How to pass the GOPs at TUM

The GOPs at TUM are fundamental examinations that you must pass within your first two attempts. If you fail any GOP twice, you are directly exmatriculated from the program, and you cannot study the same degree program anywhere else in Germany. For BSc. Aerospace, these two exams are "Advanced Mathematics for Engineers" (Math 1) and "Engineering Mechanics 1 - Static Mechanics" (EM1).

Real Stats

For the previous year 2025/2026, the first exams for the GOPs had the respective fail rates

• EM1: 48%
• Math 1: 29%

GOP Tips / General Exam Tips

I personally managed to perform very well in the GOPs (1.3 in Math 1, 1.0 in EM1) and it mainly came down to good preparation. I studied for both exams throughout the semester and always ensured I understood concepts within the week in which they were introduced. I relied very heavily on tutor help during the exercise sessions and always prepared questions beforehand.

Be quick

I also never underestimated the GOPs. You will likely feel like you know all the content over a week prior to the exams. This isn't time for you to relax, it's time for you to train your solving pace. It's pointless if you can always solve 3D NVM diagrams in static mechanics, but it takes you an hour. The exam is very fast-paced, and you have to train your timing. In the actual preparation, try to understand and be able to solve all questions before the exam phase starts, and just spend the exam preparation time ensuring you can solve the questions quickly and precisely.

Time yourself and solve the full exam!

Additionally, ensure that you can solve the entire exam in the given time limit, not just individual questions in their given limits. In EM1, it's very possible that you can be much faster than allowed on specific tasks (e.g. I solved virtual work tasks in roughly half the allowed time, but took a bit more than the allowed time for 2D NVM). Since I kept training full exams, I knew that I could budget more time for the 2D task and compensate for others. Many students just solve individual tasks in the time frame, then completely blank on the exam due to stress and fatigue. Simulate the exam situation as much as possible with an actual exam simulation to ensure everything goes smoothly.

You cannot just resolve exams that you have seen before

Save some fresh exams towards the end of your preparation as a final test. It's always worth it to save at least one exam that you haven't yet seen to be solved around 3 days before the exam. Don't leave it until the very last day before the exam though, leave a short buffer to not stress yourself out too much. It should be the test to check your precision and timing mainly, not your ability to actually solve the question. In the off chance that the exam goes poorly, you need to grind out the last couple of days to try improving.

This is why you can't save it for the day before, if you're 1 day away from the GOP and get 20% on an exam, you're going to lose your mind and perform terribly. Ensure that the final fresh exam is done with time to spare to correct issues.

Ensure you fall for all the traps in the prep and avoid those in the real exam

Make sure the exam really is one you haven't attempted before (find some online if you have none left). You will always subconsciously remember the solution steps and know if you're making a catastrophic error in a task you've seen the answer to. This is not a luxury you have in the real exam. Ensure that your simulation allows you to fall for these traps/bad errors. You should fall for them in the prep rather than in the real exam.

Tutorial Exercise Tips

During exercise sessions, especially for the GOPs, the tutorials will be full of students who are terrified of failing. This saturates the tutors quite a bit and means each tutor is very busy and you'll need to wait quite a while to get your question answered. To combat this, I suggest two things.

1. Do the exercise questions on your own time first, then show up to the tutorials and ask the tutors questions near the start.

At the start of the sessions, the students are still solving tasks and don't yet require tutor assistance. This is the best time to ask your questions since the tutor can focus more time and effort on clearing up the exact issue you're having.

2. Find a tutor that matches your style.

I personally was a university tutor for many subjects. The students that performed best were the ones that stuck with a singular tutor throughout the semester and always came to them to clear their questions. Tutors might have different explanations for why a solution is a certain way. If you go to multiple tutors, you could end up just getting confused, as all of them might answer your question slightly differently.

I suggest going to every tutor at the start, seeing which one aligns best with your study style, then asking exclusively them for help. Any tutor is going to help you. They all scored well, so all of them are knowledgeable on the subject, but one might explain things in a way better suited for you, so try to stick to that one.

Final Remarks

The GOPs are just like any other examinations you will take at the university. The structure of the course is the same, so if you can make it mentally feel the same, it's really going to help you. The fail rates may seem crazy, but it's not too extreme compared to other exams in your course and some people also really just panic (trust me, I've seen it, I supervised the EM1 exam twice). Remember that there are 400+ people registered for the courses. Look around near the end of the lecture period, there are maybe half of those people left. Most of the ones who pass are the ones who are still there. High fail rates don't mean everyone tried super hard and failed. Some did, but some also didn't try as hard as they could have. If you consistently showed up and tried your absolute hardest, the rest you just have to believe in. I did exactly that and scored very well, and you can too.