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May 04, 2024, 02:43:19 pm

Author Topic: 4U Maths Question Thread  (Read 666041 times)  Share 

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RuiAce

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Re: 4U Maths Question Thread
« Reply #1230 on: June 11, 2017, 06:47:25 pm »
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Hi, could I please get some help with 7b and 8? Would 7b relate to or use 7a's result? And I have no idea where to even start for 8! Thank you :)



RuiAce

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Re: 4U Maths Question Thread
« Reply #1231 on: June 12, 2017, 09:43:43 am »
+2
Hi, could I please get some help with 7b and 8? Would 7b relate to or use 7a's result? And I have no idea where to even start for 8! Thank you :)



I leave the formal structure of the proof as your exercise
« Last Edit: June 12, 2017, 09:47:25 am by RuiAce »

ProfLayton2000

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Re: 4U Maths Question Thread
« Reply #1232 on: June 12, 2017, 11:48:52 am »
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Help I don't even know where to begin with this one (or is this level of difficulty outside what the HSC expects of us?)

chelseam

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Re: 4U Maths Question Thread
« Reply #1233 on: June 12, 2017, 12:23:44 pm »
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I leave the formal structure of the proof as your exercise
Thank you so much for your help Rui! ;D
HSC 2017: Chemistry / English Advanced / English Extension 1 / Legal Studies (5th in NSW) / Math Extension 1 / Math Extension 2

RuiAce

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Re: 4U Maths Question Thread
« Reply #1234 on: June 12, 2017, 12:33:58 pm »
+1
Help I don't even know where to begin with this one (or is this level of difficulty outside what the HSC expects of us?)
The question looks wrong to me.

ProfLayton2000

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Re: 4U Maths Question Thread
« Reply #1235 on: June 12, 2017, 01:30:42 pm »
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johnk21

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Re: 4U Maths Question Thread
« Reply #1236 on: June 13, 2017, 06:19:51 pm »
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Could someone please help me with this question.
Thanks in advance :)

jakesilove

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Re: 4U Maths Question Thread
« Reply #1237 on: June 13, 2017, 06:48:28 pm »
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Could someone please help me with this question.
Thanks in advance :)

Hey! We start with

Now, we make the substitution


noting that c is just a constant, so disappears when we differentiate. Now, we change the limits



Therefore,



However, we can change the arbitrary variable u to the arbitrary variable x



As required
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Studying a combined Advanced Science/Law degree at UNSW

chelseam

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Re: 4U Maths Question Thread
« Reply #1238 on: June 15, 2017, 10:39:11 pm »
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Hi! Could someone please explain the process of making a trig substitution (the kind that looks like the one in this question). Thank you so much! :)
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RuiAce

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Re: 4U Maths Question Thread
« Reply #1239 on: June 15, 2017, 10:48:43 pm »
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Hi! Could someone please explain the process of making a trig substitution (the kind that looks like the one in this question). Thank you so much! :)
Most of it is like an ordinary substitution where you let x = f(u). This one isn't exactly any different so I'm not sure what you want me to explain


chelseam

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Re: 4U Maths Question Thread
« Reply #1240 on: June 15, 2017, 10:54:07 pm »
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Most of it is like an ordinary substitution where you let x = f(u). This one isn't exactly any different so I'm not sure what you want me to explain
I was confused about when and how to change the domain! Thanks Rui :D
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RuiAce

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Re: 4U Maths Question Thread
« Reply #1241 on: June 15, 2017, 11:01:06 pm »
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Ah. Usually when you have x = f(u) instead of u = f(x), you try to put a restriction on the domain of u (or in this case, theta) so that over that domain the function is invertible. (i.e. the function is "locally" invertible.) That gets out out of troubles, e.g. if you had to substitute x = u2 and your original boundaries were 4 and 9, you no longer have to worry about a ± and just use 2 and 3.

chelseam

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Re: 4U Maths Question Thread
« Reply #1242 on: June 15, 2017, 11:04:38 pm »
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Ah. Usually when you have x = f(u) instead of u = f(x), you try to put a restriction on the domain of u (or in this case, theta) so that over that domain the function is invertible. (i.e. the function is "locally" invertible.) That gets out out of troubles, e.g. if you had to substitute x = u2 and your original boundaries were 4 and 9, you no longer have to worry about a ± and just use 2 and 3.
Thanks again Rui! You've been so helpful ;D
HSC 2017: Chemistry / English Advanced / English Extension 1 / Legal Studies (5th in NSW) / Math Extension 1 / Math Extension 2

beau77bro

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4U Maths Question Thread
« Reply #1243 on: June 15, 2017, 11:23:32 pm »
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HEY GUYS I WAS WONDERING WHAT YOU THOUGHT (ESP MODERATORS) WHAT WAS THE BEST WAY TO PREPARE FOR TRIALS (OTHER THAN THAT BRILLIANT NEW TOPIC TEST FOR EXT 2 WHICH IVE ORDERED). So what is it? Textbook Qs all day or trial questions all the way? I personally did a tonne of trials before half yearlies and just didn't find them challenging in a good way... It's just a tonne of easy-ish questions with some half hard ones or ridiculously hard - I felt like I didn't cover much of the course either. And half of my study I spent quite uninterested/unmotivated (I realise trials will change that ahahahha and I need to revise- so they are a really good option). So yea what do you legends think. What's the way to go? Smash out textbooks for each topic or focus on trial papers? Or maybe something completely different hahaha just take notes?

RuiAce

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Re: 4U Maths Question Thread
« Reply #1244 on: June 15, 2017, 11:43:22 pm »
+1
HEY GUYS I WAS WONDERING WHAT YOU THOUGHT (ESP MODERATORS) WHAT WAS THE BEST WAY TO PREPARE FOR TRIALS (OTHER THAN THAT BRILLIANT NEW TOPIC TEST FOR EXT 2 WHICH IVE ORDERED). So what is it? Textbook Qs all day or trial questions all the way? I personally did a tonne of trials before half yearlies and just didn't find them challenging in a good way... It's just a tonne of easy-ish questions with some half hard ones or ridiculously hard - I felt like I didn't cover much of the course either. And half of my study I spent quite uninterested/unmotivated (I realise trials will change that ahahahha and I need to revise- so they are a really good option). So yea what do you legends think. What's the way to go? Smash out textbooks for each topic or focus on trial papers? Or maybe something completely different hahaha just take notes?
By the time it was trials for 4U I honestly gave up textbooks. Only past papers can emulate what you're going to get on the day.

Yes, doing questions from here on is the way to go. But textbooks really don't reflect what you're going to get these days. The closest to the exam style questions would be the Syd Grammar questions, which I gather that you have but presumably you have covered quite a load of them already. You can probably still do some more in the meantime if your trials are far away, especially since motivation levels do spike up in preparation for trials, but once you get to that period where you have to study for trials it won't matter too much.

You might not need to worry too much about easy questions for now, but you're going to have to practice them seriously. Because if you don't practice the easy ones, you'll find you make an embarrassing amount of silly mistakes. On the contrary, seeing as though you look as though you have all the easy content covered, (provided you can juggle your other subjects) it's time to aim high. Those really hard questions aren't meant to be things you just look at and say "oh yep duh", even though every now and then you might. Unlike scraping, training yourself enough to score well into the 90s is going to require those questions be knocked down. You should be able to develop enough skills to be able to at least give it a shot, even if you don't get the final answer out. Remember, questions won't be worth only 1 mark unless they're trivial at the end of the paper.

Now, I need to make a comment on this:
I felt like I didn't cover much of the course either.
If you do a LOT of past papers, yes you will. No guarantee that you're going to cover every cornerstone of the course, but you're going to have covered quite a fair load.

Key word is a LOT though. Extension 2 is huge; it's not as restricted as Extension 1 in what they can ask. You're gonna have to go all over the place with them papers.