Preparing for the Infi 1 exam

This is mainly about the HUJI Infi 1 exam, but the method could work in other universities and even courses.

What’s on the exam

From what I noticed, Yves’ Calculus 1 course (HUJI) includes four topics: the field of real numbers, sequences, functions and derivatives. The five questions usually follow a structure that resembles this:

Q1 - sequences
Q2-3 - the real numbers
Q4 - functions
Q5 - derivatives

Sort the material in your head by topic

To start off, make a list of all the claims and results you’ve studied and sort it by these topics. Don’t spend more than half a day on this - you shouldn’t recite the whole thing or rewrite all the theorems, just list them by name (and, if you can, the techniques and tricks that go with them).

Past exams (not simulations)

Around one to two weeks before the exam, I believe the best use of your time is grinding through past exams and patching up gaps by reverse-engineering (I’ll explain), rather than going through the material again. Material sits better once you have it in context, and even better once you remember the feeling of not being able to solve a question because you forgot that exact claim.

The goal is to meet as many question structures as you can (preferably from exams by the lecturer who’s writing yours) and reverse-engineer your studying from them: if a question uses something you don’t understand, go back and learn it. There’s a finite number of things they can ask about, and the structures repeat (say there are about 20 structures per topic - cover those 80 and you’re set). Remember that passing exams is an art of its own, and knowing the material isn’t 100% correlated with it.

Don’t treat them as full simulations yet. Keep 2-3 exams aside for full simulations at the very end, preferably the latest ones from your lecturer.

The routine for each question

How long each stage takes depends on how much time you have left. If you start 2-3 weeks out, give each stage 20 minutes. 1 week out, lower it to around 10, so you experience as many structures as possible.

Find an AI that is good for reviewing mathematics (I recommend Gemini or Claude). Remember that by default, it doesn’t know which claims your course covered and in which order, or what you are expected to explain rigorously versus what your course considers elementary - so review everything it says first from the perspective of it reviewing your answer, and then from the perspective of you reviewing its answer.

If you are solving a question that has an official solution, it’s best not to use AI at all - just hide the solution and look only at the next immediate step instead of asking AI for a hint, and read the full solution instead of asking AI for it.

Try the question on your own for 10-20 minutes.
If you are doing well, continue. If you are stuck, ask AI for a hint (mention that you want just the next immediate step rather than the solution). Then try for another 10-20 minutes.
If you get stuck again, repeat step 2.
If you solved it, move to step 5. Otherwise, ask AI for the full solution. Make sure you understand all of it, and if you don’t, go back and read the material it used, or even re-watch the relevant lectures and recitations if you have time. Then skip to step 6.
Send your solution to AI and ask for a grade out of 100. If you don’t get a 100 on that question, put the AI’s response aside, fix your solution yourself, and send it again, until you get a 100 or decide its nitpicks are irrelevant.
The next day, solve it again from scratch without looking at anything from yesterday. Then repeat step 5. If you get less than 85-90, repeat this step the next day.

The same goes for the theorems from the course. When you reconstruct a proof, treat it exactly like a question you just got on the exam: “Prove Darboux’s theorem.”

Figure out what your problem is

Everyone has their own. It could be:

Formalism - you know how to answer, but can’t write it down rigorously enough. I encourage you to read Working correctly with variables and quantifiers (Hebrew). Remember that Infi 1 is just as much about writing correct math proofs as it is about the material.
Time - you can solve the questions, just not in time. This requires work of its own: solving both single questions and full simulations with a timer, and trying to reduce your time. When you solve single questions, try to finish each one in about half an hour. When you solve simulations, try to finish within your exam’s time limit. When you finish, review what you didn’t answer in time, and think of possible reasons why. Additionally, look for tricks that save time, such as describing the existence of something rather than explicitly defining it when you don’t need to, or using words instead of formulas wherever it ends up being shorter. When you use the correct methods and precise wording, words are just as formal as quantifiers.
Material - you don’t know the material well enough. This is the most “terminal” one… You might have a fighting chance, depending on your situation. One way or another, in my personal opinion, you shouldn’t skip Moed A even if you are sure you will fail - get the initial shock over with as soon as possible (unless you have made up your mind to retake the course anyway). That said, I acknowledge there can be logistical reasons to skip Moed A, so decide what’s best for you.
Intuition - you don’t see where to start or how things connect. This is solved by just going over many questions.

Each one has a different fix. For formalism, material and intuition, I think the routine above is the best answer when you have a week or two left. Time needs its own work on top of that, as described.

Simulations

This needs to resemble your test, except for small things that could make the learning experience less exhausting - such as listening to music, or using a tablet rather than pen and paper if that’s what you prefer - because that might allow you to do more simulations. Other than that, work with a timer set to the same duration as your test. No pausing the timer, and stop writing when it rings. No phone breaks, no external help from AI or friends or anything else.

A common tip is to start with the question that is easiest for you. This is good advice, but it’s often hard to tell which one that is, and a question that looks easy can turn out to be very hard. Personally, I think going over the whole test to find the easiest one is a waste of your exam time. If one question screams at you from a quick glance that it’s easy, or if there’s a topic you are better at, start with that one - otherwise just start with the first question and go from there.

When you finish the simulation, ask AI for a grade and for your mistakes. Fix them, go back and study what you got wrong, and practice single questions on that topic if you have enough days left.

A few more general things

Study without WhatsApp.
Studying with friends may help or may hurt. A good fit could provide structure for the simulations.
Don’t try to study an impossible number of hours a day. You will be stressed and not actually achieve this.

That’s what worked for me, at least - everyone is a little different, and the same method doesn’t work for everyone. Good luck!

I strongly recommend reading: