STPM Further Maths 2009

[Johnivan]

p.s.: If you are here to search for information on STPM Further Mathematics T, please pay a visit to my blog, it might help you:
http://furthermathematicst.blogspot.com/

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Hello everyone, I'm new here...

I will be taking further maths in 2009!!

Anyone doing the same? please sign up and join this forum!
Maybe we could share some questions or thoughts, or teachers?

I'm from Johor, a very dead place for further maths...

So, i bought the books recommended by MPM, study myself...

Anyone taking further maths who has a "teacher", please let me know, and let everyone know as well! I believe many Silly people (like me) wants to take further maths, but they can't simply because they don't have resources...

Anyone who has further maths trial papers...
exercises...
notes...
Just share around and help each other!

Some tips from me:
1. Download the further maths syllabus from
http://www.mpm.edu.my/download.php?FilePoolID=119

2. Buy the text books through MPH bookstore! You either have to order them, or buy through the net... They are expensive, but that's the only way... I have 5 of them:
a. Further Pure Mathematics by Bostock, L. Chandler, S & Rourke C
b. Further Pure Mathematics by Gaulter B & Gaulter M, Oxford 2001
c. Discrete Mathematics and Its Applications (6e) by Rosen KH, McGraw-Hill
d. A concise Course in Advanced Level Statistics by Crawshaw J & Chambers J
e. Lastly, a Maths S paper 2 reference book.

I'll tell you more when more people join... Please help... Thanks!! :)

[Eurytos]

I took further mathematics last year by studying alone, uockyuf also took the subject and helped me quite a bit. Anyway further maths isn't for silly people to take ! It is actually for those that want a challenge instead of having too much time studying other subjects LOL.

For further mathematics revision books, you will need more than 5 books to study for. My school library had loads of revision books on this subject. Personally those i found useful including those you already mentioned were :
a. The list in the post above mine.
b. Matematik Lanjutan T Kertas 1 ( Malay Version )
c. Matematik Lanjutan T Kertas 2
d. A University Level Calculus Book to study the remainder theorem
e. A levels further mathematics past year collection from 1980 - 1990 and 1990 - 2000
f. STPM Past year papers with solutions if possible.
g. And many more resources that i forgot already ....

Good Luck In 2009!

[Johnivan]

Hey thanks for posting... I forgot to say that those students who took Further Maths before are always welcomed to give their tips and advices...

By the way, i have a question, about graph theory:
Are we suppose to draw the graphs on graph paper? or just on the kertas kajang...

[Eurytos]

Erm.. you may or may not be asked to draw graphs. Actually graph theory isn't your regular statistical graph, rather a diagram that consists of vertices, edges and paths.

[Johnivan]

Hmmm... I think you mean that even if we are asked to, we don't need to draw it on graph paper, just on the kertas kajang...

Thanks.

Did anyone take Further Maths in 2008? If you do, please scan the english versions and e-mail them to me in any format... My teacher wants to post it on the net...

By the way, eurytos, do you know how to solve linear congruences with x^2 or with two variables? (which came out in 2007)?

For example,

x^2 = 1 (mod 3)

I can guess the answer, but i don't know what's the correct working...
Anyone who knows, please help me to solve it. Thanks ya...

[Eurytos]

The question you asked

x^2 = 1 ( mod 3 )

Ok you start this way for
x = 0 ( mod 3 ) --> x = 0 ( mod 3 )
x= 1 ( mod 3 ) -- > x = 1 ( mod 3 )
x = 2 ( mod 3 ) -- > x = 4 ( mod 3 ) which is also 1 ( mod 3 )
so obviously the congruence of x ^ 2 mod 3
is x = 1,2 ( mod 3 ) lor

stpm 2007 got no X^ 2 mod question lar they came out with linear congruences.

[uoykcuf]

hello, it has been a long time i din come here dy after stpm 2008. haha. i dont have my scanner here right now, but i can send you my 2008 paper.
for past year papers, you can visit this website.
http://cwooi.com/index.php?option=com_remository&Itemid=28&func=select&id=2&orderby=2&page=1
i got a friend who is also taking fmt 2009, you can contact with him. i will email you his msn contact.

anything can ask me n Eurytos.

[Johnivan]

Hey thanks for your help. I'm waiting to hear from you again.

I know the website you posted, in fact, i even e-mailed him questions, and the teacher solves them for me! He's a great teacher! Except that, he hasn't replied me or even update his website since December last year... I wonder what happened to him...

Just wanted to ask you guys: How do you plan your studies for Further Maths? Did you guys finish studying everything very early? What makes you want to take further maths at that time?

[Secret]

Hai!
I'm also from klg n 18 yrs old.
I'm interested in math too.

May i know what u was study when f5?

[Eurytos]

Further maths was the only reason i wanted to study form 6, if not for FM i would have went to take A levels liao lor. Anyway i dint start to study much for my lower 6, i finished about 5 chapters only. Then starting january i finished 2-3 chapters a month and by the time may came, i finished the syllabus lor. Uockyuf got different studying method, but also damn geng, coz when we do past year he like so pro. LOL.

Try planning your schedule for further maths earlier. Just so that you can cope with both your school exams and your further maths syllabus. I personally think that for 1 month before your school exams you should study FM as if you was taking it for your school exams. But the 2 weeks before your school exams, stop all FM and study for school exam !! :))

[Secret]

To:Eurytos

As i know, A level also offer further math subject right?

[Eurytos]

Yes and this is a forum, not msn. Please do not use this to thread to chat.
Anyway i took STPM and Further maths because it would guarantee me a chance to improve on my resume with the numerous national level competitions i could participate in.

[uoykcuf]

Hey thanks for your help. I'm waiting to hear from you again.

I know the website you posted, in fact, i even e-mailed him questions, and the teacher solves them for me! He's a great teacher! Except that, he hasn't replied me or even update his website since December last year... I wonder what happened to him...

Just wanted to ask you guys: How do you plan your studies for Further Maths? Did you guys finish studying everything very early? What makes you want to take further maths at that time?

i finish studying normal math in lower six, after that only start study fmt.
the reason i take fmt is simple, i like math :)

[Johnivan]

Hai!
I'm also from klg n 18 yrs old.
I'm interested in math too.

May i know what u was study when f5?

Do you mean which school i study or what subjects did i take?
I'm from THO to STK, I took 14 subjects: all the sciences plus Bible Knowledge, Perdagangan, Geography and Chinese.

You plan to take form 6? Its a good choice. :)

Further maths was the only reason i wanted to study form 6, if not for FM i would have went to take A levels liao lor. Anyway i dint start to study much for my lower 6, i finished about 5 chapters only. Then starting january i finished 2-3 chapters a month and by the time may came, i finished the syllabus lor. Uockyuf got different studying method, but also damn geng, coz when we do past year he like so pro. LOL.

Try planning your schedule for further maths earlier. Just so that you can cope with both your school exams and your further maths syllabus. I personally think that for 1 month before your school exams you should study FM as if you was taking it for your school exams. But the 2 weeks before your school exams, stop all FM and study for school exam !! :))

Hmmm... I think i'm also the same like you! I just finished studying the 1st 5 chapters, as well as do exercises for the next 5 last year (I regret, i should have did exercises for the 1st five too...), and now i'm still in Transformation Geometry. By the way, will 3D transformation come out? I'm struggling with that now, because i still haven't go into 3D in Coordinate Geometry yet...

[Eurytos]

Do you mean which school i study or what subjects did i take?
I'm from THO to STK, I took 14 subjects: all the sciences plus Bible Knowledge, Perdagangan, Geography and Chinese.

You plan to take form 6? Its a good choice. :)



Hmmm... I think i'm also the same like you! I just finished studying the 1st 5 chapters, as well as do exercises for the next 5 last year (I regret, i should have did exercises for the 1st five too...), and now i'm still in Transformation Geometry. By the way, will 3D transformation come out? I'm struggling with that now, because i still haven't go into 3D in Coordinate Geometry yet...

Form 6 good choice ? LOL

Anyway there is no 3 D coordinate geometry for transformation, but they will test you on how to find an unchanging point and line and also the equation of the line.

[Coltzon]

2. Buy the text books through MPH bookstore! You either have to order them, or buy through the net... They are expensive, but that's the only way... I have 5 of them:
a. Further Pure Mathematics by Bostock, L. Chandler, S & Rourke C
b. Further Pure Mathematics by Gaulter B & Gaulter M, Oxford 2001
c. Discrete Mathematics and Its Applications (6e) by Rosen KH, McGraw-Hill
d. A concise Course in Advanced Level Statistics by Crawshaw J & Chambers J
e. Lastly, a Maths S paper 2 reference book.


Isit all 16 chapter in 5 references book and a Maths S paper 2 is mathematics S paper 2??:amazed:amazed

2. Buy the text books through MPH bookstore! You either have to order them, or buy through the net... They are expensive, but that's the only way... I have 5 of them:
a. Further Pure Mathematics by Bostock, L. Chandler, S & Rourke C
b. Further Pure Mathematics by Gaulter B & Gaulter M, Oxford 2001
c. Discrete Mathematics and Its Applications (6e) by Rosen KH, McGraw-Hill
d. A concise Course in Advanced Level Statistics by Crawshaw J & Chambers J
e. Lastly, a Maths S paper 2 reference book.


Isit all 16 chapter in 5 references book and a Maths S paper 2 is mathematics S paper 2??:amazed:amazed

2. Buy the text books through MPH bookstore! You either have to order them, or buy through the net... They are expensive, but that's the only way... I have 5 of them:
a. Further Pure Mathematics by Bostock, L. Chandler, S & Rourke C
b. Further Pure Mathematics by Gaulter B & Gaulter M, Oxford 2001
c. Discrete Mathematics and Its Applications (6e) by Rosen KH, McGraw-Hill
d. A concise Course in Advanced Level Statistics by Crawshaw J & Chambers J
e. Lastly, a Maths S paper 2 reference book.



Isit all 16 fmt chapter in 5 book and a Maths S paper 2 is mathematics S papaer 2??:amazed

[Eurytos]

The post above is rather confusing @<hidden>@<hidden>
I cannot understand what you are trying to convey.... Please clarify

[Johnivan]

Isit all 16 fmt chapter in 5 book and a Maths S paper 2 is mathematics S papaer 2??:amazed


:huh? I'm trying to interpret your language...---...---...

"Isit all 16 fmt chapter in 5 book"
Why not let me give you a break down:

Chapters found in Discrete Maths:
1. Logic & Proof
2. Recurrence Relations
3. Number Theory
4. Graph Theory

Chapters found in A Concise Course in Advance Statistics:
1. Sampling & Estimation
2. Chi-square Distribution
3. Correlation & Regression
4. Hypothesis Testing
(The last 4 chapters...)

Chapters found in The rest of the two books (Further Pure Mathematics):
1. Functions
2. Differentiation & Integration
3. Power Series
4. Differential Equations
5. Transformation Geometry
6. Coordinate Geometry
7. Complex Numbers
8. Matrices

However, some of the sections of certain chapters can't be found in the 5 books (Gaussian elimination, Taylor's remainder theorem, differentiability, etc).

"a Maths S paper 2 is mathematics S papaer 2??"
Yes, you are right. A maths S paper 2 is Mathematics S 'paper' 2. (:P)

[Coltzon]

So how for not include chapter??Dont study Or just leave it??

[Eurytos]

So how for not include chapter??Dont study Or just leave it??

I think i get your drift, but please use some proper english. There are certain chapters that are not included in the list of reference books suggested by MPM. Refer to the old further mathematics textbook in malay to search for those chapters not included. Part of those missing chapters are in there.

[Coltzon]

I think i get your drift, but please use some proper english. There are certain chapters that are not included in the list of reference books suggested by MPM. Refer to the old further mathematics textbook in malay to search for those chapters not included. Part of those missing chapters are in there.


sry...my english is very bad and i wan to ask where shop have sell further math malay version??MPH bookshop got or not??:amazed:amazed

[Johnivan]

To:Eurytos

As i know, A level also offer further math subject right?

Well, its true that A level also offer further maths... I think KTAR offers the subject. But their syllabus are very different (once the same), because the A level one has some simple Mechanics (Physics) in it; whereas STPM has more on theories, hard core chapters on Mathematics. :)

So how for not include chapter??Dont study Or just leave it??

Of course you can't just leave it and don't study! Anything may come out in STPM...
1. You can check out school or public libraries for College level books. Calculus (7th Edition) is an example that i found in my school library which has the sections that i mention in an earlier post.

2. Since the internet is so advance today, you could always refer to the internet to look up for what you want. :)

sry...my english is very bad and i wan to ask where shop have sell further math malay version??MPH bookshop got or not??:amazed:amazed

讲华语咯?? By the way, its an outdated book... I saw a few in the public library in Kluang. You can try out in your hometown...:)

[Coltzon]

Who known Klang have 图书馆？？:amazed

[uoykcuf]

Who known Klang have 图书馆？？:amazed

you can try your school library. i think most of the old schools have that orange book. ask your teacher and see. it is an old syllabus further math book.

[Coltzon]

为什么pelangi,oxford,...出phy,che,bio,math,...,但是没有出further mathematics T 的references book？？

[uoykcuf]

为什么pelangi,oxford,...出phy,che,bio,math,...,但是没有出further mathematics T 的references book？？

the number of candidate who take fmt not more than 50 ppl. the demand for this book so small. if they publish these books, the publisher sure rugi besar.

[Eurytos]

the number of candidate who take fmt not more than 50 ppl. the demand for this book so small. if they publish these books, the publisher sure rugi besar.

Last year 30 people took Further Mathematics T only, so pathetic. If they publish further mathematics revision book, 1 person will buy then the other 29 people will photostat. LOL

[Johnivan]

I signed up for further maths T already, yeah... So now there's no turning back...

Hmmm... It seems like there's still no voice from any other further maths takers, i hope there will be more people taking further maths in the years to come... All the best!

I just finished studying transformations... Now going into coordinate geometry... These two chapters seems easy, but when you ask me to virtualise it, it seems hard... I hope they won't ask us to 'sketch' stuff in 3 dimension... Haha...

Just a question for our few further maths seniors: What do you want to study in Uni? (Since you guys took FM, there must be something to do with maths, i think...?)

[Eurytos]

I signed up for further maths T already, yeah... So now there's no turning back...

Hmmm... It seems like there's still no voice from any other further maths takers, i hope there will be more people taking further maths in the years to come... All the best!

I just finished studying transformations... Now going into coordinate geometry... These two chapters seems easy, but when you ask me to virtualise it, it seems hard... I hope they won't ask us to 'sketch' stuff in 3 dimension... Haha...

Just a question for our few further maths seniors: What do you want to study in Uni? (Since you guys took FM, there must be something to do with maths, i think...?)

All the best to all FM candidates out there ! They won't ask you to sketch stuff in 3 dimension too, no worries there.

For your question regarding what we (I) am going to study in Uni. it most certainly won't relate much to mathematics. Probably will be doing Law locally, Pure physics if accepted to U.S. and double degree in engineering and economics if possible in Singapore.

[markwongsk]

Good luck for those taking FM. I wanted so badly to take FM but then there's a limit of 5 subjects =( so haha I did triple science =D

[Johnivan]

Hey seniors, i got some questions:

How do you solve the questions on loci in 3D in the past year papers?
Where do you learn them from?
And, how do i "show that" two lines or two planes are coincidental?

[Eurytos]

Under the chapter Coordinate Geometry in the old further maths textbook.
To show that 2 lines or planes are coincidental, the vector equations of both lines or planes when solved will have a finite solution.

E.g. : r= ai,bj,ck + u(xi,yj,zk) and r= di,ej,fk + m(pi,qr,jk)
By comparing both equations, if there is a finite value for both u and m,
then the 2 lines are coincidental.

[uoykcuf]

orange malay book.

for the line, my way is same as Eurytos
for the plane, the plane is always coincidental if and only if the plane is not parallel with each other.

[Eurytos]

Oh yeah for coincidental planes, they always have a line as an intersection, rather than a point.

[Coltzon]

i wan to ask american degree transfer programe course good or not???

[Eurytos]

Wrong thread lar, this thread is STPM further maths 2009.
Not ADTP.

[Coltzon]

有什么course是关于fmt的，还是学爽的？？

[Johnivan]

有什么course是关于fmt的，还是学爽的？？

You are an interesting guy, i would say...

In my opinion, Further Maths may help you in part of your engineering maths next time, if you plan to take engineering. It may help you a lot if you want to take Actuarial Science, Mathematics, Applied Mathematics and Statistics in Uni next time. You never 学爽...

Some people may say that since we are going to learn part of further maths in uni, then why do we need to learn it now?

I would say: 1. It is a good challenge for form 6 students to see whether they are independent enough to study on their own. But of course, i don't encourage everyone to do, cos you have to know your limits... and 2. It will help A LOT in your Maths T paper. Its more about the knowledge and experience gained, rather than whether we untung or not...:)

[uoykcuf]

有什么course是关于fmt的，还是学爽的？？

To be frank, in the beginning i just like what you have said, i学爽的. And it actually does not give you any extra course.

But after that, i found that it does help a lot in normal math. And since i know more, i could help my friends when they have problem in math. Thus i am treated as a godlike person in my school. So i enjoy learning them. lol

According to my teacher, actually it is unnecessary to take further math as you will learn them again in 1st year university. But personally i think that if you want to study oversea, it is advisable to take it as there is some tough competition among us. When you go to university, you have already gained an advantage compare to the other person. And from what i heard, in singapore, the student from China is actually 10x better than us. They not only have learnt what we have learned further math before they entering uni, they learn more than that. Singapore H3 math is harder than further math stpm as i have seen theirs syllabus and done some of their question also. So if you plan to go to singapore, and you do not learn more, you are far behind from the other. That's why many Malaysian student who study in singapore saying that studying in singapore is hard.

If you do not plan to take them, do study them in your holiday after your stpm in order to prepare yourself.

[Coltzon]

You are an interesting guy, i would say...

In my opinion, Further Maths may help you in part of your engineering maths next time, if you plan to take engineering. It may help you a lot if you want to take Actuarial Science, Mathematics, Applied Mathematics and Statistics in Uni next time. You never 学爽...

Some people may say that since we are going to learn part of further maths in uni, then why do we need to learn it now?

I would say: 1. It is a good challenge for form 6 students to see whether they are independent enough to study on their own. But of course, i don't encourage everyone to do, cos you have to know your limits... and 2. It will help A LOT in your Maths T paper. Its more about the knowledge and experience gained, rather than whether we untung or not...:)

Applied Mathematics 是什么来的？？

[Xon]

Coltzon, 我想你應該明白這一個聊天室 “STPM Further Maths 2009" 是為了幫助那些在STPM 2009 中應付中六高級數學的學生。若有別的問題, 我想你應該遊覽這兒其他的聊天室題目。謝謝您的合著。

( translation : "Coltzon, i think you should understand that this thread is mainly for those who're sitting for Further Math in STPM 2009. Please read other thread to get more info. Thanks for co-operation." )

[Eurytos]

Finally someone that has enough sense to bring the topic back on track. Oh yeah when STPM results are announced next month, check the statistics of Further mathematics subject. I personally think it will be an indication of how well next year's results will be.

The qualities of our forum depend on the mutual interaction between the programmers here and the valued members. You name it, we make it. You report it, we correct it. That's how a win-win situation being achieved. =) : Xon

[Johnivan]

Finally someone that has enough sense to bring the topic back on track. Oh yeah when STPM results are announced next month, check the statistics of Further mathematics subject. I personally think it will be an indication of how well next year's results will be.


Sure, i will check it out. I hope it won't be too hard for this year... It seems like there will be lesser candidates for fmt this year... I think even the name itself already scares so many people away from taking it...

By the way, I got questions again, something about hypothesis testings:
For questions asking to find difference of means, can the means in the hypotheses be "terbalik"?
E.g. for the alternative hypothesis,
mu1 - mu2 > 0 and
mu2 - mu1 < 0 . Do they mean the same thing?

Second question: also about finding difference of means. According to the book, small samples (n<30) with unknown variance sigma^2 should use a t-distribution. What if the sample means of the two variables are 20 and 17 respectively? when i find T ~t(n1 + n2 -2), i get 35, which is a large sample already. Does that mean that i shouldn't use t-distribution for this case?

[Eurytos]

Sure, i will check it out. I hope it won't be too hard for this year... It seems like there will be lesser candidates for fmt this year... I think even the name itself already scares so many people away from taking it...

By the way, I got questions again, something about hypothesis testings:
For questions asking to find difference of means, can the means in the hypotheses be "terbalik"?
E.g. for the alternative hypothesis,
mu1 - mu2 > 0 and
mu2 - mu1 < 0 . Do they mean the same thing?

Second question: also about finding difference of means. According to the book, small samples (n<30) with unknown variance sigma^2 should use a t-distribution. What if the sample means of the two variables are 20 and 17 respectively? when i find T ~t(n1 + n2 -2), i get 35, which is a large sample already. Does that mean that i shouldn't use t-distribution for this case?

Yes they do mean the same thing for m1 - m2 > 0 and m2 - m1 < 0.
Though i would strongly suggest you stick to > 0, because your equations would then be less confusing.

For difference of means, although you are getting a sample of > 30, you still cannot assume that it follows the central limit theorem. This is because both samples have respective sizes of <30, and though their cumulative sample sizes do exceed 30, the deviation from normal dist. still exists. It's like saying 2 wrongs don't make a right.

[Johnivan]

Thanks Eurytos, but for the 2nd question do you mean that i still have to use t-distribution? But the data booklet don't have the value of v for 38...
I got another question: How do you guys study for Logic & Proof? It seems to be a long chapter (propositions, quantifiers...) but every year only a little bit comes out...

By the way, the Further Maths T 2008 paper is up! You can get it from

http://cwooi.com/index.php?option=com_remository&Itemid=28&func=select&id=2&orderby=2&page=2

Special thanks to uoykcuf!

All the best to all further maths takers! Please show up if you can, so i won't feel that lonely...

[Eurytos]

Thanks Eurytos, but for the 2nd question do you mean that i still have to use t-distribution? But the data booklet don't have the value of v for 38...
I got another question: How do you guys study for Logic & Proof? It seems to be a long chapter (propositions, quantifiers...) but every year only a little bit comes out...

By the way, the Further Maths T 2008 paper is up! You can get it from

http://cwooi.com/index.php?option=com_remository&Itemid=28&func=select&id=2&orderby=2&page=2

Special thanks to uoykcuf!

All the best to all further maths takers! Please show up if you can, so i won't feel that lonely...

For a t-distribution with 2 sample sets, normally shouldn't have an accumulated sample set of > 30. But i am not too sure, coz my stats book return to library already, so can't help you much here.

Anyway logic and proof you just need to focus on inverse, negation those ~pvq, stuff like that forgot called what already. And also proof by mathematical induction, besides those others not too important.

[uoykcuf]

i am glad that last year paper is there dy. lol. so now other people who want the paper can go there take

just to elaborate, if you know set, you already master 70% of mantiks dy. the way how to solve is about the same, e.g. "de morgan law", the difference is the sign, a little bit of new thing like implication and some new name.

i suggest you to study proof after you have finished everything as proving this chapter need some knowlegde from the other chapter. like Eurytos said, induction is the main thing.

trust me, this chapter not hard :)

[Coltzon]

Who can help me solve this question
y=asinX^e^x,find dy/dx.

[markwongsk]

Under the chapter Coordinate Geometry in the old further maths textbook.
To show that 2 lines or planes are coincidental, the vector equations of both lines or planes when solved will have a finite solution.

E.g. : r= ai,bj,ck + u(xi,yj,zk) and r= di,ej,fk + m(pi,qr,jk)
By comparing both equations, if there is a finite value for both u and m,
then the 2 lines are coincidental.

can use matrices to do evaluation? determinant style...?

Who can help me solve this question
y=asinX^e^x,find dy/dx.

y=a sin u

u=x^e^x

dy/du = a cos u

ln u = (e^x)ln x

1/uXdu/dx = e^x(1/x + ln x)

du/dx = e^x (1/x+ln x)x^e^x

dy/dx = a (e^x (1/x + ln x) x^e^x) cos x^e^x

not sure whether correct or not because haven't touch maths for 3 months ... haha

can eurytos or uoykcuf help check?

I found another alternative solution (which doesn't amount to anything but here it is anyway)

y=a sin x^e^x

sin^-1 y/a = x^e^x

ln sin^-1 y/a = e^x lnx

1/(sin^-1 y/a) X 1/[a(1-(y/a)^2)^0.5]X dy/dx = e^x (lnx + 1/x)

simplifies to my previous answer

[Eurytos]

can use matrices to do evaluation? determinant style...?



y=a sin u

u=x^e^x

dy/du = a cos u

ln u = (e^x)ln x

1/uXdu/dx = e^x(1/x + ln x)

du/dx = e^x (1/x+ln x)x^e^x

dy/dx = a (e^x (1/x + ln x) x^e^x) cos x^e^x

not sure whether correct or not because haven't touch maths for 3 months ... haha

can eurytos or uoykcuf help check?

I found another alternative solution (which doesn't amount to anything but here it is anyway)

y=a sin x^e^x

sin^-1 y/a = x^e^x

ln sin^-1 y/a = e^x lnx

1/(sin^-1 y/a) X 1/[a(1-(y/a)^2)^0.5]X dy/dx = e^x (lnx + 1/x)

simplifies to my previous answer

Both ways are correct, though the second one involves differentiating inverse trigonometric equations which might be quite confusing.

[markwongsk]

Both ways are correct, though the second one involves differentiating inverse trigonometric equations which might be quite confusing.

well, I would love to confuse my teachers :P serves them RIGHT for giving homework XD XD XD

I remember last year I used the Cayley Hamilton theorem to get my inverse matrices haha. Serves them right =P

[Johnivan]

Hey people...

STPM results coming out tomorrow. Please let me know your Further Maths results, OK? So i can get a glimpse of what i will get next year... Anyway, I'll be glad if you all get A's... All the best!

[uoykcuf]

Hey people...

STPM results coming out tomorrow. Please let me know your Further Maths results, OK? So i can get a glimpse of what i will get next year... Anyway, I'll be glad if you all get A's... All the best!

both eurytos and i get A in further math. in fact we have made Further Math 100% A in penang and kedah. hahaha.
so u will sure get A if u take further math as it is 100% A according to statistic :D

[Johnivan]

both eurytos and i get A in further math. in fact we have made Further Math 100% A in penang and kedah. hahaha.
so u will sure get A if u take further math as it is 100% A according to statistic :D

Wow! Congrats to uoykcuf and eurytos! You guys are really great! I hope i'll learn from both of you... All your hard work has brought you all great blessings! Yay! :))

[markwongsk]

Wow! Congrats to uoykcuf and eurytos! You guys are really great! I hope i'll learn from both of you... All your hard work has brought you all great blessings! Yay! :))

The probabilty that a student will pass Further Maths is 0.01. Find the probabilty that out of 34 students, 2 students will pass with A. Given the normal distribution has mean 45 and standard deviation 30 for A and that A is >65 marks.

=D

[Eurytos]

The probabilty that a student will pass Further Maths is 0.01. Find the probabilty that out of 34 students, 2 students will pass with A. Given the normal distribution has mean 45 and standard deviation 30 for A and that A is >65 marks.

=D

Markwongsk so good in counting LOL
On the other hand if you are VERY OPTIMISTIC, all students in penang and kedah will get A in further maths if they register for the subject coz Penang and Kedah 100 % A in further mathematics Haha

Oh yeah my further mathematics < uoykcuf
His is Paper 1 A Paper 2 A
Mine is Paper 1 B+ Paper 2 A

My statistics section almost 100 liao i think, coz i everyday do statistics question until i finished all the statistics exercises in the black book @<hidden>@<hidden>

[markwongsk]

Markwongsk so good in counting LOL
On the other hand if you are VERY OPTIMISTIC, all students in penang and kedah will get A in further maths if they register for the subject coz Penang and Kedah 100 % A in further mathematics Haha

Oh yeah my further mathematics < uoykcuf
His is Paper 1 A Paper 2 A
Mine is Paper 1 B+ Paper 2 A

My statistics section almost 100 liao i think, coz i everyday do statistics question until i finished all the statistics exercises in the black book @<hidden>@<hidden>

I LOVE PAPER 1 !!!! =( don't like paper 2 :cry
um uoykcuf can you scan the test paper??? I want to do also :P

[uoykcuf]

I LOVE PAPER 1 !!!! =( don't like paper 2 :cry
um uoykcuf can you scan the test paper??? I want to do also :P

haha me too. luckily paper 2 is damn easy, if not i will get B for it also. lol
all further math paper is in this website
http://cwooi.com/index.php?option=com_remository&Itemid=28&func=select&id=2&orderby=2&page=2

[francisfu]

Hey, I am from puchong, selangor, Stpm 2008 candidate. I, too, got an A for my further maths. Congratz to Eurytos and uoykcuf for getting A too.

Looks like this year we got quite alot of A-scorers. We already have 3 in this forum. Lol. From what i heard, there was only 3 ppl who scores A in 2007, when there was 54 students taking the subject. Whereby we only have 34 students taking this year.

Eurytos and uoykcuf, where are u guys applying to? wat course? Actuarial science i suppose? O yeah, who can solve the paper 2 graph theory question? Never really mastered graph theory back then :P only touched its 皮毛 lol. I am also weak at remainder theorem, did not have the right material, just found a book on remainder theorem the day before the exam, lucky it din come out.

To all the new candidates, make sure u do well in ur statistic. Statistic consist of 50 marks out of the paper 2, which is 25 marks of the total. A great sum. And if you can do well in coordinate geometry (vector) and transformations (both are not hard), u're basically secured a A. For graph theory, the application is really hard, and you reli dunno what the question will be, proving? Applications? So dun lay much hope on it. For number theory, the questions can vary alot too. Last year's number theory question was olympiad style and it only gives out 4 marks. Comparatively, last year transformation question gives out 15 marks. So if u can score well in statistic + vector + transformation, u're an A-scorer for paper 2. Just make sure u know everything of the 6 chapters in paper 2.

[Johnivan]

To all the new candidates, make sure u do well in ur statistic. Statistic consist of 50 marks out of the paper 2, which is 25 marks of the total. A great sum. And if you can do well in coordinate geometry (vector) and transformations (both are not hard), u're basically secured a A. For graph theory, the application is really hard, and you reli dunno what the question will be, proving? Applications? So dun lay much hope on it. For number theory, the questions can vary alot too. Last year's number theory question was olympiad style and it only gives out 4 marks. Comparatively, last year transformation question gives out 15 marks. So if u can score well in statistic + vector + transformation, u're an A-scorer for paper 2. Just make sure u know everything of the 6 chapters in paper 2.

Hey, thanks for your encouragement! Wow, all my seniors who took further maths seems to get A... This gives me a lot of pressure now...
By the way, do you all have any other references for Number Theory? I'm going crazy studying it... Their questions seems to have easy answers (by guessing), but i just can't figure out why, or how the working is done. Do you all have any recommendations?

[uoykcuf]

Hey, I am from puchong, selangor, Stpm 2008 candidate. I, too, got an A for my further maths. Congratz to Eurytos and uoykcuf for getting A too.

Looks like this year we got quite alot of A-scorers. We already have 3 in this forum. Lol. From what i heard, there was only 3 ppl who scores A in 2007, when there was 54 students taking the subject. Whereby we only have 34 students taking this year.

Eurytos and uoykcuf, where are u guys applying to? wat course? Actuarial science i suppose? O yeah, who can solve the paper 2 graph theory question? Never really mastered graph theory back then :P only touched its 皮毛 lol. I am also weak at remainder theorem, did not have the right material, just found a book on remainder theorem the day before the exam, lucky it din come out.

To all the new candidates, make sure u do well in ur statistic. Statistic consist of 50 marks out of the paper 2, which is 25 marks of the total. A great sum. And if you can do well in coordinate geometry (vector) and transformations (both are not hard), u're basically secured a A. For graph theory, the application is really hard, and you reli dunno what the question will be, proving? Applications? So dun lay much hope on it. For number theory, the questions can vary alot too. Last year's number theory question was olympiad style and it only gives out 4 marks. Comparatively, last year transformation question gives out 15 marks. So if u can score well in statistic + vector + transformation, u're an A-scorer for paper 2. Just make sure u know everything of the 6 chapters in paper 2.

congratz to you also. how bout your other subj? 5A also i think :D
suddenly i see so many further math taker come out in the forum recently, even in other forum also :oops: :oops:
yeah, this year is better than last year, lol. i wonder how many ppl get A in further math.

Hey, thanks for your encouragement! Wow, all my seniors who took further maths seems to get A... This gives me a lot of pressure now...
By the way, do you all have any other references for Number Theory? I'm going crazy studying it... Their questions seems to have easy answers (by guessing), but i just can't figure out why, or how the working is done. Do you all have any recommendations?

try "Discrete mathematics and its application" by Rosen and other algebra book stated in syllabus. do some olympiad question might help you for this topic.and also, make full use of calculator :P

[francisfu]

congratz to you also. how bout your other subj? 5A also i think :grin:
suddenly i see so many further math taker come out in the forum recently, even in other forum also :oops: :oops:
yeah, this year is better than last year, lol. i wonder how many ppl get A in further math.


Nope, in fact i think i am only good at maths :D. I got B for my general paper, C for chemistry (:P i only passed once during school exam and thats lower 6 1st term exam ) , A- for physics ( disappointment, i was aiming for A ) , and A for every paper of maths and f maths. If only i could transfer some marks of maths to physics, it would be 3As already D:

Anyway, i find this year's paper harder than last year. Last year's paper was the easiest of all i think.

Hey, thanks for your encouragement! Wow, all my seniors who took further maths seems to get A... This gives me a lot of pressure now...
By the way, do you all have any other references for Number Theory? I'm going crazy studying it... Their questions seems to have easy answers (by guessing), but i just can't figure out why, or how the working is done. Do you all have any recommendations?

Hmm, the book suggested by uoykcuf is a good book, but its hard to be bought. I am using 'Schaum's Outlines Discrete Mathematics' and 'Discrete Mathematics with Graph Theory'. Schaum's Outline is a good book, the number theory is good. Covered most of the syllabus, while the graph theory isn't good. The other book was quite tough and has alot of chapters which isn't in our syllabus. Imagine buying a book which cost 60++ and just use a few chapters in it. Try borrowing and photostating from frens.

Try being really good with some chapters. Make sure u score full marks if questions from those chapters came out. In my case, i always read a few books just for 1 chapter.

[Johnivan]

STPM 2007 Paper 2



Two straight lines l1 and l2 have equations -2x+4=2y-4=z-4 and 2x=y+1=-z+3 respectively. Determine whether l1 and l2 intersect. [7 marks]
The points P & Q lie on l1 and l2 respectively, and the point R divides PQ in the ratio 2:3. Find the equation of the locus of R. [6 marks]


Can anyone please tell me how to solve the 2nd part. Or rather, how does a locus equation in 3D looks like?

[uoykcuf]

STPM 2007 Paper 2



Two straight lines l1 and l2 have equations -2x+4=2y-4=z-4 and 2x=y+1=-z+3 respectively. Determine whether l1 and l2 intersect. [7 marks]
The points P & Q lie on l1 and l2 respectively, and the point R divides PQ in the ratio 2:3. Find the equation of the locus of R. [6 marks]


Can anyone please tell me how to solve the 2nd part. Or rather, how does a locus equation in 3D looks like?



l1=(2,2,4)+t(-1/2+1/2+1), l2=(0,-1,3)+s(1/2,1,-1)
use ratio theorem
(3(l1)+2(l2))/5=.....
then remove the variable inside

the answer i get is z=6-2x
but i not sure it is correct or not.
havent checked yet. have to wait eurytos or francisfu come n check.
it is a straight line.

[Johnivan]

l1=(2,2,4)+t(-1/2+1/2+1), l2=(0,-1,3)+s(1/2,1,-1)
use ratio theorem
(3(l1)+2(l2))/5=.....
then remove the variable inside

the answer i get is z=6-2x
but i not sure it is correct or not.
havent checked yet. have to wait eurytos or francisfu come n check.
it is a straight line.

I'm sorry, but could you explain a little more on the 'ratio theorem' you used? Thanks....

[uoykcuf]

I'm sorry, but could you explain a little more on the 'ratio theorem' you used? Thanks....

just like what u have learnt in form5 for coordinate
for example, if coordinate A divides coordinate B and coordinate C in m:n ratio, then A=(nB+mC)/(m+n).

it is same as in vector, the difference is just the word "coordinate" change to "vector" only. you will touch it in math T paper 2 later.

[Johnivan]

Hey, i think i got the same answer as you! Thanks, I hope Eurytos will come and check it as well...:)

[Wright]

STPM 2007 Paper 2



Two straight lines l1 and l2 have equations -2x+4=2y-4=z-4 and 2x=y+1=-z+3 respectively. Determine whether l1 and l2 intersect. [7 marks]
The points P & Q lie on l1 and l2 respectively, and the point R divides PQ in the ratio 2:3. Find the equation of the locus of R. [6 marks]


Can anyone please tell me how to solve the 2nd part. Or rather, how does a locus equation in 3D looks like?


can anyone show the working for me?? thx

[Eurytos]

Uoykcuf just showed me the workings to the question above. Below are the workings of his solution :

From ratio theorem,

x = ... + ... t + ... s
y = ... + ... t + ... s
z = ... + ... t + ... s

From equation 1,
t = X - ... - ... s
s = Y - ... - ... t

Solving the equations above, you get
s = Y - ... -----> Notice there no longer are t terms
t = X - ... ------> Notice there no longer are s terms

substitute both equations in Z= ... + ... t + ... s
then you will get the answer.

I forgot how to do it until i asked him. Anyway his solution is probably correct.

[Johnivan]

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...

[markwongsk]

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

[Casperloo]

How much altogether that 5 books cost ? If can, hope got Photocopy set.....

[uoykcuf]

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

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

[chtan]

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 :D

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.:cry

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

Any help is greatly appreciated.thanks

[uoykcuf]

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 :D

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.:cry

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=com_remository&Itemid=28&func=select&id=2

[Johnivan]

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. :)

[Eurytos]

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.

[chtan]

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?

[Eurytos]

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.

[Johnivan]

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...

[Eurytos]

Huh? I 'am' taking further mathematics this year...

I was referring to markwongsk. Not you, good luck for your Further Mathematics ! ( other subjects fail never mind : ) )

[Secret]

mark has answered you in very detail way dy. lol



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

Hei, I'm interesting with your further math referrence book in pdf form. So, can I get a copy from u?

[keethai]

is there any further maths tuition here at cheras area? kl?

[Johnivan]

is there any further maths tuition here at cheras area? kl?

Sorry, but you have to find it out yourself. Further Maths teachers are really rare in Malaysia, but i think there will be more in the KL area...

[PsyMaths]

I am planning to take Further Maths but I am not that good at maths. I got about average of 90+ for maths and 75+ for add maths in secondary school only. I make frequent mistake and unable to answer some "out of syllabus" question in Form 4 n Form 5 textbook.

The problem here is there is no reference book for STPM further maths alone. I have those 5 uni/college level books mentioned and glance through but I couldn't understand the number & graph theory and statistics part. Furthermore, the example given is too little and some are not included in syllabus. And my weakest part of Maths is probability. Should I take further maths? And I am thinking of going for A-level Further maths tuition.

[Johnivan]

I am planning to take Further Maths but I am not that good at maths. I got about average of 90+ for maths and 75+ for add maths in secondary school only. I make frequent mistake and unable to answer some "out of syllabus" question in Form 4 n Form 5 textbook.

The problem here is there is no reference book for STPM further maths alone. I have those 5 uni/college level books mentioned and glance through but I couldn't understand the number & graph theory and statistics part. Furthermore, the example given is too little and some are not included in syllabus. And my weakest part of Maths is probability. Should I take further maths? And I am thinking of going for A-level Further maths tuition.

Hi, nice to meet you!
I would say it would be a little dangerous for you to take further maths if you get only 75+ for add maths (If you want to get an A in STPM)... But of course, if you really put in a lot of effort and understanding, i'm sure it won't be a problem. I'm not discouraging you to take further maths, but i must say that you must be very careful when you make this decision. Make sure you won't regret after that...

Graph theory is OK, but i agree with you that Number theory is hard to understand. Have you actually read thru your Maths T? If you haven't, i would encourage you to do so, cuz you won't understand a single thing without going thru your maths T. When i started studying FMT last year, i got stuck in some integration questions, but after learning it in Maths T this year, everything came to place.

I've never taken further maths tuition, but i think the A-level Further maths tuition will help, except that they don't cover graph and number theory, transformation Geometry, Logic & proof, recurrence relations and chi-squared tests (correct me if i'm wrong). You still have to work these chapters out yourself.

Hope that helps.:)

[PsyMaths]

Hi, nice to meet you!
I would say it would be a little dangerous for you to take further maths if you get only 75+ for add maths (If you want to get an A in STPM)... But of course, if you really put in a lot of effort and understanding, i'm sure it won't be a problem. I'm not discouraging you to take further maths, but i must say that you must be very careful when you make this decision. Make sure you won't regret after that...

Graph theory is OK, but i agree with you that Number theory is hard to understand. Have you actually read thru your Maths T? If you haven't, i would encourage you to do so, cuz you won't understand a single thing without going thru your maths T. When i started studying FMT last year, i got stuck in some integration questions, but after learning it in Maths T this year, everything came to place.

I've never taken further maths tuition, but i think the A-level Further maths tuition will help, except that they don't cover graph and number theory, transformation Geometry, Logic & proof, recurrence relations and chi-squared tests (correct me if i'm wrong). You still have to work these chapters out yourself.

Hope that helps.:)

Ya... everything blur. I juz finish my complex number. I haven't started the others(especially statistics) as I am waiting for teacher to finish teaching first. Now starting logic and proof. Consider to read recurrence relations after that. I found that the Further Pure Mathematics by Bostock, L. Chandler, S & Rourke C(orange in colour dictionary like) book very hard to understand. Whereas the another one Further Pure Mathematics by Gaulter B & Gaulter M, Oxford 2001 is easy to understand. Which of these 2 books is the main one actually? Another one, I heard from here that Eukyfos even need to write a letter to school for appealing to take Further Maths. Means not every school will allow students to take FM?

[Scrmath]

Ya... everything blur. I juz finish my complex number. I haven't started the others(especially statistics) as I am waiting for teacher to finish teaching first. Now starting logic and proof. Consider to read recurrence relations after that. I found that the Further Pure Mathematics by Bostock, L. Chandler, S & Rourke C(orange in colour dictionary like) book very hard to understand. Whereas the another one Further Pure Mathematics by Gaulter B & Gaulter M, Oxford 2001 is easy to understand. Which of these 2 books is the main one actually? Another one, I heard from here that Eukyfos even need to write a letter to school for appealing to take Further Maths. Means not every school will allow students to take FM?

I agree wad john said...i m not discouraging u,but i suggest u should read more math t first,and do their trial,if u think u cn do it fairly good,then only u consider take it..

btw,it is merely a suggestion..and i din take further math also...

[Eurytos]

I have finally obtained my copy of past year further mathematics STPM papers complete with solutions coupled with notes for certain FM chapters. If any of you would like a copy of the notes, feel free to PM me and i will sent you a set. Do take note though that i dont stand to make a profit from photocopying the notes for any of you.

What I would like to see is that students across the country take up further mathematics as a 5th subject. All the best for all Further mathematics candidates out there !

[markwongsk]

I have finally obtained my copy of past year further mathematics STPM papers complete with solutions coupled with notes for certain FM chapters. If any of you would like a copy of the notes, feel free to PM me and i will sent you a set. Do take note though that i dont stand to make a profit from photocopying the notes for any of you.

What I would like to see is that students across the country take up further mathematics as a 5th subject. All the best for all Further mathematics candidates out there !

What about as the 6th Subject? :))

[Scrmath]

What about as the 6th Subject? :))

bio..lolz..:nuts

[PsyMaths]

What about as the 6th Subject? :))

STPM max 5 subjects, how come got 6?

[Scrmath]

STPM max 5 subjects, how come got 6?

But i heard b4 sumbody get 6 A's for a lvl,i seen it in my taylors magazine i think..

[Boyz_Zoo]

STPM max 5 subjects, how come got 6?
I think what that fellow is referring is STPM actually can take up until 6 subjects. The extra one is MUET though it is not counted in one's GCPA.

[markwongsk]

actually it's a joke :)) STPM max can only take 5 subjects (excluding MUET)... But I mean there are those who would have liked to take FM as a 6th subject (me, for example). However, due to the subject limitations, I was forced to take triple science and do without FM :(... I really like mathematics :cry

[Eurytos]

actually it's a joke :)) STPM max can only take 5 subjects (excluding MUET)... But I mean there are those who would have liked to take FM as a 6th subject (me, for example). However, due to the subject limitations, I was forced to take triple science and do without FM :(... I really like mathematics :cry

Haha mark not everyone gets your joke lar LOL. It sure is funny to see the forumers debating over 6th subject in STPM !!! : )

Sure can take 6th subject, go back SPM can take 10 some more !!

Oh yeah a tip for Further Maths candidates out there, if you want to score an A in FM and not a paper flat, focus on statistic and ignore number theory. This strategy normally works because statistics has a guaranteed 50 / 200 marks allocation while number theory had 4 marks only last year ??

[Johnivan]

Hey everybody, I'm back after a long while...

At last, I'm done with the whole Further Maths T Syllabus. I did all the exercises, and now I had to leave it aside to focus more on my physics and chemistry...

I couldn't believe that Correlation and Regression is easy, I thought that all the chapters are supposed to be hard...

I agree with Eurytos, saying that i should focus more on the statistic parts, because not only are they relatively easy, but they consists of most marks in Paper 2.

Talking about number theory, it is the hardest part of mathematics that i have encountered, so far... It took me a few days to get the appropriate info from the net, and to understand it... :cry

Just a question for the FMT seniors: What are you all studying now? Does the FMT help YOu?

[markwongsk]

Hey everybody, I'm back after a long while...

At last, I'm done with the whole Further Maths T Syllabus. I did all the exercises, and now I had to leave it aside to focus more on my physics and chemistry...

I couldn't believe that Correlation and Regression is easy, I thought that all the chapters are supposed to be hard...

I agree with Eurytos, saying that i should focus more on the statistic parts, because not only are they relatively easy, but they consists of most marks in Paper 2.

Talking about number theory, it is the hardest part of mathematics that i have encountered, so far... It took me a few days to get the appropriate info from the net, and to understand it... :cry

Just a question for the FMT seniors: What are you all studying now? Does the FMT help YOu?

Correlation and Regression are just Maths (S) and more statistics... so easier >_< Graph theory, number theory more difficult, IMO lar

[Eurytos]

Hey everybody, I'm back after a long while...

At last, I'm done with the whole Further Maths T Syllabus. I did all the exercises, and now I had to leave it aside to focus more on my physics and chemistry...

I couldn't believe that Correlation and Regression is easy, I thought that all the chapters are supposed to be hard...

I agree with Eurytos, saying that i should focus more on the statistic parts, because not only are they relatively easy, but they consists of most marks in Paper 2.

Talking about number theory, it is the hardest part of mathematics that i have encountered, so far... It took me a few days to get the appropriate info from the net, and to understand it... :cry

Just a question for the FMT seniors: What are you all studying now? Does the FMT help YOu?

Studying physics now and in one month going off to study physics again Haha. Anyway number theory last year only got 4 marks out of 200 so insignificant.

Regarding your second question about how FM T helps in the future, i think it depends on what course you plan to take. Lets say you study Law then i don't think you will be using any part of it !! XD On a more serious note, most undergraduate degrees will involve a few chapters in FMT. Physics for instance will have 2nd order differential equations, complex numbers using De Moivre's Theorem and regression / correlation etc.
Programming will also involve graph theory to map routes in how to program stuff. I have only seen my friends use it lar, but how exactly it works not so sure.

[Johnivan]

Hi everyone, It's a long time since i left this thread... Now i got a question for the seniors:

How do you show your complete workings for this question?

12x = 20 (mod 28 )

Thanks...:)

[markwongsk]

Hi everyone, It's a long time since i left this thread... Now i got a question for the seniors:

How do you show your complete workings for this question?

12x = 20 (mod 28 )

Thanks...:)

find the minimum value of x? maybe like this?

12x = 20 (mod 29 )
3x = 5 (mod 28 )
3x - 5 = 0 (mod 28 )
This implies that 3x-5 is divisible by 28 and hence
3x - 5 = mod 28n where n = 1, 2, 3...
Taking n = 1
3x - 5 = 28
x = 11

[PsyMaths]

find the minimum value of x? maybe like this?

12x = 20 (mod 29 )
3x = 5 (mod 28 )
3x - 5 = 0 (mod 28 )
This implies that 3x-5 is divisible by 28 and hence
3x - 5 = mod 28n where n = 1, 2, 3...
Taking n = 1
3x - 5 = 28
x = 11

o this is the complete solution??? Must we take n = 1, how to know whether mayb n=101, n = 1001... has solution also???

cuz i here also got question.

Solve the following congruence:
22x = 13 (mod 44) Answer: x =1,4,7,10,13,16,19

need to try 1 by 1???

[ktan29]

mark has answered you in very detail way dy. lol



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


uoykcuf can I have the pdf form of the reference book please? Further maths is bleeding all my pocket money away :cry.

[PsyMaths]

find the minimum value of x? maybe like this?

12x = 20 (mod 29 )
3x = 5 (mod 28 )
3x - 5 = 0 (mod 28 )
This implies that 3x-5 is divisible by 28 and hence
3x - 5 = mod 28n where n = 1, 2, 3...
Taking n = 1
3x - 5 = 28
x = 11

Anyway, isn't that minimum value of x is 4?

12x = 20 (mod 28 )
3x = 5 (mod 7 )
3x - 5 = 0 (mod 7 )
This implies that 3x-5 is divisible by 7 and hence
3x - 5 = mod 7n where n = 1, 2, 3...
Taking n = 1
3x - 5 = 7
x = 4

[markwongsk]

Anyway, isn't that minimum value of x is 4?

12x = 20 (mod 28 )
3x = 5 (mod 7 )
3x - 5 = 0 (mod 7 )
This implies that 3x-5 is divisible by 7 and hence
3x - 5 = mod 7n where n = 1, 2, 3...
Taking n = 1
3x - 5 = 7
x = 4

Yeah haha :oh I guess so... I'm not too sure about the working too. I never took FM =(

[purplesun90]

actually i want to tale fur math
but no teacher and source
so finally give up
you know....i am from lousy school...shuuu....
and there was only 1+ ppl thke fur math in whole MAY
so, anyway hope who take it, gud luck, you all genius.....muack

[ling910520]

who can give me the list of futher math refrence book that cover the entire syllabus.or if any senior here want to sell them pls pm me or email me ling5102002@<hidden>

[Johnivan]

who can give me the list of futher math refrence book that cover the entire syllabus.

I thought I just posted something detail enough and similiar to what you want... You can check out the previous posts...

[Eurytos]

actually i want to tale fur math
but no teacher and source
so finally give up
you know....i am from lousy school...shuuu....
and there was only 1+ ppl thke fur math in whole MAY
so, anyway hope who take it, gud luck, you all genius.....muack

Personally i feel that you shouldnt' give up so easily. There are quite alot of references out there if you really want to take further maths. Anyway your school has 10 plus people taking FM? That's a great sign!! Don't give up yet!! You can still make up for lost time if you start now! :)
All you need are a couple of days to find the references and kickstart your preperations for FM! Refer to earlier posts for information on Futher maths

[ling910520]

who got selling futher math reference book, new book price is not affordable leh........

[purplesun90]

Personally i feel that you shouldnt' give up so easily. There are quite alot of references out there if you really want to take further maths. Anyway your school has 10 plus people taking FM? That's a great sign!! Don't give up yet!! You can still make up for lost time if you start now! :)
All you need are a couple of days to find the references and kickstart your preperations for FM! Refer to earlier posts for information on Futher maths

oo...too late loh,i take stpm this year leh...
not in my school,i mean whole malaysia o...
and....another things make me angry is in our school,they dun allow student take 5 subject....said no such package available,i know they dun wan get busy oni..but anyway,thax for your advice and encouragement
hope we all get gud result...gud luck!!!!

[Johnivan]

I shouldn't still be here in front of the computer at this point of time, when Further Maths T Paper 1 is in a week's time... But just to drop by to wish all Further Maths takers all the best! Gambateh! :)

[seahjiachen]

Hey, does anyone has any further maths notes?

[mathexpert]

hey,sea u also take further math this year?

[seahjiachen]

yeah. what about u?

[mathexpert]

well,i plan to take it but teacher asks me to consider about it seriously.do u have any tuition teacher teach further math?
by the way,u from which state?

[seahjiachen]

I'm from subang jaya, selangor. U?? I've got a tuition teacher. We can study together for Fmaths also if u want. But my Furthur maths still noob la :D

[mathexpert]

nvm.me also very noob in math.can u send me ur msn?then we can discuss further math together

[seahjiachen]

seahjiachen _ hotmail

No probs :D I just started not long ago for Fmaths. 6 person from my school are taking Fmaths but we seldom had discussions :(

[mathexpert]

wah,so many students tale further math in ur school.so envy

if I(n)=(integrate) (ln x)^n dx,

a)prove that I(n)=-nI(n-1)

b)deduce that I(n)=(-1)^n.n!

(n) is small n at the right corner of I

[markwongsk]

wah,so many students tale further math in ur school.so envy

if I(n)=(integrate) (ln x)^n dx,

a)prove that I(n)=-nI(n-1)

b)deduce that I(n)=(-1)^n.n!

(n) is small n at the right corner of I

Try integration by parts. The deduction is simple.

[mathexpert]

can u show ur working?

write each of the complex number
z1=1-(root 3)i z2=(root 3)+i
in the form re^(ix),where r is greater than 0 and x is between -(pie) and (pie)
hence, show that if z1^7 + z2^7=a+bi,where a and b are real number,then b/a=2+(root 3)


(http://s806.photobucket.com/albums/yy341/nghongwai/)

[PsyMaths]

can u show ur working?

write each of the complex number
z1=1-(root 3)i z2=(root 3)+i
in the form re^(ix),where r is greater than 0 and x is between -(pie) and (pie)
hence, show that if z1^7 + z2^7=a+bi,where a and b are real number,then b/a=2+(root 3)



I assume that you know how to convert to re^(ix)

From there,
1) expand it to cartesian form ( x + iy)
2) compare x + yi with a + bi, b/a = tan-1 theta
3) y/x = b/a. Simplify it and u will get the answer.

[mathexpert]

anyone can upload further math paper 2009?ur help is appreciated.

[seahjiachen]

http://cwooi.com/index.php?option=com_remository&Itemid=28&func=select&id=2&orderby=2&page=2

everything's here

[mathexpert]

but here don have 2009 further math paper

[Johnivan]

Sorry for disappearing for a long while...

I understand that everyone wants to get the 2009 FMT paper. Well, actually I sent it to MR cwooi but he either didn't receive my mail or he didn't upload it... So I decided to open up my Skydrive for the benefit of Further Maths takers.
Here's the link for the Further Maths 2009 paper:

http://cid-a23a577d74927c72.skydrive.live.com/browse.aspx/.Public

By the way, the Paper 1 is super hard, so please don't ask me for answers for it... While Paper 2 I still can Tahan... Results is coming out in 5 days time, only then will I know how I did for my Further Maths... Good luck to you all! :)

[divinejun]

hi.. i m new here.. planing to learn further maths.. but i cant find any suitable book in d market and d book recommended are quite expansive. i dont tink i can afford it.. i stil got 4 more frens tat are planning to learn together.. any1 got furthermaths reference notes in digital form?? thanks alot.. :D

btw i m also a candidate for stpm 2009.. school dont lets us take more den 4 subject.. therefore i canot take further maths.. result coming out in 3 days.. wish all of u good luck!!

[walrein_lim88]

Sorry for disappearing for a long while...

I understand that everyone wants to get the 2009 FMT paper. Well, actually I sent it to MR cwooi but he either didn't receive my mail or he didn't upload it... So I decided to open up my Skydrive for the benefit of Further Maths takers.
Here's the link for the Further Maths 2009 paper:

http://cid-a23a577d74927c72.skydrive.live.com/browse.aspx/.Public

By the way, the Paper 1 is super hard, so please don't ask me for answers for it... While Paper 2 I still can Tahan... Results is coming out in 5 days time, only then will I know how I did for my Further Maths... Good luck to you all! :)

How's ur further maths T result??

[Johnivan]

How's ur further maths T result??

Haha, you people mustn't have noticed The Star commenting on Further Mathematics on 26th Feb... Everything about the extract was true, except the fact that I wanted to be a doctor... Anyway, I got a B+ for paper 1, A for paper 2, so I got an A- overall.

http://thestar.com.my/news/story.asp?file=/2010/2/26/nation/5749988&sec=nation

Unlike last year we had more than 3 people scoring resounding A's, this year there are only 2 passes out of 16 candidates who took the subject. Obviously, I'm one of them... I do hope the other person who passed could show up, I want to know you as well...

I made it 100% pass in Johor, and overall CGPA 3.67 for that subject (stupid statistics, I know...). Anyway, I was really glad about my results, because for such a hard paper 1, I think I did my best.

People, don't be afraid: 2008's paper was too easy, so they made 2009's paper damn hard. What do you think will happen to 2010's paper? I leave it for you to answer. When I'm free, I'll be giving a lecture on Further Maths in this Forum, maybe in the later part of the year (haha...). Hope to help all the "adventurous" students to pass the paper. :)

[walrein_lim88]

http://cforum6.cari.com.my/viewthread.php?tid=1877436&extra=page%3D1
my notes for further maths T paper 1...hope anybody can help me too

[Johnivan]

http://cforum6.cari.com.my/viewthread.php?tid=1877436&extra=page%3D1
my notes for further maths T paper 1...hope anybody can help me too

Wow, how I hoped you appeared a little earlier, that would have helped me a lot! You said you saved all the notes in PDF format. Don't mind sharing it out? Did you do all the notes yourself? That's great!

[walrein_lim88]

Wow, how I hoped you appeared a little earlier, that would have helped me a lot! You said you saved all the notes in PDF format. Don't mind sharing it out? Did you do all the notes yourself? That's great!



my further maths T note paper 1 have completed in CARI forum.
But i still feel dissatisfied, and hope someone can give some comment so that the notes can be improved again.

[the_thinker]

I am also taking further mathematics this year. @<hidden> -Your notes are very helpful.
I'd like to know if there is any restriction regarding the type of calculator allowed during the tests.

[markwongsk]

I am also taking further mathematics this year. @<hidden> -Your notes are very helpful.
I'd like to know if there is any restriction regarding the type of calculator allowed during the tests.

Technically there is. But MPM seldom checks. I used an 991 ES but they didn't check (helps check differentiation and integration if you know how to, and matrix). But I advise you take a spare (Something acceptable, go to MPM website to find which ones are). So if they take your main calc, you still have one to work on. Of course, don't be too reliable on calculators. I only use the special function as a checking tool!

[mathexpert]

http://i806.photobucket.com/albums/yy341/nghongwai/untitled-13.gif

[markwongsk]

This is Cauchy-Euler Diff Eq. Use Chain rule and product rule to find the second order derivative. Use Fubini where appropriate.

[smallkid]

How to find the 2nd order derivative?
I've gotten (dy/dx)e^z=dy/dz

But i dunno how to get (X^2)(d2y/dx2) = (d2y/dz2)-(dy/dz) from X=e^z

Sry for the trouble! I'm a noob :p

ok. mathexpert showed me already =p thanks

[markwongsk]

dy/dt = dy/dx * dx/dt
d2y/dt2 = d/dt(dy/dx * dx/dt)
= d2y/(dx dt) * dx/dt + d2x/dt2 * dy/dx
= d2y/dx2 * (dx/dt)^2 + d2x/dt2 * dy/dx

Hope that helped

[walrein_lim88]

http://i806.photobucket.com/albums/yy341/nghongwai/untitled-13.gif
http://i895.photobucket.com/albums/ac157/walrein_lim88/Untitled-2050.png

[markwongsk]

Good job! This is exactly what Euler's equation should achieve:)

[the_thinker]

Hey, i don't have the answer to this question. So i was hoping that someone could attempt it and post their answer just to be doubly sure that my answer is correct.

The equation of
z^4 - 2(z^3) + k(z^2) - 18z + 45 = 0
has imaginary roots. Obtain all the roots of the equation and the value of the real constant k.

[walrein_lim88]

Hey, i don't have the answer to this question. So i was hoping that someone could attempt it and post their answer just to be doubly sure that my answer is correct.

The equation of
z^4 - 2(z^3) + k(z^2) - 18z + 45 = 0
has imaginary roots. Obtain all the roots of the equation and the value of the real constant k.
http://i895.photobucket.com/albums/ac157/walrein_lim88/Untitled-268.png

[the_thinker]

Can someone help me with this...

Prove that tan-1 [(1+x)/(1-x)] = π/4 + tan-1 x

[markwongsk]

but what IS n?

[fird126]

but what IS n?

i think its pi.

[the_thinker]

Apologies... the supposed 'n' is actually pi. I copied the equation off Microsoft Word and was unaware that pi looked like an n.

[walrein_lim88]

Can someone help me with this...

Prove that tan-1 [(1+x)/(1-x)] = π/4 + tan-1 x
http://i895.photobucket.com/albums/ac157/walrein_lim88/Untitled-2259.png

[the_thinker]

I attempted this question but i think its faulty... can someone try it for me?

Using Maclaurin’s expansion, and differentiation, show that:
ln(1-x) = - x - (x^2)/2 - (x^3)/3 - … - (x^r)/r - …

[Sillyboy]

I attempted this question but i think its faulty... can someone try it for me?

Using Maclaurin’s expansion, and differentiation, show that:
ln(1-x) = - x - (x^2)/2 - (x^3)/3 - … - (x^r)/r - …

Maclaurin's expansion:

f(0) + xf'(0) + ((x^2)/2!)f"(0)+((x^3)/3!)f"'(0)+ (x^4)f""(0)+.... the dash denotes the number of times f is differentiated.
It should look like -x - (x^2)/2 - (x^3)/3-.....etc

[nimo]

Have problem solving this question. Can any member here give me the solution to
this FM question.
Reply appreciated.

The number of goals scored per match by a football team during a season has a Poisson distribution with mean 1.5. The number of goals conceded per match by the same team during the season has a Poisson distribution with mean 1 Find the probability that a match involving the team produced more than 3 goals.
Answer : 0.242

[the_thinker]

The number of goals scored and conceded per match can be seen collectively and thus the mean goals per match would be (1.5 + 1) which is 2.5. Then, simply subtitute the values into the formula..

Let x be the number of goals in a match involving the team
P(X>3) = 1 - [ P(X=3) + P(X=2) + P(X=1) + P(X=0) ]
= 1 - (e^-2.5) [ (2.5^3)/3! + (2.5^2)/2! + (2.5^1)/1! + (2.5^0)/0! ]
= 0.242

[nimo]

You are great, thanks for the prompt reply. Can you also help me on this question? For this question, I can only get (i)&(ii), but could not get (iii).

6. In a packaging factory, the empty containers for a certain product have a mean weight of 400g with a standard deviation of 10g. The mean weight of the contents of a full container is 800g with a standard deviation of 15g.

(i) Find the expected total weight of 10 full containers and the standard deviation of this weight, assuming that the weights of containers and contents are independent.
(ii) Assuming further that these weights are normally distributed random variables, find the proportion of batches of 10 full containers which weigh more than 12.1kg.
(iii) If 1% of the containers are found to be holding weights of product which are less than the guaranteed minimum amount, deduce the minimum weight. (Ans: 765g)

[the_thinker]

Alright, for this question we simply use the values for the weight of the contents whereby the mean is 800g and the standard deviation is 15.

Let x be the minimum weight.
P(X< x) = 0.01
Since it is assumed to be normally distributed,
P[Z<(x-800)/15] = 0.01
Using the distribution table, (i seem to have misplaced mine)
we can find that (x-800)/15 = 2.33 (do check this value, its my rough approx.)
Hence x = 765g

On another note, are you taking further math this year?

[nimo]

Thank you very much. And yes, I just taken Further Mathematics last two weeks and my whole class is having problems with the lecturer's teaching method.

Luckily I can get your help for these two questions which I've been trying hard to figure it out for the last two weeks.

[Sillyboy]

Thank you very much. And yes, I just taken Further Mathematics last two weeks and my whole class is having problems with the lecturer's teaching method.

Luckily I can get your help for these two questions which I've been trying hard to figure it out for the last two weeks.

May I ask what problems with regards to your lecturer's teaching method?

[the_thinker]

Maclaurin's expansion:

f(0) + xf'(0) + ((x^2)/2!)f"(0)+((x^3)/3!)f"'(0)+ (x^4)f""(0)+.... the dash denotes the number of times f is differentiated.
It should look like -x - (x^2)/2 - (x^3)/3-.....etc

Ii think my problem lies in the differentiation of f(x)...
If f(x)=ln (1-x) then f'(x)= 1/(1-x) then f''(x)= (1-x)^-2 and f'''(x)= 2(1-x)^-3

Therefore f(0) + xf'(0) + ((x^2)/2!)f"(0)+((x^3)/3!)f"'(0)+ (x^4)f""(0)+....
would equal to x + (x^2)/2 + (x^3)/3 + ...

[walrein_lim88]

Ii think my problem lies in the differentiation of f(x)...
If f(x)=ln (1-x) then f'(x)= 1/(1-x) then f''(x)= (1-x)^-2 and f'''(x)= 2(1-x)^-3

Therefore f(0) + xf'(0) + ((x^2)/2!)f"(0)+((x^3)/3!)f"'(0)+ (x^4)f""(0)+....
would equal to x + (x^2)/2 + (x^3)/3 + ...

ur differentiation is wrong
f(x) =ln (1 - x)
f'(x) = -1/(1-x)
Note: differentiate: 1-x u get -1,
u left out -

[Sillyboy]

ur differentiation is wrong
f(x) =ln (1 - x)
f'(x) = -1/(1-x)
Note: differentiate: 1-x u get -1,
u left out -

And I do hope you understood where your mistake lies! The chain rule for differentiation can be a bit tricky sometimes.

[nimo]

I'm having a problem with this question.

A continuous random variable X has a p.d.f. f given by
f(x) = k/ x(4-x) 1≤x≤3
f(x) = 0 otherwise

(a)Show that k= 2/in3

Can anyone please show me the detail working solution and also explain to me what "in" means in Mathematics?
[p/s: I'm doing self-study ahead of my school syllabus, and I haven't encounter "in" before...]

Reply are appreciated. Thank you very much.

[Sillyboy]

I'm having a problem with this question.

A continuous random variable X has a p.d.f. f given by
f(x) = k/ x(4-x) 1≤x≤3
f(x) = 0 otherwise

(a)Show that k= 2/in3

Can anyone please show me the detail working solution and also explain to me what "in" means in Mathematics?
[p/s: I'm doing self-study ahead of my school syllabus, and I haven't encounter "in" before...]

Reply are appreciated. Thank you very much.

Hello nimo, I won't post the full working for you but I will provide you with some guidance.

First off, the "in" is actually ln or log to the base "e" where e is called the exponential. "e" is a real number and has the approximate value of 2.178... Also, "ln" is commonly known as the natural logarithm.

We recall that the p.d.f of a Continuous Random Variable, when integrated over the range of the Random Variable is 1.

To integrate the function given above, you will need to know two things:

1) Partial Fractions
2) The integral of 1/Ax+B where A and B are real numbers, which ties in very closely to the differentiation of natural logarithms.

For more information about the exponential read the 1st and 4th paragraph of this wiki link:
http://en.wikipedia.org/wiki/Exponential_constant

Then for natural logarithms and its properties read paragraph 1 -7 (Ignore 6!) and "the natural logarithm in integration"
http://en.wikipedia.org/wiki/Natural_logarithm

For partial fractions, have a look at the first example from this wiki link:
http://en.wikipedia.org/wiki/Partial_fraction

Ok, you should be able to get somewhere with these information! If not, I (or someone else here!) will write a detailed account of the workings.

[nimo]

Hello nimo, I won't post the full working for you but I will provide you with some guidance.

First off, the "in" is actually ln or log to the base "e" where e is called the exponential. "e" is a real number and has the approximate value of 2.178... Also, "ln" is commonly known as the natural logarithm.

We recall that the p.d.f of a Continuous Random Variable, when integrated over the range of the Random Variable is 1.

To integrate the function given above, you will need to know two things:

1) Partial Fractions
2) The integral of 1/Ax+B where A and B are real numbers, which ties in very closely to the differentiation of natural logarithms.

For more information about the exponential read the 1st and 4th paragraph of this wiki link:
http://en.wikipedia.org/wiki/Exponential_constant

Then for natural logarithms and its properties read paragraph 1 -7 (Ignore 6!) and "the natural logarithm in integration"
http://en.wikipedia.org/wiki/Natural_logarithm

For partial fractions, have a look at the first example from this wiki link:
http://en.wikipedia.org/wiki/Partial_fraction

Ok, you should be able to get somewhere with these information! If not, I (or someone else here!) will write a detailed account of the workings.

Ok, will go to the link for better understanding and information. Will come back should i need further assistance.

TQ

[louis8_8wang]

Z=x+yi, x and y are real number.|(z-1)/(z+i)|=5.

answer is 12x^2+12y^2-x+25y+25=0.

Z=x+yi, x and y are real number.|(z-1)/(z+i)|=5.

answer is 12x^2+12y^2-x+25y+12=0.


I'm not sure about the answer...anyone can show me the soluiton?

[kudis]

Z=x+yi, x and y are real number.|(z-1)/(z+i)|=5.
This will be grungy if you substitute x+iy for z from the get go. instead use the fact that |z/w|=|z|/|w| for complex variables z and w. also zz*=|z|^2
Let's rewrite z-1=f, z+i=g:
|f/g|=5 => |f|/|g|=5
ff*=|f|^2, gg*=|g|^2 so
ff*/gg*=(|f|/|g|)^2=5^2=25
Hence:
(z-1)(z*-1)/(z+i)(z*-i)=25
(|z|^2-z-z*+1)/(|z|^2-iz+iz*+1)=25
(|z|^2-2x+1)/(|z|^2+2y+1)=25
the algebra is straightforward from here

[Johnivan]

I think direct substitution is easier:

|z-1| = 5|z+i|
substitute z = x + yi,

|(x-1) + yi| = 5 |x + (y+1)i|

Hopefully you know the modulus of any complex number x+yi is
root of (x^2 + y^2).

So squaring both sides at the same time,

(x-1)^2 + y^2 = 25 [x^2 + (y+1)^2]

Solving, you will get

12x^2 + 12y^2 + x + 25y + 12 = 0

Get it?

[mathexpert]

the lifespan (in kilometres) of a tyre is defined as the distance travelled before wearing out. A tyre manufacturer claims that the mean lifespan u of its tyre is at least 50000km. In order to test this claim, a consumer association takes a ramdom sample of 121 tyres. The means and standard deviation of the lifespan for the sample are 49200km and 2500km respectively.
a)determine the distribution of the sample mean lifespan of the tyres if the lifespan of the tyres is assumed to have
i)a normal distribution
ii)an unknown distribution

[Buckminster]

Hello everyone, I'm new here...

I will be taking further maths in 2009!!

Anyone doing the same? please sign up and join this forum!
Maybe we could share some questions or thoughts, or teachers?

I'm from Johor, a very dead place for further maths...

So, i bought the books recommended by MPM, study myself...

Anyone taking further maths who has a "teacher", please let me know, and let everyone know as well! I believe many Silly people (like me) wants to take further maths, but they can't simply because they don't have resources...

Anyone who has further maths trial papers...
exercises...
notes...
Just share around and help each other!

Some tips from me:
1. Download the further maths syllabus from
http://www.mpm.edu.my/download.php?FilePoolID=119

2. Buy the text books through MPH bookstore! You either have to order them, or buy through the net... They are expensive, but that's the only way... I have 5 of them:
a. Further Pure Mathematics by Bostock, L. Chandler, S & Rourke C
b. Further Pure Mathematics by Gaulter B & Gaulter M, Oxford 2001
c. Discrete Mathematics and Its Applications (6e) by Rosen KH, McGraw-Hill
d. A concise Course in Advanced Level Statistics by Crawshaw J & Chambers J
e. Lastly, a Maths S paper 2 reference book.

I'll tell you more when more people join... Please help... Thanks!! :)


Where did you get all the books from?I know you get that through MPH bookstore,but which outlet did you go?how can I order them online?

[Johnivan]

the lifespan (in kilometres) of a tyre is defined as the distance travelled before wearing out. A tyre manufacturer claims that the mean lifespan u of its tyre is at least 50000km. In order to test this claim, a consumer association takes a ramdom sample of 121 tyres. The means and standard deviation of the lifespan for the sample are 49200km and 2500km respectively.
a)determine the distribution of the sample mean lifespan of the tyres if the lifespan of the tyres is assumed to have
i)a normal distribution
ii)an unknown distribution

I think this question is only asking you to state the distribution. So just state it with Let X be something something, then X~N(mu, sigma^2/n).
For ii, you need to state the central limit theorem before you state the answer (which is the same).

I'm not sure, but it might be a Hypothesis question too. Where did you get this question from?

Where did you get all the books from?I know you get that through MPH bookstore,but which outlet did you go?how can I order them online?

Basically, the book shops won't have the stock there waiting for you. Since my hometown doesn't has MPH, I went to Johor Bahru, and I placed an order to ask them to send the books to my house. You can log on to MPH online to purchase too. :)

[louis8_8wang]

Z=x+yi, x and y are real number.|(z-1)/(z+i)|=5.
This will be grungy if you substitute x+iy for z from the get go. instead use the fact that |z/w|=|z|/|w| for complex variables z and w. also zz*=|z|^2
Let's rewrite z-1=f, z+i=g:
|f/g|=5 => |f|/|g|=5
ff*=|f|^2, gg*=|g|^2 so
ff*/gg*=(|f|/|g|)^2=5^2=25
Hence:
(z-1)(z*-1)/(z+i)(z*-i)=25
(|z|^2-z-z*+1)/(|z|^2-iz+iz+1)=25
(|z|^2-2x+1)/(|z|^2+2y+1)=25
the algebra is straightforward from here

but I cant eliminate i....and where comes 2y?

I think direct substitution is easier:

|z-1| = 5|z+i|
substitute z = x + yi,

|(x-1) + yi| = 5 |x + (y+1)i|

Hopefully you know the modulus of any complex number x+yi is
root of (x^2 + y^2).

So squaring both sides at the same time,

(x-1)^2 + y^2 = 25 [x^2 + (y+1)^2]

Solving, you will get

12x^2 + 12y^2 + x + 25y + 12 = 0

Get it?
but the answer given is -x not +x....?

[kudis]

[quote=louis8_8wang;341085]but I cant eliminate i....and where comes 2y?

sorry about the typo there. it should be:
(|z|^2-z-z*+1)/(|z|^2-iz+iz*+1)=25
all the imaginary parts are gone. it's useful to remember these facts:
Re{z}=(z*+z)/2=x Im{z}=i(z*-z)/2=y
you can prove this by direct substitution. that's the reason why I chose this over Johnivan's "easier" method; you discover something useful. so next time you see them you don't have to sub x+iy for z. saves you a line or two(at least for tougher problems.)

[Johnivan]

but the answer given is -x not +x....?

I triple checked my answer, and I don't think there's any error. Maybe kudis could help...

[markwongsk]

I checked too... doesn't seem like anything wrong =/

[mathexpert]

is it a must for further math candidates to write all the steps accordingly (hypothesis testing, chi-square significance test) ? like must define X first ,then state null hypothesis and alternative hypothesis....... and so on ?????

[Johnivan]

is it a must for further math candidates to write all the steps accordingly (hypothesis testing, chi-square significance test) ? like must define X first ,then state null hypothesis and alternative hypothesis....... and so on ?????

SURE! You want to get marks don't you? Haha...

[the_thinker]

Can someone help with this,

In the context of Z10, please calculate the following:
12⊕4 (the answer is not 6)

[mathexpert]

what is Z10?

[Esthern]

may i know where you bought those books?

[Euclidzz]

Hi~~^^
I was the new student that just start further mathematics T.....
My here got
1)Further Mathematics T book (Paper 1&2) (Malay version)(Some chapter is out of syllabus)
2)Siri Analisa Pelangi Matematik Lanjutan A(Tulen) Jilid 1
3)Further Pure Mathematics
4)Further Mathematics
5)1 Tuition Teacher

Now , I realized that no writer are willing to write the Further Mathematics T book.....
As the result, many students that very interest the subject are force to give up......
What I write at here, If you are really interest the subject .....
Just go for it!!!!!
When I take this subject.....I was reject by my parents ,my friends ,and my teacher....haiz.....
But I still wont give up ..... Although I was not success yet in my Further mathematics T subject......^^
If you also are the student of this subject.......can we share the idea?
This is my msn.....
karfai0317@<hidden>
This world no such things impossible
Because Impossible = I'm possible!!! :P

[Johnivan]

may i know where you bought those books?

Hi, It's a long time since I last commented on this page...

I'm not sure whether you read through all the details properly, but I'm repeating here that I bought the books from MPH. I specially ordered the books from their counter, then collect them from MPH a few weeks later.

[chrono13]

very interesting thread. In fact my friend told me this evening that there is stpm further maths but i didnt believe him then == im currently in a levels incl. further maths and for the past three months ive been having an increasing interest in maths. Im thinking of taking stpm as a private candidate on nov 2011.

Question, what do you think abt fmt? I see that most of you are pros and i wanna have your opinions about this. And im planning on taking physics for a degree, will this help a lot? Count me as a normal student lah, by the way.

[Johnivan]

very interesting thread. In fact my friend told me this evening that there is stpm further maths but i didnt believe him then == im currently in a levels incl. further maths and for the past three months ive been having an increasing interest in maths. Im thinking of taking stpm as a private candidate on nov 2011.

Question, what do you think abt fmt? I see that most of you are pros and i wanna have your opinions about this. And im planning on taking physics for a degree, will this help a lot? Count me as a normal student lah, by the way.

Hi Chrono13,

There is a Further Maths T paper in STPM. But only a few students take it every year.

2008 - 36
2009 - 16 (2 passed)
2010 - 10

So there'll be only a few people who actually know about its existence. I'm presently taking a Physics degree in NUS, and I would say, with the help of Further Maths T, I could really relax a lot in lectures. Sometimes, the lecturers go through the hard core stuff too fast. No body catches him, but you know it before hand.

I'm not sure how you define "normal", but I wouldn't recommend students who can't score A in their Maths T to take this subject. Taking A-levels or STPM subjects is already a great burden. You can't possibly say that you will get an A in Further Maths (2008 is super easy, 2009 is super hard), so if you can't do well in your other subjects, Further Maths just add salt onto your wounds. But if you really have a good time management, an analytical mind, the ability to study independently and great perseverance, this subject will be rewarding. :)

[Hanqing]

can anyone help me to solve this question?
Solve,
sinh ( arcsinh x + arcosh 2x ) = 3

[KenT13]

Erm,i finieshed my spm last year. so i'm wondering how to register for further maths? i'm gonna register when i'm in lower 6 or upper 6?

[Hanqing]

Erm,i finieshed my spm last year. so i'm wondering how to register for further maths? i'm gonna register when i'm in lower 6 or upper 6?

upper six =)

can anyone help me to solve this question?
Solve,
sinh ( arcsinh x + arcosh 2x ) = 3

[ Solved, i was careless while managing the radicals]:notrust

[KenT13]

Okay i read some of the posts. And i have no idea how to solve any questions. Is it normal? or i'll learn it soon?

[Nicholasng925]

Okay i read some of the posts. And i have no idea how to solve any questions. Is it normal? or i'll learn it soon?

It's normal that you don't know how to do those questions now, cause you'd learn it soon enough.

[KenT13]

And i don't have any Fmt books to look through. but i'd found some good websites for notes. but i cant look at the computer screen for too long. i'm simply get dizzy

[Hanqing]

And i don't have any Fmt books to look through. but i'd found some good websites for notes. but i cant look at the computer screen for too long. i'm simply get dizzy

well you can buy it from bookstores but it's not cheap =/. Anyway try to cover maths T syllabus first, as far as possible =) since you have the holidays to do so before you start your lower six

[Euclidzz]

can give ur all msn to me~~~
I hope we can discuss fmt question by using msn more faster~~
Hope u can add me~~
karfai0317@<hidden>
If u no material~~ u can ask me for borrow~~ >.<
And I hope senior or fmt candidate can add me~~
please~~!!! Help me to solve some question

[Johnivan]

At the beginning, you'll start to look through the FMT paper questions and try to find the solution through notes online. Or sometimes, you looked through the papers, and you have no idea what is it about. Well that's normal, and in fact that's good. Always make sure that you MUST buy the textbooks to proceed, as reading online stuff is NOT sufficient. You gotta spend at least RM400 for this subject, and you're not sure whether you will fail it. Oh well, that's what it takes for this subject. But if you ever will study Mathematics or Physics in University, you will be thankful that you did this subject. :)

[Hanqing]

can give ur all msn to me~~~
I hope we can discuss fmt question by using msn more faster~~
Hope u can add me~~
karfai0317@<hidden>
If u no material~~ u can ask me for borrow~~ >.<
And I hope senior or fmt candidate can add me~~
please~~!!! Help me to solve some question

do you have facebook? there's a group for further maths, if possible mind to let me know your name in facebook? so i can invite you into the group

[Euclidzz]

do you have facebook? there's a group for further maths, if possible mind to let me know your name in facebook? so i can invite you into the group

This is my FB
http://www.facebook.com/profile.php?id=100000110077530
Euclid Siew Kar Fai
Hope u add me as fast as possible~~ ^^

do you have facebook? there's a group for further maths, if possible mind to let me know your name in facebook? so i can invite you into the group

before u add me~~
message me 1st~~~
I wan identify~~ ^^

[KenT13]

what's maths T??

[Nicholasng925]

what's maths T??

Maths T is one of the subjects in STPM Science stream, which you must take if you want to take Further Maths T.

[KenT13]

stpm only has these subjects? so little compared to spm-.-
* Pengajian Am (General Studies)
* Bahasa Melayu (Malay language)
* Bahasa Cina (Chinese language)
* Bahasa Tamil (Tamil language)
* Bahasa Arab (Arabic language)
* Literature in English
* Kesusasteraan Melayu (Literature in Malay)
* Pendidikan Islam (Islamic Studies)
* Syariah (Syariah)
* Usuluddin (Islamic studies)
* Sejarah (History)
* Geografi (Geography)
* Ekonomi (Economics)
* Pengajian Perniagaan (Business studies)
* Perakaunan (Accountancy)
* Mathematics S (may not be taken with Mathematics T)
* Mathematics T (may not be taken with Mathematics S)
* Further Mathematics T (may only be taken with Mathematics T)
* Computing (may only be taken at certain schools)
* Physics
* Chemistry
* Biology
* Sains Sukan (Sport science)
* Seni Visual (Visual Art)

and what's the diff between maths s and maths T

[markwongsk]

Math S involves more statistics. Both Math T and Math S have the same paper 1, but math S covers more statistics while Math T covers things like trigonometry and differential equations.

[KenT13]

erm . . .
2. Chi-square Distribution

is this chapter in the syllabus?
according to mpm the syllabus are the follwings:
1.
Logic and proof
1
2.
Complex numbers
2
3.
Matrices
2
4.
Recurrence relations
3
5.
Functions
3
6.
Differentiation and integration
4
7.
Power series
4
8.
Differential equations
5
9.
Number theory
5
10.
Graph theory
6
11.
Transformation geometry
6
12.
Coordinate geometry
7
13.
Sampling and estimation
7
14.
Hypothesis testing
8
15.
χ2 tests
8
16.
Correlation and regression
9

[Nicholasng925]

Chi-square distribution is χ2 Test?

[Johnivan]

erm . . .
2. Chi-square Distribution

is this chapter in the syllabus?


"chi" is one of the greek alphabets which looked like an X. So basically, X^2 is "chi-squared". It's the study of how you model a sample as the assumed distribution, be it Poisson, Normal, Binomial, t- or uniform... I would say it's one of the most easy and straight-forward chapters. :)

stpm only has these subjects? so little compared to spm-.-
and what's the diff between maths s and maths T

Why would you want so many subjects in STPM? You can only take 5 anyway, and 4 is already suffocating. :P

At STPM level, every subject is important in its own way, and you take it as a pre-requisite to enter the future course that you want. I don't think any university wants Ekonomi Rumah Tangga, Sains Pertanian or Pendidikan Muzik as a pre-requisite to enter it...

And yeah, Mathematics S is normally provided in Art-Stream schools, as an easier and more practical subject for Economy Students. It has more statistics than it's counter part, Maths T.
Maths T is taken by Science students with a combination of either Phy-Mat-Chem or Bio-Mat-Chem. Maths T has Trigonometry, Differential Equations, Vectors and Geometry which any Art Student would not want to take.

You can't take both subjects at the same time, and Maths T but not Maths S is required to take together with Further Maths T.

[KenT13]

so that's called chi-square .. . i got a list of books from mpm. . going mph buy soon..

Reference Books
1. Bostock, L., Chandler, S., & Rourke, C., Further Pure Mathematics, Stanley Thornes, 1982 (Reprinted 2002).
2. Gaulter, B. & Gaulter, M., Further Pure Mathematics, Oxford, 2001.
3. Poole, D., Linear Algebra: A Modern Introduction, Brooks/Cole, 2003.
4. Anton, H., Bivens, I., & Davis, S., Calculus (Seventh Edition), John Wiley, 2002.
5. Barnett, S., Discrete Mathematics: Numbers and Beyond, Addison Wesley, 1998.
6. Rosen, K. H., Discrete Mathematics and Its Applications (Fifth Edition), McGraw-Hill, 2003.
7. Scheinerman, E. R., Mathematics: A Discrete Introduction, Brooks/Cole, 2000.
8. Crawshaw, J. & Chambers, J., A concise Course in Advanced Level Statistics (Fourth Edition), Nelson Thornes, 2001.
9. Johnson, R. A. & Bhattacharyya, G. K., Statistics: Principles and Methods (Fourth Edition), John Wiley, 2001.
10. Upton, G. & Cook, I., Introducing Statistics (Second Edition), Oxford, 2001.

according to johnivan,""However, some of the sections of certain chapters can't be found in the 5 books (Gaussian elimination, Taylor's remainder theorem, differentiability, etc)(post #18).""(still dunno how to wrap quotes)
so the remaining topic can be found where?? and do we really need maths s text??

[Johnivan]

You can try Calculus 12th edition by can't-remember-who... Should be Anton I think. You can get these info from those very thick University level Calculus books. :)

[Buckminster]

Hello everyone, I'm new here...

I will be taking further maths in 2009!!

Anyone doing the same? please sign up and join this forum!
Maybe we could share some questions or thoughts, or teachers?

I'm from Johor, a very dead place for further maths...

So, i bought the books recommended by MPM, study myself...

Anyone taking further maths who has a "teacher", please let me know, and let everyone know as well! I believe many Silly people (like me) wants to take further maths, but they can't simply because they don't have resources...

Anyone who has further maths trial papers...
exercises...
notes...
Just share around and help each other!

Some tips from me:
1. Download the further maths syllabus from
http://www.mpm.edu.my/download.php?FilePoolID=119

2. Buy the text books through MPH bookstore! You either have to order them, or buy through the net... They are expensive, but that's the only way... I have 5 of them:
a. Further Pure Mathematics by Bostock, L. Chandler, S & Rourke C
b. Further Pure Mathematics by Gaulter B & Gaulter M, Oxford 2001
c. Discrete Mathematics and Its Applications (6e) by Rosen KH, McGraw-Hill
d. A concise Course in Advanced Level Statistics by Crawshaw J & Chambers J
e. Lastly, a Maths S paper 2 reference book.

I'll tell you more when more people join... Please help... Thanks!! :)

do you still have those book?I tried to find the 2nd book,but i cant find it..do you still have it?mph already out of stock..

[Johnivan]

do you still have those book?I tried to find the 2nd book,but i cant find it..do you still have it?mph already out of stock..

I'm still having all of them. The second one is really kinda old, and only a few chapters in it is really required for Further Maths T. MPH is always out of stock for those few books, but you can go to the counter in MPH and order them, either to send it to your house or you collect it from MPH. Remember to take their contact number, as that particular book took about a month to arrive my doorstep...

[Buckminster]

I'm still having all of them. The second one is really kinda old, and only a few chapters in it is really required for Further Maths T. MPH is always out of stock for those few books, but you can go to the counter in MPH and order them, either to send it to your house or you collect it from MPH. Remember to take their contact number, as that particular book took about a month to arrive my doorstep...

what do you mean only a few chapters?what about the 1st book?is it ok if I only buy it and not the 2nd one..do the 1st book have the same chapter as the 2nd one?

so that's called chi-square .. . i got a list of books from mpm. . going mph buy soon..

Reference Books
1. Bostock, L., Chandler, S., & Rourke, C., Further Pure Mathematics, Stanley Thornes, 1982 (Reprinted 2002).
2. Gaulter, B. & Gaulter, M., Further Pure Mathematics, Oxford, 2001.
3. Poole, D., Linear Algebra: A Modern Introduction, Brooks/Cole, 2003.
4. Anton, H., Bivens, I., & Davis, S., Calculus (Seventh Edition), John Wiley, 2002.
5. Barnett, S., Discrete Mathematics: Numbers and Beyond, Addison Wesley, 1998.
6. Rosen, K. H., Discrete Mathematics and Its Applications (Fifth Edition), McGraw-Hill, 2003.
7. Scheinerman, E. R., Mathematics: A Discrete Introduction, Brooks/Cole, 2000.
8. Crawshaw, J. & Chambers, J., A concise Course in Advanced Level Statistics (Fourth Edition), Nelson Thornes, 2001.
9. Johnson, R. A. & Bhattacharyya, G. K., Statistics: Principles and Methods (Fourth Edition), John Wiley, 2001.
10. Upton, G. & Cook, I., Introducing Statistics (Second Edition), Oxford, 2001.

according to johnivan,""However, some of the sections of certain chapters can't be found in the 5 books (Gaussian elimination, Taylor's remainder theorem, differentiability, etc)(post #18).""(still dunno how to wrap quotes)
so the remaining topic can be found where?? and do we really need maths s text??

do we really have to buy all the books in the list above?

[Nicholasng925]

what do you mean only a few chapters?what about the 1st book?is it ok if I only buy it and not the 2nd one..do the 1st book have the same chapter as the 2nd one?


He meant that only a few chapters are within the STPM Further Maths T syllabus, so most of the contents of whole book are technically redundant. You might just want to photocopy notes for those few required chapters and their exercises only? =) You can always find those books in library.

[Johnivan]

what do you mean only a few chapters?what about the 1st book?is it ok if I only buy it and not the 2nd one..do the 1st book have the same chapter as the 2nd one?



do we really have to buy all the books in the list above?

I think Nicholas should have answered your questions. The only chapter not in the first book is the transformation geometry (it is actually there, but no reference to the word 'transformation', and also lacks a lot of information). Since the second one is old, you can try visiting libraries to find the book and photocopy the relevant chapters.

If you own a photocopier, I suggest you not to buy all of them, but to photocopy those chapters relevant to Further Maths only.

[Chelsea]

uhm just wondering.. Is it possible to use A-level books to study for STPM Further Math T? is the syllabus similar to that of stpm?

[KenT13]

yea plausible, a level maths consists of statistics.and more

[Nicholasng925]

uhm just wondering.. Is it possible to use A-level books to study for STPM Further Math T? is the syllabus similar to that of stpm?

Well, I don't think A-Levels has its own FM books, and even A-Levels students are using some of the books used by the STPM students. Definitely the syllabus of A-Levels is a little bit different from STPM's, for example A-Levels syllabus doesn't include number theory and graph theory, while STPM syllabus does.

[Johnivan]

uhm just wondering.. Is it possible to use A-level books to study for STPM Further Math T? is the syllabus similar to that of stpm?

A-level books help, but is not sufficient to study FMT.

[KenT13]

bump bump weiliang is assigned to find the link~ i think it's here.

[melindaL]

STPM further maths is different from matematik T for science stream rite?

[chrono13]

Hi all,

Sure, Further Maths T sounds cool but with the lack of textbooks available and clear guidelines and syllabus borders, I've decided not to pursue any further in this. If you really like maths and don't mind long hours of homework, do come to Edexcel Further Maths by the way. We haven't started on statistics yet but the pure maths stuff mentioned in the FMT topic range (vectors, matrices e.g. eigenvalues, differential equations, the hyperbolic functions sinh cosh tanh) are all covered.

Those who decides to persevere i salute you :)

[yanguel]

Hi, Do you still have te Further Maths books? Do you want to sell them?

Do you still have the books on Further Maths? Wanna sell them?

Hi, Do you still have te Further Maths books? Do you want to sell them?

Do you still have the books on Further Maths? Wanna sell them?
Please call 0164903961