You are right, Bavarian Arbitur was more difficult back then. Here are two past papers in 1990 and 1980:

http://ne.lo-net2.de/selbstlernmaterial/m/abi/BY/mathlk89_A.pdf

http://ne.lo-net2.de/selbstlernmaterial/m/abi/BY/mathgk90_A.pdf

Interesting, in German, you still call Calculus “Infinitesimalrechnung”. I guess it is equivalent to “Calcul Infinitesimale” in French. A bit archaic in my humble opinion since modern analysis is no longer based on the infinitesimals.

“I also recall more obtuse questions which you could well call trick questions, for which the German term “Einserfrage” exists, literally: “A-grade question”. If you didn’t do well on it, it would be very difficult to get an A.”

Nope, trick questions that I refer to in my earlier post are logarithmic equalities, trigonometric equalities, algebraic inequalities and functional equations. The inequality part has been hugely popular in my country for decades. Just find a book like that of Cirtoaje for reference. It can be called a huge subfield in its own right.

Anyhow, you guys already have a section on probability (Wahrscheinlichkeitsrechnung). That was 10 years ahead of us. 🙂

I think multiple choice questions can work well if they are well-designed. Personally, I’d only support MC questions that are in principle as difficult as regular questions, i.e. you have to do the work. Those can even be tougher than regular questions because you won’t get partial credit for incomplete answers. The worst are MCQs where you can guess the answer by excluding the obviously bogus answers. I also dislike MCQs where you can quickly work backward from the provided answer choices. (That seems to be a big part of the entrance exams of the Indian Institutes of Technology.)

]]>I have encountered very hard ones and very easy ones.

The nastier ones was when you get a topic and then you need to chose “true/false” for four statements which relate to the topic.

You can get maximum 2 points per “topic”. (The questions are independent). If you chose 2 wrong statements you get zero points. Meaning you can have half of the test solved right and you still get zero points overall.

Dang… A+. Well done, Aaron. I think I got a 12 out of 15 at the Grundkurs in 2009.

But I jammed in the whole stochastics part in two long days at the Staatsbibliothek together with a few Red Bulls. Our teacher was crap and I just worked myself through last year’s exams until I got it. Needless to say that the nights after I was dreaming of blue and red balls which were taken out of baskets and so on^^ But it worked. Also, I knew that one topic (I think it was “errors”) would take me like 2-3 days to learn, but never accounted for more than 4-8 points ( out of I think 120) of the whole exam, so I left it out. Saved me some time for the geometry part where I gladly saw most girls fail, because they couldn’t rotate a pyramid in their head. Talking about why women can’t park cars hahahahaa

I sure hope that differential calculus is being taught in Hamburg and Berlin. However, you’ll surely stand a very good chance of passing the final examination without that knowledge. Have a look at the “Grundkurs” exams on here:

http://bildungsserver.berlin-brandenburg.de/unterricht/pruefungen/zentralabitur/abituraufgaben-2011/

https://www.isb.bayern.de/schulartspezifisches/leistungserhebungen/abiturpruefung-gymnasium/mathematik/2017/

I have had a look at some of the test samples. Interesting, notations for functions are modernized to be closer to Analysis. Overall, I think the questions are involved with much less petty tricks than exams in my country. It certainly doesn’t make students lose track of what is essential and what is not. When I was young, I was constantly in fear because questions in exams never appear to be the same as those found in standard textbooks. You can diligently solve the whole book and may not pass the exam with good grades due to these trickier questions.

Here is entrance exam in my country last year:

https://dantricdn.com/2017/de-chinhthuc-toan-k17-m101-1498310039420.pdf

Stochastic geometry? That’s interesting. I see that technology has changed significantly high school mathematic education. When I left high school a decade ago, Probability was only studied in college. Now, it was delegated to 11th grade program. In more advanced curriculum, you even find subjects of discrete Math being taught along with more traditional contents. ]]>