[speaker001:] Right can you have a look... at those... Just have at the answers to this. Did you find any difficulties at all?
[speaker002:] N no I don't.
[Malcolm:] It looks all right from here.
[speaker002:] Yeah.
[Malcolm:] Keep the tracing paper if you need it.... That's all right.... yes that's okay that's fine.... [sucks teeth] Hang on.... Oh yes alright from there.... How did you come to that conclusion?
[speaker002:] What?
[Malcolm:] the petrol station... the petrol station, isn't it?
[speaker002:] Mm. Mm five minutes.
[Malcolm:] It's five minutes and fifteen. I misread the. That's okay. [reading] in the first fifteen minutes of the journey []... Yeah er... [tut]... What's fifteen minutes... as part of an hour?
[speaker002:] Quarter of a hour.
[Malcolm:] Quarter of an hour. ... That's point two five.
[speaker002:] Mm.
[Malcolm:] You can't
[speaker002:] Mm.
[Malcolm:] You can't have time as a decimal, time is not a decimal.
[speaker002:] Mm.
[Malcolm:] Okay? I can't remember what it's called it's in sixties whatever that is.
[speaker002:] Mhm.
[Malcolm:] Yeah. S Time is not a decimal so you can't operate time as a decimal. Nobody ever used to make that mistake at one time you know why?
[speaker002:] No.
[Malcolm:] Because everything worked was wasn't in decimal.
[speaker002:] Mm.
[Malcolm:] All the distances were in twelves
[speaker002:] Mm.
[Malcolm:] and for and weights were in fourteens so
[speaker002:] Aha.
[Malcolm:] nobody ever thought about anything being a decimal.
[speaker002:] Mhm.
[Malcolm:] So nobody had any problems with that. No of course that everything's de- you know everything's decimal time
[speaker002:] Yeah.
[Malcolm:] becomes quite an awkward calculation. It didn't used to be. It didn't. [reading] not been interrupted. same constant speed. [] So you work the same the constant speed.
[speaker002:] .
[Malcolm:] Yeah w shouldn't matter,
[speaker002:] yeah.
[Malcolm:] that's fine.
[speaker002:] Aha.
[Malcolm:] Doesn't make any difference at all that doesn't. Erm so you would have done... er yeah then you've got You've got your speed of distance over time correctly.
[speaker002:] Mm.
[Malcolm:] Or time is distance over speed. It's all right, but... you've then... gone that's not nought point two five minutes the speed's per hour. Isn't it?
[speaker002:] Mm.
[Malcolm:] The speed is per hour... isn't it? So that would have been... point two five which should have been fifteen minutes.
[speaker002:] Yes that's sixtieth of an hour
[Malcolm:] Which is point two five of an hour. Be very careful with your
[speaker002:] Mm.
[Malcolm:] units.
[speaker002:] Yeah.
[Malcolm:] That's
[speaker002:] Mm.
[Malcolm:] The calculation's fine what you've done's fine just mucked
[speaker002:] Put the wrong
[Malcolm:] the units up.
[speaker002:] Yeah....
[Malcolm:] Right? So that's... How many minutes earlier? Now you've not done that you've actually done his journey time.
[speaker002:] Mm.
[Malcolm:] Mm? So careful read the question. You must read the question!... Alright, how're you getting on with them? Or have I stopped you?
[speaker002:] Didn't know what I'm supposed to be doing with that.
[Malcolm:] Your supposed to be doing them rotate them through Do this one first.
[speaker002:] How do you mean them?
[Malcolm:] Hundred and eighty degree rotation around C.
[speaker002:] doing it Do you mean drawing it on Using this drawing it?
[Malcolm:] Yeah.... You've done rotations and reflections and so forth haven't you?
[speaker002:] Mm.
[Malcolm:] Mhm. that rotated a hundred and eighty degrees about that.
[speaker002:] Mm.
[Malcolm:] brought it by isn't it?
[speaker002:] But I know what to do I don't know what you want me to do.
[Malcolm:] I want it I want it shown as a hundred and eighty degree rotation. There's an exam question [reading] Rotate that
[speaker002:] Yeah.
[Malcolm:] about that point the hu Through a hundred and eighty degrees [].
[speaker002:] Mm....
[Malcolm:] four. What your not so Fine. Yeah.... Okay yes good. That's alright. [reading] Use the patterns to write down the A three. [] A Three is that that that that that.... A four... [breath]... Lets have a look. Is it done?
[speaker002:] No I haven't done anything yet I'm on.
[Malcolm:] Look
[speaker002:] I can't do it! I can't.
[Malcolm:] You haven't done rotations have you?
[speaker002:] Yeah I have but I don't how to do them like this I've not seen it been d drawn out like that.
[Malcolm:] Right draw something from the centre of rotation to the the figure.
[speaker002:] Mm.
[Malcolm:] Rotate that bit through a hundred and eighty degrees where's it go?
[speaker002:] Over here.
[Malcolm:] Over there. There's a hundred
[speaker002:] Yes.
[Malcolm:] and eighty innit? Trace the original.... Yes.
[speaker002:] Mm.
[Malcolm:] Round the centre of rotation it to the spoke while she's up the other spoke. Dum.
[speaker002:] Mm.
[Malcolm:] Mm? Right?
[speaker002:] Yeah.
[Malcolm:] Yeah. it's as simple as that. Isn't it?
[speaker002:] .
[Malcolm:] Go on then.... as if you've drawn. Have you got a pencil?
[speaker002:] No I was looking at the other one.
[Malcolm:] No I want it actually done I want you to physically do 'em.
[speaker002:] Right erm
[Malcolm:] So they go into your brain
[speaker002:] Mm.
[Malcolm:] ... via your eyes and and finger ends and so forth.
[speaker002:] Mhm.
[Malcolm:] Okay?
[speaker002:] Mhm. [tape change]
[Malcolm:] I suppose I should put Nyah Right okay simultaneous equations.
[speaker002:] Yeah....
[Malcolm:] With some degree of er... success I trust this time.
[speaker002:] I think I messed number one up.
[Malcolm:] Ah dear.... Yes you did.... You know why?
[speaker002:] No.
[Malcolm:] You made the classic mistake the only mistake there is here you multiply everything by two
[speaker002:] Mm.
[Malcolm:] So that's twenty six.
[speaker002:] Mm.
[Malcolm:] That's the only I mean that's th that's the real problem with this thing It's one the the difficulties you end up with You see you must remember to multiply everything that's there by the number you want to multiply, not just half of it. And that's all the problem is.
[speaker002:] I think I've done the others right....
[Malcolm:] Yes that looks alright.... Yeah. Well you can always tell can't you? How do you tell? St st st just stick
[speaker002:] Go back and check it
[Malcolm:] the numbers back in. Just put the numbers back in. Yeah it's alright. [breath] Yeah it's alright. You see you managed to... plough through these quite r readily did you?
[speaker002:] Sort of.
[Malcolm:] Ah.... What on earth's that question?
[speaker002:] Two A plus
[Malcolm:] Oh it's an A is it?... Oh I beg your pardon sorry
[speaker002:] I changed it to.
[Malcolm:] That's al that's alright that's alright I'm with that. I understand what you're doing it's a substitution.
[speaker002:] It's a little like As and Bs.
[Malcolm:] Er it doesn't make any difference does it?
[speaker002:] No but I'm used to Xs and Ys.
[Malcolm:] Yes but A Yeah that's alright erm except for examples... we where do up to?
[speaker002:] Ten.
[Malcolm:] Up to ten.... Yes. Have a go at fourteen and sixteen. Whilst I sit here and admire your expertise and
[speaker002:] Ha.
[Malcolm:] general... facility at this subject.
[speaker002:] Mm. [break in recording]
[Malcolm:] And say to yourself
[speaker002:] [whispering] Nine seven nine C plus []
[Malcolm:] Yep. Or four Y minus minus nine.
[speaker002:] Yeah.
[Malcolm:] Which is probably as good.
[speaker002:] Thirteen.
[Malcolm:] Thirteen is right.
[speaker002:] [whispering] twenty six []
[Malcolm:] That's okay. Y equals
[speaker002:] Y equals... What're you gonna do? Divide it.
[Malcolm:] Yeah, whoa. Right it's two isn't it?
[speaker002:] Mm.
[Malcolm:] Okay.
[speaker002:] Substitute that back in.
[Malcolm:] Yes that's right.... Yes.... Do number seventeen.
[speaker002:] But I haven't done sixteen.
[Malcolm:] Just do number seventeen I fancy seventeen better than number sixteen.
[speaker002:] Mhm, you would.
[Malcolm:] I know.... I have this great in-built desire to make people suffer.
[speaker002:] [cough]
[Malcolm:] [breath]... There's an easier way of doing it isn't there?
[speaker002:] What get rid of the Ys?
[Malcolm:] Yes.
[speaker002:] Mm. Suppose so.
[Malcolm:] Yeah there is is There's an awful lot of suppose so about that you only gonna do one set of calculations rather than two aren't you?
[speaker002:] Yeah.
[Malcolm:] You must look at this from the minimum of Point of view of the minimum amount of labour.... Yeah.
[speaker002:] [whispering] Equals twenty six. []
[Malcolm:] No it doesn't. I beg your pardon yes it does. [LAUGHTER].
[speaker002:] Mm.
[Malcolm:] Yes it does. You're right.
[speaker002:] [whispering] []
[Malcolm:] That's right.
[speaker002:] [whispering] and X equals []
[Malcolm:] Thirty three.... Yeah. Alright we need to bother a I know you I know you can do substitution. Yeah thing about it is though when you're looking at this, you wanna be looking as to which is the Produces the smallest numbers.
[speaker002:] mm.
[Malcolm:] And which produces the minimum amount of manipulation and that was that the second one wasn't it?
[speaker002:] Yeah.
[Malcolm:] You had much less to do than anything else.
[speaker002:] Mm.
[Malcolm:] Right that's unfortunate. That I l I've forgotten to bring the other work. However.
[speaker001:] Can I Can I just interrupt and say I've forgotten. I'm sorry is that enough?
[speaker002:] Yes.
[speaker001:] thank you.
[speaker002:] Eye's funny.
[Malcolm:] Yeah.... Now look it asks you for a certain number of things It says As... The average doesn't it? How
[speaker002:] Yes.
[Malcolm:] Do you work t an average?
[speaker002:] Average is all the tests added together
[Malcolm:] Yeah,
[speaker002:] divide by the number of tests he had.
[Malcolm:] That's right. So what's the total for all his test?
[speaker002:] Hundred and twenty six.
[Malcolm:] Hundred and twenty six how many tests had he had?
[speaker002:] ... X.
[Malcolm:] X. So the average is going to be?
[speaker002:] Hundred and twenty five divide by x.
[Malcolm:] Hundred an Is it a hundred and twenty five?
[speaker002:] twenty six.
[Malcolm:] Hundred and twenty six divided by X is that.
[speaker002:] Yeah.
[Malcolm:] So what's difficult about that?
[speaker002:] Nothing.
[Malcolm:] So. Now there's another two tests.
[speaker002:] Yeah.
[Malcolm:] So what's the total now?
[speaker002:] ... Hundred and twenty eight... divide by
[Malcolm:] Where's a hundred and twenty eight come from? What's the total marks for the next two tests?
[speaker002:] Oh....
[Malcolm:] You're told what the marks are for the next two tests aren
[speaker002:] Oh nine and eight.
[Malcolm:] Nine and eight aren't they?
[speaker002:] Yeah.
[Malcolm:] So what's the total marks for the Now for the the tests? How many marks you got all together?
[speaker002:] Hundred and... [whispering] twenty thirty [] forty... [whispering] forty two [].
[Malcolm:] Mm. [cough] What's a hundred and twenty six plus nine?... No! What's a hundred and twenty six plus nine? Come on what's nine add six?
[speaker002:] Hundred and thirty six.
[Malcolm:] O What's nine add six?
[speaker002:] Eleven.
[Malcolm:] Nine add six?
[speaker002:] [LAUGHTER] Oh [] Fourteen.
[Malcolm:] And another one.
[speaker002:] Six
[Malcolm:] fifteen yeah?
[speaker002:] Yes.
[Malcolm:] Six and nine it's always one less when innit when you're adding nine? So it's fifteen do it's a hundred and twenty six plus nine is?
[speaker002:] ... hundred and thirty forty.
[Malcolm:] I want a hundred and twenty six plus nine!
[speaker002:] Oh a hundred and twenty a hundred and thirty... five.
[Malcolm:] Hundred and thirty five. What's five and eight?... Not
[speaker002:] Thirteen.
[Malcolm:] Thirteen so the answer's gonna be a hundred and?
[speaker002:] ... Forty three.
[Malcolm:] Hundred and forty three. You know what the a en end number's gonna be every time i Don't you?
[speaker002:] Yeah.
[Malcolm:] Mm. Hundred and forty three. That's right so the total's a hundred and forty three. So what's the what's the average gonna be or even the mean?
[speaker002:] Hundred and forty three... divide by
[Malcolm:] By
[speaker002:] X plus two.
[Malcolm:] Splendid. Can we have it written down like real mathematicians?... Ah wonderful. Wonderful.
[speaker002:] hundred and forty five.
[Malcolm:] Yes No I said a hundred and forty
[speaker002:] Forty three
[Malcolm:] three yes. Over
[speaker002:] Divide by X plus two.
[Malcolm:] plus two that's right. Now what's the next part of the question say?
[speaker002:] [reading] If if a If his average for the first X test was one greater than his average for
[Malcolm:] [reading] X plus two tests.
[speaker002:] plus two tests. Use results of one and two []
[Malcolm:] To form the equation and find the value of X. [] Now what it just said... think of another way of saying that.
[speaker002:] Work out what X is.
[Malcolm:] No you can't work out what X is you haven't got a c hope of working out wh
[speaker002:] Form an equation.
[Malcolm:] Form an equation. But what's one side of the equation going to be?
[speaker002:] Hundred and twenty six divide by X.
[Malcolm:] Plus?
[speaker002:] Hundred and fort
[Malcolm:] No no
[speaker002:] plus two
[Malcolm:] No no read what it says. [reading] If his average for the first X tests is one greater than the average [] Sorry beg your pardon I've got it round me round me neck. [reading] If his average for the first X t is one greater than his average for the X plus two tests []... So a hundred and twenty six over X is gonna equal?
[speaker002:] ... What he got in the first
[Malcolm:] O in the second lot... isn't it? Plus one.
[speaker002:] Mm.
[Malcolm:] Yes. So right it down.... Yeah come on! Just write it down! Hundred and twen
[speaker002:] What?
[Malcolm:] What I've just told you hundred and twenty six over X is equal?
[speaker002:] Hundred and forty three
[Malcolm:] Three
[speaker002:] divide by X plus two
[Malcolm:] Yeah. Plus one.... Yes.... Plus one.
[speaker002:] Why is it plus one there?
[Malcolm:] Cos it's says it's This is one more than that isn't it?... This is one more than that.
[speaker002:] So shouldn't that be plus one?
[Malcolm:] How do you make them equal?
[speaker002:] Oh yeah.
[Malcolm:] Yes think about it carefully. How do you make them equal.
[speaker002:] Mm.
[Malcolm:] That's right so. Now what are you going to do?
[speaker002:] ... Find the value of X.
[Malcolm:] ... I'm an extremely patient soul as you well know, [LAUGHTER] but if you say Find the value of X to me again How are you gonna [] find the value of X? What do you intend to do?
[speaker002:] ... Get rid of the denominators.
[Malcolm:] Get rid of the denominators, good. Well done. Go on then....
[speaker002:] Is that right?
[Malcolm:] No. What're you doing? What're you doing?
[speaker002:] Timesing it by X.
[Malcolm:] Alright then times it by X. Go on then if that's what you're doing go on. Keep going! Hold on a minute you've still got a this on the bottom haven't you? To start with come on. Cos your multiplying by X go on you haven't cancelled it yet go on. Carry on.
[speaker002:] [whispering] []
[Malcolm:] Eh? What are you doing? You can't do that!
[speaker002:] Why?
[Malcolm:] Multiply everything by X go on. Ju just do every term you've got multiply it by X.... Go on.
[speaker002:] I don't know how to do it though.
[Malcolm:] Course you do! Just carry on multiplying things by X instead of trying to jump to conclusions.... Where's the two X come from?
[speaker002:] Times it by
[Malcolm:] But you've got that over th on the bottom haven't you? It's X plus two there, isn't it? It's got nothing to do when multiplying You're multiplying the top by X go on. That's better.... That's right perfect. Go on then, get some stuff cancelled out. That's right. No. There's no way you can do that. [LAUGHTER]
[speaker002:] But I've got an X on the top.
[Malcolm:] Aye but you've got an X plus two on the bottom.
[speaker002:] So if I put X minus two on the top?
[Malcolm:] No it will not cancel.
[speaker002:] Why not?
[Malcolm:] You've got a hundred and forty three X over X plus two, haven't you?
[speaker002:] Hundred and forty three minus two.
[Malcolm:] Hundred and forty does not work. There's no way that works at all.... Just do what you've got there. Write a hundred and twenty six. Write a hundred and twenty six. That's right, equals. Hundred and forty three X over... X plus two. That's right. Plus X. That's perfect now what are you going to do?
[speaker002:] ... Can I move across That across to this side?
[Malcolm:] You can multiply everything through by X plus two, yes. Go on.
[speaker002:] [whispering] []
[Malcolm:] Bracket, X plus two never mind about this s Mm. Equals... that plus... Come on you're multiplying by X plus two. No... you're multiplying by X plus two.... You've missed a You've now dropped a plus sign out haven't you? And you've dropped an X out.
[speaker002:] Why?
[Malcolm:] You're multiplying this term by X plus two aren't you?... You're
[speaker002:] Mm.
[Malcolm:] gonna multiply everything by X plus X plus two. It just so happens that if multiply this term by X plus two you get rid of the X plus two at the bottom don't you?
[speaker002:] Mm.
[Malcolm:] But everything there It's the same thing as when you were doing this.... The simultaneous equations wasn't it?
[speaker002:] Why was it?
[Malcolm:] You had to me s make sure that you multiply every term out, haven't you?
[speaker002:] Yeah.
[Malcolm:] So here you've got to multiply every term out.... Do not forget that that is a term on its own it's got n connected to this yet.
[speaker002:] No.
[Malcolm:] You're a very very careful about that so start getting it tidied up then. Expand the brackets I think is probably the best thing....
[speaker002:] Hundred and twenty six X
[Malcolm:] S X that's right. Plus two hundred and fifty two.
[speaker002:] Equals
[Malcolm:] Hundred and forty three X
[speaker002:] X
[Malcolm:] Plus
[speaker002:] X squared
[Malcolm:] X squared plus two X. That's right. Right now things are getting a bit better aren't they?... Come on!... What're you gonna do now?
[speaker002:] [sniff] Do all the Xs on one side.
[Malcolm:] Well I'd collect the things together that were the same for a start I think.
[speaker002:] ... What d'you mean?
[Malcolm:] Well you've got some Xs to collect together haven't you?
[speaker002:] Oh.
[Malcolm:] Mm?... That's better. That's simplified it.
[speaker002:] Yeah.
[Malcolm:] Now s You can start you've still gotta get the every I would get everything over to one side of the equals sign. Why?... What's this?
[speaker002:] Then use your quadratic.
[Malcolm:] This is a quadratic isn't it? Yes good.
[speaker002:] Does it matter which way you put it?
[Malcolm:] Well I always like to read it from left to right but it doesn't matter really.
[speaker002:] Yeah but I mean
[Malcolm:] you can do that if you want to.... I would have put all the... the er
[speaker002:] Hundred and forty five X minus hundred and twenty six X.
[Malcolm:] Yes.... Plus x squared... minus two five two
[speaker002:] Minus two five two.
[Malcolm:] Equals nothing. Yes.
[speaker002:] So that's going to be...
[Malcolm:] Don't look at me like that!
[speaker002:] Nineteen X.
[Malcolm:] Mhm.
[speaker002:] Plus X squared.
[Malcolm:] Yeah. Minus two five two.
[speaker002:] [whispering] minus two five two Equals nothing. []
[Malcolm:] Equals nothing that's right. Now if you're gonna do this you really want it in the form of X squared first don't you?... really to make it To make... the thing easy to work, aren't you?
[speaker002:] Well that's gonna be your A.
[Malcolm:] Yeah it is.
[speaker002:] B and that's gonna be C.
[Malcolm:] It's much be It's much better to see it as A square As X squared plus te nineteen X plus minus two two five, really.... Two five two equals nothing. Right....
[speaker002:] Formula.
[Malcolm:] I don't know.... You're gonna have some tremendously large numbers if you work the formula aren't you?
[speaker002:] Yes.
[Malcolm:] I mean B squared's nineteen squares you know just under four hundred isn't it? That's twenty times twenty. You imagine four times that.
[speaker002:] A lot.
[Malcolm:] It's a lot isn't it?
[speaker002:] But they're only numbers.
[Malcolm:] that's true. But perhaps it's easier I wonder what are other factors of two hundred and fifty two?
[speaker002:] One.
[Malcolm:] One and two hundred and fifty two, yes very good yes.
[speaker002:] Two.
[Malcolm:] Yes good. We want a difference of nineteen somewhere don't we?...
[speaker002:] That's easy.... We drop the calculator everywhere.
[Malcolm:] Well you can drop the calculator if you want it would be better if you pick 'em up and stick the [LAUGHTER] numbers in.... How're you gonna do?
[speaker002:] Two hundred and fifty two divide by nineteen....
[Malcolm:] What you got?
[speaker002:] Thirteen point two six three one five
[Malcolm:] Yes.
[speaker002:] seven nine eight.
[Malcolm:] Yes. I don't think that's right. Try the square root of two five two.
[speaker002:] ... Fifteen point eight seven four five
[Malcolm:] Yes yes, a difference. Don't know... does sixteen go into it just try sixteen into two five two.
[speaker002:] ... Fifteen point seven five.
[Malcolm:] [sound of disgust] So we want something like erm... Seven and sixteen, well that doesn't work Sorry seven and twenty six.... Is that right? No.
[speaker002:] How about
[Malcolm:] No, gives a difference of nineteen. Use the formula then, we're just sitting here wasting time....
[speaker002:] [sigh]
[Malcolm:] Minus nineteen... or minus B plus or minus the square root of B
[speaker002:] Minus B
[Malcolm:] Plus or minus
[speaker002:] plus or minus the square root of
[Malcolm:] the square root of B squared
[speaker002:] [whispering] plus []
[Malcolm:] No. Minus
[speaker002:] Minus two B C
[Malcolm:] Minus four A C
[speaker002:] Four A C
[Malcolm:] All over
[speaker002:] Two A.
[Malcolm:] Two A is right.
[speaker002:] So what's A?
[Malcolm:] It's an X!
[speaker002:] Must be true.
[Malcolm:] Yes. I am delighted you agree.
[speaker002:] Yeah. Minus nineteen
[Malcolm:] Yes.
[speaker002:] plus or minus
[Malcolm:] The square root of nineteen squared minus four times
[speaker002:] nineteen squared minus four times
[Malcolm:] one
[speaker002:] ... one
[Malcolm:] times
[speaker002:] times two
[Malcolm:] No It's not times two five minus two five two.
[speaker002:] times minus two five two
[Malcolm:] Lovely.
[speaker002:] All over
[Malcolm:] Over two
[speaker002:] Two times one.
[Malcolm:] Yep.
[speaker002:] X squared.
[Malcolm:] X equals not X squared. Minus nineteen... plus or minus
[speaker002:] ... plus or minus Can I do that
[Malcolm:] Root
[speaker002:] all in one?
[Malcolm:] Yeah!
[speaker002:] I can do it on here, oops!
[Malcolm:] Hope so.
[speaker002:] Square root of nineteen squared minus four times times minus
[Malcolm:] Minus
[speaker002:] two five two.
[Malcolm:] Answer.... Nineteen squared's three hundred and ninety ninety one I think.
[speaker002:] Mm. Three hundred and sixty one.
[Malcolm:] Really? Three sixty one times... eight thousand There's summat wrong.
[speaker002:] Nineteen squared minus four times one
[Malcolm:] No it's minus It's plus It's nineteen squared plus eight... nought... one nought nought eight.
[speaker002:] Mm.
[Malcolm:] Four time two five two. Two hundred and fifty times four is a thousand Two hundred and fift
[speaker002:] It's minus!
[Malcolm:] It's minus times a minus... Isn't it?
[speaker002:] Four
[Malcolm:] four times two th two five two is one thousand and eight isn't it?
[speaker002:] Yes.
[Malcolm:] Two fifty times four is a thousand. So two five two times four is t one thousand and eight, plus three hundred and chunkety chunk Three hundred and sixty one.
[speaker002:] Mm. Which is one three six nine.
[Malcolm:] That's more like it.
[speaker002:] Yeah but what about mm. above answer.
[Malcolm:] Mm.
[speaker002:] What about that? Where do get that from?
[Malcolm:] Because what you did was you did er nineteen squared
[speaker002:] Yes.
[Malcolm:] minus four.... I don't know why I don't how that works
[speaker002:] Would that be in brackets?
[Malcolm:] Of course it is.
[speaker002:] I didn't put a brackets there.
[Malcolm:] Well you would have to although I would have though it might have worked algebraically that's certainly wrong though. What did we say? One three six... nine.
[speaker002:] Nine.
[Malcolm:] One three six nine, yes.
[speaker002:] All over
[Malcolm:] Er you want the square root of that. that's it all over two.
[speaker002:] Two.
[Malcolm:] Yep, so it's minus nineteen plus or minus
[speaker002:] Plus or minus
[Malcolm:] root one three six nine....
[speaker002:] [whispering] Square root []
[Malcolm:] One three six nine.... That's interesting. Ah! Yes go on.
[speaker002:] Yeah it is isn't it?
[Malcolm:] Yes. Go on then.
[speaker002:] You'll remember that.
[Malcolm:] I will.
[speaker002:] Thirty seven.
[Malcolm:] So the f One answer is f fourteen
[speaker002:] Don't! Just don't!
[Malcolm:] [LAUGHTER] It's not actually.... One answer's nine innit?...
[speaker002:] Minus nought point five?
[Malcolm:] Yeah.... And the other answer is?... Can you tell me how managed to produce nought point five, how you managed to produce... that?
[speaker002:] Don't know.
[Malcolm:] Minus nineteen plus thirty seven without the aid of a calculator... must be about eighteen mustn't it?
[speaker002:] Mm.
[Malcolm:] The difference between thirty seven and nineteen's about eighteen innit? Approximately?... Divide that by two, answer?
[speaker002:] Nine.
[Malcolm:] Nine.
[speaker002:] Mm.
[Malcolm:] Engage brain [LAUGHTER] Th You must regard a calculator with the greatest and gravest of suspicion. Cos it's not actually working algebraic that calculator at the present moment I don't know what you've got it programmed in What you've got it at but it's not working algebraic.
[speaker002:] Now it might work....
[Malcolm:] [thinking noise]
[speaker002:] No unless we have to Minus nineteen minus thirty seven divide by two minus twenty eight?
[Malcolm:] Yeah that's better.
[speaker002:] ... I wonder if minus.
[Malcolm:] Wait you've got minus fifty six haven't you here? this is minus fifty six if you use your brain. And divided by two is minus twenty eight.
[speaker002:] Yeah.
[Malcolm:] Yes minus twenty eight. Now if you You take the difference between nineteen and thirty seven you get the answer eighteen don't you?
[speaker002:] [sigh] Yes.
[Malcolm:] You divide that by two you get the answer nine.
[speaker002:] Nine.... Mm. But why isn't my calculator working?
[Malcolm:] Because you haven't got it in the correct mode it's not working algebraic.
[speaker002:] Which is in what function?
[Malcolm:] Who knows what your calculator and that's a such a wonderful piece of work that.
[speaker002:] Yeah but
[Malcolm:] Scie Scientific or You want it in scientific mode if it says scientific
[speaker002:] Yeah it does. In that case use it in scientific and then it will work that way. Will it?
[Malcolm:] Yeah well it should do. Anyway.
[speaker002:] . [cough]
[Malcolm:] Okay. Let's read the second part of this question cos it's taken us er quite some time to do it but excellent question. Hasn't it
[speaker002:] Right
[Malcolm:] Right let's read the second part of this. [reading] It has an average of thirteen point five marks for the first X plus one tests. His mark on the last test gave him a final average of fourteen marks for X plus two tests. What was his marks for the last test. [] How do you work out his total marks for his X plus one tests.
[speaker002:] Thirteen point five divided by X plus one.
[Malcolm:] That's his No no you've got his average as thirteen point five haven't you? How do you work out his total marks which is what we're really looking for?
[speaker002:] Times X plus
[Malcolm:] Yes, it's thirteen point five times X plus one. And how do you work out his total marks for his X plus two tests?
[speaker002:] Fourteen times thirteen plus two.
[Malcolm:] No no no.
[speaker002:] Why?
[Malcolm:] Fourteen times what?
[speaker002:] Times X plus... two.
[Malcolm:] Yeah.
[speaker002:] That's what I said!
[Malcolm:] Was it? I'm sorry I misheard you. So what it's alright.
[speaker002:] Mm.
[Malcolm:] I misheard you okay?
[speaker002:] Mm.
[Malcolm:] So, it might be a good idea to write that down and work it out.
[speaker002:] Thirteen point five
[Malcolm:] Yes
[speaker002:] times
[Malcolm:] Will you stop doing that!
[speaker002:] What?
[Malcolm:] That!...
[speaker002:] What's wrong with it?
[Malcolm:] How do you write a multiplication in algebra?... You're gonna multiply that by X plus one aren't you?
[speaker002:] Mm.
[Malcolm:] How do you write that?
[speaker002:] Hundred and thirty five X plus one.
[Malcolm:] Bracket.
[speaker002:] X plus one.
[Malcolm:] X plus one. Ha?
[speaker002:] Suppose so.
[Malcolm:] That's how you write it.
[speaker002:] Minus fourteen
[Malcolm:] Never mind about this silliness, that you've been allowed to get away with. Right go and work them out then.... Thirteen point five times one is? Thirteen point five innit?
[speaker002:] Yeah.
[Malcolm:] Mm.... That's right.... Okay. So what's your total marks?... Sorry what's the difference?...
[speaker002:] Fourteen point five.
[Malcolm:] You know what he total mark for... his X plus one test was don't you?
[speaker002:] Mm.
[Malcolm:] And you know the total mark was X plus two tests. It actually asks you for the mark he obtained for his final tests doesn't it?
[speaker002:] Yeah.
[Malcolm:] So if you take two away, one from the other, you'll have the mark
[speaker002:] Nought point five.
[Malcolm:] for his test won't you? So you'll have nought point five X plus?...
[speaker002:] Plus...
[Malcolm:] Point about it is y you can't see it, can you unless you've got it written down so write it down. it's thirteen well it's fourteen X isn't it?
[speaker002:] Mm.
[Malcolm:] Plus twenty eight minus thirteen point five X minus thirteen point five isn't it? Or minus thirteen X plus thirteen point five isn't it?
[speaker002:] Why is it?
[Malcolm:] Well you're taking the difference between the two aren't you?
[speaker002:] So don't you just minus them?
[Malcolm:] Yeah. So that's fourteen X plus twenty eight minus thirteen point five X minus thirteen point five isn't it? Yes?
[speaker002:] Mm.
[Malcolm:] So that's nought point five X, now what?... Plus Plus what's the difference here?...
[speaker002:] Hundred and thir Hundred
[Malcolm:] What's twenty eight minus thirteen point five?
[speaker002:] Oh it's point five!
[Malcolm:] Yes.
[speaker002:] ...
[Malcolm:] What's twenty eight minus thirteen poin
[speaker002:] Fourteen point five.
[Malcolm:] Fourteen point five.
[speaker002:] ...
[Malcolm:] Okay....
[speaker002:] So wouldn't
[Malcolm:] That's
[speaker002:] you times it by two?
[Malcolm:] Another student has his average as thirteen point five marks for the first blah blah blah, right. [815 1] Which marks for the last test give a final average of fourteen marks for [] So the one test is gonna give him that isn't it? That's right you agree isn't it?... That's his total marks for X plus one tests, is there. Total marks for S plus plus two tests is there. The actual mark... is that.
[speaker002:] That's for his nought... nought point five X. So to get those two up to one X
[Malcolm:] up to one X you should times by two which is twenty nine. Which I don't believe....
[speaker002:] Well do you times it by four?
[Malcolm:] No give... but his mark on his last test gave him the final average of fourteen marks for X plus two tests. So that's his total there and his total there. Yes it's gonna be doubled hasn't it to give you that?... Oh!... [sigh] [tutting] [LAUGHTER] Oh dear! How daft can you get? What's the value of X?
[speaker002:] W we worked that out somewhere didn't we?
[Malcolm:] We did didn't we?
[speaker002:] Oh!
[Malcolm:] [LAUGHTER]
[speaker002:] Oh! Nearly as bad as.
[Malcolm:] Dear oh dear! Eh?
[speaker002:] Oh.
[Malcolm:] Innit? I'm very tired [LAUGHTER].
[speaker002:] So what do you do? Times thirteen point five X by
[Malcolm:] Well you do thirteen point five times ten if you want.
[speaker002:] Yes.
[Malcolm:] And fourteen times eleven.
[speaker002:] Why eleven?
[Malcolm:] Well nine plus two is eleven isn't it?
[speaker002:] Yes.
[Malcolm:] Hundred and fifty four.
[speaker002:] Now who is being dormant?
[Malcolm:] And you've got it haven't you?
[speaker002:] Then you find the difference?
[Malcolm:] Yes. [LAUGHTER]
[speaker002:] That makes sense.
[Malcolm:] actually work here hasn't it?
[speaker002:] Does that give you the same answer?
[Malcolm:] Yes it should do. Let's just check it go on. You had thirteen point five times ten which I think is a hundred and thirty five in normal circumstances.
[speaker002:] Yes.
[Malcolm:] And a hundred and f fourteen times eleven. Go on it's a hundred and fifty four....
[speaker002:] Minus nineteen.
[Malcolm:] No minus a hundred and thirty five.
[speaker002:] One fifty four minus hundred and thirty five. Nineteen.
[Malcolm:] Nineteen.
[speaker002:] Which is wh what we would have done if we'd done
[Malcolm:] If we'd done
[speaker002:] that better.
[Malcolm:] Yeah but it we it's a spurious argument because you've got nought point five X haven't you?
[speaker002:] Yeah.
[Malcolm:] Nought point five X i Nought point five of X i is four point five isn't it
[speaker002:] Yeah.
[Malcolm:] Four point five plus fourteen point five... Answer?
[speaker002:] Nineteen.
[Malcolm:] Nineteen. We actually got it right both ways. But it would have been simpler to have done it that way I think.
[speaker002:] And quicker.
[Malcolm:] And quicker. But not as entertaining.
[speaker002:] Yes.
[Malcolm:] [whispering] Not as entertaining. []
[speaker002:] Mm. If you like.
[Malcolm:] Yes. They have a tendency to ask questions not quite as comp Not quite as... abstract as that.
[speaker002:] Intricate. Not even intric Not quite as abstract cos th the the tendency is to ask the question The average weight of nine people is whatever it is, you know somebody else has added Yeah questions.
[Malcolm:] Yeah yeah. Rather than quite as abstract as that But you can cope with abstract as that you can do A level.
[speaker002:] Yeah.
[Malcolm:] You have to cope You have to... You have to be as abstract as that. Which will not do you any harm.
[speaker002:] Good. [humming] [reading] A man bought three box of Dutch cigars. []
[Malcolm:] Good lord how appalling in this day and age!
[speaker002:] Three boxes! [reading] At X pence per box, and two boxes of Havana cigars... at Y pence per box. Calculate terms of X and Y []
[Malcolm:] [reading] Cost of the five boxes. [] So what's the cost of the Dutch ones?
[speaker002:] How many boxes? Three X.
[Malcolm:] Splendid. What's the cost of the Havanas?
[speaker002:] Two Y.
[Malcolm:] So what's the total cost?
[speaker002:] Five X two Y.
[Malcolm:] Eh?
[speaker002:] Five X plus two Y.
[Malcolm:] Five X plus two Y not just five x two Y.
[speaker002:] Plus two Y.
[Malcolm:] Five X plus two Y. Wonderful.
[speaker002:] [reading]
[Malcolm:] Go on
[speaker002:] the average... cost per box in terms of X and Y.
[Malcolm:] So what's the average b cost per box gonna be? five X plus two Y you better write that down before our brains refuse to accept any more information. Two Y is the total cost, how do you find the average? How do you find an average?
[speaker002:] Add them together and divide by the number you've got.
[Malcolm:] How many have you got.
[speaker002:] Five.
[Malcolm:] No you haven't.
[speaker002:] We've got five boxes.
[Malcolm:] No you haven't got five boxes.
[speaker002:] Why?...
[Malcolm:] Read it again.
[speaker002:] [reading] Three boxes of Dutch []
[Malcolm:] Whoops!
[speaker002:] That's supposed to be three X.
[Malcolm:] That's a three. Yes that's better. So you haven't got
[speaker002:] .
[Malcolm:] F Divide that by five.
[speaker002:] Divide that by five.
[Malcolm:] Yes.
[speaker002:] The whole of it?
[Malcolm:] Yeah. Cos that's the total price isn't? Total cost.
[speaker002:] Total of boxes you mean.
[Malcolm:] Total cost. Five's the total number of boxes but that the top one's the total cost isn't it?
[speaker002:] Yea.
[Malcolm:] That's right. Yep....
[speaker002:] [whispering] []
[Malcolm:] Yes.
[speaker002:] Oh..
[Malcolm:] [whistling through teeth] [reading] At a profit of thirty three percent of their costs [].
[speaker002:] How do
[Malcolm:] Thir
[speaker002:] work that out?
[Malcolm:] Thirty three and a third percent is a third.
[speaker002:] Yes.
[Malcolm:] So I want a third of their... their costs. So what did he sell... the Dutch box
[speaker002:] Which is the Dutch which is that half.
[Malcolm:] Well, [reading] later he sold his three boxes of Dutch cigars at a profit of thirty three of their cost. [] Mm? So
[speaker002:] So that's three X divided by
[Malcolm:] No it's not three X divided by five, it's says of their cost. Thy cost three X didn't they?
[speaker002:] Yes.
[Malcolm:] And the sold them for a third profit so what did he sell them for?
[speaker002:] ... X plus a third.
[Malcolm:] If he sold the things for
[speaker002:] Four
[Malcolm:] thirt Aye.
[speaker002:] Four thirds.
[Malcolm:] No.... I if
[speaker002:] If he's got
[Malcolm:] he bought them for three quid?
[speaker002:] Yes.
[Malcolm:] Yeah Which is highly improbable but he bought them for three pounds
[speaker002:] Yes.
[Malcolm:] In the days when a gold sovereign meant something when you went abroad [LAUGHTER]
[speaker002:] Yes.
[Malcolm:] And he sold them that was his cost was three pounds. And he h He sold them at a profit of thirty three and a third percent which is a third. What did he sell them for?
[speaker002:] Four pounds.
[Malcolm:] Four quid.... So if he
[speaker002:] four X.
[Malcolm:] No if he cost him three X, what's he gonna sell them for?
[speaker002:] Four X.
[Malcolm:] Yes.... So he sells his Dutch s cigars for four x.
[speaker002:] When he only bought them for three X?
[Malcolm:] That's right. So he sold them for four X.
[speaker002:] Yeah....
[Malcolm:] Then what did he do with his havanas?
[speaker002:] [reading] HE gave away the other two boxes as presents. []... Strange man.
[Malcolm:] A strange fellow. Well no it probably a little bit of sweetener for a business deal later one perhaps?
[speaker002:] Mm.
[Malcolm:] Yes. I used to get bottles of whisky at Christmas and so forth.
[speaker002:] And we stole it [LAUGHTER].
[Malcolm:] Yes you now what it m Yes you know all about that?
[speaker002:] Yes.
[Malcolm:] Yes. So it's a box of h s Havana cigars. So how much profit did he make on that?... He didn't did he? He made absolutely no profit at all, in fact he made a loss of?
[speaker002:] Two X.
[Malcolm:] Two Y.
[speaker002:] Yes two Y.
[Malcolm:] Yeah.
[speaker002:] [reading] Calculate the amount he received for the sale of the cigars. [] [tape change]