Maths Extension 2 Trial Exam thoughts- 2008 (2 Viewers)
- Thread starter vds700
- Start date
tommykins
i am number -e^i*pi
- Joined
- Feb 18, 2007
- Messages
- 5,730
- Gender
- Male
- HSC
- 2008
回复: Re: Maths Extension 2 Trial Exam thoughts- 2008
[f(x)]^2 is different from f(x^2).
[f(x)]^2 has "undercurves" below the line y = 1 and is more narrow towards the y axis when above the line y = 1.
f(x^2) has the same points for when f(x) = 1, the points are reached "easier" and it is an even function.
[f(x)]^2 is different from f(x^2).
[f(x)]^2 has "undercurves" below the line y = 1 and is more narrow towards the y axis when above the line y = 1.
f(x^2) has the same points for when f(x) = 1, the points are reached "easier" and it is an even function.
Re: 回复: Re: Maths Extension 2 Trial Exam thoughts- 2008
Yeh i meant f(x^2)
the question came from CSSA 4U trials question 2 part 2
any ideas of that answer for that?
also do u know where i can get the answers from
Hitommykins said:
Yeh i meant f(x^2)
the question came from CSSA 4U trials question 2 part 2
any ideas of that answer for that?
also do u know where i can get the answers from
adnan91
Member
The graph would be squished towards the y-axis and the square root of the roots of f(x) will be ur new roots and the graph should look like the original but squashed
- Joined
- Feb 16, 2005
- Messages
- 8,401
- Gender
- Male
- HSC
- 2006
Re: 回复: Re: 回复: Re: Maths Extension 2 Trial Exam thoughts- 2008
The best way to approach these is to do a bit of inspection:
Features of y = 1 - ex: (You could do the same thing if the graph is given rather than the equation)
- At x = 0, y = 0
- As x approaches ∞, y approaches - ∞
- As x approaches - ∞, y approaches 1
Features of y = 1 - ex²: (just replace x with x² and note additional restrictions)
- At x² = 0, y = 0 (i.e. at x = 0, y = 0)
- As x² approaches ∞, y approaches - ∞ (i.e. As x approaches ∞, y approaches - ∞ and as As x approaches - ∞, y approaches - ∞)
- As x² approaches - ∞, y approaches 1 => ignore this as x² is always non-negative (an additional restriction)
*Another thing to note is that it is an even function, so there is y-axis symmetry
*There is a turning point at the origin in this case as the derivative equals zero at that point
[In general x-coordinates of turning points are conserved for composite functions: i.e. differentiate f(g(x)) w.r.t x gives f'(g(x)).g'(x) so the x-coordinates of the turning points of g(x) are conserved since g'(x) = 0 is a solution to f'(g(x)).g'(x) = 0]
Using the above information, you can deduce the graph...(it should look like a negative "parabola" from the origin)
This is a graph of composite functions.Arowana21 said:
The best way to approach these is to do a bit of inspection:
Features of y = 1 - ex: (You could do the same thing if the graph is given rather than the equation)
- At x = 0, y = 0
- As x approaches ∞, y approaches - ∞
- As x approaches - ∞, y approaches 1
Features of y = 1 - ex²: (just replace x with x² and note additional restrictions)
- At x² = 0, y = 0 (i.e. at x = 0, y = 0)
- As x² approaches ∞, y approaches - ∞ (i.e. As x approaches ∞, y approaches - ∞ and as As x approaches - ∞, y approaches - ∞)
- As x² approaches - ∞, y approaches 1 => ignore this as x² is always non-negative (an additional restriction)
*Another thing to note is that it is an even function, so there is y-axis symmetry
*There is a turning point at the origin in this case as the derivative equals zero at that point
[In general x-coordinates of turning points are conserved for composite functions: i.e. differentiate f(g(x)) w.r.t x gives f'(g(x)).g'(x) so the x-coordinates of the turning points of g(x) are conserved since g'(x) = 0 is a solution to f'(g(x)).g'(x) = 0]
Using the above information, you can deduce the graph...(it should look like a negative "parabola" from the origin)
Last edited:
lyounamu
Reborn
- Joined
- Oct 28, 2007
- Messages
- 9,998
- Gender
- Male
- HSC
- N/A
Someone is desperate. But no, you won't do CSSA paper, I am sorry to say. All schools are to do their papers on the same day. Your school won't just have that privilege to do the exam on the other day unless your school alters the exam to the large extent.Arowana21 said:
And yes, even if your school does the CSSA paper to later date, (I really doubt this) I agree with vds. That's a cheating and you shouldn't be doing it. I won't feel any pleasure from getting high marks because of cheating.
solomarc20
*Yawn
- Joined
- Dec 28, 2007
- Messages
- 146
- Gender
- Male
- HSC
- N/A
Sat my 4U test 2day...
EPIC FAIL!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Could get most of Q1-4 done but went badly downhill after Q5...
EPIC FAIL!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Could get most of Q1-4 done but went badly downhill after Q5...
conics2008
Active Member
- Joined
- Mar 26, 2008
- Messages
- 1,228
- Gender
- Male
- HSC
- 2005
haha i did mine too lol..solomarc20 said:
the hall was soo empty only 4 people..
I think i did well, except for this stupid poly mistake i did..
got tested on everything except half of mechanics and harder 3unit...
my biggest/dumbest mistake was i coudn't tell the difference between
1-1/root 2 < 1 < 1+1/root 2
instead i said 1-1/root2<1+1/root2< 1
xD
ohh well 80+.. and left exactly 5 questions.
Ridiculously hard exam. Was going well until about question 5, then it kinda went bad. We had things like induction questions when we havent done them in class. The first two steps were relatively easy, but you had to use a result proved in an earlier part of the question. Proving true for n=k+1 was just not going to happen. Graphing was good, the only interesting part of that was graphing -[F(x)]^2, and then not even that interesting. Conics was straightforward, just finding foci, eccentricity and directrices, but the generalised ellipse question was harder. I think my teacher made it herself, or at least sourced it from somewhere other than the CSSA paper. All in all, hard, but interesting. Hoping to get around 70%.
[Edit]: The mechanics question confused me. I am used to questions where the retardation of the particle is proportional to the velocity, or the square of the velocity. But this was proportional to the displacement. Thoroughly confused me.
[Edit]: The mechanics question confused me. I am used to questions where the retardation of the particle is proportional to the velocity, or the square of the velocity. But this was proportional to the displacement. Thoroughly confused me.
Last edited:
J
joseph777
Guest
if acceleration is proportional to displacement it's SHM.
conics2008
Active Member
- Joined
- Mar 26, 2008
- Messages
- 1,228
- Gender
- Male
- HSC
- 2005
it was bought from some organisation.. independent. somet shit like that..vds700 said:
eliseliselise
Member
- Joined
- Apr 16, 2007
- Messages
- 268
- Gender
- Male
- HSC
- 2005
mine was today... & i feel so disillusioned!!
the questions were BIZARRE. i have no idea what breed [cssa, neap etc] of test it was.. but it was so bloody hard!! the first questions was like deadshit easy, it was laughable how easy it was... & qu 2 was moderate, but question 4 was really, really hard!! question 5, 6 & 7 were easier... but they were still hard!
i think it was more of an ego trip for whoever set it. who wasnt my teacher as there were about 8 marks of harder 3unit stuff that we dont know yet. & after memorising every single method in the phoenix book & doing 9053485784634 past trials, i did not recognise most of the questions that were in the test... it was just overly convoluted.. scabbed enough marks for a pass though. just so disheartening after having walked out of 3unit yesterday expecting 90%+, and hoping for 70%+ in this... gah! hopefully my rank as 2nd will stay the same.. if not- there's always next year!!
the questions were BIZARRE. i have no idea what breed [cssa, neap etc] of test it was.. but it was so bloody hard!! the first questions was like deadshit easy, it was laughable how easy it was... & qu 2 was moderate, but question 4 was really, really hard!! question 5, 6 & 7 were easier... but they were still hard!
i think it was more of an ego trip for whoever set it. who wasnt my teacher as there were about 8 marks of harder 3unit stuff that we dont know yet. & after memorising every single method in the phoenix book & doing 9053485784634 past trials, i did not recognise most of the questions that were in the test... it was just overly convoluted.. scabbed enough marks for a pass though. just so disheartening after having walked out of 3unit yesterday expecting 90%+, and hoping for 70%+ in this... gah! hopefully my rank as 2nd will stay the same.. if not- there's always next year!!