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15 ;" ":
9 ;"Simplify the rule-"
9 ;"Question ";j
7 ;"You scored ";sc;" out of five."
6 ;"Solve the equation-"
5 ;"Your answer: ";a$
5 ;"You only answered ";sc;" correctly"'"out of five. You need to workthrough the exercise again.":
5 ;"You only answered ";sc;" correctly"'"out of five. I suggest you lookover this lesson again later on."
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4 ;"Therefore, x="
4 ;" ":
4 ;" ":
4 (lh+rh);lh+rh:
3 ;"x y":
3 ;"PRESS S"
3 ;"PRESS R":
3 ;"Now for a short exercise of fivequestions.":
3 (c+d+e)+"x"
3 '" otherwise:-";
3 "F","U","N","D","A","M","E","N","T","A","L"
3
2 ;lh+rh+mi:
2 ;c;"x-";d;"x"
2 ;c;"x+";d;"x"
2 ;"and ";a;" in the right-hand side.":
2 ;"Your answer: x=";a
2 ;"You put ";a;" in."
2 ;"You put ";a;" in the left-hand side,":
2 ;"You put ";a;" in both sides.":
2 ;"You put ";a;" in"'"both machines."
2 ;"You put ";a;" in"
2 ;"You made b=";a:
2 ;"You made a=";a:
2 ;"Which gives the solution ";
2 ;"This can be solved by-"
2 ;"Solve the equation-";
2 ;"So the equation is now-";
2 ;"POST TEST (2)"
2 ;"Now try a short exercise of fivequestions.":
2 ;"Now try a short exercise of fivequestions."
2 ;"LESSON SIX"
2 ;"LESSON SEVEN"
2 ;" First we simplify the LHS usingwhat we have learned in previoussections.";
2 ;" ";
2 ;" "
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2 (lh-rh);lh-rh:
2 (lh+rh+mi);lh+rh+mi:
2
2
1 xx*(c+b+d)+e<1
1 xx*(b+c-d)<1
1 xx*(b+c-d)+e<1
1 usr
1 logo
1 file D|
1 f;") You did not achieve objective";'f;",so restudy lesson ";y(f);"."
1 f$=" a+b":
1 Recording
1 Created with Ramsoft MakeTZX
1 ALGP
1 ALG7 /R
1 ALG6
1 ;c;"x-";d;"x+";e;"x"
1 ;c;"x+";d;"x+";e;"x="
1 ;c;"x+";d;"x+";e;"x"
1 ;c;"x+";d;"=";c*e+d
1 ;c+d+e;"x":
1 ;c+d+b;"x=";xx*(c+d+b):
1 ;c+d+b;"x=";xx*(c+b+d)+e;:
1 ;c+d+b;"x";v$(9
1 ;b;"x-";c;"x+";d;"x+";e;"x"
1 ;b;"x+";c;"x-";d;"x+";e;"=";xx*(b+c-d)+e
1 ;b;"x+";c;"x+";d;"x+";e;"x"
1 ;;"You only answered ";sc;" correctly"'"out of ten. You need to workthrough the exercise again.":
1 ;'" 2x + 3x = 5x"
1 ;"x=";xx*(c+d+b);"
1 ;"which we can solve by dividing20 by 10 to give the solution-";
1 ;"which means 'multiply the inputnumber x by three'."
1 ;"which gave the solution-";
1 ;"so 6x=18"
1 ;"is a CHAIN of simple rules:"
1 ;"by first adding the numbers-"
1 ;"You scored ";sc;" out of ten."
1 ;"You scored ";sc;" out of eight."
1 ;"You only answered ";sc;" correctly"'"out of five. You need to workthrough the exercise again.":
1 ;"You only answered ";sc;" correctly"'"out of five. You need to workthrough the exercise again.":
1 ;"You made x equal"'"to ";a;"."
1 ;"You made x equal"
1 ;"You have now completed the PostTest and you scored 7 out of 7."
1 ;"You got the following questionswrong:":
1 ;"You only answered ";sc;" correctly"'"out of five. I suggest you lookover this lesson again later on."
1 ;"You only answered ";sc;" correctly"'"out of eight. You need to workthrough the exercise again.":
1 ;"You only answered ";sc;" correctly"'"out of eight. I suggest you lookover this lesson again later on."
1 ;"You only answered ";sc;" correctly"'"out of ten. I suggest you lookover this lesson again later on."
1 ;"You only answered ";sc;" correctly"'"out of five. I suggest you lookover this lesson again later on."
1 ;"Which gives the solution-";
1 ;"Which comes to 9, so"
1 ;"Which becomes ";
1 ;"What is the inverse rule of achain?"
1 ;"We now look at another equation-";
1 ;"We will now look at a morecomplicated combination ofmachines."
1 ;"UPPER CASE";
1 ;"Type in file name in ";
1 ;"Type in a number between 6 and9 for a."
1 ;"Type in a number between 1 and4 for b."
1 ;"Try another..."
1 ;"Try another value"'"for x."
1 ;"Try another two numbers."
1 ;"Try another number for 'x'."
1 ;"Try another number between 6 and9 for a."
1 ;"Try another number between 1 and4 for b."
1 ;"This one adds together the twonumbers you put in. So if youput 3 in the left-hand side, and4 in the right-hand side, youshould get 7.";
1 ;"This comes to 17, so"
1 ;"Therefore x=3"
1 ;"Therefore both sides of theequation are equal."
1 ;"Then we DIVIDE the RHS by 5-";
1 ;"Then we DIVIDE the RHS by 2-";
1 ;"Then apply the inverse rule tothe right hand side-";
1 ;"The left hand side simplifiesto-";
1 ;"The equation is now-";
1 ;"The LHS rule is 'multiply x by 5and add 6'."''"So first we SUBTRACT 6 from theRHS-";
1 ;"The LHS rule is 'multiply x by 2and subtract 5'."''"So first we ADD five to the RHS-";
1 ;"That completes Lesson Six."
1 ;"That completes Lesson Seven."
1 ;"That completes the Post TestPart 2."
1 ;"THEN - two is taken away from the result."
1 ;"Suppose we now"
1 ;"Stop and rewind tape"
1 ;"Solution:":
1 ;"So, if you put in 4 you wouldget out 7 (as 4 + 3 = 7).":
1 ;"So if the input number is four,then twelve (which is 3 times 4)is the number output by themachine.":
1 ;"So we can replace the rule'x+x' by the rule '2x'.";
1 ;"Simpify the rule-"
1 ;"SAVE""file"" LINE 2"
1 ;"RESULTS"
1 ;"Question 7"
1 ;"Question 6"
1 ;"Question 5"
1 ;"Question 4"
1 ;"Question 3"
1 ;"Question 2"
1 ;"Question 1"
1 ;"Put in another"'"value for x."
1 ;"PLEASE WAIT";
1 ;"Now you input a number between1 and 9."
1 ;"Notice that the output is ";a*2
1 ;"Notice that in"'"each case the"'"output number"'"is 5 times the"'"input number.":
1 ;"Notice that in"
1 ;"No,2+7=9, so 2x+7x"'"simplifies to 9x."
1 ;"Load main program"
1 ;"Let's try it..."
1 ;"Let's try it."
1 ;"Let's try another equation likethat."
1 ;"Leave tape running"
1 ;"LOAD ~ALGP~"
1 ;"LOAD ~ALG7~"
1 ;"Just as we did"
1 ;"Input a common"
1 ;"In this lesson we are going tolook at a new kind of machine,into which you can put twonumbers at the same time."
1 ;"If you would like to go over"'" Lesson six again, ";
1 ;"If you would like to go over"'" Lesson Seven again, ";
1 ;"If you would like to go over"'" the Post Test again, ";
1 ;"First work out the sum-";
1 ;"First simplify the left handside-";
1 ;"FIRST- input number 'x' is multiplied by three."
1 ;"Enter a number"'"for x between"'"1 and 9."
1 ;"Enter a number"
1 ;"Enter another"'"number for x."
1 ;"Don't forget to check all youranswers."
1 ;"Bye For Now!":
1 ;"As you did not answer all thequestions correctly,have anothergo at the Post Test.":
1 ;"As five is the"'"sum of two and"'"three,the com-"'"bined rule of"'"2x and 3x"'"would be 5x.":
1 ;"As ";v$(1
1 ;"As ";c;" minus ";d;" is ";c-d;", so ";c;"x-";d;"x=";c-d;"x"
1 ;"As ";c;" and ";d;" is ";c+d;", so ";c;"x+";d;"x=";c+d;"x"
1 ;"As ";b;"+";c;"+";d;"+";e;"=";b+c+d+e;", so ";b;"x+";c;"x+";d;"x+";e;"=";b+c+d+e;"x"
1 ;"Applying the inverse rule of 6xto 18, we get-";
1 ;"Another machine might have therule-";
1 ;"Again, notice that the output isTWICE the input number 'x'.":
1 ;"7x-3x+2x+6=18";
1 ;"7x-3x+2x+6 becomes 6x+6"
1 ;"6x+6=18";
1 ;"5x-4=6";
1 ;"5x-3x+7x=9x"
1 ;"5x-2x=9";
1 ;"5x+6=21"
1 ;"3x2-2=4, or 6-2=4"
1 ;"3x-2x+8x-3x=18"
1 ;"3x+5x+2x=20"
1 ;"3x+5x+2x+7x=";
1 ;"3x+5x+2x";
1 ;"3x+2x-4=6";
1 ;"3x+2x-4 becomes 5x-4"
1 ;"3+5+2+7"'';
1 ;"3) Check your solution by putting it into the LHS rule."
1 ;"2x-5=17";
1 ;"10x=20";
1 ;"1) Study the rule on the left hand side (LHS)."''"2) Apply the inverse rules in reverse order to the number on the right hand side (RHS)."
1 ;","'"which is twice ";a;".":
1 ;"(as 3-2+8-3=6)";
1 ;" for short), and that gaveus the solution to the equation."
1 ;" You used the inverse rule to 3xon 12."
1 ;" You have now completed the PostTest. You scored ";sc;" out of 7.";
1 ;" Which gives the solution ";
1 ;" When you are ready to begin thenext lesson, type NEW followedby-"'';
1 ;" When you are ready to begin thePost Test, type NEW followedby-";
1 ;" When we solved simple equationsearlier, we applied the inverserule of that on the LHS to thenumber on the right hand side(";
1 ;" What happens"
1 ;" Well, we work BACKWARDS,applying the inverse rules tothe number on the RHS."
1 ;" Well done! Continue to use thisPost Test as part of yourrevision programme, as outlinedin the ~Fundamental Algebra~workbook."
1 ;" We should just check that, byputting the value two into therule 3x-2:"
1 ;" Using what we have learned sofar we can now solve equationslike-";
1 ;" To summarise our method forsolving these kind of equations,here are three steps to follow."
1 ;" This shows clearly that we areputting the same number (x) inboth sides of the machine."
1 ;" This meant 'the input number xhas three added to it'.":
1 ;" This Post Test contains sevenquestions matched to the sevenminimum objectives set out inthe instruction booklet."
1 ;" Therefore we"'"can write-"';
1 ;" The number that goes into theright hand side of the machineis subtracted from the one thatenters the left hand side.":
1 ;" The larger mach-"
1 ;" That is, you divided 12 by 3,changing the equation to-";
1 ;" So 8x-5x=3x"
1 ;" Simplify:"''" 2x+4x+7x"
1 ;" Simplify the"'" rule:"'';
1 ;" Now, how are we to describewhat this machine does?":
1 ;" Now you type in two numbers(they should be between 1 and9), the first for the left sideand the second for the rightside."
1 ;" Now work through Exercise 6b inthe workbook."
1 ;" Now try exercise seven in theworkbook. Be sure to check allanswers and do all corrections."
1 ;" Now try Exercise Seven in theworkbook."''" Don't forget to check all youranswers, and do all corrections."
1 ;" Now suppose we had an equationlike-";
1 ;" Now try this last exercise."''" There are ten questions.":
1 ;" Now for a"'"short exercise"'"of eight ques-"'"tions.":
1 ;" Notice that the rule on theleft hand side (";
1 ;" Like for instance-";
1 ;" Let us try"'"with two other"'"single input"'"machines, 4x"'"and 7x."
1 ;" In this section we are going tolook at some more equations andthe methods we use to solvethem."''" First we are going to studyequations like-";
1 ;" In this section we are going tofirst look at double inputmachines with the rule-";
1 ;" In this lesson we are going tolook at even more complicatedrules and how we can simplifythem."'';
1 ;" In the earlier lessons of~Fundamental Algebra~, you wereintroduced to machines thatchanged old numbers into newnumbers using a rule...";
1 ;" If we put the same number inboth sides;call that number 'x',then in this special case we cansay the rule is-";
1 ;" If we call the number we put inthe left side 'a', and we callthe number we put in the rightside 'b', then we can write therule for this machine as";
1 ;" Here is another example. Thistime the equation is-";
1 ;" For example: 5x-3x+7x"
1 ;" For example we can simplify therule-"
1 ;" Do you remember how in theearly lessons of ~FundamentalAlgebra~, you learned how tosolve simple equations like-"
1 ;" But suppose we were asked tosolve the equation-";
1 ;" But in this equation we have achain of rules."
1 ;" Before you do an exercise, hereis one more example."
1 ;" Before continuing with thislesson, work through Exercise 6ain the workbook."
1 ;" Based on this you will be givenrecommendations for your futurestudy."
1 ;" As 9-4=5,so"'" 9x-4x=5x."
1 ;" As ";c;"+";d;"+";e;"=";c+d+e;",so ";c;"x+";d;"x+";e;"x=";c+d+e;"x."
1 ;" After you type in your answerit is checked and at the end ofthe test you will be given amark out of seven, a list of thequestions you got wrong and theobjectives not achieved."
1 ;" (as ";xx*(c+d+e);"
1 ;" (as ";xx*(c+d);"
1 ;" for short)"
1 ;" a) 6x=18-6 b) 6x=12 c) x=12
1 ;" a) 5x=6+4 b) 5x=10 c) x=10
1 ;" What will"
1 ;" We would simplify this inexactly the same way as we didwith the ones we looked atearlier on."
1 ;" We can use"
1 ;" Notice how in"'"this case the"'"value of x is"'"multiplied by 12"'"which is 3+5+4."'"So we can write"'"that:"'';
1 ;" Notice how"'"this time the"'"output is 3"'"times the in-"'"put and 8-5 is"'"3,so this time"'"we can write"'"the simplified"'"rule to 8x-5x"'"as 3x."''';
1 ;" LOADING PROGRAM
1 ;" First we must simplify theequation, and that means in thiscase we must simplify the lefthand side-"
1 ;" Before going on to morecomplicated equations, let ushave a look at other EXPRESSIONSor rules which are a mixture of'+' and '-' rules."
1 ;" Because this test uses arandomising routine, each run ofthe Post Test will produce adifferent set of questions, soit can be used to advantage inyour revision programme."
1 ;" As 2+4+7=13,"'" 2x+4x+7x=13x."
1 ;" Again we must"
1 ;" 9x-4x":
1 ;" 3x+5x+4x=12x":
1 ;" Then DIVIDE the RHS by 3-"
1 ;" 5x=21-6, which gives 5x=15"
1 ;" 2x=17+5, which gives 2x=22"
1 ;" First, ADD 2 to the RHS-"
1 ;" 3x+5x+2x+7x"
1 ;" ";
1 ;" ";
1 ;" "
1 ;" ":
1 ;" ":
1 ;" ":
1 ;" "
1 ;" "
1 6 d) x=2"
1 5 d) x=2"
1 2x-3x+2x+9=15Z
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1 );"=";xx*(c+d+b)+e:
1 );"=";c+d+e;", so ";v$;"=";c+d+e;"x."
1 (xx*(c+d+b)+e)
1 (c-d+e)+"x"
1 (b-c+d+e)+"x"
1 (b+c+d+e)+"x"
1 ((c+d+e)*xx)
1 ((c+d)*xx)
1 ((c*xx)+e)
1 '"Let the left"
1 '"4x + 7x = 11x"
1 "would be 11x,"
1 "with 2 single"
1 "which is made"
1 "what happens."
1 "up from 4x and"
1 "to ";a;"."
1 "this case, the"
1 "these ideas to"
1 "the simplified"
1 "the same numb-"
1 "the rule '5x'."
1 "the rule '2x',"
1 "the right hand"
1 "the rule '8x'"
1 "the rule 'a+b'."
1 "simple rules"
1 "rules '3x', '5x',"
1 "rule '3x'."
1 "rule be for"
1 "right one have"
1 "one has the"
1 "of the smaller"
1 "number 'x' as"
1 "number for 'x'."
1 "now if we put"
1 "machines?"
1 "like 8x."
1 "like 3x+5x to"
1 "lesson,we com-"
1 "le input mach-"
1 "input mach-"
1 "ines. The left"
1 "ines with an"
1 "ines both have"
1 "ines have the"
1 "hand one have"
1 "hand one has"
1 "er into both"
1 "enter a common"
1 "earlier in the"
1 "combined rule"
1 "combine our"
1 "clear (y/n) ?";q$
1 "both machines."'" "
1 "both machines."
1 "bined rules"
1 "bine two sing-"
1 "between 1 and 9."
1 "between 1 and"
1 "before and see"
1 "and '4x'."
1 "and let the"
1 "address ? ";x
1 "Type in a number"
1 "The small mach-"
1 "SIMPLIFY com-"
1 "Filename",a$
1 ";c+d;"=";xx;")":
1 ";c+d+e;"=";xx;")":
1 "7x, so we can"
1 "'a-b' machine."
1 "'a+b' machine"
1 Q
1 "
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