IB Math AAHL Orientation

Welcome to AAHL! First of all, I commend you for making this ambitious choice. This is a challenging course that covers many topics and demands real understanding and problem solving skills. But if you take the class seriously and put in the effort, it's so worth it. Not only will you start university with a head start, you'll also be a genuinely better problem solver and logical thinker.

The goal of this article is to give you a sense of what you can expect in the course. By the end, you'll have a picture of every unit you will cover, as well as a solid understanding of what your assessments will look like.

What's covered in AAHL?

IB Math is divided into 5 "Topics";

1. Numbers & Algebra

2. Functions

3. Geometry & Trigonometry

4. Statistics & Probability

5. Calculus

Each of these topics can be divided into units, which you will likely cover one by one in class. These topics also overlap in some places, so you shouldn't think of them as distinct. They are nonetheless good categories for understanding the syllabus at a high level.

How will I be assessed?

There are 4 components that make up your final grade in the course, each contributing a different portion:

The Internal Assessment (IA): 20%

A 12-20 page essay that uses math from the AAHL syllabus to explore a topic that interests you.

Paper 1: 30%

A 2 hour exam with 110 marks, completed with no calculator. Consists of 8-9 short answer questions, and 3 long answer questions.

Paper 2: 30%

A 2 hour exam with 110 marks, completed with calculator. Consists of 8-9 short answer questions, and 3 long answer questions.

Paper 3: 20%

A 1h15 minute exam with 55 marks, completed with calculator. Consists of 2 very long questions that emphasize sustained reasoning.

The IB has specific assessment objectives for each component:

• The IA is all about assessing your inquiry skills, so it should read like a mini mathematical adventure. You should be learning things as you write it, and communicate those learnings clearly and accurately.

• Paper 1: you don't have a calculator.

• Paper 2: you need a calculator. Essentially half your performance is determined by how skilled you are with your calculator.

• Section A vs Section B:

  • Section A has short questions that cover a broad range of syllabus topics, and are easier to prepare for. Here's what it looks like:

  

  • Section B has long questions on just a few topics, often mixed together, and are more difficult to prepare for because the challenge is in the complexity of the setup, not just the steps themselves.

  

• Paper 3: the questions are hard, and to ace it you will need thorough and flexible mastery of the whole syllabus. This works the same as section B: you answer in a separate booklet

Grade boundaries - how good do I need to be?

If the previous section was terrifying, perhaps this will be a relief: the grade boundaries are lower than you might expect.

Typically, the threshold for a 7 is around 73%. To put this in perspective, a typical 7 might look like:

• 16/20=80% on the IA (16 scaled marks)

• 92/110=83.6% on P1 (25 scaled marks)

• 85/110=77.3% on P2 (23 scaled marks)

• 42/55=76.3% on P3 (15 scaled marks)

This yields a total of 79, which historically has always been enough for a 7. But if you want a 7, or any grade for that matter, I suggest you aim 5 points above the highest historical boundary, eg 84 for a 7.

That means a weighted average of 84% across all three components, but let's just call it 85%.

What's the takeaway here? Even if you're aiming for a 7, you don't need to be perfect. What is important is knowing your strengths and weaknesses and nailing the questions which you do know how to do. No matter how well you know the material sign errors, not fully answering the question, and other silly errors can cost you dearly.

IB Mark schemes

IB Math exams are graded against a mark-scheme. Questions on the IB can have one or multiple parts, and each have an associated number of marks, roughly in line with how long that part should take to complete. The mark-scheme is a document that details what a student's work must show in order to get each available mark. There are 3 types of marks:

• M: awarded for attempting an appropriate method, technique. Basically points for working.

• A: awarded when the examiner sees a correct answer, or accurate intermediate results.

• R: awarded for evident reasoning, eg recognizing one solution is outside the domain, or making a non-obvious logical deduction.

On mark-scheme documents, you may also see AG marks, which stand for "Answer given". These are used for questions of the form "show that ...", where the answer is effectively given, and the student is asked for clear working to arrive at that answer.

Examiners can also award follow-through (FT) marks if incorrect values found in one part of a question lead to incorrect answers in subsequent parts. For example, if

• Suppose in part (a) of the problem above you found 2(x−2)2−1 instead of 2(x−23​)2−27​. You would lose the A mark in (a) for finding the wrong answer, but you would still get the M mark if you showed a correct method.

• Part (b) asks you to find the vertex, which for 2(x−2)2−1 would be

  (2,−1)

  instead of

  2(x−23​)2−27​⟹(23​,−27​)

  you will still get full marks, as long as your working is visible.

In general, you should write down as much working as possible, even for steps that seem easy to do in your head. Trying to do steps in your head is one of the quickest ways to introduce careless errors. Also, every piece of working that is visible to the examiner has a chance of earning marks. If you got 80% of a question right and made only one small error, you can either earn some points because you wrote your working clearly, or you can earn none because your steps are in your head / on a separate piece of paper.

Rounding

This is so basic but so important. Some questions will specify the accuracy with which to give your answer. Suppose you have the decimal 32.1579

• "... to 2 decimal places" → 32.16

• "... to 5 significant figures" → 32.158

• "... to the nearest 10" → 30

In other questions, it will be obvious that the answer must be an integer. For example, if you're solving for the "minimum number of years" and you find 5.23, you have to round up to 6 because that is the smallest integer greater than 5.23.

If a question does not specify a level of accuracy, you must either give your answers exactly (eg π√2​), or to exactly three significant figures (eg 0.450).

You are also required to make all "obvious" simplifications, eg

• √425​​→25​

• ex⋅e2x=e3x

• 312​→4

Technically, the IB's mark-schemes do not require that you fully simplify fractions (unless they simplify to an integer), but given how fast examiners mark exams, I strongly recommend that you do so.

This is the easiest way to lose points, and it's also the most frustrating. I struggled with this a lot. What helped me was getting in the habit of specifying any rounding I performed. For example, if I rounded 10.859 to 10.9, I explicitly wrote

10.9 (3sf)

on my paper. This habit forced me to remember that I had to round, and also made me pay attention to any rounding specified in the question.

Command terms

Every single IB Math question contains one (sometimes 2) command terms. These are words that specific the type of response you are expected to produce. Provided below is a list of the command terms that the IB uses, with the common ones bolded.

• Calculate → your answer should be a number, and you should show steps.

• Differentiate → take the derivative (you'll learn what this means later).

• Determine → find the only possible answer.

• Draw.

• Estimate → find an approximate value.

• Explain → show your understanding of what something is or why something happens.

• Find → get to an answer showing all relevant working.

• Hence → you must use work or results from the previous part.

• Hence or otherwise → basically a hint to use the previous part.

• Integrate → find the integral of an expression (you will learn what this means later).

• Interpret → what does some result or information mean, in the bigger picture?

• Justify → provide reasons or evidence for your answer.

• Label → label specific elements in a diagram or sketch.

• Prove → very strict - you must provide indisputable logical steps showing a certain result in a formal way (you will learn how to do this),

• Show that → less strict version of a proof, perform some steps to show a given result.

• Sketch → draw a diagram or graph, including any relevant features uncovered in previous parts.

• Solve → find the solutions to an equation,

• State → short, simple answer. This command term is a clue the answer should be obvious, no working is required.

• Suggest → Propose an idea or possible answer,

• Verify → check some given fact with your own working

• Write down → the answer is somewhere in the given information, and you must extract it. This command term is a clue the answer should be obvious, no working is required.

Optimize for the assessments

Understand the IB’s philosophy

The IBO is an organization that has, whether or not you agree with it, a very clear opinion about what mathematical learning should look like. The people who design the curriculum and write the exams have strong ideas about how you should think, and every assessment is built to reflect those ideas. Once you understand what the IB's objectives for you actually are, you can align your own learning with their philosophy.

The style of the exams

The IB is obsessed with problem solving, especially in situations you haven't seen before. It's not enough to memorize the formulas, repeat the drills, or master every question that's shown up on the past paper. You will need to take what you know and apply it flexibly in problems that could be abstract or rooted in a real-world scenario.

Mastering your calculator

The second part is mastering your calculator as early as possible. The IB views technology not as a crutch, but as a tool for exploration, graphing, modeling, and solving in ways you simply can't with only pen and paper.

What’s the point of the IA?

The purpose of the internal assessment is to give you ownership of the mathematical process. The IB doesn't just want you to know how to solve problems, but how to ask meaningful questions, explore them thoughtfully, and explain your findings in a way that shows both rigor and a personal angle of understanding. The best IAs take math you've learned in the course and integrate it with your own life and interests in a way the IB is unlikely to have seen before.

Understand that the IA is moderated, so even though your teacher will be the first to grade it, there's a good chance an external IB examiner will read your internal assessment and give it a new grade. That's why it's critical that the effort and personality you pour into your IA are obvious in the words you've written, not just in the conversations you've had with your teacher about it.

This is a lot, but don't be daunted. Just knowing what to expect will help you massively, whether you're just starting your IB journey, or in the final hours before your exam. I strongly encourage you to take advantage of the resources right here on Perplex.

I believe in you, and you should too.

- James

Still have questions? Email me at james@perplex.org, or join our Discord.