Further Math HL Guide

[SC2Player]

Thought I’d create this guide because of the general lack of information on the Further Math course (hereafter referred to as Further).  Suppose it’ll be useful for three more years, until Further is disbanded along with Studies.  Got a 6, so if anyone who got a 7 can improve on this, please PM me, and I’ll do my best to edit in the info.  

Overall structure:

Further consists of six topics.  Four are the options in HL, and two are additional subjects.  They are as below (order is of no significance):

• Sets, relations, and groups
• Statistics and probability
• Discrete mathematics
• Calculus
• Linear algebra
• Geometry

Haese and Harris provides textbooks on each of the topics above.  I know that most other publishers provide textbooks for each of the options, but I’m not sure about linear algebra and geometry – check the websites of the publishers. 

Difficulty in math is always subjective, but I personally found geometry to be the hardest one.  I found the textbooks to be a bit messy in how they taught that subject. 

General Guidance:

Further is not some sort of vague esoteric course that tests you on obscure math – it has a clearly defined structure and syllabus.  Use the guide here liberally: http://www.spps.org/cms/lib010/MN01910242/Centricity/Domain/853/IBFurtherMathGuide2014.pdf

Further does not test your depth of understanding – it’s your breadth that they look at, hence the large-ish variety in topics.  There’s no need to go into that much depth for each topic. You also might not need the full 48 hours - I did most of the topics in under that time.  

Further assumes that you are familiar with the entirety of the math HL syllabus, so it is generally recommended that you take math HL along with Further, and for you to finish the syllabus early, or indeed before you begin the so you can start working through the options.  However, it is possible (though usually not recommended) to take Further only, without taking math HL.  For practice, do past papers and textbook questions.  Keep in mind that Further only became HL in 2014, so past papers before are shorter. 

You can choose to either take Further as a subject in its own right (i.e. a certificate course), or have it form part of your final IB score (out of 45).  Which one you choose will depend on how confident you are in your Further exams compared to other subjects.  If you do choose to take it as a certificate course, then you may need to provide an extra fee (ask your school for exact amounts), so that’s also something to consider. 

I've noticed that the IB is starting to include some questions based on more abstract concepts, such as proofs of a few theorems (I had to prove Fermat's little theorem) and a greater use of variables.  Don't just skim over the proofs in the textbooks, as you may need them in the exams (and of course this can help immensely with actually understanding the material, which is very important).  

For November candidates specifically:

If you’re a November candidate, you can NOT take the Further exams in November (as I found out only about three months before the exams) – you MUST sit them in May.  Apparently not enough people take the exam for the IB to justify providing another set of papers for November candidates. 

This gives you two options:

• Sit it in the middle of the second year, or IB2.  If you get an unsatisfactory score, then you can do the next option, which is:
• Sit it in the year after you graduate. 

Check to see how soon you need to send off scores, and also with how confident you are in doing the course. 

How you’ll be taught:

This bit really depends on your school – you may have a dedicated Further class, or you may just need to self-study the material (as I did).  In terms of self-studying, here are some things that I’ve learned:

• Be self-motivated and manage time properly.  You don’t have a teacher to set deadlines or yell at you and stuff, so this is very important. 
• Sometimes, if you really don’t understand a theorem, concept, or problem, just set it aside and come back to it later.  You may be able to understand it better then. 
• Don’t try to rush through the material without fully understanding it.  Keep in mind that your teacher may not be able to help you as much if you’re self-studying, so you need to make sure that you understand it well. 

Hope this helps anyone who stumbles across this.  

Edited August 4, 2017 by SC2Player