2009 Question 7 & 8 (1 Viewer)

[untouchablecuz]

any ideas?

 

[gurmies]

I have an idea



























































































Hard questions...xD

 

[raniaaa]

yes, complex numbers, probability, locus, and extremely hard curve sketching

 

[untouchablecuz]

numbers arent THAT complex

 

[raniaaa]

these ones are. they have random i's and e's everywhere.. you're gonna cry when you see them

 

[addikaye03]

In 1993 they asked a Q: prove that e^x=1+x+x^2/2!+x^3/3!+...

It's expected that they will ask for the power series expansion of sinx or cosx sometime:

sinx=x-x^3/3!+x^5/5!-...

and

cosx=1-x^2/2!+x^4/4!-...

 

[-Onlooker-]

^ how very analytical of you.

+ rep

 

[addikaye03]

-Homogeneity in cosx and sinx

Example Q: sinx+cosx=1+sin2x

Solution: sinx+cosx=cos^2x+sin^2x+2sinxcosx

sinx+cosx=(cosx+sinx)^2

cosx+sinx=0 and cosx+sinx=1 etc

-Generating a telescoping sequence

Example Q: sinx+sin3x+...+sin(2n-1)x

Solution: times numerator and denominator by sinx

[(cos0-2x)+(cos2x-cos4x)+..+(cos(2n-1)x-cos2nx)]/2sinx

=sin^2nx/sinx

- First principles of integration (i.e. using upper bound and lower bounds rectangles which help generate inequalities or limits) or differentiaion (ie. log and exponential Q)

Example Q: Prove lim(n->inf) (1+x/n)^n=e^x

Solution: d/dx(Inx)=1/x.

d/dx(Inx)=lim(n->inf) [In(x+h)-In(x)]/h

1/x= lim(n->inf) In((x+h)/x)/h

1/x=lim(n->inf) In(1+h/x)^1/h

Ley y=1/x and let n=1/h

y=lim(n->inf) In(1+y/n)^n

rearranging

lim(n->inf) (1+x/n)^n=e^x

-Throw some geometry, probability, mechanics and recursion formulae

That's all i could think of/research

 

[study-freak]

Note: I've heard that the exam commitee for this year's maths is a new one.
Thus questions can be more random than you think.

 

[gurmies]

Note: I've heard that the exam commitee for this year's maths is a new one.
Thus questions can be more random than you think.

I heard this too!

 

[untouchablecuz]

should i be pleased or worried?

 

[study-freak]

should i be pleased or worried?

Neither
Everyone will be subject to identical conditions anyway.

 

[darusan92]

wen was the last time they changed it before this year?? if u can find that out u can look up the first paper they made and might be able to see how random their going to get!!!