Surviving IB: HL Mathematics

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What do I feel about HL Math?

A love/hate relationship at its finest. For the majority of my two years I felt like a lost, clueless sheep trying to wade through the subject. HL Math is frustrating and bewildering and an entire enigma on its own; nonetheless, slowly making sense of once inexplicable mathematical concepts after enough turmoil and despair practice is a feeling of great fulfilment. Life also becomes less of a conundrum with enlightening JW quotes.

Most vital survival tips to studying the subject

Practice (no easy way out, unfortunately). School assignments are not enough. Unlike other subjects, you cannot mug for math the night before and attempt to smoke through the exam the following day. It’s the repetition (and the monotony) that will help you understand the types of questions, strengthen your familiarity with different concepts, and train your mental stamina. Timed practices are extremely important, particularly in the few months leading up to the IB exams. Familiarising yourself with the exam conditions will allow you to be better prepared for the actual exam.

Calculators should help you, not hinder you (Papers 2 and 3). Time is of the essence, particularly in Paper 3. The graphic calculator is a very powerful instrument, and we often fail to maximise its potential. Learn to use its countless functions (and shortcuts) well, as this will contribute to freeing up valuable time for you in exams.

Take charge of your own learning. Math is a very individualised subject, hence it is important that you take ownership of your own learning during these two years!

  • Go through your mistakes to understand and rectify them. Practice makes permanent, so make sure you’re practicing the right thing.
  • Look through your past papers regularly, and go through your previous mistakes. Pinpoint what exactly you were doing wrong. Is it a conceptual error that seems to surface repeatedly? Don’t be afraid to consult a teacher and clarify your doubts as soon as possible. Unfortunate carelessness? Be mindful of your mistakes so as to avoid such potholes in the future!

Organise your studying. File all assignments, practices, tests and exam papers. Get notebooks solely for mathematics; this keeps all of your additional practices in one place. This will allow you to refer to past questions and mistakes (facilitating the previous point).

Most vital survival tips to doing well in the exams

The formula booklet is your best friend! Be familiar with the formula booklet: know what formulae are in it and what are not. Compile a list of important formulas / additional knick-knacks that aren’t found in the formula booklet, and commit them to memory i.e. covariance (Paper 3), formula for the test statistics in z and t-intervals (Paper 3).  

Math is a language to master. Presentation is extremely important, especially in probability / statistics, and mathematical induction questions. Understand the difference between population and sample variance / mean, and use the correct symbols in your working. Learn to draw the lambda and mu symbols properly. Refer to the school’s exam answer keys as guidelines to good presentation!

Read questions carefully (!!!!) Do not skip a whole question just because you cannot solve part (a) – the other parts may not be related to it. Break down a difficult question and look at it from different perspectives, possible formulas to use etc. Use reading time in exams to skim through the questions. Sieve out questions that can be done comfortably (i.e. typical IB questions / easy conceptual questions) and tackle them first.

Tick-tock. Many of us struggle with actually finishing the papers – this is where timed practices would have done you well! You will hone your intuition as to when exactly to skip a difficult question and move on. For the actual IB exam, try to set aside at least 15 minutes (for papers 1 and 2) for checking your answers.

Most vital survival tips to the Mathematical Exploration (ME)

Choosing a good topic is a battle half-won. It is arguably difficult to choose a topic that matches or exceeds the difficulty level of HL Math, particularly when this has to be done with less than half of the actual syllabus covered (sometime in the middle of Year 5). Here are some guiding points:

  • Look at the HL Math syllabus outline – it details the topics to be covered throughout your two years. This would give you a starting pool of possible topics and concepts to branch off from. It is important to start the research process early.
  • Read up in advance. You should fully understand whatever topic you are delving into, as well as the formulae / tests / theorems you will use i.e. statistics tests, probability distributions etc. Consulting your teacher / supervisor to decide and refine your topic into a feasible exploration will also aid you tremendously.

Understand the marking rubric thoroughly. Explorations are marked based on several assessment criteria, i.e. use of mathematics, personal engagement, mathematical presentation etc. Analysing the demands of the rubric (and the assessment) will be extremely helpful in allowing you to understand just what needs to be in your exploration, as well as certain points that IB looks out for.

Personal engagement!!! Scoring for this criterion in particular moves beyond merely using first-person pronouns (“I”, “me” etc.), or lengthy introductions detailing your fascination with your chosen topic. One of the most useful tips I have learnt is to illustrate your thought process between various steps or sections of your exploration. You could state your reason(s) for why you chose a certain test / formula / theory to use, or explain your observations. Questions are also a good way to show that you’re actively thinking about and engaged with your topic.

Here are some examples of integrating your thought process into your report:

  • I found that my data matched x and y characteristics of theory z, hence I decided to use it to calculate…
  • I noticed that beyond value x, my sample data values differed from theoretical values derived through formula y in the previous section. To what extent would assumption z have affected my results?
  • I wondered how well my sample data was an accurate representation of model / theory x, hence I decided to apply probability test y to the data to determine its accuracy.

Learn to write math, and in math, properly. As a piece of written work, presentation in your ME is extremely crucial – it is an actual criterion in the assessment rubrics. Give yourself ample time to perfect (and standardise) your mathematical notations, graphs, tables, formulae etc. Make sure you are using the accurate mathematical language: for example, the algebraic variable “x” should be typed using the “equations” function. This not only helps you secure the “mathematical presentation” criterion, but also improves readability, the overall flow and general impression of your exploration as well. This step often takes way longer than expected, so do bear that in mind!

Proofread all of the math involved in your exploration, multiple times. Check your calculations, and standardise significant figures / decimal places throughout the entire work. Most teachers will not check the accuracy of the actual math for you.

“Extending” your investigation is usually what would differentiate a HL exploration from an SL one. This section also provides the differentiation between your exploration and others’. Are there limitations to the original test / formula you used (i.e. small sample size, certain assumptions you made for the theory to hold)? Are there any other similar scenarios you can apply your findings to (i.e. from modelling a distribution of bus arrival times to that of taxi arrival times)? Can you apply another formula to the particular problem you are trying to solve?

If you are unsure, consult your teacher on how to take your exploration further! A good ME topic should provide you with a plethora of possible extensions to consider.

NB: do take a look at the sample explorations on the IB website to get a better idea of what is expected of you!

One thing to look out for

Check if your calculator is in radians or degrees mode during tests and exams, constantly. So incredibly important – it will save you a lot of heartbreak.

If I could turn back time

I would still have been as clueless as I was. Perhaps I would have practiced more – the sky’s the limit.

In short…

In terms of studying, math has one of the most straightforward and methodical processes – discipline, sheer repetition and understanding. Mental stamina will be crucial in taking you through the entire journey. Slow and steady.

Throughout the two years you will also feel way more entitled to complain about math than the SL students – embrace it wholeheartedly!

Often seen humming and waving along corridors, Grace’s interests are curiously varied. She’s set to study Politics and International Relations at the London School of Economics, and completed a Music EE on Beethovenian influence on Schubert’s Symphony no. 4, despite not taking HL music. Not your everyday 45-pointer.

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