Question Methods 1/2 to Methods 3/4

[Tomanomanous]

Hello there -- I'm quite new to these forums! So I'll just introduce myself: I'm Thomas, I'm 16 and in year 11 at the moment.

Ok, so I'm doing Methods 1/2 this year and Further 3/4, and I've done General 1/2 last year. But General/Further for this question is irrelevant.
I've been doing textbook exercises from the Maths Quest Methods 1/2 3rd edition CAS 2.0 for methods. I've found that I'm a textbook worker and I like to do exercises. I find them fairly easy. I can do Linear Functions in my sleep. I'm good at Quadratic Functions (with binomials, power functions, and intercepts method), and I can do long divsion of polynomials, the factor theorem and polynomial equations with ease, alongside graphing Cubics and Quartics. I struggled a bit at first doing my own work with the Function Notation, but I find function notation and set notation easy now and I can look at a function notation and get a mental image in my head of what is going on. I could improve on hyperbolas, truncus' and square root functions, and inversing functions seems easy. I found exponential and logarithmic functions easy. Circular functions was a breeze, except at first I struggled a little bit with trigonometric general solutions for sine, cosine and tangent. Rates of change is also easy too, but I still got kinematics and rates of change of polynomials to do. And I've started doing some differentiation, and I'm finding the concept behind that good. I still need to do some work with that.

Ok.. That was a lot to read, but I wanted to give you an idea of how I'm going. I want to know if that's how I'm finding methods 1/2, how will I cope in methods 3/4 and specialist next year from your opinions? I am finding that from working ahead in the textbook I'm doing quite good and understanding the concepts behind the functions. I can look at rules for graphs and know what each individual pronumeral does to a graph, as I train myself to do that and I always have to know what's going on between each step in question before I move on to the next exercise. So.. How will I do next year? I've already have had a look at 3/4 textbooks and I'm going to spend term 4 this year to start doing methods 3/4, as by then I'll have done the methods 1/2 work.

[xZero]

from what you said you should zoom through methods/spesh quite easily

[Tomanomanous]

from what you said you should zoom through methods/spesh quite easily

I hope so. But I'm going to have to do Specialist Mathematics next year most likely by distance education, as I'll be the only one in the school I go to doing the subject.. *sigh* and I'm not sure.. My school isn't well known for getting high ATAR scores from people. I'm a smart person (I give myself that much), but at the end of the day it mostly comes down if you can do the exams, and I hope I will be able to do the exams.

[paulsterio]

never mind, accidental post (:

[Tomanomanous]

O_o

[Lasercookie]

I'm in a similar situation to you currently - attending a not-so-great school, breezing through methods this year, teacher already started me on the 3/4 book. I'll also be doing specialist over distance - should be good fun.

What I'm doing now is that instead of doing most of the exercise questions, I'm spending more time looking at the theory. I'm going through all the worked examples in the 3/4 textbook and then having a go at the application type questions (if they look interesting). I recommend taking a look at the Essentials textbook, definitely superior to most of the VCE maths textbooks.

I've also been reading beyond year 12 at topics that interest me. Stewart's Calculus is a pretty highly regarded textbook by quite a few members on this site.

I'm also going and gaining a more solid foundation of the stuff in the course. This is stuff like looking at where a formula came from and trying to understand the proof (or at least some version of a proof) of each bit of information presented in through out the course.

Most things in the methods/specialist course will have at least one fairly simple proof (might not be as rigorous, but at least it gives you insight into where the formula came from). I know for the product rule the textbook stated 'the proof is beyond the scope of this course'. Googling gave this pretty simple derivation that relied simply on first principles and the limit theorems.

I've found a couple of the times I've ended up deriving later formulas that are presented in the book myself (the simple stuff of course), just from doing a bit of exploration with the initial theory presented. You get the best sense of satisfaction when you do this.

Definitely ask your teacher for hard questions and a faster pace, I would be honestly surprised if they don't help you out. If they don't initially comply with a faster pace, just work at your own pace and force them to comply. There's not much they can do about it - they can't punish you just because your eager to learn (though don't make them feel obsolete, they might get offended lol).

[paulsterio]

I'm in a similar situation to you currently - attending a not-so-great school, breezing through methods this year, teacher already started me on the 3/4 book. I'll also be doing specialist over distance - should be good fun.

What I'm doing now is that instead of doing most of the exercise questions, I'm spending more time looking at the theory. I'm going through all the worked examples in the 3/4 textbook and then having a go at the application type questions (if they look interesting). I recommend taking a look at the Essentials textbook, definitely superior to most of the VCE maths textbooks.

I've also been reading beyond year 12 at topics that interest me. Stewart's Calculus is a pretty highly regarded textbook by quite a few members on this site.

I'm also going and gaining a more solid foundation of the stuff in the course. This is stuff like looking at where a formula came from and trying to understand the proof (or at least some version of a proof) of each bit of information presented in through out the course.

Most things in the methods/specialist course will have at least one fairly simple proof (might not be as rigorous, but at least it gives you insight into where the formula came from). I know for the product rule the textbook stated 'the proof is beyond the scope of this course'. Googling gave this pretty simple derivation that relied simply on first principles and the limit theorems.

I've found a couple of the times I've ended up deriving later formulas that are presented in the book myself (the simple stuff of course), just from doing a bit of exploration with the initial theory presented. You get the best sense of satisfaction when you do this.

Definitely ask your teacher for hard questions and a faster pace, I would be honestly surprised if they don't help you out. If they don't initially comply with a faster pace, just work at your own pace and force them to comply. There's not much they can do about it - they can't punish you just because your eager to learn (though don't make them feel obsolete, they might get offended lol).

hahah, oh how i love going ahead and making others look like turtles, i think theres some motivational factor in that
but seriously though, yeah going beyond year 12 a tad is interesting, and sometimes it helps with understanding

proofs is important, but not really required, like there comes a point where you should just learn the rule and not worry too much about the proof
like i could probably prove the product rule/quotient rule up the top of my head now (not the chain rule though ahah!)
but it doesnt help so much

i agree though, that doing the more applications type questions, are good, theyre the best practice you can get for the exam

[Tomanomanous]

Ok, guys! Thanks. I am so glad for the help. It's so nice to have a forums with people who actually care about their VCE like me, ahahaha. I do find it satisfying in class that I know everything that the the teacher is covering that nobody else knows about (yay me), but I am also getting ahead because, the way I see it, the more of the time I'm getting ahead, the more of a chance I have of getting ahead of and breaking through that massive 68% in the bell shaped curve. Also, not many people would have my motivation and dedication to what I do. (I don't have a history of excellent A+ grades, but I do try really hard with everything I do and put in a lot of effort to get better and to achieve).

As for my teacher, he bullied me in front of my class mates and yelled at me for getting ahead in the textbook work, so now I work ahead at home because in class if I did work ahead (because he's teaching things I already know), I'd get my coordinator yelling at me again too (who hates me for some unknown reason) and trying to take awards away from me.

Yeah... Lovely school I go to. But seeing people here who do work ahead makes me feel not alone anymore (and a bit intimidated.. You all get A+ grades on exams!! O.o)

[paulsterio]

Ok, guys! Thanks. I am so glad for the help. It's so nice to have a forums with people who actually care about their VCE like me, ahahaha. I do find it satisfying in class that I know everything that the the teacher is covering that nobody else knows about (yay me), but I am also getting ahead because, the way I see it, the more of the time I'm getting ahead, the more of a chance I have of getting ahead of and breaking through that massive 68% in the bell shaped curve. Also, not many people would have my motivation and dedication to what I do. (I don't have a history of excellent A+ grades, but I do try really hard with everything I do and put in a lot of effort to get better and to achieve).

As for my teacher, he bullied me in front of my class mates and yelled at me for getting ahead in the textbook work, so now I work ahead at home because in class if I did work ahead (because he's teaching things I already know), I'd get my coordinator yelling at me again too (who hates me for some unknown reason) and trying to take awards away from me.

Yeah... Lovely school I go to. But seeing people here who do work ahead makes me feel not alone anymore (and a bit intimidated.. You all get A+ grades on exams!! O.o)

yeah, i completely understand, most teachers hate students who get ahead in work, but yelling at you is over the top
ive seen gentle reminders of not to go ahead, like "you should concentrate on knowing 100% of what we're on before moving ahead"

but ive always tried to work ahead, and its served me well, so i think the same should go for you as well...and also your attitude is good, like i think its always the people who put in the hard work and the dedication that do well, people who enjoy what they're doing and that you know, its not only the cut-throat competition you see at that top bracket - there are those that do subjects for the enjoyment (:

haha, man, im loving your school would you like to name and shame your school?

[Lasercookie]

I'm sorry to hear that you're in a really horrible situation there. I guess there's not much you can really do about it, other than keep your working away discretely. If they try to pull the same crap next year, punch your coordinator in the face (or complain directly to DEECD or the principal). http://www.education.vic.gov.au/about/contact/pcschools.htm

Or if you can/is feasible - transfer the hell out of there. That should be a last resort only though (and only if they continue the same ignorance next year). Either way, you're going to have to ignore your school. I like this quote and I've quoted it before, but here it is anyway: "I have never let my schooling interfere with my education." (Mark Twain)

I do agree with Paulsterio that knowing proofs is not required, but if you're working ahead you may as well put in the effort to study them. It'd allow you to make links between all the topics much much easier (plus it's satisfying when you can actually understand them). I think the proof of the product rule was the only time I actually used those different limit theorems outside of the dedicated exercise lol.

[Tomanomanous]

I'm sorry to hear that you're in a really horrible situation there. I guess there's not much you can really do about it, other than keep your working away discretely. If they try to pull the same crap next year, punch your coordinator in the face (or complain directly to DEECD or the principal). http://www.education.vic.gov.au/about/contact/pcschools.htm

Or if you can/is feasible - transfer the hell out of there. That should be a last resort only though (and only if they continue the same ignorance next year). Either way, you're going to have to ignore your school. I like this quote and I've quoted it before, but here it is anyway: "I have never let my schooling interfere with my education." (Mark Twain)

I do agree with Paulsterio that knowing proofs is not required, but if you're working ahead you may as well put in the effort to study them. It'd allow you to make links between all the topics much much easier (plus it's satisfying when you can actually understand them). I think the proof of the product rule was the only time I actually used those different limit theorems outside of the dedicated exercise lol.

Yeah, if it is going to happen in year 12 then I am going to complain. I think that I have been treated unfairly, especially when the coordinator basically implies you are an idiot and puts you down and tries to force you to apologise to your teacher for working ahead. I honestly wish I could transfer to another school, but the other schools in the area aren't that great too, and the private school is like $10,000 for year twelve and my family just doesn't have those sort of finances for my high school education. I'm worried enough about how I'm going to pay for my university education as it is (Hecs or whatever it is called is probably the preferable option)

I'm also going to look into proofs, but first if I could be provided some resources to start looking? Because at the moment it seems a tad confusing to me. I'd love to extend my knowledge in maths so I have that deeper level of understanding behind the concepts so I can bring a higher study score to myself for methods in year 12.

[Lasercookie]

I guess the thing would be if the nearby schools have good teachers that are actually reasonable and care about your education. Private school education doesn't really pose that much of an advantage. I'll stop talking about this now - it's irrelevant. Terrible schools and poor teachers are survivable.

For proofs really just google the topics and you'll stumble across them on wikipedia. You could also look up like 'proof of the quadratic formula'. The textbook will also sometimes explain where a formula has come from (e.g. for differentiation I think the Heinemann book did, they showed how you get two points on a graph, label one (x, f(x)), the other (x+h,f(x+h) do some more stuff and you end up with your first principles formula. I might be misusing the word 'proof' actually. I don't know.  What I'm saying is you just want a solid idea of where it came from.

But yeah, google is good. "proof of product rule" comes up with this: http://math.ucsd.edu/~wgarner/math20a/prodrule.htm
"proof of quadratic formula" also is good (don't google this yet). I reckon you should be able to derive the quadratic formula yourself. I don't know if I should give you clues or not. Just write down everything you know about quadratic functions and see if you get anywhere.

Just question everything you come across.  If you want to start on 3/4 stuff, go for it. I would finish off 1/2 calculus first - I enjoyed it a lot and doesn't take too long to get through. I've got this little A5 exercise book where I write down all the maths stuff I learn for reference/reading material.

I don't know if this will help get a higher score, but I do know it'll help you enjoy the subject a bit more. I guess that's what the important thing is.

[Tomanomanous]

I guess the thing would be if the nearby schools have good teachers that are actually reasonable and care about your education. Private school education doesn't really pose that much of an advantage. I'll stop talking about this now - it's irrelevant. Terrible schools and poor teachers are survivable.

For proofs really just google the topics and you'll stumble across them on wikipedia. You could also look up like 'proof of the quadratic formula'. The textbook will also sometimes explain where a formula has come from (e.g. for differentiation I think the Heinemann book did, they showed how you get two points on a graph, label one (x, f(x)), the other (x+h,f(x+h) do some more stuff and you end up with your first principles formula. I might be misusing the word 'proof' actually. I don't know.  What I'm saying is you just want a solid idea of where it came from.

But yeah, google is good. "proof of product rule" comes up with this: http://math.ucsd.edu/~wgarner/math20a/prodrule.htm
"proof of quadratic formula" also is good (don't google this yet). I reckon you should be able to derive the quadratic formula yourself. I don't know if I should give you clues or not. Just write down everything you know about quadratic functions and see if you get anywhere.

Just question everything you come across.  If you want to start on 3/4 stuff, go for it. I would finish off 1/2 calculus first - I enjoyed it a lot and doesn't take too long to get through. I've got this little A5 exercise book where I write down all the maths stuff I learn for reference/reading material.

I don't know if this will help get a higher score, but I do know it'll help you enjoy the subject a bit more. I guess that's what the important thing is.

Ahhk I can see what you mean with the whole school thing

Yeah, that's the idea I had of proofs. Sounds interesting!! And yes. I'm finding calculus interesting, too. (CALCULUS, INTERESTING?? SEND ME THE PSYCHIATRIC WARD!). I want to finish the year 11 calculus concepts before I start year 12 3/4 work, which will be at the end of the term (if I can get my ass into gear). Ahaha

Yeah. Thank you, anyway! You're very helpful

[Lasercookie]

Yeah, that's the idea I had of proofs. Sounds interesting!! And yes. I'm finding calculus interesting, too. (CALCULUS, INTERESTING?? SEND ME THE PSYCHIATRIC WARD!). I want to finish the year 11 calculus concepts before I start year 12 3/4 work, which will be at the end of the term (if I can get my ass into gear). Ahaha

It's surprising what you can do when you're motivated enough. I finished the calculus chapter in the two weeks over the holidays lol.
I've been refining my understanding and doing what I've mentioned above in class for the past few weeks (teacher let me sit my test early as well .

If you actually look at it, the 1/2 calculus stuff is pretty simple. There's really just a few major things you need to understand and you can pretty much breeze through the whole chapter. Limits, first principles, differentiation with that rule, tangent and normal, stationary points occur when dy/dx=0, indefinite integration (i think that's about it for 1/2 methods).

[Tomanomanous]

Yeah, that's the idea I had of proofs. Sounds interesting!! And yes. I'm finding calculus interesting, too. (CALCULUS, INTERESTING?? SEND ME THE PSYCHIATRIC WARD!). I want to finish the year 11 calculus concepts before I start year 12 3/4 work, which will be at the end of the term (if I can get my ass into gear). Ahaha

It's surprising what you can do when you're motivated enough. I finished the calculus chapter in the two weeks over the holidays lol.
I've been refining my understanding and doing what I've mentioned above in class for the past few weeks (teacher let me sit my test early as well .

If you actually look at it, the 1/2 calculus stuff is pretty simple. There's really just a few major things you need to understand and you can pretty much breeze through the whole chapter. Limits, first principles, differentiation with that rule, tangent and normal, stationary points occur when dy/dx=0, indefinite integration (i think that's about it for 1/2 methods).

Yeah, that sounds about right It is different to other stuff you'd learn in previous years, which makes it a bit of a 'differentiation' from maths you'd be used to. It's fun though. I've gone through the rest of the course with ease. I'm going to tackle the differentiation chapter in half an hour and try to get a few exercises down before I go to sleep