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Discrete or calc option? (I'm screwed)

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Ok so at the end of last term we learned that our teacher was leaving for HL maths, so we rushed our calculus option in 2 weeks and went through all the theory. Over the holidays I was honestly more concerned with completing my other subjects, IAs, and my EE, as well as my HL maths core. But now, when coming back to school, with no teacher, we have just been doing questions, but I am struggling heavily with our calc option. After looking at the discrete maths it looks SO much easier.

Is it worth switching now if i can? It would mean teaching myself the whole option, but I mean I don't understand calc at all at the moment. Or should I stick with calculus? 

If you have any resources that would make either of the option easier to understand and quicker to get through please send it. 


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it's impossible to get through Calculus thoroughly in lecture in only 2 weeks. For comparison, we went as fast as we could for Calc option and we did it in 7 weeks. In University, they generally dedicate a solid 3 months on comparable topics. Calculus has the highest boundaries among all Options you if you have to do Calc you have to study extra thoroughly. I recommend at least 6 weeks @ 1.5 hours/day of studying for any option on your own if you are looking to do well on Paper 3. With that being said, only 1 Option is sent to you for Math HL Paper 3, so if you want to switch Options you should let your coordinator know and there may be a late fee of USD$470 (AUD$ 590). 

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I'll do a comparison between discrete and calculus: 


  • Is separated into two sections: Number theory and Graph theory:
    • Number theory is the study of the integers, so you're going to learn about concepts such as integer sequences, divisibility, and primes.
    • Graph theory is the study of graphs (no, not the functions); tbh Google will give yo u a better description than I can.
  • Requires little pre-requisite knowledge compared to calculus option (you only need basic algebra and logic for most of the topics, and mathematical induction for a few).
  • A lot of memorization (probably second most, after the group theory option); you need to memorize most of the formulas in the textbook for the Discrete option, as the formula booklet only gives you three almost completely useless formulas.
  • Content is fairly straightforward to grasp for the number theory section, but the questions can sometimes be pretty hard; conversely, the graph theory section is sometimes more difficult to understand, but questions are mostly straightforward once you get the concepts.
  • Not that many calculations, as it's somewhat more proof-based - you may need to also prove some simple theorems, so it's worthwhile to understand all the proofs. 


  • Extends the calculus in core, so if you have any difficulties with the core calculus, this option can be pretty difficult.
  • A lot less memorization - the formulas in the booklet are actually useful in this option.
  • Quite a lot of calculations compared to Discrete option (use your graphing calculator to check your answers if you have time when doing this option), but minimally proof-based. 
  • Content can sometimes be quite difficult to understand, and questions are usually fairly tricky too. 

In terms of time spent, I'd say that the Discrete option requires less time - I finished the Discrete option in about 1.5 weeks of intensive study (and by intensive I meant that it was the only thing I studied for in that time period, doing absolutely no other work). With calculus it probably took me about 2 weeks of intensive study. 

Honestly, if you're considering other options besides your school one, I'd say the Sets, Relations, and Groups option is the easiest (it was for me at least). Once you fully grasp the concepts, the paper is a breeze (I mostly finished practice ones in about 30-40 minutes, out of an hour's time limit). There are virtually no calculations, and most of the paper consists of proofs. The difficulty thereby lies in understanding the concepts, but these are not that difficult IMO, as some of it is kind of obvious, while others mostly consist of memorization of definitions. Don't expect any help from the formula booklet for this option though; this has arguably the most useless formulas ever in the entire booklet (I mean seriously, schools could've saved a bunch of ink by not printing these formula, and I'm pretty sure that nobody would've been affected). It's also got perhaps the most memorization ever, so if you're not that good or hate memorization, then it's probably not the option for you. 

Ultimately, I suppose it really depends on what you're better at, calculations or proofs/memorization. If you're better at calculations, then consider either the Statistics option or the Calculus one (go with your strengths), whereas if you're better at proofs/memorization, go for either Discrete or Sets, Relations and Groups (check through). 

In terms of resources, Haese and Harris provides a pretty good overview of each option, with some nice problems too. Past papers, as usual, are perhaps the best for practice. Make sure you study out of the most recently published textbook to account for syllabus changes. 

Edited by SC2Player

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