VCE Methods Question Thread!

[Texyrialed]

What is the best way to tackle worded problems for any topic? I have an upcoming SAC on Exponents and Logarithms and my teacher said that the SAC is all application/worded problems which I am the worst at.
What are your personal tips/tricks/hacks to answer and be able to formulate an equation to get the correct answer for worded questions?

[james.358]

Hey Texyrialed!

I used to be hate worded problems as well, but I've managed to improve at these over the past year. Here are some tips that I think will be useful.

 - Immerse yourself in the situation and enjoy it! Especially if the task is creative, you should try to imagine yourself being the architect, epidemiologist, whatever your role is, rather than a mere student. Hopefully this helps you to stay more engaged with the task and be aware of domain (e.g. realise that values for lengths can't be negative, etc)

 - If you're likely to miss important information in the question, I suggest you develop a system to answer these questions. For example when reading the questions, I circle everything the question asks for (mark allocations) and underline important information you might forget (e.g. k>0, label coordinates, etc). These shouldn't take too long but will be very useful later on when checking

 - Practice extended response questions! I'm sure you can find many similar problems in chapter reviews and past exams, and trust me you'll be thanking yourself in the SAC for familiarising with this question style 

Hope this helps! If you have any other questions please don't hesitate to reply to the thread. 

James

[Corey King]

Hey guys
I find myself unable to factorize this expression: https://gyazo.com/30a5fd95ccf62fe74be4561e5f8c2db1
I got myself to this point - x^2(x-b) - a^2(x+b)
But was unable to get any further. I feel like there's a way to solve this using the difference of squares method but I do not see how.
Any help would be much appreciated
Corey

[SS1314]

Hey guys
I find myself unable to factorize this expression: https://gyazo.com/30a5fd95ccf62fe74be4561e5f8c2db1
I got myself to this point - x^2(x-b) - a^2(x+b)
But was unable to get any further. I feel like there's a way to solve this using the difference of squares method but I do not see how.
Any help would be much appreciated
Corey

Have you tried subbing in x=a to find a linear factor?

You can do long division or use the 'comparing coefficients' method after.

[p0kem0n21]

Hey guys
I find myself unable to factorize this expression: https://gyazo.com/30a5fd95ccf62fe74be4561e5f8c2db1
I got myself to this point - x^2(x-b) - a^2(x+b)
But was unable to get any further. I feel like there's a way to solve this using the difference of squares method but I do not see how.
Any help would be much appreciated
Corey

Maybe try expanding that expression and seeing if it matches that in the question (check your signs)

[keltingmeith]

Maybe try expanding that expression and seeing if it matches that in the question (check your signs)

ya cheeky bugger, can I upvote you more times?

[Corey King]

Maybe try expanding that expression and seeing if it matches that in the question (check your signs)

Well hot damn! It factorizes into x^2(x-b)-a^2(x-b)

Then I can just factorize into two binomial factors.

I get (x^2-a^2)(x-b)

I can see (x^2-a^2) as a difference of squares, so they factorize into (x+a)(x-a)

So the solution is (x+a)(x-a)(x-b).

Silly me! Thanks a bunch

Corey

[Coolgalbornin03Lo]

How come when I used the expand function my CAS says “invalid multiply”

I.e for Expand(x(x+2)(x-4))

[p0kem0n21]

How come when I used the expand function my CAS says “invalid multiply”

I.e for Expand(x(x+2)(x-4))

Did you make sure to multiply each of the factors (did you press the multiply/'x' button between factors)?

CAS can't recognize x(x+2)(x-4); it has to be typed in as x*(x+2)*(x-4)       (where * is the multiplication dot thing lol)

[Corey King]

Hey Guys.
I'm trying to cross multiply here to factorize.
Unfortunately I'm stuck. Not sure where my mistake is.
Any ideas?

[The Cat In The Hat]

Hey Guys.
I'm trying to cross multiply here to factorize.
Unfortunately I'm stuck. Not sure where my mistake is.
Any ideas?

Don't know it'll work because you've got that +3 or whatever (I can't really see it because it's fairly light writing). Can you darken it/raise the contrast and repost please?

[Corey King]

Don't know it'll work because you've got that +3 or whatever (I can't really see it because it's fairly light writing). Can you darken it/raise the contrast and repost please?

Yeah that's where I'm at right now.
I triple checked to make sure I didnt write the question down wrong, putting in an incorrect sign.

[The Cat In The Hat]

Yeah that's where I'm at right now.
I triple checked to make sure I didnt write the question down wrong, putting in an incorrect sign.

I assume this is also something you can't just shove through your CAS?

[Corey King]

Additionally,
I do not understand this method of factorising. I know how to use it, as the process is pretty  simple, but have no idea why it works.

In this shown example ( https://gyazo.com/b4658fa5679e9d1010ac50e465b661e8 )
They start with an expanded expression. Then in the process of factorizing, they don't look for factors, but actually multiply a and c of the already expanded expression, then pluck out factors of that product.
I can see what they are doing, but have no idea why it is working. It does not follow my intuition for factorizing that I have gained using the other methods. I can use this method, but don't understand it.

[Corey King]

I assume this is also something you can't just shove through your CAS?

That's a good idea, I didn't think to try that
CAS gives me this: 2*(x-1.5)*(x+2)