Mathematical Methods - Pre-Exam 1 Advice for 2012

[ilovestudying]

one more question: what is the difference beween continuous and differentiable function?

[paulsterio]

a continuous function is a function which you can draw without lifting your pen off the paper.

in other terms, it means that the left limit, right limit as well as the value of the function are all equal.

a function is differentiable when it is continuous and not sharp.

[ilovestudying]

Do you think they will ask to sketch rational power functions in VCAA exam 1? Eg: y=x^2/3 etc... How can we draw it?

and when we draw graph lines, do we have to put the arrow to indicate where the graph goes?

[pi]

and when we draw graph lines, do we have to put the arrow to indicate where the graph goes?

I did, and it takes ~1s + it looks neat


On the matter of continuous and differentiable, ensure you understand what "sharp" means. For example, this is fully continuous, but not differentiable anywhere http://en.wikipedia.org/wiki/Weierstrass_function

[ilovestudying]

How about rational power function? Do we have to know how to sketch it?

And binomial distribution is discrete random variable right?

[pi]

How about rational power function? Do we have to know how to sketch it?

And binomial distribution is discrete random variable right?

As in *any* rational power function? eg. y = x^(83209748740/483738403700274038204809) ? If so, no. If they give you a simpler one to do, just plot a couple of points out and get the shape from there as your sketch



Yes, the binomial distribution is a form of discrete probability distribution

[thushan]

If you get a hard question...remember...get your hands dirty. Don't stare at the question, scribble. Write stuff, try various methods.

[TrueTears]

a continuous function is a function which you can draw without lifting your pen off the paper.

in other terms, it means that the left limit, right limit as well as the value of the function are all equal.

a function is differentiable when it is continuous and not sharp.

Also note a more degenerate case at the endpoints, endpoints are continuous iff the left limit or right limit (notice exclusive 'or' is used here) is equal to the value of the function

[SJay]

I donno if this is the right thread to ask this but what if the answers in the examiners report are in decimals but mine were in fractions? Would I get it wrong?

[pi]

I donno if this is the right thread to ask this but what if the answers in the examiners report are in decimals but mine were in fractions? Would I get it wrong?

If they ask for decimals (which would be highly unorthodox in an exam 1) then do so. If not, exact simplified form is preferred.

Although, always double check by reading the front of the exam to see what they prefer.

[SJay]

Awesome thanks

[soccerboi]

Why is (x+2)(x+8) greater than or equal to 0

written as x+2>_0  and x+8<_0 when attempting to solve it?

Why isnt x+8>_0???

[kensan]

Becuase if you do  x+8>_ then you are mising the x>_2    Also values of less than or equal to 8 are part of the solution too and they wouldn't be counted.
This is how I do these Q


     You will get 2 solutions because of the square root, [1] and [2]
   [1]
   [2]

  [1]
  [2]
  [2]

[soccerboi]

Thanks a lot!!

So with the above, (x+2)(x+8)>_0

you have to put a negative in front of one of the brackets, but have to decide which one by seeing if one cancels out the other yeh?

since x+8>0 will cancel the solns to x+2>_0, we must put the negative sign in front of x+8 to keep all our solutions alive?

[kensan]

You know how when you do square root of 4, you get plus minus 2? It's the same thing going on here. I think in actual fact the plus minus is on the left hand side, but people just automatically move it to the right for something like