The most challenging aspect of Specialist

[dc302]

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.

[Special At Specialist]

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...

[pi]

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.

[Special At Specialist]

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.

Moderator action: removed real name, sorry for the inconvenience

[hargao]

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.

Moderator action: removed real name, sorry for the inconvenience

[pi]

Made it harder for me...

And, that question is vector calculus, not a proof. I could do those ones fine

[abd123]

Can any MHS'er Spesh veterans upload their practice spesh sacs and spesh application tasks ?

[hargao]

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: )

Moderator action: removed real name, sorry for the inconvenience

[pi]

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

Moderator action: removed real name, sorry for the inconvenience

[k3nshiinx]

Vector proofs definitely the hardest

[TrueTears]

'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.

[kamil9876]

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.

[TrueTears]

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 :\

[aes_999]

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...

[kamil9876]

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.