4U Maths Question Thread

[3.14159265359]

See the edit. It's the exact same method I use in the book

thank you so much!

[3.14159265359]

could we be asked hard simple harmonic questions and projectile questions in a 4u exam?


100 post!

[RuiAce]

could we be asked hard simple harmonic questions and projectile questions in a 4u exam?


100 post!

They combined resisted motion with projectile motion back in 2003 so I wouldn't rule it out completely

[3.14159265359]

They combined resisted motion with projectile motion back in 2003 so I wouldn't rule it out completely

so its possible, but highly unlikely that they will?

[RuiAce]

so its possible, but highly unlikely that they will?

Yeah pretty much

[cthulu]

Hey had this conics question I was stuck on:

[RuiAce]

Hey had this conics question I was stuck on:

This is just the usual reflection property of the ellipse. You should work through Q4a of the 2009 paper to attempt this.

[vikasarkalgud]

Hey Rui, got a conical pendulum question,

A smooth hollow cone with semi-vertex angle 'alpha' is placed with its axis vertical and vertex down.. A particle moves in a horizontal circle on its inner surface, making n revolutions per second. Find the radius of the circle of motion.

I got r = gtan(alpha)/(4n^2pi^2) but the answer has tan(alpha) in the denominator idk how.

Thanks for help

[RuiAce]

Hey Rui, got a conical pendulum question,

A smooth hollow cone with semi-vertex angle 'alpha' is placed with its axis vertical and vertex down.. A particle moves in a horizontal circle on its inner surface, making n revolutions per second. Find the radius of the circle of motion.

I got r = gtan(alpha)/(4n^2pi^2) but the answer has tan(alpha) in the denominator idk how.

Thanks for help

It looks like I get \(\tan \alpha\) in the denominator as well.

[kaustubh.patel]

hey Rui need some help with ext2 combinations que

[RuiAce]

hey Rui need some help with ext2 combinations que

------------------------------------------------------------


Note now, that the fact that the last goal must be scored by Mary is important. That is a deadlocked position, because otherwise either the game is not finished, or we've started considering the situation where Ferdinand wins and thus their roles have been swapped. We don't want to do that - this was the purpose of the \(2!\) earlier.

Thus, in a typical arrangement of who wins each round, Mary constantly occupies four variable positions. In the following computations, I will drop off the fact Mary wins the last one.

[itssona]

Heya:)
from 2012 HSC paper, 16 c) iii
how do we simplify this expression

[RuiAce]

Heya:)
from 2012 HSC paper, 16 c) iii
how do we simplify this expression

Did you mean the second part? (If so, note that the RHS of your expression has a mistake in the denominator)
\begin{align*} \frac{(n-1)! k }{n^k (n-k)!} &\geq \frac{(n-1)!(k-1)}{n^{k-1} (n-k+1)!} \\ \frac{k}{n(n-k)!} &\geq \frac{k-1}{(n-k+1)!}\\ \frac{k}{n(n-k)!} &\geq \frac{k-1}{(n-k)! (n-k+1)}\\ k(n-k+1) &\geq n(k-1)\\ kn - k^2 + k & \geq kn - n\\ k^2 - k -n& \leq 0\end{align*}

[RuiAce]

Hi, there this question is not attached but it is the very last question of the 2005 hsc..... I can do every part but I am struggling to understand the solutions for the last part of the question..... If anyone could somehow explain?

See this recent add to the compilation (you will need to scroll down for the last part). The main reason I didn't address this sooner was because I wanted to cover the entire question as it is somewhat demanding, but I was also on vacation until today so I wasn't feeling bothered enough to do it all.

[Dragomistress]

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?