ATAR Notes: Forum
VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: VCE_2012 on January 10, 2012, 03:34:41 pm
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Hey veteran "Specialist-ers" which topic or subtopic in specialist has posed the most challenge?
By challenge I refer to a topic that baffled you during the exams or a topic that demands more time to understand.
And for those who found specialist an absolute breeze, I say to them "step back...."
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Vector Proofs.
Do not understand them at all.
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trig functions. could not for the life of me figure out those silly transformations. D:
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trig functions. could not for the life of me figure out those silly transformations. D:
And still got a 50 :O
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hahahah complex numbers, they can come up with really creative questions, i lost 2 marks on a complex number question which i could do as i was walking out of the room, god dammit
then there's Input/Output, Concentration/Mixing, those type problems. Another 2 marks lost
Hmph.
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hahahah complex numbers, they can come up with really creative questions, i lost 2 marks on a complex number question which i could do as i was walking out of the room, god dammit
then there's Input/Output, Concentration/Mixing, those type problems. Another 2 marks lost
Hmph.
differential equations also D:
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Okay, change of pace. Whats the easiest topic?
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Complex Numbers and vector proofs, probably because I hadn't come across anything like that before. It wasn't just harder material, but new concepts and new basics that I had to grasp.
EDIT: In response to the hardest topic.
Easiest topic I would have to say was calculus since we've come across that before, it was just a little bit of a level up from previous things.
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If you learn from Dr. He and Dr. G, complex numbers is the hardest.
It also use to be the hardest topic but VCAA made it easier these few years.
To this day I still don't understand some vector proofs and didn't bother to attempt to understand it before the exam but thank god the really hard ones weren't on it.
Statics can be quite hard if you don't do physics since specialist kind of over complicates it a bit.
Graph sketching is pretty retarded some times.
Personally complex numbers is most challenging for me.
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inflow/outflow are the hardest
and the calculus becomes quite easy if you do heaps of practice questions
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Vector proofs hardly appears on the exams though right? They can be tricky but even so, they usually only give really simple questions about this. Aside from this, I'd say worded problems in general always seem out to trick you! :(
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If you learn from Dr. He and Dr. G, complex numbers is the hardest.
It also use to be the hardest topic but VCAA made it easier these few years.
To this day I still don't understand some vector proofs and didn't bother to attempt to understand it before the exam but thank god the really hard ones weren't on it.
Statics can be quite hard if you don't do physics since specialist kind of over complicates it a bit.
Graph sketching is pretty retarded some times.
Personally complex numbers is most challenging for me.
Spesh overcomplicates statics? Are you sure it's not just that physics oversimplifies statics? :P
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Okay, change of pace. Whats the easiest topic?
Euler's method
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Okay, change of pace. Whats the easiest topic?
Euler's method
LOL just need to learn one CAS line and you're done.
Though I find that most the stuff you also do in Methods a bit isn't too hard to understand.
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Okay, change of pace. Whats the easiest topic?
Euler's method
LOL just need to learn one CAS line and you're done.
Though I find that most the stuff you also do in Methods a bit isn't too hard to understand.
I used a program for spesh euler to speed up questions where they ask for say y4 or y5. Remember playing around with it and going up to y1500 one time. But yeh I still knew the one line equation for the tech-free part.
EDIT: I can up it in the resource thread if everyone thinks its a good idea.
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I never learnt euler's method until I saw it in a past exam (very close to the actual exam) and I was like wtf is this...
Anyway, I found integration to be the easiest topic for me, probably because I liked it. I ended up doing pretty much all the integration exercises in my head.
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When you talk about vector proofs, are you talking about these sorts of problems:
"Prove that the midpoint of the hypotenuse of a right-angled triangle is equidistant from the three vertices of the triangle."
Or are there other sorts of vector proofs?
Because I can't really picture seeing a question like that on a SAC/exam...
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Or are there other sorts of vector proofs?
Because I can't really picture seeing a question like that on a SAC/exam...
I'm talking about crazy MHS Dr G vector proofs that have like 5 variables in three languages and have like parts a) -> h)... Those are vector proofs.
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Or are there other sorts of vector proofs?
Because I can't really picture seeing a question like that on a SAC/exam...
I'm talking about crazy MHS Dr G vector proofs that have like 5 variables in three languages and have like parts a) -> h)... Those are vector proofs.
Can you please show me an example of a question?
All parts to the question.
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I'm talking about crazy MHS Dr G vector proofs that have like 5 variables in three languages and have like parts a) -> h)... Those are vector proofs.
Didn't the many number of parts make it easier because it told you how to do everything step by step?
and for mr special at specialist
From 2010 MHS SAC 4 Tech Active
Question 4
Two particles are moving in 3D-space. Both particles have non-intersecting straight line
paths. The position vector of particle A is given by
r(t) = i − 2j + t(2i + 3j − 4k)
where the vector 2i + 3j − 4k is parallel to the path of A.
The position vector of particle B is given by
s(t) = j + t(3i + j − 5k)
where the vector 3i + j − 5k is parallel to the path of B.
Take all distances to be in metres and t is time in seconds.
(a) The vector a = xi + yj + zk where x > 0 is a unit vector perpendicular to both
2i + 3j − 4k and 3i + j − 5k. Find the values of x, y and z.
(b) Find the coordinates of the positions for both particles at t = 0.
(c) Hence, find the minimum distance between the path of particle A and the path of
particle B.
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Made it harder for me... :(
And, that question is vector calculus, not a proof. I could do those ones fine :)
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Can any MHS'er Spesh veterans upload their practice spesh sacs and spesh application tasks :P?
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And, that question is vector calculus, not a proof. I could do those ones fine :)
wtf even part c?? you tank pi ;)
and where was there calculus?
and isn't part c a vector proof question as you need to show or prove your final result? (unlike Doctor G's solutions which assumed it was all trivial D: )
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And, that question is vector calculus, not a proof. I could do those ones fine :)
wtf even part c?? you tank pi ;)
and where was there calculus?
and isn't part c a vector proof question as you need to show or prove your final result? (unlike Doctor G's solutions which assumed it was all trivial D: )
Well, there was no calculus in this question, but it was of that type (position vectors, distances, etc.). The problems I could never do were with random shapes and making your own vectors to prove something random :(
Haha, there was a question like part c) in Dr G's spesh book, so I could do that :)
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Vector proofs definitely the hardest
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'Vector proofs' is just the vce dumbed-down version of a specific subset of linear algebra, you guys most of the time simply use vectors to prove Euclidean geometry (http://en.wikipedia.org/wiki/Euclidean_geometry) results. There are many many many non-geometric theorems which are proven using linear algebra techniques (such as using vector notation and so on), for example, showing unique basis (http://en.wikipedia.org/wiki/Basis_%28linear_algebra%29) representation: If S a set of vectors and is a basis for a vector space V, then every vector in V can be expressed in one unique way.
Now since VCE doesn't teach you any mathematics from a pure perspective, not suprised why so many kids find 'vector proofs' so hard.
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dumbed-down version of a specific subset of linear algebra
and what specific subset of linear algebra would that be?
There are many many many non-geometric theorems which are proven using linear algebra techniques (such as using vector notation and so on), for example, showing unique basis (http://en.wikipedia.org/wiki/Basis_%28linear_algebra%29) representation: If S a set of vectors and is a basis for a vector space V, then every vector in V can be expressed in one unique way.
Now since VCE doesn't teach you any mathematics from a pure perspective, not suprised why so many kids find 'vector proofs' so hard.
Really, are you saying you need to know linear algebra to do vector proofs? I don't think so. You're provided with enough tools(dot product etc.) and I've seen good students here not knowing linear algebra but being decent at vector proofs. Again as the saying goes: you don't need an atomic bomb to kill an ant.
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Really, are you saying you need to know linear algebra to do vector proofs?
no, i never said you need to know linear algebra to do vector proofs, where did i say that? I said there are more to vector proofs than just knowing a few properties and applying them to geometric proofs.
I've seen good students here not knowing linear algebra but being decent at vector proofs
ok. i never mentioned students who don't know linear algebra won't be able to do vector proofs?
just saying it's better to understand more applications with vectors rather than knowing just some, confidence rises with more knowledge, you are correct that students are able to conduct proofs with the tools necessary in spesh, but again, a passionate student would agree that it's better to know more than less
dumbed-down version of a specific subset of linear algebra
and what specific subset of linear algebra would that be?
didn't define subset very well, what i was meant to convey to students was that vectors can be utilised in different ways, ie, you're never taught in vce to consider vectors as a n tuple http://en.wikipedia.org/wiki/Linear_algebra#Vectors_as_n-tuples:_Matrix_Theory (and even if you were, you probably never learnt it from the bigger picture) where as in linear algebra you are exposed to these new ideas utilising vectors in different ways, all of this helps the student gain more confidence which would help them improve overall when dealing with vectors.
Again as the saying goes: you don't need an atomic bomb to kill an ant.
well you go use an atomic bomb to kill an ant then, don't think i ever said you had to use linear algebra techniques to do vce vector proofs.
seems you have misread quite a bit :\
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The most challenging aspect of spesh, IMO was understanding what everything meant. I did horribly at spesh unit 1 at MHS, and dropped it for a more mathematic friendly subject - Accounting...
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Ok then, we'll just wait until next semester until you start talking about how a passionate student would also picture vectors in infinite dimensional Hilbert Spaces and study bounded linear functionals on them, or consider them as just a special case of modules over a PID.
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Ok then, we'll just wait until next semester until you start talking about how a passionate student would also picture vectors in infinite dimensional Hilbert Spaces and study bounded linear functionals on them, or consider them as just a special case of modules over a PID.
so what i was talking about was simply directed towards a passionate vce kid, when did this turn into discussion regarding a passionate uni kid?
and yes if i were the passionate uni student id probs do some research into the bigger picture, but that's another matter, for now this is vce, and i suspect that a passionate spesh student wouldn't get mind fucked if they checked out some linear algebra, rather i think learning a bit of elementary linear algebra is a good supplement to year 12 spesh, especially considering students are also taught vector calculus later on in the course, i think some linear algebra ideas would be quite helpful.
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That's my point, you said that a passionate vce kid would learn about n-tuples/bases... but why stop there? how about Hilbert Spaces and modules over a PID?
Now since VCE doesn't teach you any mathematics from a pure perspective, not suprised why so many kids find 'vector proofs' so hard.
Again, "many kids" suggests more than just the one off TT who loves maths.
\endposting (let's not stray too off topic)
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That's my point, you said that a passionate vce kid would learn about n-tuples... but why stop there? how about Hilbert Spaces and modules over a PID?
Now since VCE doesn't teach you any mathematics from a pure perspective, not suprised why so many kids find 'vector proofs' so hard.
Again, "many kids" suggests more than just the one off TT who loves maths.
\endposting (let's not stray too off topic)
lol, shush you, stop teasing me already ;(
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rather i think learning a bit of elementary linear algebra is a good supplement to year 12 spesh
actually this is not so bad, would actually finally clear up the 5 page threads on linear independence.
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rather i think learning a bit of elementary linear algebra is a good supplement to year 12 spesh
actually this is not so bad, would actually finally clear up the 5 page threads on linear independence.
LMAO, true that lol
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are there any 'crazy vector proofs' in the actual exam? i finished exercise 2A of essentials for vectors and I already found it a bit hard :( did anyone else feel the same way =O is essentials vectors questions way easier than the ones on exam? or the same level?
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are there any 'crazy vector proofs' in the actual exam? i finished exercise 2A of essentials for vectors and I already found it a bit hard :( did anyone else feel the same way =O is essentials vectors questions way easier than the ones on exam? or the same level?
dw about it lol, there's hardly any on the exam and even if there are, it's normally a pretty easy one ;)
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are there any 'crazy vector proofs' in the actual exam? i finished exercise 2A of essentials for vectors and I already found it a bit hard :( did anyone else feel the same way =O is essentials vectors questions way easier than the ones on exam? or the same level?
dw about it lol, there's hardly any on the exam and even if there are, it's normally a pretty easy one ;)
:D
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I like linear algebra (Y)
btw, i wonder if we put TT and kamil in a cage and got them to out-maths eachother, who would win? :\
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rather i think learning a bit of elementary linear algebra is a good supplement to year 12 spesh
actually this is not so bad, would actually finally clear up the 5 page threads on linear independence.
The answer is UMEP Maths.
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are there any 'crazy vector proofs' in the actual exam? i finished exercise 2A of essentials for vectors and I already found it a bit hard :( did anyone else feel the same way =O is essentials vectors questions way easier than the ones on exam? or the same level?
I did really bad on vectors in GMA, but i found 2A to be pretty good actually. Essentials has really dodgy explanations so i use maths quest for explanations and I think it makes it a lot easier. I don't understand the dot product though, in both essentials and maths quest.