1,000,000 Question Thread :D

[kenhung123]

Find the value of m for which the simultaneous equations

Has:
Infinite number of solutions:

I got







How do I eliminate +5?

[TrueTears]

Sub it in.

You get 3x+5y=5

7x+5y=5

Which does not give infinite number of solutions.

[kenhung123]

Thanks

[kenhung123]

Would you define 2 equations with same gradient, x and y intercepts one which has infinite solutions?

[NE2000]

Would you define 2 equations with same gradient, x and y intercepts one which has infinite solutions?

Yes (as in they are the same so they intersect over their entire length).

Not sure if you've done much integration and stuff yet but the derivative is the gradient but you can think about it this way.

If where m(x) is the gradient and - given that the derivative gives the gradient.

Then where M(x) is an antiderivative of m(x) and where d is a constant.

Now if they both pass through a single point (so even if you only know that they pass through the same y-intercept)...Let's call this point (a,b)









Hence
and

So f(x) and g(x) are equal.

So any two equations with same gradient over all x which coincide at any one point are equal and intersect at every point

[kenhung123]

Do we need to learn simultaneous equations with more than 2 variables solving by matrices and lambda substitution?
i.e. how to solve x-y+z=4 and -x+y+x=6 in terms of a parameter of lambda

[kyzoo]

For Methods no, I don't even know what a lambda is and I did Methods 3/4 this year. But then again I did NON-CAS and that's not around next year.

[Gloamglozer]

For Methods no, I don't even know what a lambda is and I did Methods 3/4 this year. But then again I did NON-CAS and that's not around next year.

It is in the CAS course but I've never seen it asked in an exam though.

[TrueTears]

Yeah I've never ever met a question regarding parameters in any methods trial exam or VCAA exam.

[kenhung123]

Do you need to show arrows on both ends when drawing hyperbolas? As examiners emphasize that you must not show your graph curving away from the asymptotes/

[kenhung123]

Yeah I've never ever met a question regarding parameters in any methods trial exam or VCAA exam.

Ok, don't know why they included it in essentials. It seemed weird.

[/0]

Probably just a bit of breadth on matrix methods, or perhaps to introduce you to trig solutions with parameters

[TrueTears]

Yeah I've never ever met a question regarding parameters in any methods trial exam or VCAA exam.

Ok, don't know why they included it in essentials. It seemed weird.

Who knows, maybe next year they might put a question on it, you might as well learn it.

[kyzoo]

They have tons and tons of stuff in Essentials that isn't on the exam. E.g. proof for differentiation formulas, proof for Var(aX+b) = a^2Var(X), etc

I reckon they're trying to be as complete as they can, include everything that's related. But that's why I like it - it means I can fully understand stuff whereas I couldn't if I was just given a sheet of the formulas needed for Methods.

[Gloamglozer]

Yeah I've never ever met a question regarding parameters in any methods trial exam or VCAA exam.

Ok, don't know why they included it in essentials. It seemed weird.

Who knows, maybe next year they might put a question on it, you might as well learn it.

Take the god's/goddess' (take whichever one "floats your boat") advice on this one.  Definitely cover your ass with VCE exams.