4U Maths Question Thread

[clovvy]

Hi,
For all cube root of unity questions do I do:
w^3=1
w^3-1=0
(w-1)(w^2+w+1)=0
w-1=0 and w^2+w+1=0 equations and use these to find solutions?

careful dude, for cube roots of unity w is a complex number, so w-1 cannot be one as it is not purely real, although w^3 is a real number that is one... this type of proof you need to be familiar with, and 1+w+w^2 has to be zero....

[RuiAce]

Hi,
For all cube root of unity questions do I do:
w^3=1
w^3-1=0
(w-1)(w^2+w+1)=0
w-1=0 and w^2+w+1=0 equations and use these to find solutions?

[envisagator]

Hi Rui, just need help with this polynomial question.

[RuiAce]

Hi Rui, just need help with this polynomial question.

Basically, if you get lost in the formulae, keep writing \( \gamma\) and \( \delta\) but remember to sub \(\gamma = \alpha\) and \(\delta = \beta\) later on.

[zawszeyi]

Ok so im a little worried doing the 4u maths past papers. Im getting around 65's at this point.
What kind of raw marks do I need for a band 6? About 70?
Thanks.

[RuiAce]

Ok so im a little worried doing the 4u maths past papers. Im getting around 65's at this point.
What kind of raw marks do I need for a band 6? About 70?
Thanks.

Around there typically scrapes the E4 as you say.

I don't know how to help you any further without more info.

[justwannawish]

Hey, how do you solve this integral:
(xe^x) (1+x)

I tried doing by parts using u=x/1+x but didn't really get anywhere

[RuiAce]

Hey, how do you solve this integral:
(xe^x) (1+x)

I tried doing by parts using u=x/1+x but didn't really get anywhere

I’m reading this as \( \int xe^x(1+x)\,dx \) which is just \( \int (x^2+x) e^x\, dx \) and can be handled by two applications of integration by parts. Where are you getting that substitution from?

[justwannawish]

I’m reading this as \( \int xe^x(1+x)\,dx \) which is just \( \int (x^2+x) e^x\, dx \) and can be handled by two applications of integration by parts. Where are you getting that substitution from?

Sorry that was completely my fault!
It was meant to be xe^x/(1+x)

[clovvy]

Sorry that was completely my fault!
It was meant to be xe^x/(1+x)

I tried doing it with let u=1+x and it is a lot nicer than your substitution..  However integrals like e^x/x is a special property not in the syllabus...  I end up integrating e^(u-1)-e^(u-1)/u by using substitution and the final answer is a property that we don't even learn in 4U

[RuiAce]

Yeah basically that's a non elementary integral. It might be doable with appropriate boundaries but there is definitely no known antiderivative for it.

[justwannawish]

Thanks guys! It was a question on one of the trial papers our school bought (our actual trial was made up of questions from 3~ independent papers) and our teacher briefly mentioned that the question (which was originally xe^x/(1+e^x) ) was wrong and that xe^x/(1+x) was meant to be the correct q. He might have just stuffed it up, but thank you guys for all your help!

[RuiAce]

Thanks guys! It was a question on one of the trial papers our school bought (our actual trial was made up of questions from 3~ independent papers) and our teacher briefly mentioned that the question (which was originally xe^x/(1+e^x) ) was wrong and that xe^x/(1+x) was meant to be the correct q. He might have just stuffed it up, but thank you guys for all your help!

Both of them are non-elementary actually. I do vaguely recall this of this debuckle actually, but I’m fairly sure whatever the integral was supposed to be should’ve had some boundaries attached to it. Check with your teacher what the integration boundaries were because I think your integrand may have been correct...?

[justwannawish]

Both of them are non-elementary actually. I do vaguely recall this of this debuckle actually, but I’m fairly sure whatever the integral was supposed to be should’ve had some boundaries attached to it. Check with your teacher what the integration boundaries were because I think your integrand may have been correct...?

The boundaries were 1 to 0 if that helps

[RuiAce]

The boundaries were 1 to 0 if that helps

Had to consult with a friend just in case and even then it still looks not doable (damn). If you ever get to see the solutions on the independents paper please keep us updated haha