STPM Further Maths 2009

[uoykcuf]

Originally Posted by 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 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
suddenly i see so many further math taker come out in the forum recently, even in other forum also
yeah, this year is better than last year, lol. i wonder how many ppl get A in further math.

Originally Posted by Johnivan

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

[francisfu]

congratz to you also. how bout your other subj? 5A also i think
suddenly i see so many further math taker come out in the forum recently, even in other forum also
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 . I got B for my general paper, C for chemistry ( 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]

Originally Posted by 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?

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]

Originally Posted by uoykcuf

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]

Originally Posted by Johnivan

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]

Originally Posted by 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?

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...