ticket."  500 e:"Money received from (1000-q) tickets at `1 each = `(1000-q)"'"Money from q 50p tickets =`q2" V:"Total money received is:"';23;"q"'" `600 = `(1000-q) + `";23;"2" 6:19;"q"'" 600 = 1000-q + ";19;"2" -12 ;"q"'" -400 = -";12 ;"2" ?" 800 = q"''"i.e. Number of 50p tickets sold = 800."  p;"The values of p and q in the simultaneous equations:" z7:7;"4p-2q = 6";7;"3p+8q = -5"''"are:"  S6000p,"p=1 q=-1","p=0 q=1","p=1 q=0","p=-1 q=1","p=1 q=1","a",6060 $"Number the equations (1) and (2)" ;7;"4p-2q = 6 ...(1)";7;"3p+8q = -5 ...(2)" >:"It is necessary to eliminate p or q from the equations." Ff$="Multiply both sides of equation (1) by 4.":700:500 D6,6;"16p-8q = 24...(3)";7;"3p+8q = -5 ...(2)" 7f$="Add equations (2) and (3).":700:500 N9 ,0;"Add (2) and (3)";6;"19p = 19"'"i.e. p = 1" ;f$="Substitute p=1 in equation (1)":700:500 W600X:590N:13 ,0;"Substitute p=1 in (1)";6;"4x1-2q = 6" E8;"4-2q = 6"'"Subtract 4 from both sides";9 ;"-2q = 2" +"i.e. q =-1"'"Therefore p=1 q=-1" 8 d65195,1 nU"Solve the equation"'';8;"4p+10p-14 = 0"''"by completing the square. p is:" xB7,11 ;"1"'"a) 2 or -2","b) 1 or -4";11 ;"2" !12 ,0;"c) 2 or -1" jd;11 ,16;" 1";12 ,16;"d) 1 or -3";13 ,16;" 2" -15,4;"7"'"e) or -3"'" 2"  *6500d,"","","","","","d",6600 8;"4p+10p-14 = 0" :"Divide the equation by 4" =:14;"5 7";11 ;"p+p- = 0";14;"2 2" .:"Add 72 to both sides of the equation" E:14;"5 7";11 ;"p+p = ";14;"2 2" Gf$="Complete the square on the left hand side.":700:500  :"To complete the square add" C6;"1 5";6;"x to both sides";6;"2 2" ^:10 ;"5 25 7 25";5;"p + p + = + ";10 ;"2 16 2 16" ":"Form the square" ,Z:9 ;" 5 56 + 25";9 ;"p + = ";9 ;" 4 16" 62:20;"81";18;"= ";20;"16" @<f$="Take square roots of both sides":700:500 J[:20;""; 12 ;"5 81";8;"p + = ";12 ;"4 16" O'149,152:9 ,20 T0:17;"9";14;"= ";17;"4" ^J"Therefore"''" 9 5 9 5"'" p = - or --"'" 4 4 4 4" h9:"i.e.":14;"1"'" p = 1 or - 3";14;"2" r X65195,1 b-"For"';6;"v = u + 2as s equals:" lF5,20;"v-u"'"a) v-u-2a","b) ";21;"-2a" v39 ,20;"u-v"',"d) "'," 2a" 9c;9 ,0;" v-u"'"c) "'" 2a " "14,0;"e) 2a-u-v"  *7000X,"","","","","","c",7100 1"For"';3;"v = u + 2as s is required." 5:"Always do the same to both sidesof the equation" 3:"Subtract u from both sides of the equation." :6;"v-u = 2as" 4:"Divide both sides of the equation by 2a" 7:6;"v-u";6;" = s";8;"2a"   L65195,1 V"For" `B14;"";14;"l";6;"T = 2 ";12 ;" g" j-770:5,11 ;"":750 t'101e,127:9 ,20 ~5,20;"l equals:" S770:8,4;"gT"," gT"'"a) ","b) "'" 2"," 4" N12 ,4;"4g"," 2g"'"c) ","d) "'" T"," T" 4e;16,0;" Tg"'"e) "'" 4"  *7500L,"","","","","","e",7610 "Always do the same to both sidesof the equation. l is inside a square root and this is removed by squaring both sides of the equation." T750:5,15;"l";6,15;"";7,15;"g" (770:6,7;"T = 4" B9 ,0;"Multiply both sides of the equation by g" :6;"gT = 4l": "Divide throughout by 4." 4:6;"gT";6;" = l";6;"4"  o rerun this question" 2B21,0;"Use ";x;"SPACE";y;" for the next question " Z=32 d=13 1000 n 1320( x:q=0::250  h$,l$,qty  70F :f$=h$:v=3:m=((32 -f$)/2):900 -:::7;2;"Programme Content"  2010 !f$=" CELTIC REVISION SOFTWARE" v=18:m=3  900  500: k=1qty  750:65195,0  400  1000 k  9f$="End of "+h$:v=3:m=((32 -f$)/2) " 900 ,U10 ,0;x;"Press n then ENTER";y;" to auto-load programme ";2;l$ 6:::x;"Press r then ENTER";y;" to rerun thisprogramme" @1::x;"Presw b then ENTER";y;" to goto BASIC" J 800  T"k$="n"k$="r"k$="b"1700 721,0;x;"Undefined key lease re-select" h 1610J k$="n"1800 k$="r"5 L>5,2;"RETURNING TO BASIC DESTROYS";8;"THIS PROGRAMME" E::x;"Press y to return to BASIC"/'"Press any other key to abort" 0:i$= i$="y"i$="Y"  1550 /:n$=" START THE TAPE ":v=5:m=8  900 :: l$ "exec","section 1",0  &:usr defined graphics &j$="t" &n=07 &"("line ";n;" of usr graphics"),v & j$+n,v &n & &l$10 :.3,0 & 750 &"UDG"65000,536 &6"REWIND TAPE AND RE=CONNECT TO VERIFY SAVE OF ";l$ &l$:"Verfy ";l$;" O.K." &1"UDG"65000,536:"Verify code O.K." ' '!"SAVING":l$="exec":9950& xyzF STOP THE TAPE v mfRUDG K\y 8x8͞ x<͞  ~%~%|Xg~ w$<<8$((!{\6X#6V+^!w#~!VUw+!~#~+w#w$$$$$<<8$((|~$$$$$0H x 8$8p2LL28v> ~ (X~H~>Fb|>D|Rb|` @  @~D|b|>F <`~~">>0H x>F n=1f Hi$(n)=32 860\ R k$=k$+i$(n) \n f  f=990  v,m;""; 23729\,v n=1̱f$ f 23728\,m:65000 m=m+1:n  1;f$(n);: %1;5;1;f$(n);: 2;f$(n);: 5;f$(n);:  250  100d ?21,0;x;"Please select your answer";y;" "  800  ~0k$="a"k$="b"k$="c"k$="d"k$="e"1180 ?21,0;x;"Undefined Key ?";y;" Please try again"  1050 k$w$1280 w$="a"a=5 w$="b"b=5 w$="c"c=5 w$="d"d=5 w$="e"e=5  100d =f$="CORRECT":f=995:v=0:m=25:910 B20,0;"Use ";x;"ENTER";y;" for answer explanation" B21,0;"Use ";x;"SPACE";y;" for the next question "  350^ =13 1300 =32 C20,0;x;"Wrong-Correct answer is ";w$;" ";:" "  I21,0;x;"Answer explanation follows";:" ":350^  s (B20,0;"Use ";x;"ENTER";y;" to rerun this question" 2B21,0;"Use ";x;"SPACE";y;" for the next question " Z=32 d=13 1000 n 1320( x:q=0::250  h$,l$,qty  70F :f$=h$:v=3:m=((32 -f$)/2):900 -:::7;2;"Programme Content"  2010 !f$=" CELTIC REVISION SOFTWARE" v=18:m=3  900  500: k=1qty  750:65195,0  400  1000 k  9f$="End of "+h$:v=3:m=((32 -f$)/2) " 900 ,U10 ,0;x;"Press n then ENTER";y;" to auto-load programme ";2;l$ 6:::x;"Press r then ENTER";y;" to rerun thisprogramme" @M.G. Fincher E1::x;"Press b then ENTER";y;" to goto BASIC" J 800  T"k$="n"k$="r"k$="b"1700 ^721,0;x;"Undefined key please re-select" h 1610J k$="n"1800 k$="r"5 L:5,2;"RETURNING TO BASIC DESTROYS";8;"THIS PROGRAMME" E::x;"Press y to return to BASIC"''"Press any other key to abort" 0:i$= i$="y"i$="Y"  1550 /:f$=" START THE TAPE ":v=5:m=8  900 :: l$ !"Section 6","section 7",4 10 ,12 ;"Graphs": '144,24:104h,0 '144,568:104h,0 '144,88X:104h,0 (144,120x:104h,0 (144,152:104h,0 )160,160:0,-144 )192,160:0,-144 )224,160:0,-144 {1,19;1;"y";3,19;"3";7,19;"2";11 ,19;"1";19,18;"-1" f15,19;1;"0";15,23;"1";15,27;"2";15,31;"x" # (F"Plot the graph of y=2x-1. Hence solve the equation 2x-1=3."'"x is:" 2 Z42600( ," 0"," 1","-1"," 2","-2","d",2660d d 2500 nj0,0;"The graph of"'"y=2x-1 is a"'"straight line"'"and only two"'"points need be"'"plotted:" x":"When x=0,y=-1"'"When x=1,y=1" -2;18,0;"Plot the graph" 500 V156,16:2;72H,144:1,26;2;"y=2x-1" v10 ,0;"The equation"'"2x-1=3 is solved"'"by finding the"'"intersection of"'"the graphs"'"y=2x-1 and y=3" ':"Graphs intersect"'"at x = 2 "  f=152 n=15 f,16:0,159 f=f+24:n f=24 n=17 144,f:111o,0 f=f+24:n  3000 :1;0,24;"y";1,24;"6";4,24;"4";7,24;"2";13 ,23;"-2";16,23;"-4";19,23;"-6" /10 ,17;1;"-4 -2 0 2 4x"  t"Plot the graph of x-x-6=y forvalues of x=-3 to +4."''"Hence solve the equation"'';6;"x-x-6=0."'"x is:" & NR3100 ," 2 or -3","-2 or 3"," 1 or 0","-1 or 0","-1 or 1","b",3160X X 3080 b[0,0;"First work out"'"the values of y"'"for values of x"'"between -3 and 4." lS:"For x-x-6=y"';4;" x x -x -6 y";y;'"-3 9 3 -6 6"'"-2 4 2 -6 0" v4"-1 1 1 -6 -4"'" 0 0 0 -6 -6"'" 1 1 -1 -6 -6" 4" 2 4 -2 -6 -4"'" 3 9 -3 -6 0"'" 4 16 -4 -6 6" +:"When x=0.5"'"y=(.5)-(.5)-6"'" =-6.25" 2;"plot the graph" 500 &n=164:m=168:3460 &n=n+12 :m=96`:3460 &n=n+12 :m=480:3460 &n=n+12 :m=24:3460 &n=n+12 :m=24:3460 &n=n+12 :m=480:3460 &n=n+12 :m=96`:3460 'n=n+12 :m=168:3460 %n=206:m=21:3400H 82;19,0;"Draw the graph":500 2:164,168:12 ,-72H:12 ,-480:12 ,-24:6,-3:6,3:12 ,24:12 ,480:12 ,72H:z 0,0;""; ,n=121:" ":n *~0,0;"The equation"''"x-x-6=0"''"is solved by"'"finding the"'"intersection of"'"the graphs"''"y=x-x-6 and y=0" 43:"Graphs cut at"'"x=-2 and x=3"''" x = -2 or 3" > Hn=n+3:m=m+3 R!n,m:2;-6,-6 \ n=n-6 f n,m:2;6,-6 pn=n+3:m=m-3 z 3400H :500: %568,80P:0,40( &104h,80P:0,40( &168,80P:0,40( &200,80P:0,40( &568,80P:160,0 &568,96`:160,0 &568,112p:40(,0 '176,112p:40(,0 X568,80P:2:480,32 :64@,0:32 ,-32 :z #6,3;"velocity (ms)" v8,4;"60";10 ,4;"30";12 ,6;"0 30 70 90(sec)";11 ,27;"Time"  65195,1 $"A car accelerates from rest for 30 seconds, travels at constant speed for 40 seconds and then decelerates for 20 seconds (see";6,26;"graph)" . 3500 8O14,0;"The acceleration (a) ms, and deceleration (d) ms are:" B!:"a) a=3, d=2","b) a=1, d=1" L""c) a=1, d=2",d;"d) a=2, d=3" V"e) a=2, d=1" ` j*3610,"","","","","","d",3700t t~"From the graph the car accelerates from 0 to 60 ms in 30 seconds and decelerates from 60 ms in 20 seconds." ~ 3500 E13 ,17;"60"'" Acceleration = = 2ms";17;"30" E17,17;"60"'" Deceleration = = 3ms";17;"20"   f=152 n=15 f,40(:0,112p f=f+24:n  f=480 n=17  144,f:111o,0 f=f+16:n 1;2,24;"y";4,24;"6";6,24;"5";8,24;"4";10 ,24;"3";12 ,24;"2";14,24;"1" /16,17;1;"-2 -1 0 1 2x" 2:152,144:24,-480:12 ,-12 :12 ,-4:12 ,4:12 ,12 :24,480:z  " 4000 ,55,0;"The equation for"'"the graph is:" 610 ,10 ;"" @ JP4130","y = x","y = 2x","y = x+2","y = 2x-2","y = x-2","c",4200h h 4000 rJ0,0;"The shape of the graph is that of the equation y=x." |1"When x=0,y=2"'"Therefore equation"'"is y=x+2" [f$="Confirm the equation by reading the values of y for x=-2 to 2.":700:500 #6,0;"From the graph" %"When x=-2 y=6"'"i.e. y=(-2)+2= 6" ':"When x=-1 y=3"'"i.e. y=(-1)+2= 3" $:"When x=1 y=3"'"i.e. y= 1+2= 3" $:"When x=2 y=6"'"i.e. y= 2+2= 6"  xyzF STOP THE TAPE v mfUDG )K\y 8x8͞ x<͞  ~%~%|Xg~ w$<<8$((!{\6X#6V+^!w#~!VUw+!~#~+w#w$$$$$<<8$((|< 8$ 8$8p2LL28v> ~ (X~H~B$$B  $$ff"A @~D|b|>F <`~~"0H x>F n=1f Hi$(n)=32 860\ R k$=k$+i$(n) \n f  f=990  v,m;""; 23729\,v n=1̱f$ f 23728\,m:65000 m=m+1:n  1;f$(n);: %1;5;1;f$(n);: 2;f$(n);: 5;f$(n);:  250  100d ?21,0;x;"Please select your answer";y;" "  800  ~0k$="a"k$="b"k$="c"k$="d"k$="e"1180 ?21,0;x;"Undefined Key ?";y;" Please try again"  1050 k$w$1280 w$="a"a=5 w$="b"b=5 w$="c"c=5 w$="d"d=5 w$="e"e=5  100d =f$="CORRECT":f=995:v=0:m=25:910 B20,0;"Use ";x;"ENTER";y;" for answer explanation" B21,0;"Use ";x;"SPACE";y;" for the next question "  350^ =13 1300 =32 C20,0;x;"Wrong-Correct answer is ";w$;" ";:" "  I21,0;x;"Answer explanation follows";:" ":350^  s (B20,0;"Use ";x;"ENTER";y;" to rerun this question" 2B21,0;"Use ";x;"SPACE";y;" for the next question " Z=32 d=13 1000 n 1320( x:q=0::250  h$,l$,qty  70F :f$=h$:v=3:m=((32 -f$)/2):900 -:::7;2;"Programme Content"  2010 !f$=" CELTIC REVISION SOFTWARE" v=18:m=3  900  500: k=1qty  750:65195,0  400  1000 k  9f$="End of "+h$:v=3:m=((32 -f$)/2) " 900 ,U10 ,0;x;"Press n then ENTER";y;" to auto-load programme ";2;l$ 6:::x;"Press r then ENTER";y;" to rerun thisprogramme" @M.G. Fincher E1::x;"Press b then ENTER";y;" to goto BASIC" J 800  T"k$="n"k$="r"k$="b"1700 ^721,0;x;"Undefined key please re-select" h 1610J k$="n"1800 k$="r"5 L:5,2;"RETURNING TO BASIC DESTROYS";8;"THIS PROGRAMME" E::x;"Press y to return to BASIC"''"Press any other key to abort" 0:i$= i$="y"i$="Y"  1550 /:f$=" START THE TAPE ":v=5:m=8  900 :: l$ "Section 7","tests",11 H10 ,8;"Geometry";8;"Trigonometry";8;"Sets": n"Consider two triangles, XYZ and PQR. Which of the following pairs of triangles are congruent?" !:"1 XY = PQ, X = P, XZ = PR" "2 X = P, Y = Q, Z = R" "3 XY = PQ, YZ = QR, XZ = PR"  S2500 ,"1 only","2 only","3 only","1 and 3 only","all of them","d",2570 Dr=0:p=0:t=0:u=0:v=0:w=0: 2560 :2800 r=7:2800 u=7:2800 (t=7:2800 2 <"u=7:v=4:2830 n x2860, :2890J #r=7:2860, :2890J #p=7:2860, :2890J #t=7:2860, :2890J 2860,  u2,0;"The two triangles in condition 1are congruent because two sides and the included angle are equal" 'r;"XY=PQ, ";u;"X=P, ";t;"XZ=PR." 22910^ :2940| :2960 :2890J : f2,0;"The triangles in condition 2 aresimilar because corresponding angles are equal." 'u;"X=P, ";v;"Y=Q, ";w;"Z=R." "22910^ :2970 :2960 :2890J : ,d2,0;"The triangles in condition 3 arecongruent because corresponding sides are equal" 6'r;"XY=PQ, ";p;"YZ=QR, ";t;"XZ=PR." @2910^ :2940| : J$500:590N:2560 : THr;80P,80P:p;-20,-100d:t;-60<,20: ^10 ,40(:2900T hD16,0;"X";6,10 ;"Y";19,10 ;"Z" r | 150,40(:2900T G16,17;"P";6,27;"Q";19,28;"R": c20,37%:u;0,13 ,1:160,37%:u;0,13 ,1: P150,40(:60<,60<:-15,-75K:-45-,15 E16,17;"P";8,27;"Q";19,25;"R" e71G,31:w;-10 ,-6,1:195,34":w;-10 ,-6,1 d80P,108l:v;6,-4,1:200,90Z:v;6,-4,1: 240,64@:-120x,0:120x,78N:0,-78N:-8,0:0,8:8,0 r3,31;"M";9 ,31;"3";14,15;"L";14,22;"4";14,31;"N"  3000 $3,0;"In triangle LMN" 76,0;"Sin MLN is:":12 ,0;""  83050 ,"1","0.6","0.75","0.3","0.8","b",3100  3000 &p$=" Side opposite MN" 0#q$= " MLN = = " :r$=" Side adjacent LN" Ds$=" Hypotenuse LM" Nu0,0;"In LMN, N=90."''"By Pythagoras' theorem"''"LM = LN+MN"'" = 16+9"''"LM = 25"'" = 5" Xq16,10 ;p$'"Sin";q$;11 ;s$:500:11 ,0;"Sin MLN"'" 3"'" = = 0.6"'" 5" b500:590N l:"Remember" v,2,10 ;p$'"Sin";q$;11 ;s$ ,6,10 ;r$'"Cos";q$;11 ;s$ -10 ,10 ;p$'"Tan";q$;10 ;r$ J14,11 ;"Sin MLN"'"Tan MLN = ";11 ;"Cos MLN"  P128,88X:120x,0:-40(,64@:-80P,-64@ '192,88X:16,64@ /203,147:3,-1,1 .206,143:7,1,1 d1;2,26;"M";10 ,15;"L P N";6,22;"3 4"  3500 ,2,0;"In LMN, MP bisects M." :"LM=3cm, MN=4cm" 06,0;"The area of"'"LMN = 14cms" :"The area of"'"LMP is:" 10 ,0;"": B3560 ,"7cm","3.5cm","6cm","10cm","12cm","c",3620$ $ 3500 .\0,0;"The area of a is equal to halfthe base times the perpendicularheight." 8Ef$="Draw the perpendicular of height h":700:500 =E600X:19,0;2;"Investigate the ratio LP:LN" B 3800 L@4,0;"Area of MLN"'" 1"'"= xLNxh = 14cm"'" 2" V'"Area of LMP"'" 1"'"= xLPxh"'" 2" `p3;"Area MLN 0.5xLNxh LN";3;" = = ";3;"Area LMP 0.5xLPxh LP" j;:15;"14xLP"'" Area LMP = ";16;"LN" t 500: ~3500 :3800 0,0;"The bisector of an angle in a divides the side opposite in theratio of the sides"'"containing the angle." ?" ML LP 3"'2;" = = "'2;"MN PN 4" (" 4"'" PN = LP"'8;"3" "Now"'" LN = LP+PN" ^10 ;"4 7 LP 3"'" LN = LP+LP=LP or = ";10 ;"3 3 LN 7" Q:15;"LP 3"'"Area LMP = 14x = 14x = 6cm";15;"LN 7"  v208,152:0,-64@:216,88X:0,8:-8,0:7,27;"h"  =168,160:80P,-128:0,112p ;-80P,16:0,-64@:80P,-16 B245,104h:4100:245,108l:4100 B165,124|:4100:165,128:4100 s192,158:3,-3:-3,-3:192,94^:3,-3:-3,-3 ҿ1;2,20;"Q";3,31;"M";10 ,20;"P";9 ,23;"5";10 ,28;"4";12 ,31;"N";11 ,25;"R";17,31;"S"  %3,3:3,-3: V2,0;"Parallelogram MNPQ"'"is 18 cm in area."'"R divides NP so"'"that:" 76;"NR 4";6;" = ";6;"RP 5" ""MN produced meets"'"QR at S" ,:"The area of RNS=" 6"4000:12 ,0;"" @ JM4110,"3.2 cm","4 cm","2.22cm","10 cm","6.4 cm","a",4200h h 4000 rz0,0;"The area of a is half the areaof a parallelogram on the same base and between"'"the same parallels" |"Area MNPQ = 18cm" 5"Area QRP"'" 5 18"'" = x = 5cm"'" 9 2" j"In 'sQRP, RNS"''"QRP = NRS (vert."'"opposite 's)"''"PQR = NSR (alternate"'"'s, MN parallel QP)" #:"RPQ = RNS (sum of 's of )" V2;"'s QRP and RNS are similar. Usethis to find the area of RNS.":500 :4000 |0,0;"The ratio of areas of similar triangles is equal to the ratio of the squares on"'"corresponding sides" 9:"Area RNS NR"'" = "'"Area QRP RP" ?:12 ;"16x5"'"Area RNS = ";11 ,13 ;"25" :10 ;"= 3.2cm"  192,88X,568 x248,88X:-112p,0:568,568:568,-568:-100d,-35#:44,,91[ r192,84T:0,3:162,118v:4,-4:215,118v:4,4 q1;11 ,16;"L O M";5,24;"N";15,17;"P";0,0;""   4500 L2,0;"In the following diagram, LOM isa diameter and"'"LN=NM." &6,0;"Angle NPM is:"''""  94550,"90","60","45","15","10","c",4600  4500 M"The in a semicircle is a rightangle. In LMN, LOM is a diameter."  :" LNM = 90" \:"Now LN = NM"'"(given)"''" NLM = NML"'" = 45"'"(Base angles"'"of isosceles )"  U:" NPM = NLM"'" = 45"'"('s subtended by"'"the same arc, NM, are equal)"  |192,88X,568 u136,88X:112p,0:-35#,524:-77M,-524:30,480:47/,4 N152,120x:5,-4:184,140:0,-5 p1;11 ,16;"X";11 ,30;"Y";10 ,18;"40";4,19;"W Z"   5500| \2,0;"XY is a diameter of the circle."''"ZXY = 40"''"XW = WZ"'''"WXZ is:"  95550,"40","70","35","25","90","d",5600  5500| `0,0;"In WXZ, WX=WZ(given)"'" WXZ is an isosceles triangle"'"Hence WXZ = WZX" :"Let WXZ = y" 0:"Now XZY = 90"'"(angle in a"'"semicircle)" ?:"Also"'"WXY+WZY=180"'"(opposite 's"'"of a cyclic quad)" !:"WXZ+ZXY+WZX+XZY = 180" "y + 40 + y + 90 = 180" &A18;"2y = 50";19;"y = 25";14,18;" " 0 p)65195,1:"If";18;"3" z$11 ;"Tanx = "'18;"4" 9"Without using tables the values of Sinx and Cosx are:" O:"a)";5;"1";12 ;"2";17;"b)";22;"16";30;"9" -"Sinx=,Cosx=";17;"Sinx=,Cosx=" :5;"5";12 ;"5";22;"25";30;"25" P::"c)";5;"5";12 ;"4";17;"d)";22;"3";30;"4" -"Sinx=,Cosx=";17;"Sinx=,Cosx=" :5;"9";12 ;"9";22;"25";30;"25" H:e;"e) 3";12 ;"4"'"Sinx=,Cosx="'5;"5";12 ;"5"  *6000p,"","","","","","e",6100 ["Given 3";26;"9"'" Tanx= then Tanx=";12 ;"4";26;"16" C"Now";17;"Sinx";11 ;"Tanx=";17;"Cosx" )"Also"'"Sinx+Cosx=1 or Cosx=1-Sinx" f:15;"Sinx";25;"9"'" Tanx = = "'13 ;"1 - Sinx";25;"16" :" 16Sinx = 9 - 9Sinx" =28;"3"'" 25Sinx = 9 Sinx = "'28;"5" '"Now";19;"9 16";31;"4" D" Cosx =1-Sinx=1-= Cosx="'19;"25 25";31;"5"  d65195,1 n"A man at the top of a cliff, h feet above the beach sees a boatin the sea at an angle of depression of y. The distance of the boat from the base of thecliff, vertically below the man is:" x:"a) hTany","b) hSiny" 112 ,4;"Cosy"'"c) "'" h" ad;12 ,16;" h ";13 ,16;"d) ";14,16;" Tany" :"e) hCosy"  *6500d,"","","","","","d",6600 /"Let distance of boat from base of rock = d" b64@,144:120x,-502:-120x,0:0,+502:502,0 m88X,141:3,3:-3,3:88X,91[:3,3:-3,3 764@,100d:6,0:0,-6 [75K,140:2,4,1:170,95_:2,4,-1 [1;4,4;"MAN y";7,2;"CLIFF h";9 ,18;"y" $11 ,13 ;"d BOAT" d14,12 ;"h";24;"h"'" Tany = d = ";12 ;"d";22;"Tany"  X"A car drives from a town M on a bearing of 060 for 10km and then travels for a further 10km on a bearing of 040 to a town NThe bearing of N from M is" b g>7000X,"050","060","020","100","040","a",7020l l 7300 vx"The car travels for 10km along"'"MO on a bearing of 060. It"'"then travels for 10km along"'"ON on a bearing of 040" :"LMO = MOY (alternate"'"'s, LM parallel to XY)"'"XOY = 180 (XOY is a"'"straight line)"'"XOM = 180-60 = 120"'"MON =120+40 = 160" 4:"Now MO=ON (given)"'"MON is an "'"isosceles " 7:2;"Calculate the"'"value of NMO":500 :7300 :"As MON is isosceles, its base"'"'s are equal."'"i.e." " NMO = MNO = y" i"Now"'"NMO+MNO+MON = 180 (sum"'"of the 's of a )"''" 180 = 160 + y + y"'" 20 = 2y"'" 10 = y" %'"Now"'" LMN=60-y"'" LMN=50" )"i.e."'"Bearing of N"'"from M = 050"  y120x,568:0,-24:128,128:-40(,-80P:-88X,-480:0,-10 M247,144:0,25:208,64@:0,32 1;2,31;"N";8,28;"10km";9 ,25;"X";12 ,26;"O";14,15;"L";14,26;"Y" 1;18,15;"M";16,19;"10km";18,20;"LMO=60";19,20;"XON=40";0,0;""  Lj770:62>,94^:0,62>:136,0:0,-62>:-136,0 V<115s,126~,25:145,126~,25 `:1;3,6;" X";3,21;"Y" j/2:128,110n:6,0 t'124|,114r:12 ,0 ~'122z,118v:16,0 '121y,122z:18,0 '121y,126~:18,0 '121y,130:18,0 '122z,134:16,0 '124|,138:12 ,0 &128,142:6,0 z   7500L 911 ,0;"The shaded area is represented by:"  D7650,"X Y","X Y","X' Y'","X Y","X Y","d",7700 V13 ,0;"The shaded area represents the intersection of the sets X and Y" "7500L:500:590N (T:"Remember"''"X Y means X is a subset of B"''"y E Y means y is an element of Y" 2r:" is the universal set from which all subsets are formed"''"X Y is the intersection of thesets X and Y"  ~ (X~H~B$$B@   $$ff"A @~D|b|>F <`~~"0H x>F n=1f Hi$(n)=32 860\ R k$=k$+i$(n) \n f  f=990  v,m;""; 23729\,v n=1̱f$ f 23728\,m:65000 m=m+1:n  1;f$(n);: %1;5;1;f$(n);: 2;f$(n);: 5;f$(n);:  250  100d  018,20;2;"[";s(k);" marks]" ?21,0;x;"Please select your answer";y;" "  800  ~0k$="a"k$="b"k$="c"k$="d"k$="e"1175 ?20,0;x;"Undefined Key ?";y;" Please try again"  1050 k$w$(k)1280 w$(k)="a"a=5 w$(k)="b"b=5 w$(k)="c"c=5 w$(k)="d"d=5 w$(k)="e"e=5 mark=mark+s(k) noans=11260 cor=1:100d 018,20;2;"[";s(k);" marks]" =f$="CORRECT":f=995:v=0:m=25:910 B21,0;"Use ";x;"SPACE";y;" for the next question "  300, =32 noans=11260 F20,0;x;"Wrong-Correct answer is ";w$(k);" ";:" "  1260 d)2;0,3;"part(i)":: ncor=11395s p q=q-1 s?2;0,0;"Q";q;0,3;"part(ii)": u x7:q=0:mark=0:noans=0::250  h$,l$,qty  70F :f$=h$:v=3:m=((32 -f$)/2):900 -:::7;2;"Programme Content"  2010 !f$=" CELTIC REVISION SOFTWARE" v=18:m=3  900  21004 k=1qty -750:65195,0:cor=0  400  1000 k  noans=19000(# 7:4;0,7;"You obtained ";mark;" %" 9f$="End of "+h$:v=3:m=((32 -f$)/2) " 900 ,U10 ,0;x;"Press n then ENTER";y;" to auto-load programme ";2;l$ 6:::x;"Press r then ENTER";y;" to rerun thisprogramme" @M.G. Fincher E1::x;"Press b then ENTER";y;" to goto BASIC" J 800  T"k$="n"k$="r"k$="b"1700 ^721,0;x;"Undefined key please re-select" h 1610J k$="n"1800 k$="r"5 L:5,2;"RETURNING TO BASIC DESTROYS";8;"THIS PROGRAMME" E::x;"Press y to return to BASIC"''"Press any other key to abort" 0:i$= i$="y"i$="Y"  1550 /:f$=" START THE TAPE ":v=5:m=8  900 6:::2;" At the beginning of SIDE ONE.":: l$ "Tests","directions",29 /8,4;"20 sample test questions": 4w$(29,1) >n=129 Hw$(n) Rn \u"c","b","e","e","b","c","d","a","a","b","d","d","c","c","b","e","b","b","c","c","a","d","b","b","c","b","c","b","e" f s(29) pn=129 zs(n) n 2,3,2,3,2,3,5,5,2,3,3,2,5,5,3,2,5,5,3,2,3,2,5,5,5,3,2,5,5  500: x;"INSTRUCTIONS" :"To use this test as a mock examination the answers are displayed at the end of the testotherwise the answers appear after each question." j:"Do you wish to use this test as a mock examination? "'';x;"Press y for yes"''"Any other key for no." ""2240 =""2250 ="y"Ŧ="Y"2300   .0,8;4;"MOCK EXAMINATION" ,5,6;x;"Answer all questions" 210 ,3;x;"Time allowed - 1hr 30min." $noans=1 500: 65195,1 1380d O"Simplify 3q+5p q-4p"'10 ;" - "'12 ;"3";19;"2" S:4;"4q+p"," 3q+22p"'"a) ","b) ";5;"5";22;"5" 111 ,20;"2q+p"',"d) "'," 6" =c;11 ,0;" 3q+22p"'"c) "'" 6 " ":" 2q+p"'"e) "'" 5"  "","","","","" 1390n "A cricketer scores 21,35,0,40,12in 5 successive innings."'"What does he score in his sixth innings, if his average for the 6 innings is 26?"  "18","48","31","24","27" H 1380d R8;"28.08 0.001 is"  ("2.808","28.08","280.8","2808","28080"  1390n >9 ;"4.5 x 0.01 is"'9 ;""'13 ;"3" j t!"150","15","1.5","0.15","0.015"  1380d '3;"0.0810 in standard form is" 2"81x10","8.1x10","8.1x10","0.8x10","0.08x10"   1390n #5;"1011 + 1010 + 111 =" '"10111","11011","11100","1101","1011"  h]"A boy sells a motor bike for `1800 making a loss of 10%"'"The boy bought the bike for:" i r)"`1500","`1620","`1980","`2000","`2120" 0C"Calculate the simple interest "'"on `656 at 12.5% for 4.5 years" : D+"`369","`738","`553.50","`73.80","`55.35"  1380d "The rateable value of a house is`55 and the owner pays `49.50 inrates for the year."'"The rate at which the rates are levied is:"   G"90p in `1","`1.11 in `1","55p in `1","5.5p in `1","85p in `1"  1390n y"The average of five numbers = 60"'"The average of another three numbers = 40"'"The average of all eight numbersis:"  8 "50","52.5","25.3","50.6","25"  1380d "A car travels for 2 hours at 50mph and then for 1 hour at 80mph. The average speed of the car for the whole journey is:"  *"65mph","30mph","55mph","60mph","130mph" P65195,1 Q 1390n R"`96 is divided between two people X&Y so that the ratio "'""'"money for X : money for Y = 5:3"'""'"The money received by each is:" S:4;"X";10 ;"Y"''"a) `5";9 ;"`91"''"b) `40";9 ;"`24"''"c) `3";9 ;"`93"'';d;"d) `60";9 ;"`36";y;''"e) `8";9 ;"`88" Z d"","","","","" "The volume (V) of a gas varies directly as its temperature (T) and inversely as its pressure(P)"''"When T=288 and P=2atm, V=800cc"''"When T=297 and P=3atm, V=" " ,,"400cc","1238cc","550cc","2475cc","1100cc" $"The factors of 10p-11pq-6q are"  T"(2p+3q)(5p-2q)","(10p+q)(p-6q)","(5p+2q)(2p-3q)","(10p-q)(p+6q)","(2p+3q)(5p+2q)"  1380d @10 ;"5.8 - 2.1"'10 ;" ="'13 ;"0.74"  "0.5","5","2","50","0.02" p 1390n z 6;"2(5m-3n) - 3(m-n) ="  +"13m+3n","7m+9n","13m-3n","7m-9n","7m-3n" 865195,1 9p"In the equation"'""'6;"11m-5 (3m+3)"'6;" - = -4"'8;"4";16;"5"'"m is" ::"a) 1";8;b;"b) -1";y;''12 ;"67"'"c) 0";8;"d) -"'12 ;"43"'""'3;"117"'"e) "'3;"67" B L"","","","","" J"Factorize p+p-6"'"Hence the value of p in"'""'11 ;"p+p-6=0 is"   8"3 or -2","-3 or 2","-6 or 1","6 or -1","1 or 0"  1380d $"The product of p,5p and -2p is:"  ""-4p","4p","-10p","p","6p-2p"  1390n /"The sum of the angles of a hexagon is:"  %"540","360","720","1080","180" X 1380d Y"A newsagent buys pencils at `28.80 a gross and sells them at25p each. If the total selling price for all the pencils is `108, the newsagent will make a total profit of:" b l)"`21.60","`79.20","15p","45p","`136.80"  1390n !"If k = 4x10, then k =" * 4,"8x10","16x10","8x10","16x10","16x10" 65195,1 s"The values of p&q in the simultaneous equations"'""'9 ;"3p + 2q = -26"'9 ;"5p - q = 0"'"are" f;3;"p";8;"q"''"a 0 1"'';b;"b -2 -10";y;''"c -1 0"''"d -5 -2"''"e -1 1"  "","","","","" 65195,1 /"The equation"'"for this graph"'"could be:" 1:"In the "'"following"'"k & c are"'"constants" 6;"kx"'"a y= (k=positive c=positive)"'6;"c"';b;"b y=kx+c(k=negative c=positive)";y;'"c y=kx+c(k=negative c=negative)"'"d y=kx+c(k=positive c=negative)"'"e y=kx+c(k=positive c=positive)" 127,127:96`,0:175,175:0,-80P:143,167:72H,-72H:6,15;"x":0,22;"y":1;6,21;"0"  "","","","","" xY"In LMN"'""'"MLN=60"'"POL=50"'"PNO=30"'""'"OP is"'"parallel"'"to MN"''"PNM is" z247,104h:-80P,64@:-88X,-104h:168,40(:-128,8:88X,24 o160,120x:3,3:-3,3:160,80P:3,3:-3,3 0,19;"L";4,27;"P";10 ,30;"N";13 ,8;"M";7,13 ;"O";12 ,0;""   "130","30","70","60","40" @ 1380d A191,112p,568 Jv191,568:0,112p:546,-480:-95_,30:41),-94^:546,64@ T&170,568:80P,0 ^i1;0,23;"Y";3,17;"O";6,31;"X";15,24;"T P" hr2,0;"In the diagram"''"PT is a tangent,"'"TY a diameter"'"of the circle,"'"TOX = 50."''"YTX is:" i r"90","40","50","20","25"  1390n b"XY is a fixed line and a point P moves so that"';6;"XY = XP+YP"''"The locus of P is"  "perpendicular bisector of XY","line perpendicular to XY at Y","a circle, radius half XY","the bisector of angle XPY","a line parallel to XY" p"L,M,N,O,P are five points on thecircumference of a circle in that order."'"LMN=130 and OLN=80"'"OPL="  !"30","130","80","50","100" !D"220 people went to night classesin painting, writing and pottery" !\"120 went to painting classes"'"80 went to writing classes"'"70 went to pottery classes" !i"20 went to painting and writing"'"25 went to writing and pottery"'"12 went to painting and pottery" !Z:"The number of people who attended painting, writing and pottery classes was:" ! !"15","200","57","220","7" #( :12 ;5;"ANSWERS" #2q=1:n=1 #<$9100#:9190#:9100# #F$9200#:9190#:9100# #P$9200#:9300T$:9190# #Z 500: #f=12 #9400$:f # # 9400$ #f=12 #9300T$:f $ $T"Q";q;4;w$(n) $^n=n+1:q=q+1: $M"Q";q;4;"part (i) ";w$(n),"Q";q;20;"part (ii) ";w$(n+1) $n=n+2:q=q+1: xyzF STOP THE TAPE v mfUDG FK\y 8x8͞ x<͞  ~%~%|Xg~ w$<<8$((!{\6X#6V+^!w#~!VUw+!~#~+w#w$$$$$<<8$((|< 8$ 8$8p2LL28v> ~ ~$<  $$@ "A @88(< 8$0H xBBBBB<