Hard Questions (1 Viewer)

[leehuan]

Here's a funny one from Fort Street Leaving Certificate trial 1959 Question 3a:

Differentiate x^xx

y=x^x^2

ln(y)=x^2.ln(x)

Meh...

1/y dy/dx = x(2ln(x)+1)

 

[InteGrand]

I suppose logarithmic differentiation was explicitly taught before?

 

[Nailgun]

Here's a funny one from Fort Street Leaving Certificate trial 1959 Question 3a:

Differentiate x^xx

this question wouldve been so scary before integrand and drsoccerball taught me logarithmic differentiation ahahah

 

[leehuan]

No. y=x^x^x

Anyway, here is the correct answer:

x^xx(x^x-1+x^xlnx(1+lnx))

That's what happens when I can't see the question clearly enough because it is too small.

ln(y)=x^x.ln(x)

result quoted here out of laziness: d/dx x^x = x^x(1+ln(x))

1/y dy/dx = x^x(1+ln(x)).ln(x) + x^(x-1)

 

[Carrotsticks]

Actually this was not the first time this was examined. It was also in the Fort Street 1960 Leaving certificate trial Question 5a.

So that's interesting that the HSC in 1975 pinched a question from a school trial question 15 years prior - and from a Leaving certificate trial too!

I don't think the HSC would have pinched it from a school trial.

Almost all standard courses dealing with infinite series will at some point have the proof of the p-series converging for p>1, and it most likely would have been the typical integral test proof.

 

[dan964]

OP is a Year 12 student Extension 1. These are not in the scope of the HSC syllabus.

Also, these aren't particularly difficult problems. I am almost certain that my Year 11 class, who just learned Chain Rule less than a week ago, could do the second problem, given a 30 second introduction on how to compute partials.

yeah I know (they aren't too difficult, and not in the scope of syllabus), this thread is in the extra-curricular section.

 

[KINGOM 885]

Why?
I am an extension 1 student

 

[leehuan]

Why?
I am an extension 1 student

You're an Ext 1 student and you posted here. Are you saying you want hard Ext 1 maths questions or questions that are actually hard for real mathematicians

 

[Paradoxica]

Why?
I am an extension 1 student

You're an Ext 1 student and you posted here. Are you saying you want hard Ext 1 maths questions or questions that are actually hard for real mathematicians

Prove or disprove the existence of a universal method to determine whether or not a given equation that defines elliptic curves over ℚ, has finitely, or infinitely many solutions in ℚ.

 

[seanieg89]

Prove or disprove the existence of a universal method to determine whether or not a given equation that defines elliptic curves over ℚ, has finitely, or infinitely many solutions in ℚ.

Went to an amazing lecture on this by Venkatesh last year. Fascinating problem.

 

[InteGrand]

You're an Ext 1 student and you posted here. Are you saying you want hard Ext 1 maths questions or questions that are actually hard for real mathematicians

I think it was originally posted elsewhere (in Maths Extension 1 forum if I recall correctly), but got moved to this area by a Moderator.

 

[Paradoxica]

Went to an amazing lecture on this by Venkatesh last year. Fascinating problem.

I know. I've already read up on a similar problem for general diophantine equations and was disappointed (but it didn't go against my expectations) that the answer was a negative.

I won't be surprised if the answer to that problem is a negative though.

 

[kev@year1223]

Hello @tywebb , would like to buy Cambridge worked out solutions for Maths Extension 1 from you. Could you please advise?