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Advanced Higher Maths 2011-2012 : Discussion and Help

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I have a small issue with a vector question (year 2008, Qu 15--->http://www.sqa.org.uk/pastpapers/papers/papers/2008/AH_Mathematics_all_2008.pdf)

I am able to the whole question except the last bit, to get the acute angle, where I keep getting a negative number (therefore having cos(x)= -5/(55)sqrt) which would give me an obtuse angle... Where am I going wrong?
Reply 1161
Avatar for Slumpy
Slumpy
16
Original post by SameerM
I have a small issue with a vector question (year 2008, Qu 15--->http://www.sqa.org.uk/pastpapers/papers/papers/2008/AH_Mathematics_all_2008.pdf)

I am able to the whole question except the last bit, to get the acute angle, where I keep getting a negative number (therefore having cos(x)= -5/(55)sqrt) which would give me an obtuse angle... Where am I going wrong?


What've you got as the equation of the plane? And then what's your working?
I'll do a wee breakdown of my solutions:

a) -4i-2j+0k
b) Co-ordinates= (0,3,7) getting eqn of intersection as: 2i-4j-10k
c) To get the acute angle I used (-4,-2,0) and (1,3,-1)
Reply 1163
Avatar for Slumpy
Slumpy
16
Original post by SameerM
I'll do a wee breakdown of my solutions:

a) -4i-2j+0k
b) Co-ordinates= (0,3,7) getting eqn of intersection as: 2i-4j-10k
c) To get the acute angle I used (-4,-2,0) and (1,3,-1)


For a), that's not the equation of a plane, it's just some numbers. And, on looking(haven't yet done the Q), I'm pretty sure it's wrong.
Original post by Slumpy
For a), that's not the equation of a plane, it's just some numbers. And, on looking(haven't yet done the Q), I'm pretty sure it's wrong.


Sorry I didn't make myself clear when I said that, I tried the whole question: I marked it aswell, and everything was correct except for the last bit, about the acute angle.
The marking instruction is slightly bizarre as it explicitely says:

-6-4/2*(55)^sqrt (which I got)

and then goes to: 5/(55)^sqrt (without a negative...- which I don't get).
Reply 1165
Avatar for Slumpy
Slumpy
16
Original post by SameerM
Sorry I didn't make myself clear when I said that, I tried the whole question: I marked it aswell, and everything was correct except for the last bit, about the acute angle.
The marking instruction is slightly bizarre as it explicitely says:

-6-4/2*(55)^sqrt (which I got)

and then goes to: 5/(55)^sqrt (without a negative...- which I don't get).


Your normal to the first plane is (-4,-2,0). For simplicity I'd always just consider this as (4,2,0), which then gives you the right answer. Otherwise, just got with 180-the answer you get(think about the planes; they meet, and there are 2 angles between them, an obtuse and an acute one, the sum is 180 degrees).
Does anyone know where to find the "understanding standards" from the SQA for last year? Both my maths teacher and my business teacher told us to look at them, but I can't seem to find them on the SQA site...
Original post by Slumpy
Your normal to the first plane is (-4,-2,0). For simplicity I'd always just consider this as (4,2,0), which then gives you the right answer. Otherwise, just got with 180-the answer you get(think about the planes; they meet, and there are 2 angles between them, an obtuse and an acute one, the sum is 180 degrees).


Yeah now that I looked at the question again it's actually told me to give the acute angle regardless of me attaining a negative answer and thus having an obtuse angle...
And your right! Thanks for that explanation at the end it's given me a better understanding of planes.
Reply 1168
Avatar for Calum14
Calum14
a paper lik 2008 or 2010 would be good :P

just hope inverse of 3x3 doesnt come up :P
Yay, finally properly get vectors. It's actually a pretty easy part of the course if you learn it properly. :tongue:

Edit:

OK, if I had an equation like z^3 = -8, could I use z^3 = 8e^(i*pi) = 8e^(i*3pi) = 8e^(i*5pi) ?

I much prefer doing it that way, but I'm not sure the SQA would be happy.
(edited 11 years ago)
Like 23 hours to go ! :O
Original post by laughylolly
Like 23 hours to go ! :O


Shut up

D:
Original post by JordanR
Shut up

D:


Okay, I'm sure you'll do fine though! I'm just hoping no really horrible like 6+ marker comes up.
Yeah I'm feeling alright about it. I keep panicking and thinking I don't know things, then doing questions on them and being like, "oh, I do know that!" So hopefully that remains constant.

If intersection of 3 planes comes up I'm not gonna be happy though. :tongue:

Edit: also just found out that my calculator can solve equations like z^3 = 8. Happy days.
(edited 11 years ago)
Original post by JordanR

Edit: also just found out that my calculator can solve equations like z^3 = 8. Happy days.

Is it a Casio? Mines has a complex mode but I have no idea how to use it. I type in 8^{1/3} and it only returns 2... :frown:
Original post by Quintro
Is it a Casio? Mines has a complex mode but I have no idea how to use it. I type in 8^{1/3} and it only returns 2... :frown:


Yes. FX-991ES PLUS.

To solve something like z^3 = -8 hit "mode", then press 5 for eqn mode. Then enter in your equation (in this case, z^3+8 = 0) into the appropriate equation "solver" in the list (it'll be number 4).

:smile:
Original post by JordanR
Yes. FX-991ES PLUS.

To solve something like z^3 = -8 hit "mode", then press 5 for eqn mode. Then enter in your equation (in this case, z^3+8 = 0) into the appropriate equation "solver" in the list (it'll be number 4).

:smile:

Ooh, that's the same calculator as mine. I get slagged for it because I decided to pay an extra few quid for it compared to the dark blue one everyone else has :tongue:

OH MY GOD IT WORKS that is the best feature ever! Thanks haha!
Original post by Quintro
Ooh, that's the same calculator as mine. I get slagged for it because I decided to pay an extra few quid for it compared to the dark blue one everyone else has :tongue:

OH MY GOD IT WORKS that is the best feature ever! Thanks haha!


You can also do simplifications of complex numbers and stuff like that with it too. So when you're outside your exam tomorrow, just before you go in, show them all that stuff. :tongue:
Original post by JordanR
You can also do simplifications of complex numbers and stuff like that with it too. So when you're outside your exam tomorrow, just before you go in, show them all that stuff. :tongue:

They will regret ever laughing at my calculator muahaha :colone:
(edited 11 years ago)
Original post by Quintro
They will regret ever laughing at my calculator muahaha :colone:


If you want to be a complete ass, show them it solves the inverse of a 3x3 matrix, does gauassian elimination, vector dot and cross products, matrix operations, conversions between number systems, definite integration, differentiation at a point...


:biggrin:

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