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STPM Further Maths 2009

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markwongsk Male
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  #71 Old 30-04-2009 Default Re: STPM Further Maths 2009

Quote:
Originally Posted by Johnivan View Post
Hey brothers, another question:

Given 3 eigenvectors:
v1 = (1 -1 0)
v2 = (1 0 -1)
v3 = (1 1 1)

c) show that v1, v2 and v3 are linearly independent.
I don't know what is it talking about...

d) Express the vector (a b c) as a linear combination of v1, v2 and v3 with coefficients in terms of the constant a, b and c.
The answer given was
1/3(a-2b+c)v1 +
1/3(a+b-2c)v2 + 1/3(a+b+c)v3
I've no idea how to show it...
(c) three vectors are said to be linearly independent if the only solution forarbitrary numbers x,y,z forming the equation xv1 + yv2 + zv3 = 0 in otherwords, the determinant of the matrix must be non-zero. Try finding the determinant for the eigenvectors' matrix, you will get determinant = 3 I think... and since it's non-zero, the eigenvectors are linearly independent

Based on the extension of our knowledge in (c), it follows that eigenvectors which are linearly dependent has a determinant of zero. Since the new vector (a,b,c) can be expressed in terms of other vectors v1, v2, v3, it follows that this vector (a,b,c) is linearly dependent of v1, v2, and v3.

If we take v1, v2 and (a,b,c) and form a Matrix, we solve the determinant = 0 to get the vector (a,b,c) in terms of v3. (the answer for this is (a + b + c)v3 which is trivial considering v3 = (1,1,1) ) Using similar methods and finding determinant for the matrices of v1,v3 and (a,b,c) & also v2, v3 and (a,b,c) we get the following solutions:

(a,b,c) = (a+b+c)v3
(a,b,c) = (a+b-2c)v2
(a,b,c) = (a-2b+c)v1

therefore 3(a,b,c) = (a+b+c)v3 + (a+b-2c)v2 + (a-2b+c)v1
(a,b,c) = 1/3 [(a+b+c)v3 + (a+b-2c)v2 + (a-2b+c)v1]

simplifying to the answer given

Note that although the calculation involving matrix with v1,v3 and (a,b,c) yields a determinant of 2c-b-a, since the determinant is = 0 we can change this form into a+b-2c and get the second equation. I hope you understand my method since I din take FM exams so I dono whether it's really correct or not. I hope eurytos and/or uoykcuf can verify this for me

Last edited by markwongsk; 30-04-2009 at 08:44 PM. Reason: Automerged Doublepost
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Casperloo Male
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  #72 Old 01-05-2009 Default Re: STPM Further Maths 2009

How much altogether that 5 books cost ? If can, hope got Photocopy set.....
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uoykcuf
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  #73 Old 01-05-2009 Default Re: STPM Further Maths 2009

Quote:
Originally Posted by Johnivan View Post
Hey brothers, another question:

Given 3 eigenvectors:
v1 = (1 -1 0)
v2 = (1 0 -1)
v3 = (1 1 1)

c) show that v1, v2 and v3 are linearly independent.
I don't know what is it talking about...

d) Express the vector (a b c) as a linear combination of v1, v2 and v3 with coefficients in terms of the constant a, b and c.
The answer given was
1/3(a-2b+c)v1 +
1/3(a+b-2c)v2 + 1/3(a+b+c)v3
I've no idea how to show it...
mark has answered you in very detail way dy. lol

Quote:
Originally Posted by Casperloo View Post
How much altogether that 5 books cost ? If can, hope got Photocopy set.....
each book range from rm100-200
so total is rm500-1000
i got one book in my computer in pdf form, if you want u can pm me.
if u can come kedah, u can find me to ask me for the book

Last edited by uoykcuf; 01-05-2009 at 11:31 PM.
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chtan Female
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  #74 Old 02-05-2009 Default Re: STPM Further Maths 2009

Hi everyone! i'm considering taking further maths as my 5th subject for stpm. However I realized that there are not many books on further maths. From the list of recommendations that i saw, i have a few questions:

1. Is there a book which contains the complete stpm further maths syllabus? U guys listed so many different ones and it's gonna be costly to buy since my school's library is hopeless.

1a.if there isn't could u guys recommend the top 3 ones which u find most useful? I'm on a tight budget here

2. Which book did u guys used to do exercises? maths T had this Q&A book which i find quite useful but that publisher does not produce any further maths ones.

3. where can I find a collection of past yrs questions?

Any help is greatly appreciated.thanks
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uoykcuf
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  #75 Old 02-05-2009 Default Re: STPM Further Maths 2009

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Originally Posted by chtan View Post
Hi everyone! i'm considering taking further maths as my 5th subject for stpm. However I realized that there are not many books on further maths. From the list of recommendations that i saw, i have a few questions:

1. Is there a book which contains the complete stpm further maths syllabus? U guys listed so many different ones and it's gonna be costly to buy since my school's library is hopeless.

1a.if there isn't could u guys recommend the top 3 ones which u find most useful? I'm on a tight budget here

2. Which book did u guys used to do exercises? maths T had this Q&A book which i find quite useful but that publisher does not produce any further maths ones.

3. where can I find a collection of past yrs questions?

Any help is greatly appreciated.thanks
1. there is no such a book. you have to buy different kind of book and pick the useful topic to study.

1a. Further Mathematics, author: Bostock & Chandler
Discrete Mathematics, author: Rosen
Statistic, author: Crawshaw J Chambers
these are the book i think are enough for you to cover all syllabus dy. go search the old orange further math book in your school library. i think your school library got if your school is old enough. it is the text book for further math before the syllabus change. it is very useful but it is in malay version.

2. our local publisher do not publish any further math book as every year less than 100 ppl taking it. what you have to do is to see the example in the book listed above and try to understand the way to solve the question.

3. download from here http://cwooi.com/index.php?option=co...nc=select&id=2
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  #76 Old 02-05-2009 Default Re: STPM Further Maths 2009

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Originally Posted by Edmundkj
Yeah...Thank yOU for replying me.Actually, I did try to check the books online in the MPH website but couldn't find any. There's a MPH bookstore in Mid Valley right in KL. But it's SOOOOO... big that I dun think I'll succeed finding these books. I also know that the books are expensive..
Hi again...

Actually you might not be able to "find" them in MPH itself, these books are too rare to be in the shop itself. You need to go to the customer service counter to order, either to send it to MPH, and you collect; or you ask them to send it to your house (extra RM20). If you really want to take Further Maths, I would say that you really have to PAY to get the books. And, it won't be easy: because just physics and chemistry can make you upside down... Try to BUY these if you can:

1. Gaulter, B. & Gaulter, M., Further Pure Mathematics, Oxford, 2001.
It covers Complex Numbers, Matrices, Functions, Differentiation and integration, Power series, Differential equations,Coordinate geometry.


2. Bostock, L., Chandler, S., & Rourke, C., Further Pure Mathematics, Stanley Thornes, 1982 (Reprinted 2002).

This book acts as the helper for the previous one. The only important thing in this book is actually Transformation Geometry. But because the previous book is a "book of little words", This one gives the explanations.


4. Rosen, K. H., Discrete Mathematics and Its Applications (Fifth Edition), McGraw-Hill, 2003.
or
5. Scheinerman, E. R., Mathematics: A Discrete Introduction, Brooks/Cole, 2000.
You need this book to do Logic and Proof, Recurrence Relations, Number Theory and Graph Theory. But the rest are far out of the syllabus. Can't help, cos STPM Further Maths don't have a all-in-one book... This is the most expensive one.

The above 3 is very important. They cost around RM90 to RM110 each. You must have them to study. Then you might not need to buy these below, but just look for them, because you only need a little from them:

3. Anton, H., Bivens, I., & Davis, S., Calculus (Seventh Edition), John Wiley, 2002.
You need it for reference on Taylor's Polynomial, Continuity and Differentiability and Parametric and Implicit Derivation of d2y/dx2.

6. Crawshaw, J. & Chambers, J., A concise Course in Advanced Level Statistics (Fourth Edition), Nelson Thornes, 2001.
I won't stop you if you want to buy this, because it is really complete for the statistics part. I have this in my school library, so i asked permission from my library teacher for photocopy for chi-squared, Sampling & Estimation, Correlation & Regression, Hypothesis Testing.

Can you see it now? How leceh it is just to study Further Maths: a subject which you don't have a teacher beside you, and full of uncertainty when it comes to scoring... It's all up to you to decide.
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A few links worth checking out:
My Life Story
Further Mathematics T Blog (2003-2011 Syllabus)
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Eurytos Male
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  #77 Old 02-05-2009 Default Re: STPM Further Maths 2009

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Originally Posted by Johnivan View Post
Hi again...

Actually you might not be able to "find" them in MPH itself, these books are too rare to be in the shop itself. You need to go to the customer service counter to order, either to send it to MPH, and you collect; or you ask them to send it to your house (extra RM20). If you really want to take Further Maths, I would say that you really have to PAY to get the books. And, it won't be easy: because just physics and chemistry can make you upside down... Try to BUY these if you can:

1. Gaulter, B. & Gaulter, M., Further Pure Mathematics, Oxford, 2001.
It covers Complex Numbers, Matrices, Functions, Differentiation and integration, Power series, Differential equations,Coordinate geometry.


2. Bostock, L., Chandler, S., & Rourke, C., Further Pure Mathematics, Stanley Thornes, 1982 (Reprinted 2002).

This book acts as the helper for the previous one. The only important thing in this book is actually Transformation Geometry. But because the previous book is a "book of little words", This one gives the explanations.


4. Rosen, K. H., Discrete Mathematics and Its Applications (Fifth Edition), McGraw-Hill, 2003.
or
5. Scheinerman, E. R., Mathematics: A Discrete Introduction, Brooks/Cole, 2000.
You need this book to do Logic and Proof, Recurrence Relations, Number Theory and Graph Theory. But the rest are far out of the syllabus. Can't help, cos STPM Further Maths don't have a all-in-one book... This is the most expensive one.

The above 3 is very important. They cost around RM90 to RM110 each. You must have them to study. Then you might not need to buy these below, but just look for them, because you only need a little from them:

3. Anton, H., Bivens, I., & Davis, S., Calculus (Seventh Edition), John Wiley, 2002.
You need it for reference on Taylor's Polynomial, Continuity and Differentiability and Parametric and Implicit Derivation of d2y/dx2.

6. Crawshaw, J. & Chambers, J., A concise Course in Advanced Level Statistics (Fourth Edition), Nelson Thornes, 2001.
I won't stop you if you want to buy this, because it is really complete for the statistics part. I have this in my school library, so i asked permission from my library teacher for photocopy for chi-squared, Sampling & Estimation, Correlation & Regression, Hypothesis Testing.

Can you see it now? How leceh it is just to study Further Maths: a subject which you don't have a teacher beside you, and full of uncertainty when it comes to scoring... It's all up to you to decide.
Probably the best written Guide to Further Mathematics Books I have ever read. The MPM should revise their official list of recommended books to include detailed explanations such as this. You really should have taken FM seeing that you had already put so much effort into the subject.
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chtan Female
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  #78 Old 03-05-2009 Default Re: STPM Further Maths 2009

1. Gaulter, B. & Gaulter, M., Further Pure Mathematics, Oxford, 2001.
It covers Complex Numbers, Matrices, Functions, Differentiation and integration, Power series, Differential equations,Coordinate geometry.


2. Bostock, L., Chandler, S., & Rourke, C., Further Pure Mathematics, Stanley Thornes, 1982 (Reprinted 2002).

This book acts as the helper for the previous one. The only important thing in this book is actually Transformation Geometry. But because the previous book is a "book of little words", This one gives the explanations.


is 2 sufficient without 1? besides the examples in the books where can i find more exercises?
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Eurytos Male
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  #79 Old 04-05-2009 Default Re: STPM Further Maths 2009

Quote:
Originally Posted by chtan View Post
1. Gaulter, B. & Gaulter, M., Further Pure Mathematics, Oxford, 2001.
It covers Complex Numbers, Matrices, Functions, Differentiation and integration, Power series, Differential equations,Coordinate geometry.


2. Bostock, L., Chandler, S., & Rourke, C., Further Pure Mathematics, Stanley Thornes, 1982 (Reprinted 2002).

This book acts as the helper for the previous one. The only important thing in this book is actually Transformation Geometry. But because the previous book is a "book of little words", This one gives the explanations.


is 2 sufficient without 1? besides the examples in the books where can i find more exercises?
You can't. That's the problem with Further maths, unless you have notes from further maths classes way back. Where are you from actually ? If you are from Penang i could give you a set of notes and books complete with past years, exercises for every chapter, solutions and even several sets of FM trial papers. It was my compilation and have passed it on to a Further Maths teacher in Chung Hwa. Anybody interested in having the complete syllabus and willing to meet me. PM Me, i would be glad to help.

It is my greatest regret that during my times of need there wasn't someone there to guide me through it. Hopefully you won't need to go through what i had to.
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Johnivan Male
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  #80 Old 08-05-2009 Default Re: STPM Further Maths 2009

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Originally Posted by Eurytos View Post
PYou really should have taken FM seeing that you had already put so much effort into the subject.
Huh? I 'am' taking further mathematics this year...
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Further Mathematics T Blog (2003-2011 Syllabus)
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