VCE Methods Question Thread!

[Irving4Prez]

Is there a rote method for calculating the shortest distance from the origin to a point on the graph? I spent 5 minutes to get the answer whereas another student managed to do it considerably faster...

[alchemy]

Is there a rote method for calculating the shortest distance from the origin to a point on the graph? I spent 5 minutes to get the answer whereas another student managed to do it considerably faster...

Example?

[M_BONG]

(Re-post)
Do Methods examiners take a mark off if you don't simply fractions?

Ie Can we leave 5/60 as it is? Or does it have to go down to 1/12 (cuz it's not immediately obvious that it's simplifiable.. for me, at least)

Also, just confirming: no rationalising is required in Methods; but it's required in Spesh?

[IndefatigableLover]

(Re-post)
Do Methods examiners take a mark off if you don't simply fractions?

Ie Can we leave 5/60 as it is? Or does it have to go down to 1/12 (cuz it's not immediately obvious that it's simplifiable.. for me, at least)

I would think they would take a mark off if you don't simplify fractions to its simplest form. Mainly when you have questions they'll ask to give your answer in simplest form and to me that means simplifying till you can't anymore.. if it's with the case you put up there (5/60 - 1/12) then I would think they'd take off a mark.. just what I think though :|

[paper-back]

I would think they would take a mark off if you don't simplify fractions to its simplest form. Mainly when you have questions they'll ask to give your answer in simplest form and to me that means simplifying till you can't anymore.. if it's with the case you put up there (5/60 - 1/12) then I would think they'd take off a mark.. just what I think though :|

Apparently they do, according to our teacher

[swagsxcboi]

Is there a rote method for calculating the shortest distance from the origin to a point on the graph? I spent 5 minutes to get the answer whereas another student managed to do it considerably faster...

do you mean by using pythag?

[Irving4Prez]

Example?

Last year's Written Examination 2, Q 4b

http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2013/2013mmcas2-w.pdf

do you mean by using pythag?

I had a look at the solutions and I'm pretty sure they used pythag. However, wouldn't the hypotenuse be the longest distance from the origin and a point on the graph?

[swagsxcboi]

when I've sketched a graph on my CAS, how do I find the point at an exact value?  eg. at x=pi

[keltingmeith]

Also, just confirming: no rationalising is required in Methods; but it's required in Spesh?

No rationalising is required in either unless they ask you to. For example, sometimes they'll ask you to put something in the form , which is essentially them asking you to rationalise. Otherwise, though, you're fine to leave your surd in whatever way you want.

Only exception I can think of is complex numbers in specialist - you should ALWAYS rationalise complex numbers.

[swagsxcboi]

Last year's Written Examination 2, Q 4b

http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2013/2013mmcas2-w.pdf

I had a look at the solutions and I'm pretty sure they used pythag. However, wouldn't the hypotenuse be the longest distance from the origin and a point on the graph?

LOL I got no clue what's going on 

[EspoirTron]

Oooh, so basically limits is sort of saying like what the value of f(x) is approaching if you take a number really close to x? Is if possible for a function to not have a limit?

Thanks so much, it cleared up a lot of things for me

Yep, that's the general idea! Yes, it is possible for a function to not have a limit. This occurs at places like an endpoint. For example, if I am looking at a graph and beginning my view from the right-hand side, where this graph is continuous on the interval [a,b], then the right-sided limit would not exist at the value x=b since essentially there is nothing of the graph on that side. I hope that helps!

[keltingmeith]

when I've sketched a graph on my CAS, how do I find the point at an exact value?  eg. at x=pi

For a TI-nspire:

Menu ---> 5: Trace ---> 1: Graph Trace, then enter your value and push equals.

I'm not sure about the Classpad, sorry.

[swagsxcboi]

For a TI-nspire:

Menu ---> 5: Trace ---> 1: Graph Trace, then enter your value and push equals.

I'm not sure about the Classpad, sorry.

yep nspire. absolute legend!

[swagsxcboi]

The sum of two positive numbers is 8. Find the numbers if the sum of the cube of one and the square of the other is a minimum.

[b^3]

If the two numbers are and then for the sum of the two to be , we have , so . Now denote a function that is the sum of one and the cube of the other, lets say , . Now you can substitute eq into eq to get it in terms of only, and then note that it will be a minimum at the turning point (as the domain will be restricted to satisfy ). Then you can differentiate that and set it to zero to find the value(s) of , sub back to find the values of and whether they fit the constraints and pick the set that satisfy both.

Spoiler

https://www.desmos.com/calculator/q3wgxdesid