Maths Methods 3/4 Help Thread 2011

[nacho]

Quick question, what's the best way to set out domain of a function?

1) Df = (-1, 2) u (2, inf)
2) x c (-1, 2) u (2, inf)
3) {x: x c (-1, 2) u (2, inf) }

Just don't wanna get tripped up on this sort of thing!

i use option 1 or 2, 3 is ... i dont see why one would use that, but it's good to familiarise yourself with it, i guess.

Technically, the only correct solution in those 3 options, is option 3, because 3 gives you a set (which is what a domain is), whereas 1 gives you a condition on no variable, and 2 gives you only 1 number (the number x). However, I think VCAA accepts them all anyway so it shouldn't matter.

edit: also, I assume your 'c's are meant to be epsilons? Or whatever you call the E like symbol.. haha

lol good to know
so its like more mathematical

[Greatness]

hmm i suppose it might be a good idea to write it in the 3rd form, just in case they are super pedantic this year! Especially in exam 1...

[luken93]

Quick question, what's the best way to set out domain of a function?

1) Df = (-1, 2) u (2, inf)
2) x c (-1, 2) u (2, inf)
3) {x: x c (-1, 2) u (2, inf) }

Just don't wanna get tripped up on this sort of thing!

i use option 1 or 2, 3 is ... i dont see why one would use that, but it's good to familiarise yourself with it, i guess.

Technically, the only correct solution in those 3 options, is option 3, because 3 gives you a set (which is what a domain is), whereas 1 gives you a condition on no variable, and 2 gives you only 1 number (the number x). However, I think VCAA accepts them all anyway so it shouldn't matter.

edit: also, I assume your 'c's are meant to be epsilons? Or whatever you call the E like symbol.. haha

Cheers, that's what I thought, but in all of the solutions they really don't seem to be too pedantic about it...

[nacho]

f (x) = sin (4x) + 1 with domain [0, pi/2]

i) what is the new domain after a dilation by a factor of 3 from the x -axis
ii) ''                                                                                                 '' y-axis
iii) ''                                              '' tranlastion of 3 units parallel to the x-axis             
iv)"                                                                                                         " y-axis          (with the last two, just wanted to know if the domain actually changes, or remains the same)


edit:
there's only two days left till exam 2, but i can never answer 'explain why....' questions in words.
any suggestions on how to tackle these questions? Are diagrams allowed to be used for them?



ALSO TO ADD, HOW DO YOU DO VCAA 2008 EXAM 2 QUESTION 3F) ?
how do you obtain coordinates for the y-value of C?? i got it right, but i just estimated by looking at the graph... which isnt mathematical?

also how do u do 3g of the same q/paper

[homosapiens]

I'm a little iffy about transformations...

1. f(x) is sin(x). What would the transformed equation be after:
a) a dilation in the x direction by 3, then horizontal translation to the right by 2
Is sin(1/3*(x-2)) correct?
b) horizontal translation to the right by 2, then a dilation in the x direction by 3
Is the answer the same as a?

c) a reflection in the y-axis followed by horizontal translation to the right by 2
f(-x-2) or f(-(x-2)
d) horizontal translation to the right by 2, followed by a reflection in the y-axis
f(-(x-2)) ?

e) vertical translation by 2 up followed by reflection in the x-axis
-(f(x)+2) ?
f) reflection in the x-axis followed by vertical translation of 2 units up
-f(x)+2 ?

[homosapiens]

f (x) = sin (4x) + 1 with domain [0, pi/2]

i) what is the new domain after a dilation by a factor of 3 from the x -axis
ii) ''                                                                                                 '' y-axis
iii) ''                                              '' tranlastion of 3 units parallel to the x-axis             
iv)"                                                                                                         " y-axis          (with the last two, just wanted to know if the domain actually changes, or remains the same)

I'm pretty sure the y-axis one will stay the same, the x-axis one is debatable though... I interpret it as shifting the whole graph 3 units to the right so the domain will now be [3, pi/2+3] - not entirely sure though

[dc302]

f (x) = sin (4x) + 1 with domain [0, pi/2]

i) what is the new domain after a dilation by a factor of 3 from the x -axis
ii) ''                                                                                                 '' y-axis
iii) ''                                              '' tranlastion of 3 units parallel to the x-axis             
iv)"                                                                                                         " y-axis          (with the last two, just wanted to know if the domain actually changes, or remains the same)


edit:
there's only two days left till exam 2, but i can never answer 'explain why....' questions in words.
any suggestions on how to tackle these questions? Are diagrams allowed to be used for them?



ALSO TO ADD, HOW DO YOU DO VCAA 2008 EXAM 2 QUESTION 3F) ?
how do you obtain coordinates for the y-value of C?? i got it right, but i just estimated by looking at the graph... which isnt mathematical?

also how do u do 3g of the same q/paper

3f) The amount of antidote he takes is always 16 units. So find how much antidote is left at the end of day 1, and then add 16 to it. To do this, sub in d = 1 for z, to find that z = 8 at the end of the first day. So the next day he must have 8+16 = 24 units of antidote.


edit: and for 3g)

It is simply a matter of 2 translations: 1 to the right and 8 up.

So from z = 16/(d+1)

We must change z to z-8 and d to d-1

So this becomes z - 8 = 16/d, which is z = 16/d + 8

[Lucas111]

Hey guys,

Could you please just revise me through solving m or k for Infinite solutions and for one solution (which it exists in)?

Cheers

[b^3]

Hey guys,

Could you please just revise me through solving m or k for Infinite solutions and for one solution (which it exists in)?

Cheers

Something I and a couple of others typed out not too long ago -> Re: What do, unique, infinite and no solutions mean?

[Lucas111]

haha cheers man

[Sal]

Quick question,
are we required to rationalise the denominator of ALL answers in the exam, or is it fine if we leave it in another form?

[Greatness]

If it asks for a certain form then yeah you might have to rationalise, but otherwise it doesnt matter... Well you might want to in case they decide to take marks off for not rationalising...

[che0061]

hi!
im having problems with this question in 2011 mav trail exam 1 and i was wondering if anyone can help me please?!
question is :
find the antiderivative of (4(e^2x +1))/ (e^2x +2x)?
thanks guys!

[Greatness]

integral of f'(x)/f(x) dx = loge(f(x))  use that

[che0061]

thanks swarley
greatly appreciated!