ZXTape! 2Mathematics - Side B*Celtic Revision Software / Sphere SoftwareE.J. Perkins, M.G. FincherEnglish EducationalMpmeOriginal Release%TZXed by Andrew Barker For Gary Poole0$Examination Practice & Tests O Levelsection 5 2C B4C8x=7:y=6:z=0:y:y:z::1400x g64999:x=7:y=6:z=0:y:y:z::5,3;"Please leave tape running" "UDG"65000,536 Q:70F:f$=" 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 )qK\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 FFK\y 8x8͞ x<͞  ~%~%|Xg~ w$<<8$((!{\6X#6V+^!w#~!VUw+!~#~+w#w$$$$$<<8$((|< 8$ 8$8p2LL28v> ~ ~$<  $$@ "A @88(< 8$0H xBBBBB<