VCE Methods Question Thread!

[Only Cheating Yourself]

My Belief - you have an obsession with CTS but you also seem to be lacking confidence in using it. Maybe watch a Khan Academy video on CTSing?

Isn't my owner right?

[hobbitle]

I missed one of your posts where you explained - sorry.
You are right in your 'simplification', but you can't solve for x over the reals.
The form you found ((x-2)^2 + 4) isn't really any different or more useful than the original quadratic.
We had our wires crossed.
To solve for x you would need imaginary numbers.

[SunnyB]

The question you produced can only be solved use imaginary numbers.

If you look at something as x^2+8x+16 it is simply (x+4)^2

[Only Cheating Yourself]

I missed one of your posts where you explained - sorry.
You are right in your 'simplification', but you can't solve for x over the reals.
The form you found ((x-2)^2 + 4) isn't really any different or more useful than the original quadratic.
We had our wires crossed.
To solve for x you would need imaginary numbers.

What are imaginary numbers?

[SunnyB]

whats CTS?

[hobbitle]

What are imaginary numbers?

You'll learn about them in Specialist Maths or Uni Maths if you do it.

Simply put they are a way to do things that you can't do with regular numbers, like finding the square root of a negative number.

CTS = complete the square

[Orb]

You'll learn about them in Specialist Maths or Uni Maths if you do it.

Simply put they are a way to do things that you can't do with regular numbers, like finding the square root of a negative number.

CTS = complete the square

Yeah, furthering on from hobbitle, imaginary numbers are something like square root of -1.

From current Methods knowledge, it's impossible to know/find out what that is.

However, in Specialist they define that as something called i.

As far as I know (which isn't that much), imaginary numbers don't pop up in any Methods exams.

[spectroscopy]

"x:" means "where x is"
Besides set difference, you can also use it to describe restrictive/maximal domains.

For instance:
A question such as "Find all the values for x where f(x)>4, where f(x)=x²"
An answer can be x: {x<-2 U x>2}

thanks

[hobbitle]

imaginary numbers don't pop up in any Methods exams.

Correct, they aren't part of the Methods curriculum.
They are defined by the imaginary unit i, which is defined by the property that i² = -1
You can therefore do things like find the square root of a negative number eg.

[Only Cheating Yourself]

Guys I'm really struggling with worded questions!  This is what i hate, the methods book is filled with the same questions all the way from 1-10 and its all fine but then when i have ago apply the concept i've learnt in a worded question i really struggle. 

A rectangular piece of metal with length 6cm and width 4cm is to be enlarged by increasing both of these dimensions by x cm as at right(which is a diagram…)
a.) if the value of x is 2, describe the change in area that occurs

This could seriously be the difference from me reaching my potential in methods, not being able to answer worded questions is really hurting me!  This question is the chapter of quadratics and null factor law so, I'm assuming it has to be relevant to that right?  Now how can i put that question into the form of a general quadratic expression so i solve it? 

[hobbitle]

  This question is the chapter of quadratics and null factor law so, I'm assuming it has to be relevant to that right?  Now how can i put that question into the form of a general quadratic expression so i solve it?

This is good that you're thinking this way, how to get the worded question into a form you are familiar with.
It sounds to me perhaps like you aren't drawing enough diagrams and writing things down.  Like perhaps you get overwhelmed by the words in the worded questions.  Try to sort it out in terms of numbers. 

Break down the question into parts.

Okay, so you have a rectangle.  And the question is asking you about a 'change in area'.  Cool, you know how to find the area of a rectangle!  Work with what you know at the start... a 6cm x 4xm rectangle. 

So the area of this rectangle is:
6cm X 4cm = 24cm square.

Awesome, so now you have some information that you know you're going to need later, because the question is asking you to compare/describe a change.

Moving on.  The question wants you to add x cm onto each side and find the new area.  The formula for the new area is the same, except we have a variable now!  If we add x to the length of each side of the rectangle, the formula for the area becomes
(6 + x) X (4 + x) = A (area)

Now, you're told that x is 2cm.  Convenient!  Now you can just substitute x=2 in and find the new area.

(6 + x) X (4 + x) = A (area)
(6 + 2) X (4 + 2) = A (area)
8cm X 6cm = 48cm square

So the question ultimately asks you to describe the change in area if you increase each side length by 2cm.  So you started with 24cm², and you added 2cm to each side, and the new area is 48cm².  The area of the rectangle has doubled.

I'm sure you know how to do these simply sums - the problem seems to be, for you, sorting out the information provided in the worded questions.  Don't get scared by them.  Just take them one sentence at a time.  Each sentence will give you a piece of information (or two).  Write down relevant formulas (like in this case, you see the word 'area', so you should think "Aha!  The formula for area of a rectangle is...." etc).  Go through them a few words at a time, don't try to see the big picture immediately.  When questions get more complicated, you won't be able to see the bigger picture until you've processed the information you're given a bit.

[TrueTears]

the 3/4 textbook has some notation i havent seen before can someone please clarify

when its talking about set difference of two sets A and B, and how its denoted A\B, it says

A\B={x:x is an element of A, x isnt an element of B }

what does the x: mean exactly? (you can sorta tell) and also when do i use it?
cheers

the colon literally reads as "such that".

[Only Cheating Yourself]

This is good that you're thinking this way, how to get the worded question into a form you are familiar with.
It sounds to me perhaps like you aren't drawing enough diagrams and writing things down.  Like perhaps you get overwhelmed by the words in the worded questions.  Try to sort it out in terms of numbers. 

Break down the question into parts.

Okay, so you have a rectangle.  And the question is asking you about a 'change in area'.  Cool, you know how to find the area of a rectangle!  Work with what you know at the start... a 6cm x 4xm rectangle. 

So the area of this rectangle is:
6cm X 4cm = 24cm square.

Awesome, so now you have some information that you know you're going to need later, because the question is asking you to compare/describe a change.

Moving on.  The question wants you to add x cm onto each side and find the new area.  The formula for the new area is the same, except we have a variable now!  If we add x to the length of each side of the rectangle, the formula for the area becomes
(6 + x) X (4 + x) = A (area)

Now, you're told that x is 2cm.  Convenient!  Now you can just substitute x=2 in and find the new area.

(6 + x) X (4 + x) = A (area)
(6 + 2) X (4 + 2) = A (area)
8cm X 6cm = 48cm square

So the question ultimately asks you to describe the change in area if you increase each side length by 2cm.  So you started with 24cm², and you added 2cm to each side, and the new area is 48cm².  The area of the rectangle has doubled.

I'm sure you know how to do these simply sums - the problem seems to be, for you, sorting out the information provided in the worded questions.  Don't get scared by them.  Just take them one sentence at a time.  Each sentence will give you a piece of information (or two).  Write down relevant formulas (like in this case, you see the word 'area', so you should think "Aha!  The formula for area of a rectangle is...." etc).  Go through them a few words at a time, don't try to see the big picture immediately.  When questions get more complicated, you won't be able to see the bigger picture until you've processed the information you're given a bit.

Thanks!  I've got a few more worded questions in this chapter i'll try my hardest to solve them using what you tole me, step my step etc…  One quick question why do we expand and why do we add, to find 48cm?  As in how do i know to expand.

[hobbitle]

You aren't expanding... You're just adding 2cm to each side... 6 plus 2 and 4 plus 2... And then multiplying them to find the area.  I was just kind of 'spelling it out' but perhaps the formatting confused you.

[Only Cheating Yourself]

You aren't expanding... You're just adding 2cm to each side... 6 plus 2 and 4 plus 2... And then multiplying them to find the area.  I was just kind of 'spelling it out' but perhaps the formatting confused you.

Yep i'm confused, if you add then you get 14, then what do you multiply it by?