[FYAPSUNK]
[UNCLEAR] get this sorted out .
WMN: FYA_143
Dialogue: FYA
[PS25S]
[UNCLEAR] it tends to stick on , it 's never done that , I do n't think , yet .
[PS25T]
Yeah .
[PS25S]
Now , have you had a chance to look at anything since last time ?
[PS25T]
I have n't and I 've I 've meant to , but [UNCLEAR]
[PS25S]
Ah . [UNCLEAR] [UNCLEAR] you know
[PS25T]
I 've been like mad mad busy w one thing and another .
[PS25S]
Yeah . Oh I know what it 's like .
[PS25T]
Even of an evening .
[PS25S]
[UNCLEAR]
[PS25T]
Well mainly cos of me mum of an evening , cos she 's not been too good , so I 've been up and down .
[PS25S]
Oh is n't she ? Yeah . Yeah it 's erm
[PS25T]
Ca n't seem to get a chance .
[PS25S]
It 's really
[PS25T]
I mean I want to
[PS25S]
Yeah .
[PS25T]
to get i and do some of this and do these
[PS25S]
Yeah .
[PS25T]
problems ,
[PS25S]
Yeah .
[PS25T]
it 's getting the time to do it .
[PS25S]
But you need to be
[PS25T]
Mm .
[PS25S]
When we cover something in the lesson , you need to go over it yourself ,
[PS25T]
Yeah .
[PS25S]
work out the exercises in it , erm maybe get a little bit stuck , sort it out yourself , and then think , Oh yeah
[PS25T]
Yeah .
[PS25S]
I know I see how you do it . And maybe if you 're totally stuck , then I can go through it again next time , but
[PS25T]
Yeah .
[PS25S]
It 's really the more you do
[PS25T]
Mm .
[PS25S]
on your own . Because when it
[PS25T]
Well
[PS25S]
comes to the exam [UNCLEAR] you 're gon na be on your own .
[PS25T]
Yeah . I 'll have I mean I 'm having er a weekend in Lytham so I might er take stuff up with me , you know for for the odd
[PS25S]
Yeah .
[PS25T]
revising . Kids are on the beach and that . So I can work I I can still work through on these ones .
[PS25S]
Okay . You happy with the trig then ?
[PS25T]
Erm yeah I 'd I 'd say it 's trig and geometry and the bearings , using trig with the bearings is the
[PS25S]
Yeah .
[PS25T]
thing that I need to
[PS25S]
Okay .
[PS25T]
Cos I know they 're the things that seem to
[PS25S]
Okay .
[PS25T]
have the big marks on .
[PS25S]
Take a take a bearing on me then , if North is that window .
[PS25T]
Erm North 's that window ,
[PS25S]
Right yeah , do n't forget [UNCLEAR] , go
[PS25T]
Yeah .
[PS25S]
clockwise even though it means coming the long way round [UNCLEAR]
[PS25T]
Yeah .
[PS25S]
They put it on every question and they all come out of the exam and they say , Oh it was fifty degrees wa No , it was all the way , it was three hundred and ten . Oh . There goes the marks on that one .
[PS25T]
Yeah .
[PS25S]
So [UNCLEAR] if you remember nothing else , remember that one .
[PS25T]
Yeah .
[PS25S]
[UNCLEAR] to make sure you go clockwise . Okay , have you come across anything else that you 've I suppose you have n't had , you have n't been coming across much at all .
[PS25T]
No . [UNCLEAR]
[PS25S]
[UNCLEAR]
[PS25T]
I mean I had act I wanted to er hopefully have a fortnight off before the exam , to revise , but the way this work' looking , I do n't what I 'm going .
[PS25S]
Mm .
[PS25T]
I 'm definitely gon na take a few days off , but I wanted
[PS25S]
Yeah .
[PS25T]
to get into it properly . You see I 've not really got the same trouble with English , because well English is a written thing is n't it , [UNCLEAR]
[PS25S]
Yeah , and you 've been doing that for many many years , English
[PS25T]
Yeah .
[PS25S]
have n't you ?
[PS25T]
Yeah . Erm
[PS25S]
Right so [UNCLEAR] right . So you 're okay on graphs , because there 's usually a question on graphs which er if you you you know if you 're okay on them , pretty easy marks ?
[PS25T]
Erm not too bad , I mean we 've done a The last thing I done at at the night school , was a historogram .
[PS25S]
Okay . Yeah .
[PS25T]
Is that is that the right name for it ?
[PS25S]
Hist hist histogram . Yeah . [UNCLEAR] statistics .
[PS25T]
Erm there 's a lot of us starting [UNCLEAR]
[PS25S]
Okay , what does that mean then ?
[PS25T]
Well I I worked out at school well actually the teacher worked out .
[PS25S]
Is is that [UNCLEAR] .
[PS25T]
Erm no only partly finished , it would have
[PS25S]
Okay .
[PS25T]
gone to about here .
[PS25S]
What 's
[PS25T]
Yeah .
[PS25S]
Right . What 's the main thing missing from it at the moment ?
[PS25T]
Erm well apart from like , the next few columns ?
[PS25S]
Mm .
[PS25T]
[UNCLEAR]
[PS25S]
The bit they give you marks for .
[PS25T]
Er
[PS25S]
What 's what 's this measuring up here ?
[PS25T]
Oh right , that 's erm
[PS25S]
And what 's that measuring along there .
[PS25T]
[UNCLEAR] I ca n't remember .
[PS25S]
Right . Now if you do that in real life
[PS25T]
Yeah .
[PS25S]
erm you 're doing a perhaps you 're doing a histogram of some jobs that you 've been doing ,
[PS25T]
Mm .
[PS25S]
to see which ones are giving you the good profits , [UNCLEAR] sort of thing .
[PS25T]
Yeah . This this was a weight .
[PS25S]
Right .
[PS25T]
Weights and measures .
[PS25S]
Yeah , it can be almost anything , but if
[PS25T]
Mm .
[PS25S]
you have n't marked on what it is , erm and then you come make [UNCLEAR] get some interruptions , which you 're going to do , and you
[PS25T]
Yeah .
[PS25S]
come back to it next week ,
[PS25T]
Mm . Yeah , what is that ?
[PS25S]
What was this ? And it 's So one of the first thing to do is to get your axes marked so that when you 're putting stuff in , you know which is which . Cos you can put these the other way up .
[PS25T]
Yeah .
[PS25S]
You know , with almost any graph , you can put them whichever way up you like . So
[PS25T]
I did n't do that one .
[PS25S]
No . Decide on suitable scale first . Right . And watch out with the scale on these , on histograms , and on any graphs because , what happens I mean I was watching somebody do this a couple of days ago . They 're marking off along here , erm every square is two , say ,
[PS25T]
Mhm .
[PS25S]
and they go , Two , four , six , eight , twelve
[PS25T]
Mm er
[PS25S]
Two , four , six , f around ten
[PS25T]
Mm .
[PS25S]
is where most people go wrong . Two , four , six , eight , nine , ten , eleven , twelve , thirteen , fourteen [UNCLEAR]
[PS25T]
Yeah . And [UNCLEAR]
[PS25S]
[UNCLEAR] and it 's it 's rubbish then , it 's rubbish because the scale does n't mean anything . One part of the scale it 's double , and the other part it 's not .
[PS25T]
Yeah .
[PS25S]
And all the results come out all wrong . And it 's so s I mean it does n't need a lo any mathematical skill at all really .
[PS25T]
Mm .
[PS25S]
It 's just a question of you know , marking off every second square . But you 'd be surprised how many people do n't .
[PS25T]
Yeah .
[PS25S]
[UNCLEAR] they get it wrong . Cos it is a boring thing . And you stop concentrating ,
[PS25T]
Mm .
[PS25S]
get it wrong .
[PS25T]
Yeah .
[PS25S]
So erm mark your axes , work out what your scale is going to be , to fit it all on , I mean that that looks like a nice fit .
[PS25T]
Mm .
[PS25S]
Just gone on and a little bit left over . That 's fine . Erm if it 'd all been down here , you could think , Oh well I can make it twice that , take it out to about here .
[PS25T]
Yeah .
[PS25S]
Okay . That looks fine , a good fit . What about erm graphs of functions .
[PS25T]
Erm
[PS25S]
I think we 'd better have a look at equations actually .
[PS25T]
I 've done some Now where is it ? I 've done some functions .
[PS25S]
Right . Functions .
[PS25T]
Yeah . One function er that that yo you 're given a function ,
[PS25S]
Right .
[PS25T]
You 're told that that particular function is equal to that .
[PS25S]
Mm .
[PS25T]
And then they ask you to find the function , and do something with it , you have to use that function there , you have to use that in it .
[PS25S]
Mm . Well there 's a definition of a function there .
[PS25T]
Yeah .
[PS25S]
What 's a function ?
[PS25T]
Er a function is [UNCLEAR] is a set a set sum that you 're given . A function of a number .
[PS25S]
Mm .
[PS25T]
Er as a end result that number , that 's a function but you have to do something with it .
[PS25S]
Er Mm . Tell me some of the things that happen when you 're you 're working out a function , what would what would be the the overall picture if someone was going to work out a function ?
[PS25T]
Erm
[PS25S]
What would you
[PS25T]
Well you [UNCLEAR] given the function .
[PS25S]
You 're given a function , okay , whatever that is .
[PS25T]
Mm .
[PS25S]
It might be a bit like a rabbit or something , it 's a function , right . And what would you do with it ?
[PS25T]
Er I 'd store it and use it with whatever I 'm asked to use it with .
[PS25S]
So you 'd be asked to use it with something . You 'd be given some input .
[PS25T]
Mm .
[PS25S]
Okay , what would you do with that input ?
[PS25T]
I 'd either , plus it , multiply it , divide it .
[PS25S]
So you 'd do some mathematical operations on it .
[PS25T]
Mm .
[PS25S]
And is that it or
[PS25T]
Either that
[PS25S]
Would that produce an would that produce anything ?
[PS25T]
It 'd produce a different answer .
[PS25S]
And it gives an answer , an output ,
[PS25T]
Mm .
[PS25S]
okay . So the input comes in , the function , you do something with it ,
[PS25T]
Mm .
[PS25S]
And you get an output . So that 's a sort of overall picture of a function . And what 's going inside the function ? Can it be anything , or what ?
[PS25T]
Pretty much it can be anything , it could be in brackets , it could be a minus in brackets ,
[PS25S]
Mhm . Okay , I 'll give you a I 'll give you a number .
[PS25T]
And [UNCLEAR]
[PS25S]
Erm three hundred and sixty .
[PS25T]
Yeah .
[PS25S]
Right . You give me all its factors . Or a few factors , give me some factors .
[PS25T]
Er erm well er twenty ,
[PS25S]
Okay yeah .
[PS25T]
five ,
[PS25S]
Yeah .
[PS25T]
erm ten ,
[PS25S]
Okay . Now is that a function ?
[PS25T]
Mm ?
[PS25S]
Is that a function , what you 're doing ? I give you a number and you give me some other numbers that are tied up with it in some way . Is that a function ?
[PS25T]
Not sure . Possibly .
[PS25S]
Right . It 's not .
[PS25T]
Yeah .
[PS25S]
Okay . What does your what does this say , for a function ? When you take a number , follow a set of instructions , and end up with End up with what ?
[PS25T]
Er
[PS25S]
You 'd end up with
[PS25T]
End up with one answer .
[PS25S]
On answer .
[PS25T]
Mhm .
[PS25S]
If you end up with more than one answer , then it 's not a function .
[PS25T]
Yeah .
[PS25S]
Okay , so that 's the that 's the big thing about it . It 's an input , a set of rules to follow , that will guarantee , that you get one output .
[PS25T]
Mhm .
[PS25S]
Okay , erm so suppose I ask you to square the number . Whatever number I give you , you multiply
[PS25T]
Mm .
[PS25S]
it by itself . Okay ? Three ?
[PS25T]
Nine .
[PS25S]
Minus four ?
[PS25T]
Minus twelve . Twelve .
[PS25S]
Erm yeah , four fours ?
[PS25T]
Sixteen .
[PS25S]
Okay so it 's
[PS25T]
Sixteen .
[PS25S]
Right so if I give you minus
[PS25T]
[UNCLEAR]
[PS25S]
four , you give me plus sixteen .
[PS25T]
Yeah because it 's multiplied .
[PS25S]
Right .
[PS25T]
Yeah .
[PS25S]
Plus four ?
[PS25T]
Erm
[PS25S]
What would you give me ?
[PS25T]
Er sixteen .
[PS25S]
Yeah .
[PS25T]
Yeah .
[PS25S]
Okay . Is that a function ?
[PS25T]
Yeah .
[PS25S]
Yeah . Cos you 're following the instructions , and you 're giving me one answer .
[PS25T]
Mhm .
[PS25S]
Now you 've given me the same answer for two different inputs , but that 's okay . That 's fine .
[PS25T]
[UNCLEAR]
[PS25S]
That 's still a function . But if you 're giving me different inputs , different outputs for for one input , then that 's not a function .
[PS25T]
Mhm .
[PS25S]
So if I say , what 's the square root of sixteen ?
[PS25T]
And I said four .
[PS25S]
You could say , Well it 's either four or minus four , which one do you want ?
[PS25T]
Yeah .
[PS25S]
Two answers , so that 's not a function . If I say , Well you 'll give me the only ever give me the negative version of the square root , so if I give you sixteen , you give me minus four . If I give you nine , you give me ?
[PS25T]
Er minus three .
[PS25S]
Right that 's a function .
[PS25T]
Mm .
[PS25S]
There 's only ever one answer . Or I could have been a bit less awkward , and said , you just give me the positive one .
[PS25T]
Mm .
[PS25S]
The plus four or the
[PS25T]
Yeah .
[PS25S]
the plus three . That would be a function , but a function , there 's only one answer to it . [UNCLEAR] thought of as a a recipe , for any number . Okay erm the input need not be a number , it can be all sorts of funny things .
[PS25T]
Mm .
[PS25S]
And you get one funny thing as the answer . But we can , at this level , we can restrict it to numbers .
[PS25T]
Yeah .
[PS25S]
Erm
[PS25T]
It 's [UNCLEAR] a few Xs in there and there .
[PS25S]
Right now .
[PS25T]
[UNCLEAR] went down to like this kind of stuff here .
[PS25S]
Right .
[PS25T]
Twelve over three and
[PS25S]
Okay . Now the notation , do you understand the notation ?
[PS25T]
Where 's the notation ?
[PS25S]
Two types of notation it gives here . A and B.
[PS25T]
Yeah well erm they 're basically different functions [UNCLEAR] different questions .
[PS25S]
Erm those are the same function . But he 's given it to you in two different types of notation , and you need to know both . So w how would you read this first on ?
[PS25T]
X squared plus four
[PS25S]
You have n't read the first bit though .
[PS25T]
Oh . Function X in brackets
[PS25S]
Mm .
[PS25T]
So that x , whatever you use it with , has to be X squared plus four .
[PS25S]
Mm . Okay how would you read this one ?
[PS25T]
And that one is written out , just a different way .
[PS25S]
[UNCLEAR]
[PS25T]
That 's got the two dots .
[PS25S]
Yeah .
[PS25T]
Right . But he normally sticks to brackets rather than , he 's got X is it X squared plus four , it 's exactly the same .
[PS25S]
Mm .
[PS25T]
He 's just wrote it out different . He 's used the two dots
[PS25S]
Right . Okay .
[PS25T]
and [UNCLEAR]
[PS25S]
This nota this notation , is mapping notation , because amongst other things , a function is a special case of a mapping . We wo n't go into
[PS25T]
Mm .
[PS25S]
mappings , but you can have they 're very often non mathematical .
[PS25T]
Mhm .
[PS25S]
Erm you have four types of matt of mapping . And two of those types er you can they can possible be functions .
[PS25T]
Mm .
[PS25S]
So this is read , A function F , such that the double dot is just read as , such that , A function F such that X maps to X squared plus four .
[PS25T]
Mm .
[PS25S]
So that any X any number you give to me , you give me X , I 'll g say if I 'm the function , if you give me X as the input , I 'll give you X squared plus four .
[PS25T]
Mhm .
[PS25S]
You give me three , as the input , I 'll give you three plus four . Okay . So if you gave me six as the input , what would I do with it ?
[PS25T]
Six squared plus four .
[PS25S]
Okay , and this is in function notation .
[PS25T]
Mhm .
[PS25S]
Where that is what the answer is , F of X.
[PS25T]
Mhm .
[PS25S]
F of X is the answer . F of X is what F has done to X.
[PS25T]
Yeah .
[PS25S]
Someone gave it X , as its input , and it gave you , as an answer , F of X.
[PS25T]
Mhm .
[PS25S]
And F of X in this case will be X squared plus four . Exactly the same mechanism ,
[PS25T]
Mhm .
[PS25S]
the same rules for that . It 's a different notation and you
[PS25T]
Mm .
[PS25S]
do need to know both . Both of them mean , take a number , square it and add four . And that 's your answer . Okay ?
[PS25T]
Mhm .
[PS25S]
When you find an answer for the function , at a particular number , erm I would
[PS25T]
It 's called the evaluation of the function .
[PS25S]
Right . And we 'll call it the and we 'd have said and You find you find the value of the function , for a particular number , a particular input , a particular value of X. And that 's evaluating function . Finding the value of the function . Given that F of X is X squared plus four , work out F of two .
[PS25T]
Mhm . That 's two times two is four plus four .
[PS25S]
Okay . And all of these . F of nought .
[PS25T]
That 's er nought squared plus four is four .
[PS25S]
Okay . Right . Now gets interesting , and you need to know what the notation is , when you 've got more than one function .
[PS25T]
Mm .
[PS25S]
Right ?
[PS25T]
Yeah .
[PS25S]
So this is where you sort of sort out if you really know what 's going on . Three functions . Find F of this , G of that , H of that . And you wo n't have any problem with that .
[PS25T]
Mhm .
[PS25S]
Okay is that okay ?
[PS25T]
These are them there .
[PS25S]
Let's have a quick look . Erm so on one , A , B and C
[PS25T]
This is this is one .
[PS25S]
Right .
[PS25T]
There .
[PS25S]
There okay . Erm
[PS25T]
F worked out at a half .
[PS25S]
Problems one .
[PS25T]
Oh .
[PS25S]
F of five ?
[PS25T]
F of five is one . what was it , two X
[PS25S]
Right [UNCLEAR] two times five okay . Right . So all these have been marked and they 're okay are they ?
[PS25T]
Yeah .
[PS25S]
Erm right . Now five
[PS25T]
These ones here though , I was surprised I I got them right .
[PS25S]
Mm ?
[PS25T]
[PS25S]
[UNCLEAR]
[PS25T]
Because I was like well it was n't quite gelling , but I just done it anyway and it
[PS25S]
Follow the rule [UNCLEAR]
[PS25T]
[UNCLEAR] Yeah .
[PS25S]
tells you . Square it , multiply it by two , subtract , whatever it is , just do it .
[PS25T]
Yeah .
[PS25S]
And you get the answer . Erm right .
[PS25T]
I think three might be on another page .
[PS25S]
F maps to next prime number greater than X. Find F of seven .
[PS25T]
What number 's that , A ? A on three . Well F of seven was eleven .
[PS25S]
Yeah . Right . F of seven , what 's the next prime number , well it 's not worth trying the evens , nine obviously is n't prime , so eleven is the next one .
[PS25T]
Yeah .
[PS25S]
Okay . F of fourteen ? It 's not fifteen
[PS25T]
That was seventeen .
[PS25S]
Seventeen . Yeah . And F of three , next one up is five .
[PS25T]
Yeah .
[PS25S]
Ooh no . No that 's erm it 's not five .
[PS25T]
Why not ?
[PS25S]
F of seven is fine , F of fourteen is fine , Right . We need two people for this , to work out this function . We 're both doing the same job , we 're both the same function , which is , find the next prime number up , from whatever number you 're given . Now F of F of
[PS25T]
Mhm .
[PS25S]
three .
[PS25T]
Yeah .
[PS25S]
You work it from the inside out . What goes into this F of , is whatever came out of that F of .
[PS25T]
Yeah .
[PS25S]
So I 'll be the inside one ,
[PS25T]
Mhm .
[PS25S]
the one that works out F of three . Right so , you 're the gaffer if you like , you 're the outside one . You 'll come along and you say , right I will I 'm going to You 're going to take as your input , whatever I give as output . My input was three .
[PS25T]
Yeah .
[PS25S]
And so F of three is five .
[PS25T]
Mm .
[PS25S]
And that 's what I hand on to you as your input .
[PS25T]
Mhm .
[PS25S]
Okay . So you 've now got to work out F of five .
[PS25T]
Function of five ?
[PS25S]
And the function is , find the next prime number that 's greater than .
[PS25T]
Well do n't I just go the next one great than three ?
[PS25S]
No because that 's what that 's not your input , that 's my input .
[PS25T]
Yeah .
[PS25S]
That 's my input .
[PS25T]
Mm .
[PS25S]
You 're waiting there ,
[PS25T]
Mm .
[PS25S]
You ca n't do anything , until I 've produced my output . Right I 'm that first I 'm that function , Mhm . And you 're this one , outside the gates if you like ,
[PS25T]
Yeah .
[PS25S]
outside the brackets .
[PS25T]
Mhm .
[PS25S]
Waiting until that one 's been worked out .
[PS25T]
Oh if that 's one 's five then they go to the next on e after that , which is seven .
[PS25S]
Seven . Right now a function of a function there .
[PS25T]
Mhm .
[PS25S]
It 's the same , it 's the same function . I think it 's probably easier to see it , when you use a different function . Now we do n't he has n't given you any of those here . Er I 'm pretty sure they do give you them . Just check the level [UNCLEAR]
[PS25T]
Yeah he has n't has n't [UNCLEAR]
[PS25S]
If he gives you that , if he gives you F of F , then he can give you F of G , and I 'm pretty sure that you do need to know that , so I wo n't bother checking . I 'll just give you some on those .
[PS25T]
Mhm .
[PS25S]
And you can see what [UNCLEAR] this this is in function notation , which is most commonly used , and it 's easier to understand , than the mapping notation , most people find .
[PS25T]
Yeah .
[PS25S]
So think of a function , keep it nice and simple , cos you 're gon na have to work it out .
[PS25T]
Yeah .
[PS25S]
Okay . Think of a function .
[PS25T]
Er X squared
[PS25S]
F of X equals X squared
[PS25T]
plus ten .
[PS25S]
plus ten . Well do you want to make , do you want to make it plus one ?
[PS25T]
Yeah .
[PS25S]
Plus one might be a bit easier . Okay . And I 'll think of a function . Which is three X minus two . Okay ?
[PS25T]
Right .
[PS25S]
Okay . Now what I want you to do , is to find F of G of X. And to find G of F of X. Now we 'll try a few examples first .
[PS25T]
Mm .
[PS25S]
With actual numbers . Before we go into that .
[PS25T]
Yeah .
[PS25S]
What 's F of G of three ? How would you work that out , sort of talk about it before you get started . What what are you going to do with that ?
[PS25T]
Er m well if if function was three , it 'd be
[PS25S]
Function is n't three , input , the number that 's going in is three .
[PS25T]
Mhm .
[PS25S]
[UNCLEAR] Right .
[PS25T]
G three
[PS25S]
G of three .
[PS25T]
G of three , G of three squared plus one .
[PS25S]
G of three . So that F has got to wait outside , the brackets , till the stuff inside 's been worked out .
[PS25T]
Mhm .
[PS25S]
So we 'll just leave this down here . Waiting to see
[PS25T]
Mhm .
[PS25S]
what it comes to .
[PS25T]
Mm .
[PS25S]
It 's F of something . It does n't know what yet .
[PS25T]
Mhm .
[PS25S]
Right , so what 's G of three ?
[PS25T]
G of three is er G three squared plus one .
[PS25S]
It 's not G three squared .
[PS25T]
G of
[PS25S]
It 's just No , G of three , is three squared plus on .
[PS25T]
Yeah .
[PS25S]
Right . It 's very important to be precise and know exactly what you 're talking about on these , cos you 'll get
[PS25T]
Mhm .
[PS25S]
you 'll just finish up with rubbish if you do n't .
[PS25T]
Yeah .
[PS25S]
And it 's why they put these in
[PS25T]
Mm .
[PS25S]
To m to sort out if you were really on top of it and know what you 're doing .
[PS25T]
Mm .
[PS25S]
Okay . So now we 're looking for F of three squared plus one . And what 's No we do n't . That 's right not right . I should have have checked that before I wrote it in . G of G of X is three times X
[PS25T]
Yeah Yeah G
[PS25S]
Three times X minus two .
[PS25T]
G of X is three ti three X three times X
[PS25S]
So it 's three
[PS25T]
minus two .
[PS25S]
times three , minus two .
[PS25T]
Mhm .
[PS25S]
Okay . Erm let's change that , let's make that four , so we do n't get confused with this three that 's already in there .
[PS25T]
Yeah okay .
[PS25S]
So it 's three times X which is three times four .
[PS25T]
Mhm . Plus two .
[PS25S]
Okay . Minus two . G of X
[PS25T]
Right so it 's three fours are twelve take away two is is ten .
[PS25S]
Well okay . That 's what we 've got so far . Now we want to do F of that . Now what does F of that come to ?
[PS25T]
The function of that is X squared
[PS25S]
Well that 's X. That lot is X.
[PS25T]
So it 's ten squared .
[PS25S]
So it 's three times four minus two , squared
[PS25T]
Plus one .
[PS25S]
plus one . So that 's F of G of X.
[PS25T]
Mhm .
[PS25S]
Now I 'd like you that 's F of G of X , to work out G of F of X.
[PS25T]
Mhm .
[PS25S]
Er the same X. G of F of three . [UNCLEAR] of four sorry . So Right . What 's that going to come to ?
[PS25T]
G
[PS25S]
That 's what that 's what F of X comes to , and that 's what G of F G of X comes to .
[PS25T]
Right so first of all I work out what 's inside these brackets yeah ?
[PS25S]
Yeah .
[PS25T]
Leave the G there .
[PS25S]
Good .
[PS25T]
Now F of four is four squared plus one .
[PS25S]
Right .
[PS25T]
Yeah ?
[PS25S]
Do n't work ou Yeah that 's great . Do n't work out what that comes to , leave it as four squared plus one .
[PS25T]
Right .
[PS25S]
Okay .
[PS25T]
So then G G of X er is ,
[PS25S]
Now you you can only write exactly what 's on there , in here .
[PS25T]
Mhm .
[PS25S]
Because that 's what G of that 's G of thins number .
[PS25T]
Mhm .
[PS25S]
And this is G of the same number . So you do n't need the G on it now . When when you went from there to there , the F of four disappeared .
[PS25T]
Yeah .
[PS25S]
Cos four squared plus one , is F of four .
[PS25T]
Right .
[PS25S]
So when you go from there to there , the G will disappear .
[PS25T]
Mhm .
[PS25S]
And the brackets .
[PS25T]
Yeah .
[PS25S]
Okay . That will all disappear .
[PS25T]
Yeah .
[PS25S]
Hello
[FYAPSUNK]
Hi .
[PS25S]
How are you then ?
[FYAPSUNK]
Fine thanks .
[PS25S]
[UNCLEAR] having a nice rest are you ?
[FYAPSUNK]
Well [UNCLEAR] I am now now anyway .
[PS25S]
I mean , you know in general , are you sort of sitting back , you know , letting the house run itself and everyone rushing round . [UNCLEAR]
[FYAPSUNK]
Oh well [UNCLEAR] not quite really no .
[FYAPSUNK]
[UNCLEAR]
[PS25S]
You get some troublemakers here sometimes do n't you .
[FYAPSUNK]
[PS25S]
Thanks very much for
[FYAPSUNK]
Okay .
[PS25S]
the coffee . So what would G of seven be , it would be three times seven minus two . But what 's G of this lot ?
[PS25T]
Well is it I 'd have to work it out would n't I ?
[PS25S]
No .
[PS25T]
Four fours are sixteen but th that would be seventeen .
[PS25S]
Okay do it like that .
[PS25T]
So it 'd be three seventeen minus two .
[PS25S]
Right so write it as about here write it as three times seventeen , minus two . Okay , but there 's no reason why you ca n't write it as We 're doing G of F of , that was F of , and G of is [UNCLEAR]
[PS25T]
G of F of
[PS25S]
That 's X so we 've got three times , four squared plus one .
[PS25T]
Yeah . Minus two .
[PS25S]
Minus two .
[PS25T]
Yeah .
[PS25S]
Yeah Okay ? Right .
[PS25T]
That 's [UNCLEAR] I put them just [UNCLEAR]
[PS25S]
That 's fine . Now
[PS25T]
So it helps to put that in the brackets . It helps to put that in a smaller bracket , when I go three times that , minus that . Yeah .
[PS25S]
Right . G of F of X is going to be what ? It 's going to be G of What 's F of X ?
[PS25T]
X squared plus one .
[PS25S]
Right , what do you do with when you 're doing G , you do three times it
[PS25T]
Minus two .
[PS25S]
and then subtract two .
[PS25T]
Right .
[PS25S]
Right now you worked out F of four .
[PS25T]
mhm .
[PS25S]
G you worked out G of F of four . This should be a general thing now . Er G of F of X is equal to that . So if we put four in there , we should get the same answer that you got . Three seventeens minus two , forty nine . Is that right ? Looks about it . Yeah .
[PS25T]
Mhm .
[PS25S]
Okay . So if we put four in there , that 'll be seventeen , three seventeens . Yeah . That works okay , that .
[PS25T]
Yeah .
[PS25S]
And G of F of four , would come to forty nine . Now I 'm pretty certain that you do that and it 's it 's a bit of erm there 's qui quite a bit in it . Getting sort of
[PS25T]
It does , the functions can see seem quite advanced really do n't they . [UNCLEAR] . Or is it just cos it 's fresh stuff ?
[PS25S]
Er
[PS25T]
[UNCLEAR] bit like algebra is n't it ?
[PS25S]
But they 're not so much Yeah . They 're not so much advanced , as they are very very basic .
[PS25T]
Mm .
[PS25S]
They 're more basic than algebra ,
[PS25T]
Yeah .
[PS25S]
more basic , and the more basic things are , the more strange and sort of
[PS25T]
Mm .
[PS25S]
more awkward to get your head round it . Er just see what they say on functions here . [UNCLEAR] . look in the table . Page eight . Coverage of topics . Topics , relevant to basic level . Higher level , intermediate level . So intermediate , rounding , simultaneous equations by graph . They 're all on that . [UNCLEAR] want to look at , on the graphs . Bearings , transformations , probability , I ca n't see functions . Should be right at the beginning . Erm , rounding off . It still ne [UNCLEAR] Yeah . Drawing bearings , transformations , rotations [UNCLEAR] . [UNCLEAR] functions , [UNCLEAR] fractions .
[PS25T]
Functions .
[PS25S]
Functions and combinations of functions , at the higher level . N E A , level R. You 're doing Q are n't you ?
[PS25T]
Yeah .
[PS25S]
Are you all doing Q at on your night school course ?
[PS25T]
Yeah . They might have just threw in a bit er more from paper three .
[PS25S]
Erm
[PS25T]
Cos he reckons that paper three does give you some
[PS25S]
Well I I thought , that functions came into it , I must say . this one does n't give it and er
[PS25T]
Is this one er
[PS25S]
Oh this is an eighty eight . [UNCLEAR] eighty eight . I mean they they can change in a year . Can change in a year .
[PS25T]
In this one ? [UNCLEAR]
[PS25S]
Er probably the best way to tell , is did he give you a syllabus at some stage ?
[PS25T]
Yeah . He did .
[PS25S]
Mm . [UNCLEAR] it 'll be in here . Cos it 's
[PS25T]
[UNCLEAR]
[PS25S]
on definitely on the higher level . It 's just that I I 'm quite sure that you need . See he 's given you a function of a function .
[PS25T]
Mhm .
[PS25S]
F of F of erm and I think you do need it on that . But erm
[PS25T]
See I do n't know where he got it from , because he did n't give us th questions out of this book .
[PS25S]
No .
[PS25T]
He he 'd obviously done them in school
[PS25S]
Yeah .
[PS25T]
and brought them in on you know , erm sort of
[PS25S]
Are you reasonably happy with that ?
[PS25T]
Yeah . I mean at first I did n't know what you mean , but I do now .
[PS25S]
So it 's getting used to , for a start , being able to read it .
[PS25T]
Mm .
[PS25S]
Cos it 's it 's hieroglyphics .
[PS25T]
Mm yeah .
[PS25S]
Is n't it ? It 's just
[PS25T]
Mm .
[PS25S]
funny squiggles and you 've got to sort of like when you first see X squared , and you think , What 's that ? X with a little two up in the air .
[PS25T]
Yeah .
[PS25S]
Erm then you gradually get used to it , and when you read it , you 've read it several times , it means something to you then . So this 'll come to mean something . Erm er They 're all okay , they 're all okay . [UNCLEAR] . He 's only given you one of those . Do do do n't bother about that one . Er when do you see him next ? Wednesday ?
[PS25T]
Tues Tuesday .
[PS25S]
Tuesday . Ask him whether you need to do that C whether you
[PS25T]
Mhm .
[PS25S]
need to do that ?
[PS25T]
Yeah .
[PS25S]
G G of F of X.
[PS25T]
Mhm .
[PS25S]
Erm if you do , we 'll have a look at it a bit more .
[PS25T]
Right .
[PS25S]
Erm I think you 're okay on the basic functions . You 've got that
[PS25T]
Mhm .
[PS25S]
so we 'd be better off , spending the time on on graphs .
[PS25T]
Now he give me that .
[PS25S]
Three posts on a building site . Er let's have a look . Er one Right You okay on number one ?
[PS25T]
I have n't even read it . Er the cash price for double glazing the windows was three nine five oh . He decided to pay by hire purchase . Pay a deposit of twenty percent . Calculate the amount of the deposit . Well I mean I know that twenty percent is twenty pound in a hundred , but what 's a quick way of doing it on the calculator . What is the quick formula .
[PS25S]
Have you got a well there are several way of doing it , but have you got er a percent button ? That 's one that 's probably th simplest . Which you do n't tend to have Oh you have got one there on the equal . Erm what 's that ? Shift and pers shift and equal ?
[PS25T]
Mm .
[PS25S]
Er let's see . One hundred plus two shift percent . Is there an alt or a another funny key that you use instead of ? Not that one . One hundred erm maybe it 'll only work with the times , generally on scientific ones , they do n't use the percent [UNCLEAR]
[PS25T]
Mm .
[PS25S]
[UNCLEAR] times
[PS25T]
Something to do with a hundred times the amount is n't it .
[PS25S]
Two see you 've got a percent key marked there , how do you get
[PS25T]
Mhm .
[PS25S]
these , upper ones . Oh you put it into a different mode .
[PS25T]
Ah yeah [UNCLEAR]
[PS25S]
That 's what you do .
[PS25T]
Mhm .
[PS25S]
You put this into a different mode , and it 's not worth messing about with that at all .
[PS25T]
No cos it mess it up
[PS25S]
Because , you put that into a different mode , you ca n't get back to your normal mode , and your calculator 's useless for the rest of the exam .
[PS25T]
Yeah .
[PS25S]
So do n't use your percent button .
[PS25T]
Mhm .
[PS25S]
Erm right equivalents of percentages and fractions . [UNCLEAR] . What does four percent mean ?
[PS25T]
Oh four parts of a hundred .
[PS25S]
Okay four percent is a fraction .
[PS25T]
Mhm .
[PS25S]
Four out of a hundred . That 's it . Simple as that . So if I said , Find four percent of two hundred and forty pounds . Right .
[PS25T]
Mhm .
[PS25S]
It 's it 's four hundredths of do n't forget that times is of .
[PS25T]
Yeah .
[PS25S]
You do n't you do n't ever need to know that that is pronounced times .
[PS25T]
Mhm
[PS25S]
You can always say of .
[PS25T]
Yeah .
[PS25S]
Three of four . Three of four is twelve . Three sets of four , three lots of four , three boxes of four ,
[PS25T]
Mhm .
[PS25S]
bags of four . Three of four , is twelve . Four of three , is twelve .
[PS25T]
Mm .
[PS25S]
Right . Four hundredths of two forty is the same as two forty of four hundredths .
[PS25T]
Mhm .
[PS25S]
Does n't matter which way you round you do it , that of , you can just switch them and get the same answer . Which you know from your your three fours and four
[PS25T]
Yeah .
[PS25S]
threes . [UNCLEAR] so that 's all you do . How would you do that on your calculator ?
[PS25T]
Er two forty times a hundred times four ? No .
[PS25S]
How would you find
[PS25T]
Oh two forty over a hundred , times four .
[PS25S]
Right . Yes . Yes . You 've got . Are you okay multiplying fractions ? Of of-ing fractions ?
[PS25T]
Yeah . Yeah . Er not a hundre
[PS25S]
Not a hun
[PS25T]
Not brilliant No .
[PS25S]
Not a hundred percent that 's
[PS25T]
yeah .
[PS25S]
a fraction so you must have some idea of fractions . Right . Easiest thing to do with fractions , is to multiply them .
[PS25T]
Mhm .
[PS25S]
It 's the easiest thing to do . Cos you do what you think you 're suppo you know what you 'd expect .
[PS25T]
Yeah .
[PS25S]
Is you just multiply the two top ones together .
[PS25T]
Yeah . [UNCLEAR]
[PS25S]
Right ? And you multiply
[PS25T]
Yeah .
[PS25S]
the two bottom ones together . [UNCLEAR] .
[PS25T]
Right so that 's
[PS25S]
So what 's Have a guess , what would be erm
[PS25T]
So nine hundred , it works out at nine pound odd [UNCLEAR]
[PS25S]
What would two thirds of three quarters come to roughly . Just sort of thinking about it having a guess .
[PS25T]
A half .
[PS25S]
How did you get that ? Did you work it out here ?
[PS25T]
No it just seemed to spring to mind .
[PS25S]
Okay , what would three quarters of two thirds be ?
[PS25T]
Three quarters of two thirds , be a half .
[PS25S]
Right . Are you happy with that ?
[PS25T]
Yeah .
[PS25S]
Yeah . Okay . Just just have a quick look at it . In real life instead of squiggles on bits of paper .
[PS25T]
Right If we multiply that up it would come out to a half
[PS25S]
Yeah .
[PS25T]
would n't it .
[PS25S]
[UNCLEAR]
[PS25T]
But I never , it just seemed to click as a
[PS25S]
What are we doing . Erm two thirds of three quarters , or three quarters of two thirds . Right . So how much is there ?
[PS25T]
Er three quarters .
[PS25S]
How big is that ?
[PS25T]
That 's that 's a third .
[PS25S]
Right and that 's also a third . It does n't look it cos it 's
[PS25T]
Mm .
[PS25S]
it 's a s different colour , but it is the same size as that .
[PS25T]
Mhm .
[PS25S]
So we 've got two thirds there .
[PS25T]
Yeah .
[PS25S]
What would a quarter of that look like ? If you shared that two thirds out evenly between four people ,
[PS25T]
Mm .
[PS25S]
how much would they get each .
[PS25T]
About that .
[PS25S]
Great . If you shared out that two thirds right that 's that 's
[PS25T]
Yeah .
[PS25S]
one piece there , two thirds . Share that out between four people , how much would they get each ?
[PS25T]
Er one of these .
[PS25S]
One of these . Okay ?
[PS25T]
Mhm .
[PS25S]
So that 's one quarter .
[PS25T]
Mhm .
[PS25S]
So three quarters , would be three pieces like this .
[PS25T]
Mhm .
[PS25S]
It would be one two three .
[PS25T]
Yeah .
[PS25S]
That 's the half .
[PS25T]
Mm .
[PS25S]
Okay . Now what 's two thirds of three quarters ? Here 's your three quarters . What would one third of this be ? If we shared that three quarters equally between three people , how much would they get ?
[PS25T]
Between three people .
[PS25S]
Mhm .
[PS25T]
They 'd get erm let's see they 'd get that .
[PS25S]
Right . So they 'd get they 'd get that much .
[PS25T]
Mm .
[PS25S]
That 's one third of three quarters . So two thirds of three quarters , would be two pieces like that .
[PS25T]
mhm .
[PS25S]
Okay ? One two . Which is a half .
[PS25T]
Mhm .
[PS25S]
So it does work out .
[PS25T]
Yeah .
[PS25S]
It always works out with fractions . It 's the easiest thing to do with them . Multiply one by the other .
[PS25T]
Mhm .
[PS25S]
[UNCLEAR] leave them there . But it 's all all this is okay , but it sort of makes your brain ache after a bit and to just see something real that relates to it it 's makes it stick in your
[PS25T]
Yeah .
[PS25S]
mind .
[PS25T]
Mm .
[PS25S]
So any number , divided by one , is just the same number , so if we
[PS25T]
Yeah . So if we got two , four , O multiplied by four , equal to so what it is nine sixty
[PS25S]
Do n't do n't need to do the equals , you can go straight on to the divide by a hundred .
[PS25T]
And if we divide that by one , nought , nought , and then we do the equals , it becomes nine point six .
[PS25S]
Right . Okay . Good .
[PS25T]
I say I thought it was about nine pound odd .
[PS25S]
Right . [UNCLEAR] So
[PS25T]
So the the formula ,
[PS25S]
To calculate what erm
[PS25T]
Percentage [UNCLEAR]
[PS25S]
P P percent if you like . Well
[PS25T]
Mhm .
[PS25S]
we wo wo n't use X. P percent of thirty five pounds , [UNCLEAR] that 's thirty five times P over a hundred .
[PS25T]
Yeah . That 's it ? Yeah .
[PS25S]
[UNCLEAR]
[PS25T]
Good [UNCLEAR]
[PS25S]
That works , so if you want a twenty
[PS25T]
Mhm .
[PS25S]
percent , it 's thirty five times twenty and divide by a hundred .
[PS25T]
Mhm .
[PS25S]
Some of them you you might do in your head , like you think , Well I know twenty percent is one fifth , so I 'll just divide that by five and that 's seven pounds .
[PS25T]
Mhm .
[PS25S]
Erm so you can do that , you can work out total payments , and subtract that , and what it should have been . What about number two ?
[PS25T]
Let's see erm The diagram above , represents a rectangular lawn , fifteen by ten , with a circular flower bed diameter six [UNCLEAR] . Taking pi as three Er taking pi as three , calculate the area of the flowerbed . Area of a circle is pi R squared . So it 's three times the radius , squared ?
[PS25S]
Mhm . Yeah . So calculate the area of the flowerbed . Okay ?
[PS25T]
Er so the the flower bed has a diameter of six metres . So the radius is three metres .
[PS25S]
Right .
[PS25T]
So pi is three , times three squared .
[PS25S]
Right . Okay ?
[PS25T]
Well
[PS25S]
Yeah ?
[PS25T]
Three squared is nine , so it 's three nines , which is twenty seven .
[PS25S]
Right . Okay , twenty seven square metres .
[PS25T]
Mhm .
[PS25S]
And then what about B ?
[PS25T]
Please calculate the area of lawn remaining . So we have to take away , twenty seven metres . Square m
[PS25S]
[UNCLEAR] all the way round
[PS25T]
Yeah .
[PS25S]
is the perimeter . Area is the short one . That 's not all the way round , that 's just multiplying one by the other .
[PS25T]
Mhm .
[PS25S]
Okay . That gives you a [UNCLEAR] the length by the breadth or if you 're working out er painting a ceiling or something ,
[PS25T]
Mm .
[PS25S]
length by the breadth to work out how may square metres , then you have a look on the can , [UNCLEAR] one can will cover thirty square metres or whatever .
[PS25T]
Mm .
[PS25S]
Okay ? So that 's okay . So you should n't be having any problem with those anyway . In the diagram , a rhombus , each side of length three centimetres , put X in inside . Given that X is less than three centimetres from here mm mm mm mm , indicate the region in which X must lie . Mm .
[PS25T]
[UNCLEAR]
[PS25S]
Now , any of these geometry ones , have a look , if you ca n't get it very quickly , just leave it .
[PS25T]
Yeah .
[PS25S]
Erm you can come back to it at the end if you 've done everything else , but there 's something about these that er I think you 're one . Erm some people get hooked on geometry , and they , I 'm gon na get this one if it kills me .
[PS25T]
Yeah .
[PS25S]
It does n't kill you , but it means you spend an hour on it when you could be doing the rest of your exam .
[PS25T]
Yeah . It does n't help . Yeah .
[PS25S]
Okay ?
[PS25T]
Er what what they 're saying is , P Q P going round this way , P Q R S , is a rhombus . What does it mean a rhombus ? That 's the name of that shape ?
[PS25S]
Yeah .
[PS25T]
Yeah . Cos I 've not come across that .
[PS25S]
Okay .
[PS25T]
I have seen that shape , but not called a rhomb But each side of length is three centimetres . So three , six ,
[PS25S]
They will
[PS25T]
twelve .
[PS25S]
each of those is three , alright ?
[PS25T]
Twelve centimetres . For the whole thing .
[PS25S]
The the perimeter would be twelve centimetres
[PS25T]
Yeah .
[PS25S]
Yeah .
[PS25T]
A point X lies inside the rhombus . It is given that X is less than three centimetres from P . Right ?
[PS25S]
Yeah Right .
[PS25T]
And that the distance P X , is greater than the distance R X.
[PS25S]
Right .
[PS25T]
So it 's got to be down here . Indicate clearly , by shading it the diagram , the region in which K must lie , down here .
[PS25S]
Clearly shade in the diagram .
[PS25T]
Is that worth about [UNCLEAR] . A point at X lies inside the rhombus . It 's given X is less than three centimetres from P . So it means it 's not Ah so it means it 's got to be up the top end .
[PS25S]
But you just said it 's down the bottom end ?
[PS25T]
I did . But I 'm reading it again .
[PS25S]
Mhm .
[PS25T]
And it says , It 's given that X is less than three centimetres from P . Well these are three centimetres long .
[PS25S]
Right .
[PS25T]
So if it 's less than three centimetres from P it 's got to be up this end . And that the distance P X ir greater than the distance R X. Well that does throw me because then
[PS25S]
Right .
[PS25T]
Yeah . Because it 's like equal distances .
[PS25S]
Okay . Right . So you get to that stage , and you think forget this .
[PS25T]
Mm .
[PS25S]
Right ?
[PS25T]
Right .
[PS25S]
How many marks for it ? Not many . There would n't be many for that .
[PS25T]
Mm .
[PS25S]
And you could waste an awful lot of time on it .
[PS25T]
Wh what was the answer for that ?
[PS25S]
Well I think I 'll leave you that one .
[PS25T]
[UNCLEAR] .
[PS25S]
Erm
[PS25T]
Are you taking the mickey ?
[PS25S]
I 'll give you I give you a clue . Shall I give you a clue ?
[PS25T]
Er
[PS25S]
No . It 's geometry question , what sort of things do you normally use with , when you 're doing geometry ?
[PS25T]
[UNCLEAR] like pi and stuff like that ? You know .
[PS25S]
Mm . What sort of instrument did you normally use ?
[PS25T]
A protractor .
[PS25S]
Yeah . Anything else ?
[PS25T]
Compass .
[PS25S]
That 's more like it .
[PS25T]
Mm . [UNCLEAR]
[PS25S]
Erm nearly all of these , geometry questions
[PS25T]
Yeah .
[PS25S]
wh where there 're constructions , a compass comes into it . So do n't spend much time on that . Cos
[PS25T]
Mm .
[PS25S]
you 've got lots of other work in this that you should be doing .
[PS25T]
Yeah . Right .
[PS25S]
But if you 're really absolutely cheesed off , then give yourself am maximum of five minutes on that ,
[PS25T]
Mhm .
[PS25S]
and then leave it and go and do something else .
[PS25T]
Yeah .
[PS25S]
And it 'll probably come to you . But erm do n't get stuck on those in the exam .
[PS25T]
Right .
[PS25S]
If you ca n't do it right away , leave it .
[PS25T]
Mhm . Right .
[PS25S]
Student asks thirty people , how long it had taken them And you draw a frequency table , which you 've just been doing there .
[PS25T]
Mhm .
[PS25S]
Okay ? So that should be okay . That would be a good one for you to try on your own .
[PS25T]
Yeah .
[PS25S]
Erm right I I would say , just leave that . Just forget it
[PS25T]
Yeah .
[PS25S]
Just forget that sort of problem altogether
[PS25T]
Mhm .
[PS25S]
because you can really get stuck on them .
[PS25T]
Yeah .
[PS25S]
That you 'll get you can pretty much guarantee you 'll get one , and it 'll be almost the same as that . There 'll be different numbers , it wo n't be a football match , it might be weights of pizzas , it might be the length to french sticks , you know it could be anything . But
[PS25T]
Yeah .
[PS25S]
it 'll be very similar to that . Same technique . I think you 'll also get something like this . Using the root which is not drawn to scale , write down the reading running up there , running up there , running up there , giving the total [UNCLEAR] . Find the numbers of litre petrol . Now you should be able to do that one .
[PS25T]
Mhm .
[PS25S]
Completely on your own . So this i this is a good thing to work through , this one . Now look . A field is in the shape of a quadrilateral , [UNCLEAR] . Use the scale [UNCLEAR] one to ten . Make an accurate drawing Now if you get one like this ,
[PS25T]
Mm .
[PS25S]
like six , and you will usually get one of these on , [UNCLEAR] do an accurate scale drawing , then go for that .
[PS25T]
Yeah .
[PS25S]
They tell you what to do , do an accurate scale drawing . They will often tell you what scale to use as well . Which they do here . And then all you have to do , is measure off something , a diagonal or
[PS25T]
Mhm .
[PS25S]
how far is this one from that ? And put your answer in . If your diagram is pretty reasonable , you 'll get most of the mark . Erm if your diagram 's pretty reasonable and you measure the wrong thing , you can still get quite a lot of the marks .
[PS25T]
Mm .
[PS25S]
So it 's a And it does n't take all day . It 's a good one . [UNCLEAR]
[PS25T]
Yeah . So it 's a good one to go for . Yeah .
[PS25S]
Right . Now probability . If you do n't understand it , just leave it .
[FYAPSUNK]
[PS25T]
Yeah . This was the
[PS25S]
Erm
[PS25T]
tree thing is n't it ?
[PS25S]
Yeah . Erm Write the appropriate probabilities on the branches of the tree diagram . And we 'll have a quick glance at that now . See what you make of it . Three blue and one red . And two draws are made , at random in each case . Draw one , a bead is taken from bag A. And it 's put in bag B.
[PS25T]
Well bag A
[PS25S]
I think that 's a bit nasty that .
[PS25T]
Yeah . Bag A contains three blue beads
[PS25S]
Mhm .
[PS25T]
and one red bead . Bag B contains three blue beads and three red beads . Two draws are made [UNCLEAR] Draw one , a bead is taken from bag A and put in bag B. Right . A bead is taken from bag B. Write the appropriate probability on the branches of the tree diagram . Draw one ,
[PS25S]
And they wo n't be giving you a lot of marks for that I do n't
[PS25T]
Mm .
[PS25S]
think . Erm I think that 's slightly tricky . It 's it 's unusual .
[PS25T]
Yeah .
[PS25S]
Erm
[PS25T]
I mean you 're obv er to me you 'd there 's more chance of you getting a blue bead out .
[PS25S]
Well we 're not bot too bothered about , is there more chance or less chance ? We want to know exactly .
[PS25T]
Mm .
[PS25S]
Exactly how much chance . Erm this is this is real this stuff . This is
[PS25T]
Mm .
[PS25S]
erm not you know , silly mathematics , it 's probability is based on , it 's to do with gambling .
[PS25T]
Mm .
[PS25S]
It 's all about [UNCLEAR] getting your money . Now there was a bloke called Chevalier de Mer . Who was
[PS25T]
Sounds French .
[PS25S]
He wrote to Pascal . Was it Pascal ? Er yes . Pascal . Erm who was a a mathematician , a very brilliant mathematician . Erm saying I 've got this gambling problem , I do n't know whether how much it 's worth betting on this . You 're a mathematician ,
[PS25T]
Mm .
[PS25S]
you work it out for him . For me . And he he more or less laid down the whole theory of probability , in a few days , Pascal
[PS25T]
Yeah .
[PS25S]
did . Erm in the letters that he wrote to this bloke . Who then went on to win quite a lot of money , cos he could
[PS25T]
Yeah .
[PS25S]
he knew what the odds were and everyone else did n't . Erm let's say . A pack of cards . You draw four cards out , one after the other .
[PS25T]
Mm .
[PS25S]
Okay ? Now it 's gon na cost you a pound to play this game . Okay . If you get four aces out , We make sure it 's a fresh deck of cards and everything else , and nothing 's fixed .
[PS25T]
Mm .
[PS25S]
If those cards that you get are four aces , I 'll give you a thousand . Okay ? a thousand pound . If they 're not , then I get your pound . Do you want to play ?
[PS25T]
No .
[PS25S]
Would you you know , would you play that ?
[PS25T]
Yeah . I 'd probably I 'd have a go . Yeah .
[PS25S]
You 'd have a go .
[PS25T]
Mm .
[PS25S]
Okay . Well
[PS25T]
Probably lose me pound like , but I 'd have a go .
[PS25S]
You 'd probably lose more than that .
[PS25T]
Mm .
[PS25S]
Cos you 'd keep having , Ah it 's only another pound [UNCLEAR] . You 've got fifty off me
[PS25T]
Yeah .
[PS25S]
so far , I 'll have another go , to try and get
[PS25T]
Mm .
[PS25S]
that thousand . Well you 'd need about nearly round round about a million goes .
[PS25T]
Mm .
[PS25S]
You 'd think something like three chances in a million of getting four aces . So if someone had come up to you , and said , Well look , you you bet three pound , to have a go and if you get a four aces , I 'll give you a million pound , then it 's worth it . That 's a that 's a reasonable that 's a fair balanced
[PS25T]
Mm .
[PS25S]
deal . That 's okay . But usually , it 's very very much loaded in favour in favour of the the banker
[PS25T]
Yeah .
[PS25S]
the person who 's offering you the game , and he knows the odds .
[PS25T]
Mm .
[PS25S]
You do n't . You just think , Ooh [UNCLEAR] thousand to one , that sounds good odds . Ca n't get much better than that .
[PS25T]
No .
[PS25S]
But he should be giving you a million to three .
[PS25T]
Yeah .
[PS25S]
Which which is a lot more . So we want to know exactly what the odds are , on this one . A blue one or a red one . Draw one . What are the odds . [UNCLEAR] red . I I like writing them writing them on the nodes like that . That 's a red one , and that 's a blue one . Right . Draw one , it 's from bag A. Bag A has got three blue , and one red .
[PS25T]
Yeah .
[PS25S]
[UNCLEAR] start off here with three blue and one red .
[PS25T]
Mhm .
[PS25S]
What 's the chances of getting a red , what 's the chances of getting a blue ?
[PS25T]
Well there 's one chance of getting a red . And there 's three chances
[PS25S]
Well mark the probabilities on here . Where they 've put the
[PS25T]
Oh right .
[PS25S]
Right .
[PS25T]
Three blue , one red .
[PS25S]
Now this looks like a good game to bet on , because a probability of one , is an absolute certainty . A probability of three is just totally unheard of .
[PS25T]
Mm .
[PS25S]
You ca n't have a probability of greater than one .
[PS25T]
Yeah .
[PS25S]
So this is n't the probability . What 's the chances of getting a red ?
[PS25T]
The chances of getting a red . There 's there 's one chance .
[PS25S]
One chance in a million ?
[PS25T]
One chance in three .
[PS25S]
One chance in ?
[PS25T]
Four .
[PS25S]
Right . So the chance of getting a red , is one in four .
[PS25T]
Ah .
[PS25S]
The chance of getting a blue ?
[PS25T]
Is three in four .
[PS25S]
And the chance of getting either a red or a blue , If I say , Here you are , I 'm gon na you 've got this bag and it 's got three blue and one red in it . And I 'm gon na pick one at random , and I 'm gon na have this bet with you that I will get either a red or a blue . And what odds are you gon na Are you gon na play ?
[PS25T]
Yeah . If you 've got .
[PS25S]
There 's the bag has got , three blue and one red in it .
[PS25T]
Yeah .
[PS25S]
I 'm gon na take one out without looking .
[PS25T]
Mhm .
[PS25S]
And I 'm gon na bet you that I 'll either get a red one or a blue one .
[PS25T]
Mm .
[PS25S]
Now I 'll pay you ten pounds to play this game , and I only want a pound if I win .
[PS25T]
Yeah . I 'd play it but it 's possible that the red one will go when you take it out . And there 'll only be blue left .
[PS25S]
Well it 's a certainty that I 'll get either a red or a blue .
[PS25T]
Yeah .
[PS25S]
Right .
[PS25T]
Mhm .
[PS25S]
Cos there 's only a red or a blue in there , so if I
[PS25T]
That 's right yeah .
[PS25S]
If I say , I 'll bet you I 'll get either a red or a blue .
[PS25T]
Mhm . Yeah .
[PS25S]
[UNCLEAR] I 'm I 'm onto a good , I ca n't lose .
[PS25T]
Yeah .
[PS25S]
So I 'll just keep raking it in wo n't I ?
[PS25T]
Mm .
[PS25S]
Because we add up the probabilities , to find out the chances of getting that or that . We get three quarters , add a quarter ,
[PS25T]
One .
[PS25S]
which is one . [UNCLEAR] A probability of one , is an absolute certainty .
[PS25T]
Mhm .
[PS25S]
One out of one . A hundred times out of a hundred , a million times out of a million .
[PS25T]
Yeah .
[PS25S]
Cos probability is always expressed as a fraction . Right . Now this is where the tricky bit comes in . Whatever one we get , goes into the next bag .
[PS25T]
Mhm .
[PS25S]
So if we did get Three out of four chances we get a blue .
[PS25T]
Yeah .
[PS25S]
If we get a blue one , we put it in the bag , and what would the bag cont what would the second bag contain now ? Bag B , it had got three blue and three red , so it 's now going to have four blue and three red . Okay ?
[PS25T]
Mhm .
[PS25S]
Looking at this one , if we pulled a red one out of bag A and put it into bag B , bag B would now have three blue , and four red . Take that one next as we 're down here . Blue at the top . Now what 's the chance of getting a blue ? How many are there in the bag ?
[PS25T]
Three . And four red .
[PS25S]
Four red . So what 's the chances of getting a blue one ?
[PS25T]
Three in seven .
[PS25S]
That 's it . Three out of seven . And the chances of getting a red ?
[PS25T]
Four out of seven .
[PS25S]
Four out of seven . Okay ?
[PS25T]
Mhm .
[PS25S]
Going back to the beginning again . Three blues on red . Mot likely , three times out of four it 'll be a blue . We put it in the second bag , and that 's now four blue and three red . So the chance of getting
[PS25T]
[UNCLEAR]
[PS25S]
a blue is ?
[PS25T]
Four out of seven .
[PS25S]
Four out of seven . And the chance of getting a red ?
[PS25T]
Three out of seven .
[PS25S]
Down here . Three out of seven . Okay ? Right . What 's the chance of getting either a blue or a red ? On this on this pick ?
[PS25T]
Erm
[PS25S]
Four sevenths , add three sevenths , how many sevenths is that ?
[PS25T]
Seven sevenths are one .
[PS25S]
Which is one . So it 's a certainty that we get a blue or red .
[PS25T]
Yeah .
[PS25S]
It 's just a check that we 've got that covered .
[PS25T]
Mhm .
[PS25S]
That we have got the right probabilities .
[PS25T]
Yeah .
[PS25S]
Same down here , three sevenths add four sevenths , that 's okay . Now what 's the chance , that we 'll get a blue out of the first bag , and a blue out of the second bag ?
[PS25T]
Erm Three and four and four and seven , so it 's
[PS25S]
What do you mean by , Three and four and four and seven ?
[PS25T]
I was gon na add them up to see how [UNCLEAR]
[PS25S]
Were you ?
[PS25T]
Yeah .
[PS25S]
What happens if I added erm an eighth to three quarters ? Would the three quarters get bigger or less ? Bigger or smaller ?
[PS25T]
Bigger .
[PS25S]
So you 're saying , there 's more chance of getting the blue out of out of the second , than there is of just [UNCLEAR]
[PS25T]
Mhm .
[PS25S]
Right , and your next one , if you put it back , is four out of fifty two . And the next one four out of fifty two . So you 're saying the chances of getting four aces , provided you put it back each time and shuffled them again , would be sixteen out of fifty two .
[PS25T]
Mm Yeah . No .
[PS25S]
Your o your chances are n't getting better , they 're getting a lot worse
[PS25T]
Mhm .
[PS25S]
are n't they ?
[PS25T]
Mhm .
[PS25S]
With each complication .
[PS25T]
Yeah .
[PS25S]
Each other unlikely event that 's got to happen . There 's a good chance we wo n't even be there .
[PS25T]
Mhm .
[PS25S]
We wo n't there 's there 's a good chance we do n't even get the first blue .
[PS25T]
Yeah .
[PS25S]
So having got it , it 's not a certainty that we 'll get the next one . We 've got to combine these two probabilities , by multiplying them .
[PS25T]
Mhm .
[PS25S]
So the chance of getting here , is three quarters times four sevenths . Okay ?
[PS25T]
Yeah .
[PS25S]
Which will come to three sevenths . The chance of getting here , is three quarters times three sevenths . Now might as well leave them as as twenty eighths . So that' nine twenty eighths there .
[PS25T]
Mhm .
[PS25S]
Twelve twenty eighths up here . This one , the chance of coming down this way , was a quarter . We can only only start off from here ,
[PS25T]
Mhm .
[PS25S]
if we 've come down there . And most of the time we wo n't . We will have gone up there three times out of four .
[PS25T]
Yeah .
[PS25S]
So to even get a chance of picking a a blue , after we 've had a red ,
[PS25T]
Mhm .
[PS25S]
Only that 'll one happen one time in in four , on there . So this is going to be a quarter times three sevenths .
[PS25T]
Mhm .
[PS25S]
[UNCLEAR] . And that 's going to come to three out of twenty eight . And this one , will be what ?
[PS25T]
Where [UNCLEAR] one one quarter times four sevenths .
[PS25S]
That 's it .
[PS25T]
Four over twenty eight .
[PS25S]
And they , what do they add up to ? Four and three is seven ,
[PS25T]
Seven
[PS25S]
and twelve is nineteen
[PS25T]
So it 's six sixteen plus twelve .
[PS25S]
And nine .
[PS25T]
[UNCLEAR] twenty eight .
[PS25S]
Right . Okay .
[PS25T]
Yeah . Twenty eight twenty eighths is one . That 's right .
[PS25S]
Right . It means we 've covered them all and we 've got the probability correct . Twelve and nine , twenty one , twenty four , twenty eight out of twenty eight . If we 'd have added them
[PS25T]
mm .
[PS25S]
The way you wanted to do , and then we added all this lot up , we 'd find well , w the chance is more than a certainty . More than one , that we 'd finish up there . And very very much more than one , that one of these would happen . At each stage in your tree vertically ,
[PS25T]
Yeah .
[PS25S]
if you add them up , they should come to one . When you work out the probability of arriving at that point . So if we call that point blue , red , and we call this one here , blue , blue . Right ? That 's a blue followed by a blue . And this one is a blue followed by a red , A red followed by a blue . And a red followed by a red . That 's R R. Okay ?
[PS25T]
Yeah .
[PS25S]
Erm that 's a q sorry that 's a quick look at it . Now the reason this is a bit messy , is that at that stage , depended on which one you get out of here , you putting in the second bag . Erm I have n't seen one before like that at this level .
[PS25T]
Yeah .
[PS25S]
[UNCLEAR]
[PS25T]
He may be giving us harder papers just to
[PS25S]
I suspect that you do n't that you do n't ne Yeah . I think he is .
[PS25T]
As he gears up .
[PS25S]
I think you do n't need that bit . Erm try it again . Do it yourself , that one .
[PS25T]
Mhm .
[PS25S]
But do n't when you 've made your draw ,
[PS25T]
Yeah .
[PS25S]
Do n't bother putting the ball in the next bag , in bag B. Bag B 's got three blue and three red . just leave it like that .
[PS25T]
Mhm .
[PS25S]
When you 've drawn the first one , just put it back in the first bag and forget about it and go on . And see how you work your tree out .
[PS25T]
Yeah .
[PS25S]
Okay . That 's erm [UNCLEAR] . But you need you need to be practising a lot of things now .
[PS25T]
Mm .
[PS25S]
A lot . Erm Right . Using the distances and bearings , draw a scale diagram and measure things . Good one to go for .
[PS25T]
Mhm .
[PS25S]
You should get full marks on that and on that other one .
[PS25T]
Yeah .
[PS25S]
They 're good ones to go for . That one No way . You know ?
[PS25T]
Yeah .
[PS25S]
You can really get tied up in it and you [UNCLEAR] and I 'll just try this now . [UNCLEAR] I know I 've been a long time on this but I 'll I think it 's nearly there .
[PS25T]
Yeah .
[PS25S]
They can be nearly there for an hour and a half .
[PS25T]
Mm .
[PS25S]
And you keep , Oh yeah I 'll just No .
[PS25T]
Yeah .
[PS25S]
Just leave it . Leave it . And what 's Mrs Pink doing ? Alright , again , this is the same sort of thing you get . Average speed before the car broke down . average speed between then and then . The length of the time that she spent in Cambridge . That 's a good one to look at . Er now he 's get Ms and Ss and Ns on this . So that 's Midlands and Southern and Northern . That was a Northern was it ?
[PS25T]
What does he mean by that ?
[PS25S]
Northern paper .
[PS25T]
Oh right .
[PS25S]
Northern paper , Southern paper , Midlands paper .
[PS25T]
Oh yeah .
[PS25S]
Erm Okay . Yeah I think I think have a go at those , you should be able to . You should be able to do all of those . I would le definitely leave that .
[PS25T]
Mhm .
[PS25S]
There wo n't be a lot of marks on it .
[PS25T]
Yeah .
[PS25S]
So you can really just you know
[PS25T]
Mm .
[PS25S]
you can just throw the exam away getting stuck
[PS25T]
Yeah .
[PS25S]
on one of those . Erm bearing You should be fine on that and on that . Now , drawing graphs of functions . Have you done inequalities ? Less X is less than or equal to six ? No .
[PS25T]
No .
[PS25S]
Cos that is definitely on [UNCLEAR] erm . Mm . You 've done drawing graphs of er Y equals
[PS25T]
Done vectors
[PS25S]
Y equals two X minus three . Things like that . Draw a graph of that .
[PS25T]
No .
[PS25S]
No ?
[PS25T]
Does n't ring a bell , no . Not a graph of it , no .
[PS25S]
[UNCLEAR] you have you has he done any drawing graphs ?
[PS25T]
Yeah he 's done some graph work . Erm
[PS25S]
Yeah . Yeah . You 'll be given a function like given in that form , Y equals some function of X. And then draw a graph .
[PS25T]
There 's some sort of graphs here . I d Oh these [UNCLEAR] .
[FYAPSUNK]
[UNCLEAR]
[PS25S]
quick look at that one .
[PS25T]
[UNCLEAR]
[PS25S]
Yeah this is it . Yeah . draw a graph of that equals that for that .
[PS25T]
No .
[PS25S]
Okay ?
[PS25T]
Is that a vector ? No ?
[PS25S]
No . No . Let's have a look . No . It 's just a graph of a function which happens to be a straight line . Erm
[PS25T]
[UNCLEAR] my lines I think I 've possibly got them
[PS25S]
Mm .
[PS25T]
[UNCLEAR] .
[PS25S]
Yes . I think so .
[PS25T]
Yeah
[PS25S]
I would n't have said wrong , but not correct . So X is minus one . Four X plus one is minus three . One and five [UNCLEAR] Okay those points are right . So putting those on the graph , you 've got minus one , minus three . Minus one right One one point should be here .
[PS25T]
Mhm .
[PS25S]
You 've got nought , one , which is there . Okay . I 'll just put a ring in pencil , round the ones that are okay . Nought , one , that 's okay . [UNCLEAR] Y equals three X plus five , okay . And you 're doing , Y equals four X plus one . Oh I see . Yeah . But erm
[PS25T]
They 're [UNCLEAR]
[PS25S]
Mm . This one This minus one , three , just is n't shown anywhere .
[PS25T]
Yeah .
[PS25S]
Minus one minus three does n't even go down to minus two .
[PS25T]
Yeah . I d I did n't actually complete this .
[PS25S]
No . Okay .
[PS25T]
In fact I I 've got a feeling this may
[PS25S]
Erm
[PS25T]
have been , written down to actually do
[PS25S]
Mm .
[PS25T]
on ano separate pieces of graph paper .
[PS25S]
Yeah . That 's what I th or well what I was just about to suggest . It would be well worth you doing that , because they give you , you can almost guarantee a question on graphs . They 'll give you some
[PS25T]
Mm .
[PS25S]
Nice standard functions like this , that you can feel at home with .
[PS25T]
Yeah .
[PS25S]
And draw your graph . Erm let's see . If you 've got any different , use two colours there , how many have you got ? One , two , and three , Yeah . I would do them on separate ones . Erm If you have n't got graph paper , erm pick a bit of s squared paper [UNCLEAR]
[PS25T]
Mhm .
[PS25S]
Just a normal sort of squared exercise book . I have n't got any with me , and I was just looking at graphs for someone else earlier .
[PS25T]
Yeah .
[PS25S]
Erm that 's I mean I would really recommend that you make the time .
[PS25T]
Yeah .
[PS25S]
It 's getting
[PS25T]
To do that .
[PS25S]
It 's getting very very close , and you 've got an awful lot to do .
[PS25T]
Mm .
[PS25S]
You 've got a tremendous amount to for you , not for me to go through with you ,
[PS25T]
Mm .
[PS25S]
but just for you to do , on what we 've done so far ,
[PS25T]
Mm .
[PS25S]
to consolidate that , before we can move on really .
[PS25T]
Yeah . Yeah erm .
[PS25S]
Erm . I ca n't find time for you ,
[PS25T]
Yeah .
[PS25S]
you you 'll have to make the time somewhere ,
[PS25T]
Mm .
[PS25S]
pinch the times from something . Erm to do cos you 're gon na , you 're gon na be struggling if you
[PS25T]
Mm .
[PS25S]
if you ca n't do a lot more work .
[PS25T]
Yeah .
[PS25S]
Er how d how do you feel , you 're doing with with the maths ?
[PS25T]
Erm well I feel I like you say , I can do with more more sitting down and doing it myself so it it sinks in .
[PS25S]
Mm . You could do with a lot a lot more . A lot more exercises
[PS25T]
Mm .
[PS25S]
and a lot more Because otherwise , you 're gon na come to that exam , you 're gon na sit down , and you 're gon na say , Oh I did something a bit like this with John , I remember that . I understood it at the time .
[PS25T]
Yeah .
[PS25S]
It 's gone now . Cos you have n't done it yourself ,
[PS25T]
Yeah .
[PS25S]
on your own , several times , to practise it , to shake it up and down , get all the bits out of it
[PS25T]
Mm .
[PS25S]
and sort of store it away
[PS25T]
Yeah .
[PS25S]
where you can just pull it in . You think , Yeah , I know what I 'm doing with this . Completely in control of it .
[PS25T]
Yeah .
[PS25S]
Okay ?
[PS25T]
Yeah .
[PS25S]
Erm . What more can I say ?
[PS25T]
Well
[PS25S]
You you need
[PS25T]
I 'll
[PS25S]
to You need to have a good go at these . Go through that paper , and
[PS25T]
Mhm .
[PS25S]
erm and do those graphs .
[PS25T]
Yeah . And I 'll have a a good read of this , and try and write down , things that I 've got a block about I mean
[PS25S]
Do do more writing and trying things and reading at the moment .
[PS25T]
Mhm .
[PS25S]
You can catch up on the [UNCLEAR] I mean you can do those graphs without reading anything else about it .
[PS25T]
Yeah .
[PS25S]
Do one on each sheet of paper . Erm [UNCLEAR] Reuben might have some graph paper [UNCLEAR]
[PS25T]
I 've got gr I 've got graph paper .
[PS25S]
Right .
[PS25T]
Yeah .
[PS25S]
Okay ? Great well use on sheet for each .
[PS25T]
Yeah .
[PS25S]
And do some graphs on that . Cos we 've got , really we 've got a a lot more that I 'd like to cover .
[PS25T]
Yeah .
[PS25S]
Erm we 've only had a a glimpse really of probability .
[PS25T]
Mhm .
[PS25S]
You can guarantee there 'll be one question on that .
[PS25T]
Yeah .
[PS25S]
Erm you could probably do with revising the statistics bit . Erm you should also be practising , manipulating equations .
[PS25T]
Mhm .
[PS25S]
Changing the subject of equ of an equation .
[PS25T]
Yeah .
[PS25S]
Yeah . If I give you something like , now can you remember how to do that sort of thing ? That 's that 's
[PS25T]
Make R the subject .
[PS25S]
Call that three . Two erm Make Y the subject . So that you get Y equals something . And again there . R equals something . Now in that one , erm one , this is the easiest one , I thought , Well , better give you some easier ones so you can work into that .
[PS25T]
Mhm .
[PS25S]
Erm And make X the subject of that . X equals Okay . No . Have a go at that one first , and work up that way , how 's that sound ? There 's more work in doing these but you you should be sort of practising equations all the time .
[PS25T]
Yeah .
[PS25S]
Erm , doing awkward ones that have got fractions in . So that you 're keeping up with the fractions . Doing ones that have got percentages in . Doing ones that have got maybe a mixture , of percentages . I mean it was , a couple of years ago , a favourite question , things like , erm , What 's twenty five percent of a quarter ?
[PS25T]
Mhm .
[PS25S]
Er how would you go about that ? What 's twenty five percent of a quarter ?
[PS25T]
A quarter of a quarter .
[PS25S]
Right good , okay , and what will that come to ?
[PS25T]
A quarter once one is one .
[PS25S]
A quarter of a quarter
[PS25T]
[UNCLEAR] Du n no .
[PS25S]
One times one ?
[PS25T]
One .
[PS25S]
One .
[PS25T]
Sixteen .
[PS25S]
Four times , do n't forget , four times .
[PS25T]
Yeah .
[PS25S]
Er very tempting to add them .
[PS25T]
Mhm .
[PS25S]
Especially when you 'd rather work with eights than sixteenths .
[PS25T]
Yeah .
[PS25S]
Okay ?
[PS25T]
Yeah .
[PS25S]
It 's all this sort of the bias that you 've got through how you 've worked things , and [UNCLEAR] fiddle about with sixteenths . Erm when you once y once you 've got out of the habit of sixteenths and thirty seconds , and things like that , you find that I mean , we found the other week , did n't you , that you were thinking , Oh these millimetres [UNCLEAR] a bit of a pain . He was much
[PS25T]
Yeah .
[PS25S]
happier when it was back in the old feet and inches .
[PS25T]
Mm .
[PS25S]
But if you try and go back to it , when you have n't done it for years , you realize how complicated it was .
[PS25T]
Yeah .
[PS25S]
With the yards , feet and especially all the , How many yards in a a furlong and
[PS25T]
Mm .
[PS25S]
a chain , and mile and
[PS25T]
Yeah .
[PS25S]
Then nautical mile and everything else .
[PS25T]
Mm .
[PS25S]
It 's er it 's a pain . That 's a paper . [UNCLEAR] . Never mind . That 's paper [UNCLEAR]
[PS25T]
Yeah .
[PS25S]
That one was for how old is er Is that yours ?
[PS25T]
No .
[PS25S]
Oh that 's probability , it 's where it starts . [UNCLEAR] functions did n't we .
[PS25T]
Yeah .
[PS25S]
And again , these scribbles , I mean my excuse is they 're supposed to be like that , but These wo n't mean a thing
[PS25T]
Mhm .
[PS25S]
in maybe two or three days time .
[PS25T]
Yeah .
[PS25S]
But in a d within the next day or so , perhaps over the weekend , if you can make your notes about what this was Put it in your own words , what was happening here . What does F of G of X mean ? Erm [UNCLEAR] just put a tiny note on it . erm you were all right on those .
[PS25T]
Mm .
[PS25S]
I would ask him about that [UNCLEAR]
[PS25T]
Yeah .
[PS25S]
Ask him if you need to know F of G of X and G of F of X.
[PS25T]
Mhm .
[PS25S]
I mean I f I I feel that you do . But it was n't there
[PS25T]
Yeah .
[PS25S]
on that syllabus that I 've just looked at , so
[PS25T]
Mhm .
[PS25S]
[UNCLEAR] do n't want to load you up , with
[PS25T]
Yeah .
[PS25S]
more stuff if it 's not on your syllabus .
[PS25T]
Right .
[PS25S]
So [UNCLEAR] that one should be . Rrr . How do you feel about it ?
[PS25T]
Mm er not too bad , but I feel , you know , I need to
[PS25S]
You you you really
[PS25T]
I need to work on it .
[PS25S]
You really do I mean And what 's what 's the last time
[PS25T]
It 's remembering the formulas and stuff that 's er is the is the major thing , because I know , like in the class , I 've not actually had a lesson where I 've done bad . But it 's memory of er
[PS25S]
If you just have that one lesson , and he explains it to your properly , and he sets you some exercises , on what you 've just done , half an hour or an hour ago , you 'll get through them .
[PS25T]
Mm .
[PS25S]
But if he gives you the s exactly the same numbers even , same exercise , same number
[PS25T]
Yeah .
[PS25S]
If he gives you [UNCLEAR]
[PS25T]
Yeah .
[PS25S]
a month later , you would n't know where to start .
[PS25T]
Yeah .
[PS25S]
Unless [UNCLEAR]
[PS25T]
[UNCLEAR]
[PS25S]
time from somewhere , and just had I mean , five or six goes , an the same sort of question , until you get to the stage where you just go , Oh yeah , Okay . Bang bang bang bang .
[PS25T]
Mm .
[PS25S]
And then you 've got to the stage where you do n't need to . I mean you know , with other jobs that you do , when you need to practise it , and when you do n't .
[PS25T]
Yeah .
[PS25S]
Erm if you 've got something complicated to wire up or something .
[PS25T]
Mm .
[PS25S]
Or [UNCLEAR] work out what I 'm doing here , maybe make a little , few little notes to yourself .
[PS25T]
Mm .
[PS25S]
I must do that bit and that before that . And make sure this bit is earthed , but that must n't be earthed and
[PS25T]
Yeah .
[PS25S]
You do that same job , half a dozen times ,
[PS25T]
Mm .
[PS25S]
in the end , you 're just whizzing through it , you 're thinking about what you 're having for your tea . And you 're talking to your mate and it 's all just happening by magic .
[PS25T]
Mm .
[PS25S]
Yeah . And you 're not really concentrating very much at all . But it only comes with practice , and it 's
[PS25T]
Yeah .
[PS25S]
exactly the same with this .
[PS25T]
Mm .
[PS25S]
It will you know , you see it done once and do it once yourself . You think , Right I 've got it . Come the exam , you will be kicking yourself ,
[PS25T]
Yeah .
[PS25S]
cos you 'll think , I did one of these , when was it ?
[PS25T]
Mm .
[PS25S]
Oh a couple of months ago I did one of these , now er how do I get into it ? Where do I start ?
[PS25T]
Yeah .
[PS25S]
What 's the trick on this one ? Hey . So
[PS25T]
Yeah . Right
[PS25S]
I do n't I mean I know I I 'm very busy , I 've got stuff that I should have done , months and months ago , that I have n't got round to doing yet , cos there 's been all sort of interruptions . So er But I 'm the one who suffers , cos I 'm not getting round doing it .
[PS25T]
Yeah .
[PS25S]
So I ca n't you know , ca n't advise you
[PS25T]
Mm .
[PS25S]
in how to find time . And you really need do it . I 've gone on a bit but
[PS25T]
[UNCLEAR]
[PS25S]
you do need
[PS25T]
Mm .
[PS25S]
to find yourself , several hours a week .
[PS25T]
Mhm .
[PS25S]
Erm as well as just going to night school .
[PS25T]
Yeah .
[PS25S]
So it 's up to you . Erm I 'm you know , I 'm quite sure , if you do n't , if you do n't put a lot of work in , then you will finish up not getting through .
[PS25T]
Mm .
[PS25S]
And you [UNCLEAR] just sort of have it all hanging over you and
[PS25T]
Yeah .
[PS25S]
do it again next year . So
[PS25T]
Mm . How long is there ?
[PS25S]
A month and a bit .
[PS25T]
Yeah .
[PS25S]
There 's a bank holiday coming up now , there 's another one the end of May ,
[PS25T]
Mhm .
[PS25S]
there 'll be all sort of interruptions and
[PS25T]
Yeah .
[PS25S]
There 's there 's no time at all . It 's gon na fly by and very soon , you 'll be sort of strolling into that exam
[PS25T]
Yeah .
[PS25S]
thinking , Oh if only I spent a bit more time [UNCLEAR]
[PS25T]
Yeah I 'll find the time
[PS25S]
Okay
[PS25T]
yeah .
[PS25S]
Okay I mean , it 's not for
[PS25T]
Yeah .
[PS25S]
me . It 's for you it 's for you .
[PS25T]
No no . Yeah . Yeah .
[PS25S]
Erm cos if you do n't it 's then either , be thinking of , Oh well
[PS25T]
Yeah it 's a lot of effort going nowhere if I do n't [UNCLEAR]
[PS25S]
Exactly it 's all wasted , what you have put in has just gone then .
[PS25T]
Yeah .
[PS25S]
And you start all over again .
[PS25T]
Yeah .
[PS25S]
Okay . Anyway I 'll better get off . And erm let you have a a little
[PS25T]
Right .
[PS25S]
break from , coming in from work , starting on this [UNCLEAR] . [UNCLEAR] ten past ten again .
[PS25T]
[UNCLEAR]
[PS25S]
[UNCLEAR]
[PS25T]
Next Friday then [UNCLEAR]
[PS25S]
Yeah I 'll I 'll