[coolstorybrother]

question 7 jan 09 fp1 aqa


(link if wanted) http://store.aqa.org.uk/qual/gceasa/...W-QP-JAN09.PDF

i understand the theory i.e i have to prove it is linear interpolation however i can't seem to obtain the rearranged version for r - mainly the c-d part why is that needed and not just d for the similar triangles?, could someone walk it through please.

Also, on q3 am i right in thinking i have too minus the (pi divided by 2) then divide by -3?

[TenOfThem]

Oh yeah ... horrible question

[coolstorybrother]

(Original post by TenOfThem)
Oh yeah ... horrible question

so i shouldn't feel that annoyed that i was stuck and spent a lot of time on this?

[TenOfThem]

I seem to remember that I spent ages doing convoluted adding of stuff to make it work

Then when I was showing the class I saw a really obvious way

[TenOfThem]

(Original post by coolstorybrother)
so i shouldn't feel that annoyed that i was stuck and spent a lot of time on this?

I spent time using the little triangles .... then in class I thought ... hang on and used this

[coolstorybrother]

(Original post by TenOfThem)
I seem to remember that I spent ages doing convoluted adding of stuff to make it work

Then when I was showing the case I saw a really obvious way

im not sure but is the really obvious way using similar triangles (r-a)/c = (b-r)/d ? could you help on q3?

[TenOfThem]

(Original post by coolstorybrother)
im not sure but is the really obvious way using similar triangles (r-a)/c = (b-r)/d ? could you help on q3?

It is about using the correct similar triangles

see ^^^^^^

[TenOfThem]

What is arctan(rt3)

[raheem94]

(Original post by TenOfThem)
I seem to remember that I spent ages doing convoluted adding of stuff to make it work

Then when I was showing the case I saw a really obvious way

Which part of the question is difficult?

[TenOfThem]

(Original post by raheem94)
Which part of the question is difficult?

none of it

[raheem94]

(Original post by TenOfThem)
none of it

On which part did you spent ages?
I may like to have a go at it.

[TenOfThem]

(Original post by raheem94)
On which part did you spent ages?
I may like to have a go at it.

The initial proof

As I said I used the 2 small triangles and then had to do manipulation to get the format required

But ... as my diagram shows it was very easy

[raheem94]

(Original post by TenOfThem)
The initial proof

As I said I used the 2 small triangles and then had to do manipulation to get the format required

But ... as my diagram shows it was very easy

I did the 1st part in this way,

The gradient of the line(using points P(a,c) and Q(b,d) ) is,

Now form the equation of the line, using the point R(r,0),


Now sub in P(a,c), this gives,



How is this solution?

[TenOfThem]

I did Purple ratio = Green ratio



so



so

[TenOfThem]

(Original post by raheem94)

How is this solution?

I did similar to this before I realised the easy way I have shown above

That is what I meant when I said it took too much manipulation

[raheem94]

(Original post by TenOfThem)
I did similar to this before I realised the easy way I have shown above

That is what I meant when I said it took too much manipulation

Your way is better, but it is difficult to realize that technique. Similar triangles aren't much used at A-Level, so the students will probably not spot the easy technique.

Though my way is also not very long, it only takes around a minute.

[TenOfThem]

(Original post by raheem94)
Your way is better, but it is difficult to realize that technique. Similar triangles aren't much used at A-Level, so the students will probably not spot the easy technique.

Though my way is also not very long, it only takes around a minute.

Yeah ... from experience I just knew it should be "see-able" rather than "workable"


Once I "saw" it I was like "OMG how obvious"

[coolstorybrother]

(Original post by TenOfThem)
It is about using the correct similar triangles

see ^^^^^^

i kind of understand this... everything except why it is c-d?

(Original post by TenOfThem)
What is arctan(rt3)

umm i really dont know, should i?

[TenOfThem]

(Original post by coolstorybrother)
i kind of understand this... everything except why it is c-d?



umm i really dont know, should i?

c-d ... yeah I had to think ... but d is already a negative number


Yes you should

[f1mad]

(Original post by raheem94)
Your way is better, but it is difficult to realize that technique. Similar triangles aren't much used at A-Level, so the students will probably not spot the easy technique.

Though my way is also not very long, it only takes around a minute.

Similar triangles is widely used as a method for linear-interpolation.