VCE Methods Question Thread!

[qazser]

No matter how much you love the writer of Essentials/how much he is an examiner, I would defs not say that Essentials is the minimum you must know.


I doubt they'd give it to you outright, but I reckon they could lead you into it. (Eg, part a would be "write in this form", then part b would describe the transformations)

Hehe

[huehue]

This looks absolutely delightful
To do this, you need to make both sides look like they're the result of a translation.

Part a:
If you're going to translate x^3 to the left or right, you're going to get (x+a)^3 = x^3 + 3ax^2 + 3a^2 x + a^3
So let's match this up with the RHS
1/3 x^3 - 3x^2 + 9x - 13 = 1/3 (x^3 - 9x^2 + 27x) - 13
If you look carefully, this is just 1/3 ((x-3)^3 - 27) - 13, which is 'completing the cube' so to speak. Hence, 1/3 x^3 - 3x^2 + 9x - 13 = 1/3 (x-3)^3 - 13 - 27/3
You should be able to identify the translations now from x^3/3 (3 to the right, -13 - 27/3 down)

Part b:
2/x to (-3x+14)/(x-4) = -3 + 2/(x-4)
Does that simplification sort of make the translations clearer? Translate 4 to the right and 3 down

wait, for part b, how did you get -3 +2/(x-4)? thanks.

[keltingmeith]

wait, for part b, how did you get -3 +2/(x-4)? thanks.

This can also be done by inspection:

[qazser]

This can also be done by inspection:

not everyone is a genius Euler 

[keltingmeith]

not everyone is a genius Euler 

This is a technique used by at least 80% of the people on here. Got nothing to do with me being smart.

In fact, usually I'm the one reminding people of long division, not the other way round.

[friedchromosome]

Could someone please give detailed answers to this?
A building block is sketched on a cartesian plane. The boundaries of the block are x=0, y=0 and y= -s/128(x-16)^2(x-4)+50. All lengths are in metres.
1. sketch the graph of the building showing the turning points and axes intercepts
2. use a triangle to find the best estimate of the area of the block
3 use calculus to find the area of the block

[keltingmeith]

Could someone please give detailed answers to this?
A building block is sketched on a cartesian plane. The boundaries of the block are x=0, y=0 and y= -s/128(x-16)^2(x-4)+50. All lengths are in metres.
1. sketch the graph of the building showing the turning points and axes intercepts
2. use a triangle to find the best estimate of the area of the block
3 use calculus to find the area of the block

... What's s?

[Caesius]

Here is (IMO) a first-principles way of solving this question.
When do you have no or infinitely many solutions? When the two linear equations, representing straight lines, have the same slope.
So as the slope is related to the y coefficient/x coefficient, we can say m/3 = 5/(m+2) -> m(m+2) - 15 = 0
Solve for m; you should find m = 3 or m = -5
Now, plug in both of these m values. If you get identical equations, you have infinitely many solutions (think about it; the lines y = x and 2y = 2x intersect at infinitely many points)
If you have lines with the same slope but different intercepts, they never intersect.
This is the easiest way of thinking about it if you're new to this kind of question. Using matrices is actually not necessary at here. Try the same thing with the other question.

Thank you!

[Biology24123]

... What's s?

Looks like a typo

[friedchromosome]

... What's s?

apologies that was 5 not s

[qazser]

Could a kind soul do Q12 please? Do i complete the square, because that will give a perfect square or does the whole eqn have to be a perfect square. Attached below is pic of question

Thanks in advance,
Qazser

[keltingmeith]

Could a kind soul do Q12 please? Do i complete the square, because that will give a perfect square or does the whole eqn have to be a perfect square. Attached below is pic of question

Thanks in advance,
Qazser

You could do that, but that's going to be a lot of trouble!! Hint: if something if a perfect square, what value is its discriminant? You might want to consider the perfect square (x-a)^2

[nadiaaa]

Hey yall,
im really really struggling with identifying the domain and the range of graphs.
Is there like a fool proof method that i can apply to every graph i see??
Or can someone just tell me how to find the domain and range??
Im just super confused.. lol
thanks in advance

[keltingmeith]

Hey yall,
im really really struggling with identifying the domain and the range of graphs.
Is there like a fool proof method that i can apply to every graph i see??
Or can someone just tell me how to find the domain and range??
Im just super confused.. lol
thanks in advance

Easiest way to find the range is to just graph the function and see what y values it takes on. This might also work for the domain if you're good at memorising graphs!

Otherwise, for the domain, you just need to look for "problem areas". The main two are the following:



In the first case, you can't divide by 0, and so the domain won't be defined when f(x)=0. For the second, you can't square root a negative number, and so the domain won't be defined when g(x)<0.

[nadiaaa]

Easiest way to find the range is to just graph the function and see what y values it takes on. This might also work for the domain if you're good at memorising graphs!

Otherwise, for the domain, you just need to look for "problem areas". The main two are the following:



In the first case, you can't divide by 0, and so the domain won't be defined when f(x)=0. For the second, you can't square root a negative number, and so the domain won't be defined when g(x)<0.

Thank you so much