VCE Methods Question Thread!

[S200]

Thanks all.

This question was a part of a VCE Methods booklet that was downloaded by another member of my methods class.
The question asked us to sketch the graph, but didn't mention with or without a calculator.

We assumed that it would be without.
So this should definitely not be on our exam?

[keltingmeith]

So this should definitely not be on our exam?

Absolutely not.
It shouldn't even be on a specialist exam, tbqh.

[RuiAce]

Absolutely not.
It shouldn't even be on a specialist exam, tbqh.

Did you just provide evidence that spesh isn't even at MX1's level

[Sine]

definitely not a methods question but possible (but not likely) to be on a spesh exam.

[snowisawesome]

I wouldn't say it "seperates people" I think across Sacs + 120 exam marks that seperates people organically enough at least on the level of 30 - 40. People could get the last question wrong and still get 47+ so you can't say anything on the final result based on a single quesiton.

Graph the function if you aren't too sure of the range, it's a reciprocal function (that may help graphing)

Can you please elaborate on how the reciprocal function works?
Also, do you know how to sketch the graph of y = cube root of x without a calculator?
Thanks

[Bri MT]

Can you please elaborate on how the reciprocal function works?
Also, do you know how to sketch the graph of y = cube root of x without a calculator?
Thanks

 cube root of x is the same thing as saying   x^1/3 , and you can learn rules for x^p/q      if you experiment with your CAS you should be able to see rules they have in common, such as passing through (1,1). When q>p draw the shape based on your experience with sqrt(x).    I had a list of rules but I can't find it right now unfortunately

[snowisawesome]

cube root of x is the same thing as saying   x^1/3 , and you can learn rules for x^p/q      if you experiment with your CAS you should be able to see rules they have in common, such as passing through (1,1). When q>p draw the shape based on your experience with sqrt(x).    I had a list of rules but I can't find it right now unfortunately

So would the negative cube root of x basically just be the graph of x^1/3, but reflected?

[Bri MT]

So would the negative cube root of x basically just be the graph of x^1/3, but reflected?

if y1= f(x)  and y2= -f(x)     y2 and y1 will be reflections of eachother
if y3 = f(x) and y4= f(-x)     y3 and y4 will be reflections of eachother

so yes 

[Sine]

Can you please elaborate on how the reciprocal function works?
Also, do you know how to sketch the graph of y = cube root of x without a calculator?
Thanks

hmm it's not really in the methods course so i'll go through very breifly.

A reciprocal function is in the form f(x) = 1/g(x) so basically "1 over a function" we can use g(x) to sketch f(x) such as when g(x) = 0, f(x) has asymptotes. When g(x) = 1, f(x) = 1.

[snowisawesome]

hmm it's not really in the methods course so i'll go through very breifly.

A reciprocal function is in the form f(x) = 1/g(x) so basically "1 over a function" we can use g(x) to sketch f(x) such as when g(x) = 0, f(x) has asymptotes. When g(x) = 1, f(x) = 1.

So do you know any other way to find the range of 1/(x^2-4) without graphing?
I graphed it, but still found it confusing to find the range, and it could come up in exam 1?

[Bri MT]

So do you know any other way to find the range of 1/(x^2-4) without graphing?
I graphed it, but still found it confusing to find the range, and it could come up in exam 1?

It could very easily come up in exam one. If you know the general shape use that, to draw a rough sketch and see the relationship between x and y and how that changes over the specified domain (eg when x increase does y increase or decrease). It's then very simple o find the range, just sub and solve

In situations where you don't know the general shape you can use differentiation to find when they will be increasing or decreasing

[snowisawesome]

It could very easily come up in exam one. You know it's a truncus and the general shape of those, so draw a rough sketch and see the relationship between x and y and how that changes over the specified domain (eg when x increase does y increase or decrease). It's then very simple o find the range, just sub and solve

Will there always be a specified domain (regardless of whether it's in exam 1 or exam 2)?

[Bri MT]

Will there always be a specified domain (regardless of whether it's in exam 1 or exam 2)?

The domain can be R in either exam

[snowisawesome]

Not exactly related to methods but can someone who does both spesh and methods end up with below 40 raw for methods? Or do they have a much higher chance of getting 40+ raw in methods than someone who only does methods? (feel free to move this to appropriate subforum if needed mods)

[Shadowxo]

Not exactly related to methods but can someone who does both spesh and methods end up with below 40 raw for methods? Or do they have a much higher chance of getting 40+ raw in methods than someone who only does methods? (feel free to move this to appropriate subforum if needed mods)

I found spesh and methods to be quite different in many ways. Typically someone who does spesh will do well in methods, but a lot of that can be attributed to their strength in maths. There are plenty of people that do both spesh and methods that get below 40 in methods.
Doing just methods won't place you at a disadvantage