4U Maths Question Thread

[Kle123]

Fair warning: My activity is reduced for this month. I won't be able to get to everything and when I do it might take a while to get there.

Thanks Rui.
NOOOOoooo...my life saver. Thankfully, its only for a month. Good luck with whatever your up to!

[RuiAce]

Thanks Rui.
NOOOOoooo...my life saver. Thankfully, its only for a month. Good luck with whatever your up to!

Ahh I'll still be around, just not as regularly. Besides Jake's floating around too

[Mahan]

How many numbers between 1 and 2002 such that the sum of the digits is divisible by 5?

[jakesilove]

How many numbers between 1 and 2002 such that the sum of the digits is divisible by 5?

Hey Mahan! Just before we answer these questions, just wondering, are they questions you struggle with? Are they homework questions? Because they all seem far beyond any curriculum I know of.

[Mahan]

Hey Mahan! Just before we answer these questions, just wondering, are they questions you struggle with? Are they homework questions? Because they all seem far beyond any curriculum I know of.

Hey Jakesilove! These questions are not directly out of HSC related textbooks but apparently in order to solve them we don't need any knowledge beyond HSC.I agree that they are tricky but after spending some time they should be doable.All the questions that I have posted are either come from other sources, Not HSC related but can be solved using only HSC knowledge, or I heard it from my friends.Sometimes I post them to share them with others or sometimes I'm curious to see whether someone comes up with a different idea or I might not know the answer to that question. For this particular one, I'm curious to see whether someone comes up with some interesting idea to solve it, because there are always multiple methods to solve counting questions, at the same time share some rather unusual and challenging question for those who like challenge.

[RuiAce]

Please reserve the questions thread for those students require assistance with.their studies. There are challenge marathon threads for these types of questions that exist purely for the sake of testing students.

Note: For that one, I'd just use techniques I was taught in discrete maths because I don't have the time to figure out the clever way. Stars and bars + inclusion/exclusion principle. Long winded because we are considering the number of solutions to b+c+d = 4, 5, 9, 10, 14, 15, 19, 20, 24 or 25 though.

[Kle123]

Hey, this question relates to the question in posted in the 3U thread. The answer 126deg 52min for part (V). How can we deduce the angle is obtuse?

[RuiAce]

Hey, this question relates to the question in posted in the 3U thread. The answer 126deg 52min for part (V). How can we deduce the angle is obtuse?

Honestly, I could not see how this is possible unless you drew a diagram that was reasonably to scale. I simulated the scenario on GeoGebra and there was no way that a free-hand diagram would've implied it.

[cutiepie30]

Use a substitution and an integration by parts to evaluate each of the following

For this question and answer attached where am i going wrong?
Why is my answer different to the supplied answer?

[RuiAce]

Use a substitution and an integration by parts to evaluate each of the following

For this question and answer attached where am i going wrong?
Why is my answer different to the supplied answer?

It's not. They're the same answer.

They just simplified it further. Because cos(...) is a common factor so you can factorise it further

[cutiepie30]

For the error in this question.(attached)

i said the working out forgot to add an integration constant(ie +c)
 when an +c is added the value of c=-1

therefore the equation becomes loge(|x|)=loge(|x|), which is true .

Would this be right/ enough ?

[RuiAce]

For the error in this question.(attached)

i said the working out forgot to add an integration constant(ie +c)
 when an +c is added the value of c=-1

therefore the equation becomes loge(|x|)=loge(|x|), which is true .

Would this be right/ enough ?

Pretty much, +C is the cause of it. Because in indefinite integration, we always have to keep in mind that the statement is true to within a constant.

If you ask me though, "true to within a constant" is the key thing that needs to be stated. Of course, you can, by computation, find the value of C (which is -1 or 1, depending on if your C is on the LHS or RHS) to reunite the solutions if you wish.

[VydekiE]

Hi, it would be great if I could get some help on this question
1) Find the equations of the tangent and normal to the ellipse x=4cos theta, y=2sin theta at the point where theta= -pi/4
Thank you!!

[RuiAce]

Hi, it would be great if I could get some help on this question
1) Find the equations of the tangent and normal to the ellipse x=4cos theta, y=2sin theta at the point where theta= -pi/4
Thank you!!

[jakesilove]

Hi, it would be great if I could get some help on this question
1) Find the equations of the tangent and normal to the ellipse x=4cos theta, y=2sin theta at the point where theta= -pi/4
Thank you!!

First, we need an equation. We know that



Clearly,




We want to find the tangent at the point



Honestly Rui, I thought I'd get this one.

But your way is 100% faster.

Far out.