Hyperblade01 Question Thread

[hyperblade01]

Starting to get active so need one of these  


First question  

can be split:

When
When

Don't fully understand how they got this, has it got something to do with the property of an absolute function being two functions? If so.. don't know how they split it this way



Thanks in advance

[kamil9876]

yes. if u is positive, (e.g: |2|=2) however |-2|=-(-2) (if u is negative |u|=-u).

you know that is positive when a is negative(assuming x is positive or zero). So apply the properties above.

also, when a=0 x^2-ax is obviously positive.

Edit: you must be more careful, the positiveness/negativness also depends on the value of x. SO be careful of the domain of x too when doing this

[hyperblade01]

A ribbon (the blue thing) is wrapped around a cuboid. There is no overlapping and the ends meet at on the base.

What is the length of the ribbon?

?

Or does the have anything to do with it...

[Stroodle]

Looks right. Don't know why they wrote

[lacoste]

It shouldnt affect anything, the x/2 represents where the ribbon is placed. (middle of length of 'x').

Normally, the y value must be given in order to work out the length of the ribbon or else its impossible.

[hyperblade01]

Haha yea i was just a bit suspicious when they added in that extra information

So the volume was




We were asked to sketch over a 'suitable domain' - any key features missing? Should the Y coordinate to the endpoint be in fractional form?

[ilovevce]

For the first question (about modulus):

The functions is given in terms of x and therefore must be split in terms of x.
The function f(x) = x²-ax defines a positive parabola with x-intercepts at 0 and a. If a>0 the x-intercept falls to the right of 0, if a<0, it falls to the left.

It SHOULD state:

f(x) = |x²-ax| can be split:

When a>0, if x<0, x> a then f(x)= x²-ax
When a>0, if 0 <x< a then f(x) = ax-x²

When a<0, if x< a, x>0, then f(x)= x²-ax
When a<0, if a < x<0, then f(x) = ax-x²

[hyperblade01]

When a<0, if x< a/2, x>0, then f(x)= x²-ax

When:
A is less than zero
X is less than a/2
X is greater than zero


If a is less than zero, then a/2 will be negative. How could x be less than a negative but greater than zero :S?

[lacoste]

y coordinate should be in fractional form if they ask for it or if part of the question stem has it.

where is your stated domain?

[0, 50]?

and range?

those to add in and you should be right!

[ilovevce]

We were asked to sketch over a 'suitable domain' - any key features missing? Should the Y coordinate to the endpoint be in fractional form?

When they say 'sketch over a suitable domain', I don't think that means you have to restrict the maximum value of x.
(0, ∞) is a suitable domain. I think all they want you to do is recongise that x can't be negative. But you should probably check with your teacher to find out what they want.

[ilovevce]

When a<0, if x< a/2, x>0, then f(x)= x²-ax

When:
A is less than zero
X is less than a/2
X is greater than zero


If a is less than zero, then a/2 will be negative. How could x be less than a negative but greater than zero :S?

Firstly, I don't know why I put a/2, it should be a. Now edited. I had turning points in my head!

Secondly, think of it being a parabola with an x-intercept at 0 and some point a. When a is negative, the graph will dip below the x-axis between a and 0. So when x < a, f(x) is positive and when x> 0, f(x) is also positive.
Between a and 0, f(x) is negative. The modulus function reflects these negative values of f(x) across the x-axis.

[hyperblade01]

It finally 'clicked' 

I understand much much better now - thanks for that!

[hyperblade01]

I've been negleting methods in a sense that I haven't been going ahead and just keeping up schoolwise (I'm not behind )


Our school spent the last week of term on the long SAC and as of now, we are only half-way to three-quarters of the way through differentiation. We've got rates of change to go and some other minor things from the Essentials Textbook.


- What are other people up to schoolwise?
- I guess this one only applies to specialist students, I'm picking one maths subject to try and finish these holidays, which should it be?
- If I were to go ahead in methods, what would be the hardest thing coming up?


Thanks in advance guys

[TonyHem]

I've been negleting methods in a sense that I haven't been going ahead and just keeping up schoolwise (I'm not behind )


Our school spent the last week of term on the long SAC and as of now, we are only half-way to three-quarters of the way through differentiation. We've got rates of change to go and some other minor things from the Essentials Textbook.


- What are other people up to schoolwise? Reaching the end of anti-differentiation
- I guess this one only applies to specialist students, I'm picking one maths subject to try and finish these holidays, which should it be? Your choice, for me, i'm trying to finish both. Probably specialist IMO, methods is probably much easier to get done during school
- If I were to go ahead in methods, what would be the hardest thing coming up?


Thanks in advance guys

[TrueTears]

I've been negleting methods in a sense that I haven't been going ahead and just keeping up schoolwise (I'm not behind )


Our school spent the last week of term on the long SAC and as of now, we are only half-way to three-quarters of the way through differentiation. We've got rates of change to go and some other minor things from the Essentials Textbook.


- What are other people up to schoolwise?
- I guess this one only applies to specialist students, I'm picking one maths subject to try and finish these holidays, which should it be?
- If I were to go ahead in methods, what would be the hardest thing coming up?


Thanks in advance guys

My school is up to integration for methods.
I'd say finish spesh as I found that very helpful and made methods much easier.
If you were to go ahead in methods I'd say maybe probability but to be honest nothing is very hard.