Preliminary mathematics marathon (4 Viewers)

[hscishard]

New question:

Is this prelim only?

 

[SpiralFlex]

New question:

Is this prelim only?

Probably, I hope not. Does James Ruse Preliminary count? I see little Year 12 Year 11s.

 

[ohexploitable]

New question:

Is this prelim only?

Anything goes.

 

[kooliskool]

lol what expand ( p -a) ( p-b) (p-c) ( p-d), where a, b, c, d are roots


its a little less work i guess

There's actually another way that only takes really a few lines only,

If you look at the as product of roots, we can create a new equation with as roots like follows:

The relationship between the new roots and the old one is

Hence

Substitute this back into the old equation which will be:



and expand to get the leading coefficient and the constant term will give you the product of roots then.

Leading coefficient will be:

Constant Term will be:

So if I'm not mistaken, is the answer just 1?

 

[ohexploitable]

shameless revive

spiralflex or someone, get in here

 

[SpiralFlex]

shameless revive

spiralflex or someone, get in here

Yes Sir!

a) Since it is Preliminary, Preliminary student's only answer this!

I will start with a basic question.

Express the following fraction in the partial form,

. Where and are constants.


The fraction is


For Preliminary students,

b) The roots of the equation are in the ratio of . Show that


For HSC students, [Sorry this question was on the thread already. Didn't know. Attempt it if you want anyway. No cheating. ]

c) Differentiate with respect to ,

. Hence find the differential coefficient of

[Hint: Don't differentiate normally.]


For HSC students,

d) Show that and hence evaluate

Remarks: HSC students! Don't answer the Preliminary sections! Preliminary students! Attempt HSC questions if you can!

 

[Drongoski]

c) is a very interesting question.

 

[AAEldar]

I think I've still got the working for b) on my pc. I shall let someone else answer it though.

Well, it's question c now.

 

[SpiralFlex]

I think I've still got the working for b) on my pc. I shall let someone else answer it though.

Well, it's question c now.

Good times...

 

[ohexploitable]

i think question c has already been asked in this thread

 

[SpiralFlex]

i think question c has already been asked in this thread

Really? What are the odds. In Preliminary too! I see little Ohexploitable on the first page of this thread!

 

[ohexploitable]

Really? What are the odds. In Preliminary too! I see little Ohexploitable on the first page of this thread!

New Question:

Differentiate...

 

[SpiralFlex]

What?! What are the odds!

 

[ohexploitable]

was it khorne?

 

[powlmao]

I Want to know!

 

[ohexploitable]

Find the value of k:
The remainder is 25 when:
is divided by
I know P(k) = 25 but im unsure what to do after.

solve for k

 

[Hermes1]

Find the value of k:
The remainder is 25 when:
is divided by
I know P(k) = 25 but im unsure what to do after.

sub in x = k, then get a quadratic equation in terms of k^2 and solve it, then you should get 4 solutions for k.

 

[Hermes1]

solve for k

yeh like this

 

[Drongoski]

Note: for real k (no complex for MX1):

 

[powlmao]

Not sure which program everyone uses, but solve it normally