Maths Extension 2 Trial Exam thoughts- 2008 (1 Viewer)

[Arowana21]

it is [f(x)]^2 but it is f(x^2)
anyone have any ideas for the graph?

 

[tommykins]

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.

 

[Arowana21]

Re: 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.

Hi

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

 

[tommykins]

回复: Re: 回复: Re: Maths Extension 2 Trial Exam thoughts- 2008

Hi

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

I haven't had my trials.

 

[Arowana21]

Re: 回复: Re: 回复: Re: Maths Extension 2 Trial Exam thoughts- 2008

I haven't had my trials.

Lets say you have a graph
f(x)= 1- e^x

and the question asked you to draw f(x^2)
what would be the solution

 

[adnan91]

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

 

[Trebla]

Re: 回复: Re: 回复: Re: Maths Extension 2 Trial Exam thoughts- 2008

Lets say you have a graph
f(x)= 1- e^x

and the question asked you to draw f(x^2)
what would be the solution

This is a graph of composite functions.
The best way to approach these is to do a bit of inspection:
Features of y = 1 - e^x: (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 - e^x²: (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)

 

[lyounamu]

Hey, i will be doing the trial this week. Are there any tips you can give me?
Also can you briefly tell me the questions that were in the exam, as much as you can?

Thanx a lot. However i am not sure whether my school uses Neap or CSSA papers

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.

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]

Sat my 4U test 2day...

EPIC FAIL!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Could get most of Q1-4 done but went badly downhill after Q5...

 

[conics2008]

Sat my 4U test 2day...

EPIC FAIL!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Could get most of Q1-4 done but went badly downhill after Q5...

haha i did mine too lol..

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.

 

[vds700]

haha i did mine too lol..

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.

was that your schools paper or a bought one?

 

[Js^-1]

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.

 

[joseph777]

if acceleration is proportional to displacement it's SHM.

 

[Js^-1]

It wasn't acceleration, per se. The retardation of the particle was proportional to the displacement. So the the further the particle travels, the slower it gets.

 

[conics2008]

was that your schools paper or a bought one?

it was bought from some organisation.. independent. somet shit like that..

 

[tau281290]

Is there a reason why my school is not buying papers like CSSA or Independent for the trials? We are doing exams that are made by our [shit] teachers.

 

[vds700]

anyone think q5 to q8 were hard??

Hell yeah, the harder 3 unit killed me!

 

[eliseliselise]

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!!

 

[- Jul -]

is everybody doing CSSA paper... hey guys Im currently doing CSSA paper for 3unit and till now I havnt made a mistake or got one wrong.. im currently on 4 .. xD

can some one link me to some cssa paper for ext 2 ..

Nah, I did the Independent Paper. I was wondering what scores everyone is getting coz I'm still not sure whether I should drop 4-U or not. Can I get just as good a mark if I do well in ext 1?

 

[- Jul -]

No. It's cheating and would give u an unfair advantage over your classmates.

yeah.