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12 vD@ZZZZZZZZZDu
6 scroll=8550
6 innum=8240
6 inchar=8360
6 flag=flag+1
6 concatenation
6 clear=8180
6 b$=F$(v,N)
6 @@@@@@@@@@@@@@@@@@@@Du
6 @@@@@@@@@@@@@@@@@@@@D
6 ;a;" ";b$
6 ;;;;;;;;;;;;;;;;;;;
6 ;"x y"
6 ;"What is the RULE that adds 3 to
6 ;"What do you think this MACHINE does ?":
6 ;"Type in a whole number between 0 and 10":
6 ;"PRESS S"
6 ;"PRESS R":
6 ;"In this case, the MACHINE is obviously adding TWO to the numbers you are putting in. So we can write it's RULE as ....":
6 ;"If the MACHINE was adding 5 to your number x , then we would write the RULE as:-";:
6 ;"<<and see what happens>>":
6 ;" ---------"
6 ;" ":
6 ;" "
6 '" otherwise:-";
6 "F","U","N","D","A","M","E","N","T","A","L"
6 "&","[","_","]","&","^","{","|","}","@"
5 ;" When you are ready to begin thenext lesson, type NEW followedby-";
4 x y":
4 table=8480
4 mdown=8200
4 delay=8160
4 d$=".....":
4 d$="....":
4 arrow=8500
3 SYMBOL SHIFT
3 Correct !":
3 And another...":
3 '''" Now solve the equation."
2 z,c;" "(
2 x,c;" "(
2 n1+"x"+("+"
2 m$="objective 6."
2 m$="objective 5."
2 m$="objective 4."
2 del=del-0.5
2 del=del-.3
2 d$=".......":
2 Try another number.":
2 Try another number."
2 Let's see..."
2 And another..."
2 ;"Score ";scr;"."
2 ;"POST TEST (1)"
2 ;"LESSON TWO"
2 ;"LESSON THREE"
2 ;"LESSON ONE"
2 ;"LESSON FOUR"
2 (inverse rule)"
2 '''" FOURTHLY-write the answer as a sentence."
2 ''" What is the equation ?"
2 '"
2 No, the equation is ";e$;".":
2 and pressingthe
1 your number
1 x=75-27
1 x divided by2
1 w$=".x+.":
1 usr
1 subtext=2100
1 subtext=2030
1 subtext=2000
1 since x times the number of oranges is 48."
1 scr=scr+fflag:
1 s$="x/"+n$
1 s$="x-"+n$
1 s$="x+"+n$
1 s$="3x-2":
1 s$="2x+1":
1 r$="x-"+n$
1 r$="x+"+n$
1 q$="subtracts":
1 q$="divides by":
1 q$="000000000":
1 q$(qp)="1":
1 pmach=8800
1 pmach=8700
1 pmach=7000
1 outbot=8700
1 m$="objective 3."
1 m$="objective 2."
1 m$="objective 1."
1 m$="You got all the questions wrongso I suggest you do all thelessons again."
1 m$="Well done, but you did get thesequestions wrong."
1 m$="This was the question you gotwrong."
1 m$="Not too bad but you still gotall these questions wrong."
1 m$="Not so good, you got all thesequestions wrong."
1 logo
1 isthe same as the rule
1 intop=8600
1 flag2=flag2+1
1 file
1 d$="...............................":
1 d$=".........":
1 d$="........":
1 cross=8100
1 cross=7350
1 counter=counter+1
1 codet
1 code4
1 code3
1 code2
1 answer=7200
1 a$="x+"+k$(3
1 You must have entered differentnumbers, try again.":
1 Yes,the equation is ";e$;".":
1 Yes, the inverse rule is x+";nm;".":
1 Yes, the equation is 7x=";y;".":
1 Yes, the rule for the bottommachine is
1 Yes, it would be ";e$;".":
1 Yes, it subtracts 4.":
1 Yes, it doubles the number youput in.":
1 Yes, it adds 3.":
1 Yes, ";i$;",now what is the answer?":
1 Where 'x' is the number you putin. But this is still a littlelong, so we could replace theword 'minus' with the '-' sign,which is obtained by holdingdown
1 What do you think the rule isfor a machine that multiplies anumber by 3?"
1 What do you think the rule isfor a machine that multipliesa number by ";nm;"?"
1 Use your list to enter the samenumbers in the same order. Startwith the first now:"
1 Type in a whole number between 1 and 9."
1 Type in a whole number between1 and 9."
1 Two magazines cost ";y;"p. If one cost ";nm;"p, what was the cost of the other ?"
1 To halve a number you mustdivide by two,therefore we couldwrite:"
1 To describe what the lastmachine was doing we couldwrite:"
1 To describe what the lastmachine did we could write:"
1 This means that the rule '
1 The cost of the book is 48p."
1 That's right, the inverse ruleis
1 That's right!":
1 That ends this Post Test.It maybe a good idea to have anotherlook at the lessons you do notfully understand."
1 Suppose you made x equal 11.What would the y number be?"
1 So,the rule for the top machineis
1 So, the rule '
1 So, let the rule for the secondmachine be
1 Recording
1 Question two.
1 Question three.
1 Question six.
1 Question seven.
1 Question one.
1 Question nine.
1 Question four.
1 Question five.
1 Question eight.
1 Question ";q;".";
1 Question ";q;". Score ";scr;"."
1 Question ";q;". Score ";scr;"."
1 QUESTION ";o
1 QUESTION ";i;
1 Press any key when you havecompleted the exercise and Iwill begin the second part ofLesson One."
1 PRESS ANY KEY WHEN YOU HAVE COMPLETED EXERCISE FIVE."
1 Now we must find a way for youto write the rule for this sortof machine, so that I canunderstand you easily.":
1 Now try another machine.":
1 Now three questions for you totry.":
1 Now the next number."
1 Now the last."
1 Now five questions for you toattempt.":
1 Now you have completed thefirst part of lesson one youshould attempt exercise 1a inthe instruction booklet beforeproceeding with the second part."
1 No,the rule would be
1 No,in fact it doubles the numberyou put in."
1 No, x=";nm;", because ";y;"/7=";nm;".":
1 No, the rule is ";a$;"."
1 No, the rule is ";
1 No, the output would be ";ans;"."
1 No, the magazine cost ";a;"p.":
1 No, the inverse rule is x+";nm;"."
1 No, the answer is ";a;"."
1 No, the answer is ";nm+y;" since ";y;"+";nm;"=";y+nm;"."
1 No, it would be 3x-2."
1 No, it would be 31, since 2x15is 30, plus 1, makes 31."
1 No, it would be ";a;".":
1 No, it would be ";a;"."
1 No, it was 31 because, 11 times3 is 33, minus 2, makes 31."
1 No, in fact it subtracts 4."
1 No, in fact it adds 3."
1 Look at the machine above, itactually multiplies the numberyou put in by two.We could writethis as:
1 Let's try another...":
1 Let's try two more machinesjoined together.":
1 If x is 15, what will y be?":
1 If x is 15 what will y be?"
1 If the rule is x-3 and theoutput is 2,what would the inputx be ?"
1 However , this is confusingbecause it has too many x's. Therefore we must remove thefirst 'x' to leave:"'"
1 Here is a machine with the rule
1 Good, that proves that thismachine does the same as thelast two joined together.":
1 Eight oranges cost 48p. Whatdoes one orange cost ?"
1 Did you get the same results asyou did with the two machines?"'"Press
1 Created with Ramsoft MakeTZX
1 Correct, let's try another.":
1 Correct, it would be 3x-2.":
1 Correct !";
1 But, before we do, copy theresults table onto a piece ofpaper."
1 But this is too long, so let'sstart by replacing '
1 But this is too long, so wecould start by replacing 'yournumber'by the letter'x',to give:"
1 As you have probably realized,the top machine doubled yournumber x, while the bottom onethen added 1."
1 ALGT 4f
1 ALG5
1 ALG4
1 ALG3
1 ALG2 Uo
1 ALG1
1 A machine has the rule ";w$;"."'"What will its output be if"'"x is ";nm;"?"
1 A book and pen cost 75p. If thepen cost 27p, what was the costof the book ?"
1 ;"Yes,that's right,because
1 ;"What is x if ";e$;"?"
1 ;"UPPER CASE";
1 ;"Type in file name in ";
1 ;"That completes Lesson Two."
1 ;"That completes Lesson Three."
1 ;"That completes Lesson One."
1 ;"That completes Lesson Four."
1 ;"That completes Lesson Five."
1 ;"That completes the Post TestPart One."
1 ;"Stop and rewind tape"
1 ;"Solve the equation, ";e$;".":
1 ;"SCORE ";scr
1 ;"SAVE""file"" LINE 2"
1 ;"PLEASE WAIT";
1 ;"No, it is ";x;", because
1 ;"Load main program"
1 ;"Leave tape running"
1 ;"LOAD ~ALGT~"
1 ;"LOAD ~ALG6~"
1 ;"LOAD ~ALG5~"
1 ;"LOAD ~ALG3~"
1 ;"LOAD ~ALG3~"
1 ;"LOAD ~ALG2~"
1 ;"LESSoN FIVE"
1 ;"LESSON FIVE"
1 ;"In this lesson we are going to see how to apply all we have learned to solving simple problems."
1 ;"If you would like to go over"'" the Post Test again, ";
1 ;"If you would like to go over"'" Lesson Two again, ";
1 ;"If you would like to go over"'" Lesson Three again, ";
1 ;"If you would like to go over"'" Lesson One again, ";
1 ;"If you would like to go over"'" Lesson Four again, ";
1 ;"If you would like to go over"'" Lesson Five again, ";
1 ;"(b) What is x if ";l$;" ?"
1 ;" You probably did most of thequestions in that exercise byintelligent guess work,but thereis a more mathematical way."
1 ;" When you are ready to begin thePOST TEST (1), type NEW followedby-";
1 ;" What rule does a machine haveif its input x and output y areas shown below?"
1 ;" What is the equation ?":
1 ;" What do you think the x numberis ?"
1 ;" We have:
1 ;" We can write these questions ina slightly different but shorterway."
1 ;" Type in a whole number between1 and 9 and see what happens."
1 ;" Type in a number between 1 and9 and see what happens."
1 ;" This Post Test contains ninequestions which are matched tothe minimum objectives, set outin the instruction booklet."
1 ;" The combined rule for a machineis ";k$;"."
1 ;" THIRDLY-solve the equation:-"
1 ;" THIRDLY-solve the equation."
1 ;" Suppose the rule is '3x' andthe output is 12."
1 ;" Now you have completed lessonfive you should attempt exercisefive in the instruction booklet."
1 ;" Now one for you to try...":
1 ;" Now one for you to try..."
1 ;" Now an example without using amachine."
1 ;" Now that you have completedlesson four you should attemptexercise four in the instructionbooklet, before continuing."
1 ;" No, it is ";i$;",so what is the answer ?"
1 ;" Here's another example...":
1 ;" (b) What is x if ";l$;" ?"
1 ;" (a) Solve the equation ";k$;"."
1 ;" ";no;" apples cost ";cost;"p."
1 ;" Well done, you got all thequestions right. You are nowready to start the second partof ~Fundamental Algebra~." :
1 ;" PRESS ANY KEY WHEN YOU HAVE COMPLETED EXCERCISE ONE."
1 ;" PRESS ANY KEY WHEN YOU HAVE COMPLETED EXCERCISE TWO":
1 ;" LOADING PROGRAM
1 ;" Two machines are joinedtogether. The rule for the firstmachine is ";a$(
1 ;" PRESS ANY KEY WHEN YOU HAVE COMPLETED EXCERCISE THREE."
1 ;" Press any key to put in the x number.";
1 ;" ":
1 ;" "
1 ;" "
1 ;" "
1 2 times your number."
1 2 times x."
1 2 times x
1 .Thisleaves us with:"
1 . Now suppose x was 11 whaty value would the machineoutput?"
1 . Butthe second machine is special.";
1 ,so we will test to see if itdoes the same as the last twomachines, by putting in the samenumbers.":
1 , sowhat do you think the rule isfor the second machine?"
1 , since3x is the same as
1 );".The table belowshows three input numbers x andthree output values y."
1 );" and the rule forthe other is ";a$(2
1 (cost/no):
1 ((no*n1)+n2)
1 'by the letter'
1 '.Which gives us:"''"
1 '''''" Now you try one...":
1 '''''" Now a short exercise of fivequestions like this one.":
1 ''''"Here is an example...":
1 ''''" The rule for a machine is ";k$;"."'''" What is the inverse to this rule?"
1 ''''" SECONDLY-make the equation:-"
1 ''''" A machine has the rule ";r$;"."
1 '''"What is the inverse rule ?"
1 '''" The rule for a machine is ";no;"x."''"What is the inverse rule?"
1 '''" Now one for you to try..."
1 '''" Let x be the unknown number."
1 '''" Here is another example...":
1 '''" A number divided by ";n1;" is equalto ";n2;". What is the number?"
1 '''" (a) Solve the equation ";k$;"."
1 '''" So
1 ''"First, what is the inverse rule."
1 ''" What is the output y, if x=";:
1 ''" What is the cost (in pence) of one apple ?"
1 ''" Well, the inverse rule will be'x/3'."
1 ''" We can solve it..."
1 ''" Using the inverse rule we get:"''"
1 ''" Therefore the number is 6."
1 ''" SECONDLY-make the equation:-"
1 ''" Now solve the equation."
1 ''" Let x pence be the cost of apencil."
1 ''" Let x pence be cost of themagazine."
1 ''" Here is an example:-"
1 ''" First let the number we aretrying to find be '
1 ''" FIRST-let x pence be the costof the book."
1 ''" FIRST-let x pence be the costof one orange."
1 ''"
1 '"Now let x be ";y;" and work out theanswer."
1 '" Your answer to each question ischecked. At the end, you will betold which questions you gotwrong and the objectives thathave not been achieved. Based onthis you will be given a guideto further study."
1 '" What is the equation ?"
1 '" We can rewrite the question as:"
1 '" We call 'x+3=5' an EQUATION. Wecall it an equation because ofthe equals sign."
1 '" We have written '
1 '" The idea is to use the inverserule and put in the number wewere given as output."
1 '" Sometimes we ask the samequestion by saying 'Solve theequation x+3=5'."
1 '" So, 12 divided by 3 is 4."''" Therefore x=4."
1 '" Let's try some examples..."
1 '" Instead of asking ""What is xif the output from the rule x+3is 5?"" we write, ""What is x ifx+3=5?""."
1 '" In this lesson we are going toput unknown numbers into themachines and you have to workout what the number was."
1 '" Because this program producesdifferent questions each time itis loaded, it can be used togreat advantage in your revisionwork."
1 '" What is the rule for thecombined machine?"
1 '"
1 '"
1 ' sign.To give:"''"
1 ' is the same as the rule'
1 ' is the same as the rule
1 ' by the '
1 ' be the number."
1 ' is thesame as the rule '
1 ' for 'thenumber' and '
1 ' for 'is'. "''"
1 #"a\*a\"c\*c\"e\
1 "clear (y/n) ?";q$
1 "address ? ";x
1 "Which tested ";m$
1 "If it outputs the number ";y;", whatis the input number x?"
1 "Filename",a$
1 " Now five questions for you totry..."
1 " If ";nm;" is added to a certain number, the answer is ";y;"."''" What is the number ?"
1 " I cut ";nm;"cm off a piece of wool.If the wool is now ";y;"cm long,how long was it before ?"
1 " A number divided by ";nm;" is equal to ";y;"."''" What is the number?"
1 " (";z;") ";
1 " ";nm;" apples cost ";y;"p"''" What is the price of one apple?"
1 so the inverse rule shouldbe
1 is the inverse"'"rule to
1 is the inverse"'"rule of
1 because the cost of the book plus the cost of the pen equals 75p."
1 and the rule for the bottommachine is
1 and pressing
1 You scored ";nr;" out of 9."
1 Yes, x=";nm;".":
1 Yes, x=";a;".":
1 Yes, the magazine cost ";a;"p.":
1 Yes, the equation is ";e$;".":
1 Yes, it halves the number youput in.":
1 Yes, each pencil costs ";a;"p.":
1 Yes, because
1 Where 'x' is the number you putin. But this is still a littlelong, so we could replace theword 'plus' with the '+' sign,which is obtained by holdingdown
1 When a rule undoes what anotherrule has done, then we say thatit is an INVERSE rule.":
1 What is the rule for a machinethat ";q$;" ";nm;"?"
1 What do you think the machineis doing to the numbers you putin?":
1 What do you think the machinedoes to the number you put in?"
1 What do you think the inverserule to
1 What do you think the rulewould be if the two machineswere replaced by one that doesthe same job?"
1 We must now find a way for youto enter your answers so thatI can understand you easily.":
1 Try another number.":
1 Try an exercise of 10 questionslike the ones you have justdone.":
1 Three times a number is 18.Whatis the number ?"
1 This machine has the rule
1 This is a machine that turnsold numbers into new ones.":
1 Therefore, if we could combinethe two macines its rule wouldbe
1 Therefore the rule
1 The rule is ";r$;" and the output is ";y;"."
1 The rule for the top machine is
1 The cost of one orange is 6p."
1 So, the inverse rule to
1 So, just as
1 So far you have put numbersinto machines and they have beenturned into new ones."
1 See if you can spot what isspecial about it.":
1 Remember,the rule '
1 Question ";q;".";
1 Put in a number between 1 and9 and see what happens."
1 PRESS ANY KEY WHEN YOU HAVE COMPLETED EXCERCISE FOUR.":
1 Now we can replace the word'
1 Now try another chain of machines.":
1 Now you have completed lessonone you should attempt exercise1b in the instruction booklet."
1 Now that you have completedlesson three, you should attemptexercise 3 in the instructionbooklet."
1 Now that you have completedlesson two you should doexercise 2 in the instructionbooklet."
1 No,in fact if halves the numberyou put in.":
1 No, x=";a;".":
1 No, the rule would be
1 No, the equation is 7x=";y;".":
1 No, the INVERSE rule would be
1 No, it's 5, because
1 No, it would be ";e$;".":
1 No, it should be 23, because 2times 11 is 22, plus 1,makes 23.Let's try another example."
1 No, each pencil costs ";a;"p.":
1 Let's try another.":
1 Let's try another. In this casethe first machine has the rule
1 It does the opposite of
1 In this lesson we are going toput two machines together andthen see what happens.":
1 In this chain of machines thefirst has the rule
1 If seven times a number is ";y;", what is the number ?"
1 However,this still contains toomany words, so let's replace'divided by' by the '/' symbol.Which is obtained by holding
1 However we had better checkthis."'"
1 First you multiply 15 by 3which makes 45,then you subtract2,which leaves 43."
1 Find the input number x."
1 Correct !!!":
1 As you probably realised, thesecond machine changes the newnumber back into the originalone."
1 A machine has the rule x-";nm;" and the output is ";y;"."
1 ";y;" pencils cost ";nm;" pence.What isthe cost of one pencil ?"
1 and the rule for thebottom machine is
1 and see what"'"happens.";
1 your number divided by 2"
1 x minus 4"
1 THIS IS AN EQUATION !"
1 x plus 3"
1 x divided by 2"
1 x+27=75
1 x=6."
1 x/2"
1 Q
1 "