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#1 2012-01-26 07:11:29

zetafunc.
Guest

Linear Interpolation FP1 Formula

Is this formula okay to use for linear interpolation (finding the root of a function in an interval [a,b])?

However, in one mark scheme (in a Jan 2007 paper) I saw them use this formula, but with absolute values.

Thanks.

#2 2012-01-26 07:33:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,665

Re: Linear Interpolation FP1 Formula

Hi;

Have you tried that formula for something simple like

It is reasonably close to a root. You would need the root to be bracketed between a and b.

Like all formulas that are derived from theory it sometimes fails laughingly.

Try it out on f(x) = x^2

Give it a = -1 and b = 1.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2012-01-26 07:51:58

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Thanks for the reply.

I've been using it for every linear interpolation question I've encountered in the FP1 exam. They recommend the similar triangles method, but it's a bit tedious because you have to do some manipulation to get the root on its own... but with this formula it's a bit easier. However, I can't find anything about this formula online...

It appears that they take the absolute value of f(a) or f(b) (replace the f(a) and f(b)s with |f(a)| and |f(b)|) in these older past papers though... for example, for f(x) = ln(x) + x - 3, they said to use linear interpolation to find a root between 2.0 and 2.5.

f(2) gives you a negative value (about -0.3069) and f(2.5) gives you a positive value (about 0.4163). But they've taken the absolute values of both and used those for f(a) and f(b) instead...

Maybe it's better if I use the similar triangles method but then check my answer using this shorter formula?

#4 2012-01-26 07:54:06

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Sorry for not seeing your f(x) = x[sup]2[/sup] example.

Sorry, forgot to specify, it doesn't work if f(a) = f(b) since denominator would be 0.

#5 2012-01-26 08:08:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,665

Re: Linear Interpolation FP1 Formula

Hi;

Other than that it seems to be okay, what is it derived from?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#6 2012-01-27 09:50:57

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Not sure... I found it on the internet somewhere on some discussion forum so it's probably pretty unreliable because someone could have just made it up without justification. But I figured out the official formula that's accepted;

Will probably worry about the derivation until after the exam has finished, as they're not allowed to ask us any proof questions on that topic (only proof by induction questions will come up for series, sequences and proving some function produces some multiple of a number, luckily).

Exam is on the morning of 30th Jan, last exam... really want it out of the way. Maths is so boring when you're just doing past papers all the time.

#7 2012-01-27 10:24:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,665

Re: Linear Interpolation FP1 Formula

Hi;

That one works pretty good on the example given, but I still do not recognize it. I have rearranged it:


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#8 2012-01-27 20:05:37

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Thanks, I will write the re-arrangement out in the exam! (after I write the non-re-arranged formula out first)

#9 2012-01-27 23:53:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,665

Re: Linear Interpolation FP1 Formula

Hi zetafunc.;

Okay, and good luck on your exam. Let me know how you do.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#10 2012-01-30 08:21:39

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Had the exam today and didn't even need this formula because it didn't come up! Strangely it was an unusually easy paper... I think I got everything correct but there were some slight issues that worried me and may have cost me a couple of marks. One question asked about using Newton-Raphson twice on some function and give the final value to 3 d.p., but didn't know if you should round after doing it the first time. You got the same answer if you rounded or not, though. And then there was plotting complex roots on an Argand diagram... I did them as points not lines! I thought, for example, 1 + i is just the point (1,i), whereas |1 + i| is a line joining (0,0) and (1,i). I'm probably wrong, I don't know...

The paper was 90 minutes long, most people left after about 40 minutes! I stayed the full 90 minutes and checked everything as relentlessly as I could but didn't find anything. Unfortunately, because it was so easy, grade boundaries will be high and tiny mistakes could be incredibly costly...

Only got 1 more chemistry exam to go and then no more until May...

#11 2012-01-30 08:23:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,665

Re: Linear Interpolation FP1 Formula

Sounds like you did well.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#12 2012-01-30 08:23:32

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Hmm, I just checked my FP1 textbook and sometimes they're drawn as dots and sometimes they're drawn as lines... but in the FP2 textbook they're always lines. I think lines might be the correct thing to do, then... looks like I lost a couple of marks.

#13 2012-01-30 08:24:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,665

Re: Linear Interpolation FP1 Formula

I would think they are points and not vectors.

I left some stuff over in your other thread on matrix transformations.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#14 2012-01-30 08:28:38

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

bobbym wrote:

I would think they are points and not vectors.

Ah, that makes sense... thanks. Most people in my class drew lines though.

Summer will be stressful though so I hope I can take it one step at a time. I have started some revision for those since I have a lot to do, but only baby steps.

#15 2012-01-30 08:32:14

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,665

Re: Linear Interpolation FP1 Formula

Why will summer be stressful? Summer is a time of barbecues and parties in castles thrown by Dukes and Barons.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#16 2012-01-30 08:37:17

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

bobbym wrote:

Why will summer be stressful? Summer is a time of barbecues and parties in castles thrown by Dukes and Barons.

Summer up until mid-July at least. 2 months of exams from mid-May to early July (around 22 of them). Then I can take maybe a month off and relax and prepare for the next year. If everything goes to plan I should have 4 exams in Jan 2013 and 2 or 3 in June 2013, which would give me time to just sit back and enjoy maths for a bit rather than train to pass an exam. Then of course there is the issue with this girl in my class but that's something else... anyway.

I am supposed to get the results on March 8th. All mark schemes, grade boundaries, exam statistics etc come out on March 1st. I wish it wasn't so far away!

#17 2012-01-30 08:40:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,665

Re: Linear Interpolation FP1 Formula

There is always a girl in class to distract you. Nothing can turn a mans mind faster into a big bucket of mush than a girl.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#18 2012-01-30 08:41:11

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

bobbym wrote:

There is always a girl in class to distract you. Nothing can turn a mans mind faster into a big bucket of mush than a girl.

I suppose... she sits in front of me in all of my exams, literally within touching distance! It's a distraction but I don't mind...

#19 2012-01-30 08:43:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,665

Re: Linear Interpolation FP1 Formula

Same thing happened to me. She was DDG and sat in front me. I guess it is some kind of test that God gives all guys.

Just do not dip her hair in the inkwell!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#20 2012-01-30 08:46:10

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

bobbym wrote:

Same thing happened to me. She was DDG and sat in front me. I guess it is some kind of test that God gives all guys.

That's the real test we have to pass, I guess... what does DDG stand for?

I don't know why but I keep trying to find ways to talk to her and end up wasting my time for nothing.

#21 2012-01-30 08:46:44

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

DDG = drop-dead gorgeous?

#22 2012-01-30 08:48:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,665

Re: Linear Interpolation FP1 Formula

DDG means drop dead gorgeous. They start off being a little bit unsure of themselves and cautious the first week or two that they know you are sitting behind them. Trying to figure you out. But as their confidence grows, watchout!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#23 2012-01-30 08:54:19

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,523

Re: Linear Interpolation FP1 Formula

hi zf

Y U NO BECOM MEMBAR???


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#24 2012-01-30 08:55:56

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

bobbym wrote:

DDG means drop dead gorgeous. They start off being a little bit unsure of themselves and cautious the first week or two that they know you are sitting behind them. Trying to figure you out. But as their confidence grows, watchout!

Hmm... in the exam hall I sit behind her but in the classroom we're at completely opposite corners... the furthest possible distance apart!

It's sort of a strange dynamic. I'm in a class with year 13 kids and I am a year 12 (they're all 1 year older than me). I've talked to everyone in my class except for three people. She is one of those three. I do sort of feel like my brain is going mushy or recognising similarities that mean nothing. She's a year older than me but we got identical GCSE grades, identical module scores, we seem to get stuck on the same questions and we're both quick, and we seem to talk the same way. Doesn't really mean anything though. Oh look, I've just spent half an hour thinking about it instead of doing something more productive! Ah well...

#25 2012-01-30 08:58:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,665

Re: Linear Interpolation FP1 Formula

Hi;

It is normal do not worry about it. Happens to everybody so we all wasted and are wasting are time. The playing field is level.

You are 12? Meet anonimnystefy he is 14.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

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