HSC Stuff > HSC Mathematics Extension 2
4U Maths Question Thread
jakesilove:
--- Quote from: katherine123 on February 17, 2016, 11:28:12 pm ---For the poly ques how do u find the leading coefficient? I only know that there are 2 known roots
and for the trig ques i dont know how to simplify it after implicitly differentiating
please help thank you
--- End quote ---
Katherine, these questions were insanely difficult. I wasn't even able to properly get the last one (I'm incredibly tired right now, so I'll blame it on that). Still, as I'll explain that second question should NOT be a multiple choice. If you find yourself spending too much time on a multiple choice, MOVE ON, because it isn't worth the marks. Still, my head hurts and I'm going to go sleep...
If someone else can come up with a better, proper answer please feel free to contribute!
Spencerr:
exsiny + eysinx = 0
After differentiating with respect to x and grouping the dy/dx onto one side we get
dy/dx = -(exsiny + eycosx) / (excosy + eysinx)
Going back to the main equation that they give us (this was the tricky part) Rearranging we get.
exsiny = - eysinx
Then subbing that in to:
dy/dx = -(exsiny + eycosx) / (excosy + eysinx)
We get
dy/dx = -(-eysinx + eycosx) / (excosy - exsiny)
= (eysinx - eycosx) / (excosy - ex siny)
Factorise out the ey from the top and ex from the bottom and you get the answer
This was a pain to type up haha, what program or website do you use jake to post the solutions?
brenden:
--- Quote from: diiiiiiiii on February 18, 2016, 12:15:11 pm ---exsiny + eysinx = 0
After differentiating with respect to x and grouping the dy/dx onto one side we get
dy/dx = -(exsiny + eycosx) / (excosy + eysinx)
Going back to the main equation that they give us (this was the tricky part) Rearranging we get.
exsiny = - eysinx
Then subbing that in to:
dy/dx = -(exsiny + eycosx) / (excosy + eysinx)
We get
dy/dx = -(-eysinx + eycosx) / (excosy - exsiny)
= (eysinx - eycosx) / (excosy - ex siny)
Factorise out the ey from the top and ex from the bottom and you get the answer
This was a pain to type up haha, what program or website do you use jake to post the solutions?
--- End quote ---
Hey dii!
Try the tex code :)
--- Code: ---[tex][/tex]
--- End code ---
When you type things in between it it looks like this.
It's super easy to learn, here are a list of resources: List of LaTeX Resources
In particular, this one is great for learning: LaTeX typeset in Maths boards
jakesilove:
--- Quote from: diiiiiiiii on February 18, 2016, 12:15:11 pm ---exsiny + eysinx = 0
After differentiating with respect to x and grouping the dy/dx onto one side we get
dy/dx = -(exsiny + eycosx) / (excosy + eysinx)
Going back to the main equation that they give us (this was the tricky part) Rearranging we get.
exsiny = - eysinx
Then subbing that in to:
dy/dx = -(exsiny + eycosx) / (excosy + eysinx)
We get
dy/dx = -(-eysinx + eycosx) / (excosy - exsiny)
= (eysinx - eycosx) / (excosy - ex siny)
Factorise out the ey from the top and ex from the bottom and you get the answer
This was a pain to type up haha, what program or website do you use jake to post the solutions?
--- End quote ---
Wow, that's beautiful! I initially did the same thing Diiiiiii, but didn't think to substitute the original equation back in! Absolute genius.
I literally use Word, then screenshot my response and upload it to Imgur so I can upload it to the forum. On Word, there is an "equation" feature which is actually very intuitive. I would highly recommend it; it's super useful!
Or, use to Tex code! I'm not as proficient at that, but it is also quite intuitive.
Again, thanks for the brilliant answer.
Jake
RuiAce:
Also, to ALL MX2 students I suggest purchasing the calculator CASIO fx-100 AU PLUS for it's ability to do COMPLEX NUMBER OPERATIONS in the exam! This calculator is indeed, board approved!
For the multiple choice question, whilst the method provided by Jake is essentially what a short response requires, multiple choice can be hastened by simply SUBSTITUTING x=1-2i directly in! If what I typed into the calculator is right, A, B and C ALL don't equate to 0.
Multiple choice tricks.
FURTHER EDITING: In fact, there is one last trick. A and B are automatically wrong because the last root has to be a fraction! Not an integer! Non integral (adjective for integer in this case) roots are the only cause the leading to coefficient to deviate from 1.
In the long method, this means that the (ax+b) could be SAFELY written as (x+b)! Then, only constants have to be equated.
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