3U Maths Question Thread

[RuiAce]

ABC is an acute-angled triangle. Squares BAHK and CAXY are constructed on AB and AC respectively and outside the triangle. The diagonals HB and XC meet when produced at P. Prove that angle BPC + angle BAC= 90

(Yes, this question has been asked on this forum by someone else but I wasn't able to access the solution).

It's just angle chasing.



Note: The question in itself is a contradiction. You never actually need to produce both diagonals. (In fact, if you need to produce both diagonals, its because you didn't have an acute-angled triangle to begin with.) This is why I just chose which one I wanted to produce; the proof follows similarly if you produce the other diagonal

[006896]

Hi
Please help me with the attached log questions. Can you show me how to do one or two questions from the attachment?

[RuiAce]

Hi
Please help me with the attached log questions. Can you show me how to do one or two questions from the attachment?

Seeing as though you decided to walk into the 4U territory (AKA Extension section) of Cambridge, are you familiar with logarithmic differentiation?

(If you are not familiar with it and don't know how to continue from here, please re-post in the 4U question thread for a full solution.)

[Caleb Campion]

Help! I was wondering if a series question or financial question could be in the MX1 exam? I do extension 1 & 2 so instead of using my ttime learning those subjects I could be studying for the subjects/topics that will actually be in my exam. I haven't found any past questions on series at all, except for a grouped 5/6 marker in the 2009 mx1 exam. Please help!

[RuiAce]

Help! I was wondering if a series question or financial question could be in the MX1 exam? I do extension 1 & 2 so instead of using my ttime learning those subjects I could be studying for the subjects/topics that will actually be in my exam. I haven't found any past questions on series at all, except for a grouped 5/6 marker in the 2009 mx1 exam. Please help!

Of course it very well could be.

But yeah, you're right to suspect that the likelihood of it would be very low. If it gets examined in 3U, it's because it's being treated as harder 2U for the 3U student. You could probably get away with not studying it for a class test or something but it's your own risk you're taking if you avoid it for the trials/final HSC exam.

(Having said that, whilst a 4U student would potentially find it more agonising than a 2U student, it should also be easier to just rote learn it in case it does appear. It is technically far more boring to 4U students, but it's really just the same thing as integration by reduction formulae; we're just relying on recurrence. A select few from 2U papers is a reasonable amount in preparation for a 3U exam.)

[clovvy]

Seeing as though you decided to walk into the 4U territory (AKA Extension section) of Cambridge, are you familiar with logarithmic differentiation?

(If you are not familiar with it and don't know how to continue from here, please re-post in the 4U question thread for a full solution.)

That question caught my attention, so I would like to see the fully worked solution at the 4U thread (I can wait)

[RuiAce]

That question caught my attention, so I would like to see the fully worked solution at the 4U thread (I can wait)

Please re-post it there. I don't reply to questions that might look non-existent.

[owidjaja]

Hey guys,
I'm not entirely sure how to do b). I found the stationary points (x=0, x=3) but I'm not sure what x-values I'm supposed to sub in.

Thanks in advance

[RuiAce]

Hey guys,
I'm not entirely sure how to do b). I found the stationary points (x=0, x=3) but I'm not sure what x-values I'm supposed to sub in.

Thanks in advance

It's another bad maths in focus question - in the exam they'll always give you a starting point.

For this one, you could observe that x=0 gives you something positive but x=3 gives you something negative. So you could (perhaps, a bit angrily,) use the 'common-sense' guess and start at x=1.5 and keep working your way down. And then keep using Newton's method until you can get a 1 decimal place approximation.

Code: [Select]

1. Submit 1.5 into the calculator
2. Continue to do:   
    ANS - (2 ANS^3 - 9 ANS^2 + 7)/(6 ANS^2 - 18 ANS)

Edit: I just realised it wanted you to find "all" intercepts. So you could probably start at x=4 and x=-1 for the other ones. There's no real intuition on how to guess that though.

[Jane20]

Can someone help me with this binomial question please ?

In the expansion (1+x+kx^2)^9 the coefficient of x^2 is zero. What is the value of k ?

Thanks alot guys !

[RuiAce]

Can someone help me with this binomial question please ?

In the expansion (1+x+kx^2)^9 the coefficient of x^2 is zero. What is the value of k ?

Thanks alot guys !

Exercise: Fill in the missing details of all the reasoning above. If you have trouble with it, elaborate on where the trouble is.

[Jane20]

I got it now !
Thanks a lot

[Dragomistress]

How do you do this?

[RuiAce]

How do you do this?

\begin{align*}\int \cos^3\theta\,d\theta &= \int \cos \theta \cos^2\theta \, d\theta\\ &= \int \cos \theta (1-\sin^2\theta)\,d\theta\end{align*}
Now you should be able to make the substitution \( u = \sin \theta\), or reverse chain rule it.

[hassrax]

Hi, I had a question about finiding limits when graphing functions. I have learnt many methods for example, the polynomial divsion method, finding the limit at infinity ect.. I was wondering if you could give me a simple guide on how to find limits for all power functions, eg Horizontal and oblique asymptotes, not vertical because thats simple. Also, in terms of graphing, how do you know if it crosses the horizontal asymptote, because sometimes it does. Thank you.