IB HL Mathematics
Words of wisdom
Contributors: Amy Take, Ellen Hao, and Lena Chen
Updated in 2016 by Anson Miu
Updated in 2016 by Anson Miu
What did you wish you’d known before choosing HL Maths?
"HL Maths has been known to be one of the more challenging higher levels; therefore, before choosing to take this subject, think very carefully! You should at least be getting A* in GCSEs! But also, don’t be too put off by HL Maths... you do not have to be a genius! Maths can be quite fun when you are trying to figure out really hard problems!" - Lena
"It’s nothing like GCSE maths, even for those in set 1 or 2. The pace is so much faster and there’s much more content stuffed into one lesson. Just because GCSE maths was super duper easy doesn’t mean IB HL Maths will. Don’t choose it because you like maths, since it was easy before. It most likely (definitely) won’t be easy in IB.
Just for record, you should choose HL Maths if you:
Your performance on the core iGCSE course is, by no means, an accurate prediction of your performance in HL Maths. Also, you should have some form of passion for maths-- if you hate the subject, it is going to be a tough two years.
"HL Maths has been known to be one of the more challenging higher levels; therefore, before choosing to take this subject, think very carefully! You should at least be getting A* in GCSEs! But also, don’t be too put off by HL Maths... you do not have to be a genius! Maths can be quite fun when you are trying to figure out really hard problems!" - Lena
"It’s nothing like GCSE maths, even for those in set 1 or 2. The pace is so much faster and there’s much more content stuffed into one lesson. Just because GCSE maths was super duper easy doesn’t mean IB HL Maths will. Don’t choose it because you like maths, since it was easy before. It most likely (definitely) won’t be easy in IB.
Just for record, you should choose HL Maths if you:
- Think GCSE maths is too easy and would like a challenge
- Really like maths
- Need it for the field you want to enter in university
- Are willing to actually put in extra time revising and doing practice problems." - Amy
Your performance on the core iGCSE course is, by no means, an accurate prediction of your performance in HL Maths. Also, you should have some form of passion for maths-- if you hate the subject, it is going to be a tough two years.
How do you approach studying for HL Maths?
"QUESTIONS, PROBLEMS, PRACTICE PAPERS! To excel in HL Maths, it is best that you familiarize yourself with the problems that IB gives you, so that you will know exactly what to do in the test! You want to be super duper skilled in all of the topics! Get your basics right - you have to be able to do calculus in your sleep!" - Lena
"This is the truth, the whole truth, and nothing but the truth. I can forget an entire month’s worth of maths after a 4-day weekend. It’s easy to forget what work you’ve done for maths, simply because HL Maths accelerates through so much content, which makes revising that much more annoying. Practice! Break out the review sets and go through the “Exam-style Questions” in the textbook. There’s an online resource with all of the worked out solutions for the textbook questions as well! Also, LISTEN IN CLASS. Missing even just one class is enough to set you back a lot when you revise for tests, and oh hey, what do you know, teachers actually know their stuff so you can ask them questions!" - Ellen
"Not that I did this, but do the practice problems in the textbook that correspond to every lesson. Don’t leave all the practice problems to the day before the exam/unit test. Expect to ask the teacher questions, because the sample worked-out questions in the textbook (the ones you will most likely go over as a class) don’t do justice to the practice problems later on in the section and those you’ll see in the exams/unit tests. Notes are pretty easy to take. Just copy everything the teacher writes on the board and whatever helpful tips they say." - Amy
Start with doing exercises/review sets from the textbook-- they don’t resemble exam-style questions by any means, but they give you a chance to practice and fine-tune your technique. Then, move onto past papers. Get used to the style/wording of the questions and know that they combine a range of topic areas in one question, so you need to readily apply different areas of the syllabus to one question. - Anson
"QUESTIONS, PROBLEMS, PRACTICE PAPERS! To excel in HL Maths, it is best that you familiarize yourself with the problems that IB gives you, so that you will know exactly what to do in the test! You want to be super duper skilled in all of the topics! Get your basics right - you have to be able to do calculus in your sleep!" - Lena
"This is the truth, the whole truth, and nothing but the truth. I can forget an entire month’s worth of maths after a 4-day weekend. It’s easy to forget what work you’ve done for maths, simply because HL Maths accelerates through so much content, which makes revising that much more annoying. Practice! Break out the review sets and go through the “Exam-style Questions” in the textbook. There’s an online resource with all of the worked out solutions for the textbook questions as well! Also, LISTEN IN CLASS. Missing even just one class is enough to set you back a lot when you revise for tests, and oh hey, what do you know, teachers actually know their stuff so you can ask them questions!" - Ellen
"Not that I did this, but do the practice problems in the textbook that correspond to every lesson. Don’t leave all the practice problems to the day before the exam/unit test. Expect to ask the teacher questions, because the sample worked-out questions in the textbook (the ones you will most likely go over as a class) don’t do justice to the practice problems later on in the section and those you’ll see in the exams/unit tests. Notes are pretty easy to take. Just copy everything the teacher writes on the board and whatever helpful tips they say." - Amy
Start with doing exercises/review sets from the textbook-- they don’t resemble exam-style questions by any means, but they give you a chance to practice and fine-tune your technique. Then, move onto past papers. Get used to the style/wording of the questions and know that they combine a range of topic areas in one question, so you need to readily apply different areas of the syllabus to one question. - Anson
What are your tips for acing the exam?
“There are many times where there will be one question that YOU DO NOT GET/can’t get the right answer. Do not spend ages on a question; go back to it later, because something might click!” - Lena
"I’m not sure if I’m even qualified to give advice here, since I haven’t aced my exams (yet. *crosses fingers*). But as I said in the last question, practice, practice, practice. Oh, and make sure you know how to use all the formulae in the formula booklet! (The formula booklet is wonderful. Take full advantage of it.) Know all the calculator tricks (nsolve, nCr(0,0), graphing stuff, etc.). Make sure you remember all the tedious little tricks/rules you have to memorize (remainder theorem etc.)" - Amy
"Time management! Time is so precious in a HL Maths exam! Don’t panic! There are many times where there will be one question that YOU DO NOT GET/can’t get the right answer. Do not spend ages on a question; go back to it later, because something might click! Use your formula booklet! Know how to use your calculator! BE CAREFUL when you answer your question, at times it is the careless mistakes that bring people down, because your brain is so exhausted from thinking about how to solve a problem that you get 3*2 wrong!!" - Lena
"First things first, I don’t think it’s… possible… to ace the HL Maths exam. It’s hard. That’s why it has a reputation. But based on my experience, I think the #1 most important thing is not to panic. A lot of the mistakes I make in maths come from dumb calculation errors e.g. stating the answer in degrees instead of radians, or stupid mistakes like “33-2=1”. (This is not a joke. This is the truth.) Maths questions are HUGE so the paper practically turns into a test of endurance, but if you’re in a state of panic, you won’t be able to think through things clearly! If you can’t do a question, write out a few starting ideas -- this might earn you that one point! -- and move on. Attack questions from different angles, and make sure you read the question for specific information; are they asking for the length or the area?" - Ellen
Confidence is key. It might sound unrealistic to be confident for any IB exam, let alone HL Maths, but you need to have faith in what you’re doing. 2 hours go by very quickly in the exam setting, and that confidence will help you breeze through the questions you know you can do in your sleep (surprisingly, there are quite a few of these in Section A), which gives you the time you need to digest the long ~20-mark questions in Section B. Persistent past paper practice will help you develop that confidence, as well as an intuition of knowing how to approach unfamiliar questions - e.g. having an idea of knowing when to use specific differentials for substitution integration. - Anson
Is there anything else that you feel like students should know?
“People will look at you with newfound respect! People always seem to be amazed when they hear that someone takes HL Maths… Remember, YOU ARE A WARRIOR!” - Lena
Time management on both papers may be slightly illogical. Both papers have Sections A and B, with each section covering 60 marks. However, applying the “1 minute per mark” strategy is extremely risky, because you’ll definitely need more time to digest the Section B questions and understand what you are actually asked to do. Section A can be covered in 45 minutes, which leaves you enough time to carefully read and understand Section B. If it helps, highlight the key words/numbers/phrases in the Section B questions so you remember what you’re asked to do when you write your answers.
Also, treat your GDC well. YOU RELY ON IT FOR 70% OF YOUR COURSE (including the Exploration), so you will be spending a lot of time with it. Familiarise yourself with the functions, from the famous “nSolve” and “polyRoots” to the duo of “zTest” and “tTest” that you will be using in Paper 3. Make sure to check your angle settings in both the graph settings and the general document settings. Remember to charge your GDC regularly -- superior mental maths won’t get you through even a quarter of Papers 2 and 3. - Anson
"ONE THING: THE MATHS EXPLORATION. YOU HAVE TO WRITE AN ESSAY IN MATHS (this goes for SL Maths as well), but HL Maths requires a more advanced level of maths. Searching for topics is very difficult, and it feel sort of like an aimless wandering in the dark. This is what makes planning so crucial; for the topic you pick (which has to have ~personal engagement~, aka some sort of link or explanation for your selection of topic besides ‘I LOVE Fibonacci, Fibonacci is my MAIN MAN BRO’), make sure that there is a complex enough level of maths to carry you forward. Don’t leave the exploration to the last moment to write -- you’re actually given an entire summer and autumn term to complete it!
Another thing: HL Maths can be a very strong bonding experience. Every single HL Maths student is tied together by a spirit of self-deprecation (as well as subtle pride for being able to put up with the syllabus), but mostly that feeling of camaraderie when each person knows that they’ve screwed up but can’t do anything about it. Class sizes are SMALL -- my HL Maths class went from 10 people to 7.
Last thing: Don’t be discouraged by one test grade. Maths is split up into units, so you’ll have subjects that you’re much stronger in, and some that you’re weaker in. Between one test and the next, you can go from a 5 to a 7! Even if you’re not doing so great in HL Maths, like Lena said, take pride in the slight fear and respect you can see in people’s eyes when you carry around the textbook!" - Ellen
Also, treat your GDC well. YOU RELY ON IT FOR 70% OF YOUR COURSE (including the Exploration), so you will be spending a lot of time with it. Familiarise yourself with the functions, from the famous “nSolve” and “polyRoots” to the duo of “zTest” and “tTest” that you will be using in Paper 3. Make sure to check your angle settings in both the graph settings and the general document settings. Remember to charge your GDC regularly -- superior mental maths won’t get you through even a quarter of Papers 2 and 3. - Anson
"ONE THING: THE MATHS EXPLORATION. YOU HAVE TO WRITE AN ESSAY IN MATHS (this goes for SL Maths as well), but HL Maths requires a more advanced level of maths. Searching for topics is very difficult, and it feel sort of like an aimless wandering in the dark. This is what makes planning so crucial; for the topic you pick (which has to have ~personal engagement~, aka some sort of link or explanation for your selection of topic besides ‘I LOVE Fibonacci, Fibonacci is my MAIN MAN BRO’), make sure that there is a complex enough level of maths to carry you forward. Don’t leave the exploration to the last moment to write -- you’re actually given an entire summer and autumn term to complete it!
Another thing: HL Maths can be a very strong bonding experience. Every single HL Maths student is tied together by a spirit of self-deprecation (as well as subtle pride for being able to put up with the syllabus), but mostly that feeling of camaraderie when each person knows that they’ve screwed up but can’t do anything about it. Class sizes are SMALL -- my HL Maths class went from 10 people to 7.
Last thing: Don’t be discouraged by one test grade. Maths is split up into units, so you’ll have subjects that you’re much stronger in, and some that you’re weaker in. Between one test and the next, you can go from a 5 to a 7! Even if you’re not doing so great in HL Maths, like Lena said, take pride in the slight fear and respect you can see in people’s eyes when you carry around the textbook!" - Ellen
Notes / Resources
Mathematics HL Course Book Solutions
"Your textbook is a great resource, and you can find longer solutions for the questions at this website. It doesn't always cover each step, but it's pretty detailed. There are examples, explanations, review sets etc., and even superfluous sections about ~real life applications~ of calculus and the backgrounds of historical mathematicians." - Ellen
Math is Fun and Purplemath
"They look pretty juvenile, but when you're desperate, beggars can't be choosers. However, I don't turn to these websites for study guides or anything like that, since they're not tailored to the IB. Usually it's just to clarify the formulae or operation of a well-established system, like integration by parts." - Ellen
"Your textbook is a great resource, and you can find longer solutions for the questions at this website. It doesn't always cover each step, but it's pretty detailed. There are examples, explanations, review sets etc., and even superfluous sections about ~real life applications~ of calculus and the backgrounds of historical mathematicians." - Ellen
Math is Fun and Purplemath
"They look pretty juvenile, but when you're desperate, beggars can't be choosers. However, I don't turn to these websites for study guides or anything like that, since they're not tailored to the IB. Usually it's just to clarify the formulae or operation of a well-established system, like integration by parts." - Ellen
For the Over-Achievers
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