MATH HL tips, tricks, any kind of help ?

[IB231997]

i have just started the IB curriculum and have my exams in 2014.

do you have any good resources or tips that would help me survive

IB math though out this curriculum ?

i have already started to regret my choice ! :'(

thankyou

[Sammie Backman]

Do maths every day. I see people with well above average mathematical ability get 2's and 3's simply because they do not practice enough.

Do past paper questions, they are normally much harder than the questions in your textbook.

[Hanadai]

Prepare yourself for two-year tortures.

By the way - good luck!

Edited August 18, 2012 by Hanadai

[Fermat]

I'm also taking math HL when I start the IBID (which is on 2 weeks) and I bought the IBID Math HL book and studied during the summer holiday.

So would recommend you to buy the IBID Math HL book, I've heard that it's great and from my experience (even though I don't know what HL math is like) it IS great, it explains everything very well and it has good questions and all.

Good luck

[macrofire]

I recommend going to a local university and looking up some advanced mathematics. Start simple: find some beginners' guide to abstract algebra or topology. When you return to the IB curriculum, HL math will seem much easier.

[aldld]

Start simple: find some beginners' guide to abstract algebra or topology. When you return to the IB curriculum, HL math will seem much easier.

Euh, if you want to study more advanced math I'd recommend starting with basic logic and set theory (which many math books have a review of at the beginning). Logic because you'll need it to follow proofs and and set theory because that's the language of advanced mathematics and you might have a hard time understanding algebra or topology without it. Also if you haven't studied real analysis (the theory behind calculus) you might find topology a bit unmotivated without ideas like nearness and continuity, since most students' first exposure to topology is in the context of real analysis.

If you are intent on studying ahead a bit, I'd recommend basic set theory and familiarizing yourself with the language of mathematical proof. Then study calculus (even if you've already learned some) paying attention to the proofs. (Spivak's book is good for this.) You'll learn calculus with much more rigour than the IB curriculum requires but it will be worth it.

I think this would also put you in a position to learn a bit of linear algebra as well, if you have time. IIRC, unfortunately matrices were removed from the HL curriculum and lin alg was added to further math.

Edit: If your only goal is to get a good mark in school, then this is all a waste of time for little benefit. But if you have any interest at all in understanding mathematics, then try what I said above.

Edited August 19, 2012 by aldld

[Fermat]

Start simple: find some beginners' guide to abstract algebra or topology. When you return to the IB curriculum, HL math will seem much easier.

Euh, if you want to study more advanced math I'd recommend starting with basic logic and set theory (which many math books have a review of at the beginning). Logic because you'll need it to follow proofs and and set theory because that's the language of advanced mathematics and you might have a hard time understanding algebra or topology without it. Also if you haven't studied real analysis (the theory behind calculus) you might find topology a bit unmotivated without ideas like nearness and continuity, since most students' first exposure to topology is in the context of real analysis.

If you are intent on studying ahead a bit, I'd recommend basic set theory and familiarizing yourself with the language of mathematical proof. Then study calculus (even if you've already learned some) paying attention to the proofs. (Spivak's book is good for this.) You'll learn calculus with much more rigour than the IB curriculum requires but it will be worth it.

I think this would also put you in a position to learn a bit of linear algebra as well, if you have time. IIRC, unfortunately matrices were removed from the HL curriculum and lin alg was added to further math.

Edit: If your only goal is to get a good mark in school, then this is all a waste of time for little benefit. But if you have any interest at all in understanding mathematics, then try what I said above.

Are you saying that matrices have been removed from HL math?! I spent a SOO much time learning this summer

[macrofire]

Start simple: find some beginners' guide to abstract algebra or topology. When you return to the IB curriculum, HL math will seem much easier.

Euh, if you want to study more advanced math I'd recommend starting with basic logic and set theory (which many math books have a review of at the beginning). Logic because you'll need it to follow proofs and and set theory because that's the language of advanced mathematics and you might have a hard time understanding algebra or topology without it. Also if you haven't studied real analysis (the theory behind calculus) you might find topology a bit unmotivated without ideas like nearness and continuity, since most students' first exposure to topology is in the context of real analysis.

If you are intent on studying ahead a bit, I'd recommend basic set theory and familiarizing yourself with the language of mathematical proof. Then study calculus (even if you've already learned some) paying attention to the proofs. (Spivak's book is good for this.) You'll learn calculus with much more rigour than the IB curriculum requires but it will be worth it.

I think this would also put you in a position to learn a bit of linear algebra as well, if you have time. IIRC, unfortunately matrices were removed from the HL curriculum and lin alg was added to further math.

Edit: If your only goal is to get a good mark in school, then this is all a waste of time for little benefit. But if you have any interest at all in understanding mathematics, then try what I said above.

Beginner guides to abstract algebra all start with the basics, the primal axioms and build ideas logically from there. A good one is Introduction to Abstract Algebra by W. Keith Nicholson. As for topology, it's something to look at for fun. I'm sure topology might not be your "hussle in the hay" but you can't deny that after reading an article, even, on beginner topology, you would refute that you learned something cool.

Yet both of these ideas are more advanced than those in high school. If you limit yourself to basic logic and set theory, you're only going to bore yourself. Keeping an open mind and opinion on what you might like to took at will make your life (academic highschool, mind you) more interesting.

Besides, we can't assume that people are mathematically challenged.

[flinquinnster]

Try not to regret your choice! Even though to be honest I may be regretting doing higher maths now. Particularly after my exams. Anyway, at risk of just repeating everything that has been repeated before, here are some of the things that I would recommend:

1. Read your textbook 'for fun'. In fact, try to read more than one maths textbook - you'd be surprised, they can be somewhat interesting, particularly when there are awkward puns and attempts to be humorous/witty.

2. Yes, do the past paper questions. But it is absolutely critical that you don't have the mark scheme in front of you when you do it! There's nothing wrong looking it up after a decent attempt, but do not study with it in front of you and just copy down the solution without trying it for at least as much time you would get in an exam. (Another thing - 1 mark in IB paper is about 1 minute, so aim to get a 5-mark question done in 5 minutes or something like that)

3. Keep your maths notes neat. I know some people like to have separate books, but for me the discovery of colour-coded pens and highlighters has been a miracle in helping me keep track of my already slightly messy notes.

4. Do your homework. Ask your teachers any questions you have - though a reasonable amount, because you don't want to scare them. Generally, you have a better chance at getting an email response to your maths questions if you send a short 100-word email as opposed to a 1000-word email (believe me, I've tried it).

5. Don't panic! (yep, I should take my own advice). If you believe it is hard, it will probably be hard. Otherwise, keep positive - think 'how hard can it be?'. Really, in my view, maths is not that much harder conceptually compared to other subjects - most of it comes done to practice and understanding in application. Which is pretty hard...

To be honest, my appreciation of mathematics is pretty shallow as well - I sound so condescending here, but it is my least 'intellectual' (read: pretentious) subject in IB. At least I find it somewhat engaging and motivating to do maths. So good luck - particularly with the new IA format that looks ridiculously fun compared to our set questions...

Also, although matrices is out of the new syllabus it's still very useful in terms of simultaneous equations and planes, so just learning the fairly basic manipulations is really useful. I think it's one of the easier topics in the old syllabus.

[IB231997]

Try not to regret your choice! Even though to be honest I may be regretting doing higher maths now. Particularly after my exams. Anyway, at risk of just repeating everything that has been repeated before, here are some of the things that I would recommend:

1. Read your textbook 'for fun'. In fact, try to read more than one maths textbook - you'd be surprised, they can be somewhat interesting, particularly when there are awkward puns and attempts to be humorous/witty.

2. Yes, do the past paper questions. But it is absolutely critical that you don't have the mark scheme in front of you when you do it! There's nothing wrong looking it up after a decent attempt, but do not study with it in front of you and just copy down the solution without trying it for at least as much time you would get in an exam. (Another thing - 1 mark in IB paper is about 1 minute, so aim to get a 5-mark question done in 5 minutes or something like that)

3. Keep your maths notes neat. I know some people like to have separate books, but for me the discovery of colour-coded pens and highlighters has been a miracle in helping me keep track of my already slightly messy notes.

4. Do your homework. Ask your teachers any questions you have - though a reasonable amount, because you don't want to scare them. Generally, you have a better chance at getting an email response to your maths questions if you send a short 100-word email as opposed to a 1000-word email (believe me, I've tried it).

5. Don't panic! (yep, I should take my own advice). If you believe it is hard, it will probably be hard. Otherwise, keep positive - think 'how hard can it be?'. Really, in my view, maths is not that much harder conceptually compared to other subjects - most of it comes done to practice and understanding in application. Which is pretty hard...

To be honest, my appreciation of mathematics is pretty shallow as well - I sound so condescending here, but it is my least 'intellectual' (read: pretentious) subject in IB. At least I find it somewhat engaging and motivating to do maths. So good luck - particularly with the new IA format that looks ridiculously fun compared to our set questions...

Also, although matrices is out of the new syllabus it's still very useful in terms of simultaneous equations and planes, so just learning the fairly basic manipulations is really useful. I think it's one of the easier topics in the old syllabus.

also could you tell me some good reference books for maths ?

you told me to read many books ...

you must be reading them to right ?

could you name some ?

thanks

[aldld]

Start simple: find some beginners' guide to abstract algebra or topology. When you return to the IB curriculum, HL math will seem much easier.

Euh, if you want to study more advanced math I'd recommend starting with basic logic and set theory (which many math books have a review of at the beginning). Logic because you'll need it to follow proofs and and set theory because that's the language of advanced mathematics and you might have a hard time understanding algebra or topology without it. Also if you haven't studied real analysis (the theory behind calculus) you might find topology a bit unmotivated without ideas like nearness and continuity, since most students' first exposure to topology is in the context of real analysis.

If you are intent on studying ahead a bit, I'd recommend basic set theory and familiarizing yourself with the language of mathematical proof. Then study calculus (even if you've already learned some) paying attention to the proofs. (Spivak's book is good for this.) You'll learn calculus with much more rigour than the IB curriculum requires but it will be worth it.

I think this would also put you in a position to learn a bit of linear algebra as well, if you have time. IIRC, unfortunately matrices were removed from the HL curriculum and lin alg was added to further math.

Edit: If your only goal is to get a good mark in school, then this is all a waste of time for little benefit. But if you have any interest at all in understanding mathematics, then try what I said above.

Beginner guides to abstract algebra all start with the basics, the primal axioms and build ideas logically from there. A good one is Introduction to Abstract Algebra by W. Keith Nicholson. As for topology, it's something to look at for fun. I'm sure topology might not be your "hussle in the hay" but you can't deny that after reading an article, even, on beginner topology, you would refute that you learned something cool.

Yet both of these ideas are more advanced than those in high school. If you limit yourself to basic logic and set theory, you're only going to bore yourself. Keeping an open mind and opinion on what you might like to took at will make your life (academic highschool, mind you) more interesting.

Besides, we can't assume that people are mathematically challenged.

I think set theory is interesting (especially if you get into topics such as countability and the continuum hypothesis) Same with logic, it shouldn't take that long to grasp the basics, but once you have that it's possible to stretch towards topics such as Gödel's incompleteness theorems. Of course I intended these as simply being a starting point. Once you grasp the important ideas you should be able to move on to pretty much any area of math.

As for topology, by all means study whatever interests you. Though I think there was some confusion about learning topology vs. reading articles on the subject (I assume you mean those intended for a popular audience.) I'd recommend reading those sorts of articles/books as they may draw your interest to study the subject in more detail. But that is quite different from seeing the development of a theory through from first principles to the interesting theorems.

I mean if you're really motivated you could dive right into topology if that's what interests you. But if you haven't seen any set theory before, when going through a proof you're going to have to go back and look at set theory to understand any of the details. Fortunately most introductory topology books include a review of set theory at the beginning.

[aldld]

also could you tell me some good reference books for maths ?

you told me to read many books ...

you must be reading them to right ?

could you name some ?

thanks

Our school uses the Haese & Harris textbook... and I don't really like it. It contains hardly any rigour and uses hand-wavy explanations, and subtle but confusing inaccuracies.

I mentioned this somewhere above, but for calculus, Calculus by Michael Spivak is excellent. It really goes into the details if you're interested in learning the proof of why something is true. Plus the questions are good for review because they aren't just the boring "plug and chug" formulaic questions, but rather they ask you to actually solve problems and prove (often important/useful) theorems.

I don't have any specific recommendations for the other topics. Though for vectors (and matrices which were unfortunately removed) it might be interesting to look at some basic linear algebra. I haven't used it myself but I've heard good things about Gilbert Strang's book, although it contains way more than what you'd need for Math HL.

[macrofire]

All in all, the best Math practice is to play around with numbers and find patterns. I had a friend who proved a connection between the Fibonacci numbers and the number of patterns of finite strings of binary numbers with the restriction that the numbers 0 and 1 must appear in groups. It was cool and it really stretched all of our minds when he presented the proof. Of course, we all knew group theory and he used this idea to support his proof.

So experiment with numbers and try proving random number facts. It'll be good for your logical capability.

[sachinkotecha]

Let me simply say this, there are things which you can do to help yourself. Firstly if you did not understand something in class, make sure you do and can do problems on it by the next one or else you will be in trouble. The one thing they didn't say is that everything is related, and even details which are thought to be unimportant may eventually come back. I would say PatrickJMT is a good source on the internet in helping understand topics however your textbook, and others you can find online are the real key