Test yourself with the accompanying Maple Learn worksheet here: learn.maplesoft.com/doc/iefswls387/trm---abitur-geometry-q1

@BlackStarASMR

Жыл бұрын

Why are you so handsome?

@BlackStarASMR

Жыл бұрын

Is "The river flows in you" your favorite melody?

@Supremebubble

Жыл бұрын

Both circles have the same radius so given that they intersect, the midpoint of the intersection circle is the midpoint of the given center points and the radius can be calculated using pythagoras. Pretty sure that would have been the intended solution.

@Rocky712_

11 ай бұрын

I am wondering if this a Math LK exam or Math Grundkurs exam. Germany's Abitur students have to choose usually 2-3 Leistungskurses (advanced courses) for their Abitur, but some might take Math as Grundkurs Exam (basic course). Also, not everyone has to take Maths in Abitur if they take other STEM (or german: MINT) courses, but the very specific rules are different between the 16 states.

@alexg3607

11 ай бұрын

@@Rocky712_ that is not true for bavaria and the given year, in G8 in Bavaria there was only one abiture and it was only the first part with the not so complex questions.

You need to keep in mind, that after part 1 (the part done in the video), there's at least another one, where you are allowed to use a calculator.

@techwithjoe8636

11 ай бұрын

but what dies this change? The calculator doesnt help that much.

@Nerdmind

11 ай бұрын

@@techwithjoe8636 yeah it does, atleast in nrw (region around cologne) we had graphic calculators, so the question can not only contain much harder numbers but you can also quickly do complex integrals/derivatives and show knowledge of a few special functions of the calculator.

@justarandomgothamite5466

11 ай бұрын

​​@@techwithjoe8636ave you ever sat the Abi? Calculators are vital for part B. It is not in the _slightest_ like Part A. Part A is the easy stuff you can do in your head. Part B is where your numbers stop being easy to work with, round numbers and the questions get more complex. It is possible to do it by hand, but not in the permitted time frame. Like if you gotta fifure out the square root 69 you better hope you have a calculator. The two parts are for testing two very different skill sets.

@ZimmermannA3

11 ай бұрын

@@justarandomgothamite5466 exactly

@mudi2000a

11 ай бұрын

@@Nerdmindkeep in mind that those calculators are not used everywhere in Germany. I am from Hessen and where my kids go (went, 1 already finished last year) only normal calculators are used.

As someone who likes maths and now studies chemistry, I can confidently say that taking this exam was one of the worst days in my life. I spent the full 6 hours available thinking and writing my heart out and when I got home, I dropped dead on my bed and slept for like 4 hours.

@kiseimhl1379

11 ай бұрын

Took (not exactly) this exam aswell twice actually since I didnt get my Abitur first try.. (thanks maths and 1 freaking point missing)

@blackhelltv8634

11 ай бұрын

im wievielten Semester Chemie bist du?

@hammerth1421

11 ай бұрын

@@blackhelltv8634 Zweites.

@Exotic69420

11 ай бұрын

​@@hammerth1421ist was für? ich bin mir nicht ganz sicher, was ich als LK wählen soll... ob Informatik oder Chemie kannst du n Einblick Geben? wäre supi

@marvin2678

11 ай бұрын

Nur 4 Stunden ? Ist doch stark 😂

As many others already mentioned, this is only the first part of two. As a whole the exam is about 5-6 hours long and therefore harder than only this first part. Your teacher decides whether you'll work on Aufgabenstellung 1 or 2 as it depends on the focus he gave his class in his lectures. Looking back on the exam it used to be fun :)

@kiseimhl1379

11 ай бұрын

Funnily enough we were given the choice which part to work on ourselves and could freely change between those as we want (as long as you mark the tasks you want to be noted on an extra sheet).

@bodo887

11 ай бұрын

Fun? Oh my god, I wish had had your outlook on math exams back in school... xD

@cco9162

11 ай бұрын

Hä? Das heißt man kann Abi machen ohne den schwierigeren Teil B zu machen?

@kiseimhl1379

11 ай бұрын

@@cco9162 ne, aber durften frei zwischen den 2 verschiedenen Aufgaben der einzelnen Themen wechseln, jenachdem was man persönlich einfacher fand

@orbitstayoncereveluv1960

11 ай бұрын

​@@kiseimhl1379omg kimlip pfp tasteeeee

Just want to point out that, as you correctly stated, there exists no "german" Abitur or "german" maths exam. Every german state has its own school system and own exams. The level of difficulty, the contents, the type of questions, can be quite different from state to state...

@awpetersen5909

11 ай бұрын

Es gibt doch ein Einheitsabitur?

@jesschronicles

11 ай бұрын

@@awpetersen5909 nein gibt es nicht, hin und wieder verwenden unterschiedliche Bundesländer gleiche Aufgaben aber es gibt kein Einheitsabitur

@cassandra8620

11 ай бұрын

⁠Nein, und wie wir alle wissen, hat Bayern das schwerste Abitur😊

@BerndKlein-ef1dg

11 ай бұрын

@@cassandra8620 Nein, Sachsen. Die Bildungsungleichheit ist nur nicht so hoch in Sachsen.

@BerndKlein-ef1dg

11 ай бұрын

@@awpetersen5909 "Als Zentralabitur wird eine Abiturprüfung bezeichnet, bei der die schriftlichen Prüfungsaufgaben von einer zentralen Behörde vorbereitet werden. In Deutschland ist dies in der Regel das Kultusministerium des Landes." Im Prinzip sind die Themen in Deutschland gleich. Die Gewichtung und Aufgabenverteilung innerhalb dieser Themen sind unterschiedlich.

Great Video! Theres actually a B part to the Abitur in which you can use a calculator. Id say that the B part is a bit more challenging so it might entertain you a bit more👍

@LJMahomes

11 ай бұрын

I don’t know how it developed over the years, but for us from bavaria the A part in the exam was pretty much a joke when I took my Mathe Abi in 2019. Being the same for all of Germany where standards are a bit lower. I don’t think many of us missed a lot of points there. The second part is way more interesting as it’s both harder and more abstract with fun ideas and topics that follow through the entire sections

@1zzystay9

11 ай бұрын

I had my Abitur last year. Many of us thought that the A part last year was actually more difficult than part B

@peters2404

10 ай бұрын

​@@1zzystay9Glückwunsch zum Abi

@graup1309

10 ай бұрын

Is this rule new that you're not allowed to use the calculator in part A? BC when I wrote it in 2017 in Bavaria we were very much allowed to use the calculator/ we were allowed to chose and I think had we chosen to not use the calculator we'd get an extra 30min or so on that part. Which led to not a single person choosing choosing to not use the calculator BC people were either bad enough at maths to be worried that calculating things themselves would take too much time or they were good enough at maths so the 30min really did not matter so of course you use the calculator for extra security

@LJMahomes

10 ай бұрын

@@graup1309 2019 Bavaria here. I think we were the first year that did the non calculator part mandatory, but it might also be 2018 when they changed it

Watching this video is such a full-circle moment for me. I took this exact test back in 2019 in Bavaria and now I just finished the first year of my MPhil at Oxford Uni. Seeing you doing the test that is part of what brought me here to Oxford is quite surreal - thank you for this :)

@paulkopold6364

Жыл бұрын

I took it too! So fun to watch, I am having a similar experience

@k.m.8190

11 ай бұрын

@@paulkopold6364 Hehe I love that all of us reunite in this comment section :D

@aqwaa3057

11 ай бұрын

Meinen Respekt. Mathe in Oxford studieren hat echt was an sich. Da kann ich als NRW Abiturient im Grundkurs nur drüber staunen haha

@TomRocksMaths

11 ай бұрын

Amazing

@stiller_jungmann

11 ай бұрын

Stark Respekt

I passed the Abitur-Test almost 10 years ago without struggling and its shocking how much I simply forgot. I think I wouldn't be able to get a single point in this test anymore😅

@user-nh4lc1qo6c

10 ай бұрын

Same… despite working as an engineer, too.

@youarebeautiful7434

8 ай бұрын

good to hear that i’ll only have to go through it once in a lifetime😂

@Krolted

8 ай бұрын

Studiere Maschinenbau im fünften Semester und ich schwöre dir ich würde nicht mehr als 30% schaffen. Die Unimathe Module habe ich auch schon lange durch und erinnere mich nur noch verschommen dran. Zeigt wie schlecht strukturiert die Inhalte sind. Wir lernen Mathe nur um die Prüfung zu bestehen und nicht für das spätere Berufsleben. Wozu gehe ich dann überhaupt studieren wenn nicht als Vorbereitung für den späteren Beruf

@syedhaidar6291

5 ай бұрын

@@KroltedJa, ich dachte das auch 😆

It should also be mentioned that everyone who wants to study must take this exam. No matter whether art or mathematics! Considering this fact, I find it a lot what is required from the topics. Individual tasks are partly easier but there are just many topics.

@kevlon_

11 ай бұрын

Is that a bavarian thing? Because I definitely did not have to take maths in my Abitur.

@kakao2711

11 ай бұрын

​@@kevlon_no its a new thing, math used to not be mandatory for the 13th year but now is, at least in my state, namely hessen

@kevlon_

11 ай бұрын

@@kakao2711 That might be another reason. It's been 13 years...

@timhh86

11 ай бұрын

@@kakao2711 Well in Hamburg it was always mandatory to take a class in maths, but you didn't have to take a exam in it. You had a 5 hour written exam in your 2 advanced course. And 4 hour exam in another subject of your choice and a 30 minute oral exam in another subject of your choice. One Exam had to be a language, one had to be either maths, physics, chemistry or biology. That was atleast the rules 16 years ago.

@techwithjoe8636

11 ай бұрын

@@kevlon_ Yes, it depends. At some schools you can replace subjects such as mathematics with others. But in most cases you need to pass it.

I finished my Abitur 6 years ago, and I am crying tears of joy right now because I NEVER HAVE TO DO THIS STUFF AGAIN😭❤️ I wasn't even that bad at maths back then, but looking at this.... I do not understand a single thing, I would get literally 0 points

@steph4369

10 ай бұрын

Same omg, I was never interested in maths as much as in other subjects, but still could get by, but looking at it now, I basically forgot everything it seems 😂 Had my Abitur in Saxony in 2017 😂

@TheCr0nix

10 ай бұрын

Same actually

@nanipanini

10 ай бұрын

ja man, quit that kackscheiss

@kartmannhelmut6323

10 ай бұрын

​@@nanipaniniYes, you need no smartphone. That is kackscheiß.

@lisamarie5339

10 ай бұрын

Baden-Württemberg 2018 here🥳🙋🏼‍♀️ man I feel old now

On Marking the Abitur: As other people already told, you didn't do the B part of the test. A+B together gives a total of 120 Points. (Just divide / multiply by 3 foronly the A Part with 40 Points) The test ist rated on a scale from 0 to 15, where 15 ist the best. (Normal german marks are on a 1-6 scale, where 1 is the best. I will include these marks in brackets.) 120-114: 15 (1+) 113-108: 14 (1) 107-102: 13 (1-) 101-96: 12 (2+) 95-90: 11 (2) 98-84: 10 (2-) 83-78: 09 (3+) 77-72: 08 (3) 71-66: 07 (3-) 65-60: 06 (4+) 59-54: 05 (4) 53-48: 04 (4-) 47-40: 03 (5+) 39-32: 02 (5) 31-24: 01 (5-) 23-0: 00 (6)

@NoNameAtAll2

11 ай бұрын

how to know a true german? by the use of ist in place of is)

@yetischwein

11 ай бұрын

you got me there :-)

@Henning_S.

11 ай бұрын

​@@NoNameAtAll2actually a lot of younger Germans use "is" instead of "ist" in text messages or when talking to each other.

@lulu111_the_cool

11 ай бұрын

​@@Henning_S.That does not make sense tbh

@Henning_S.

11 ай бұрын

@@lulu111_the_cool I think it is just because it is shorter. They also use shorter versions of other words, for example nichts -> nix (=nothing)

Would really like to see you trying the second part of our Abitur - the first part are actual things you can do in your head, the second part is where you see who understands maths. Typically this part you did makes up around a third of the total exam.

It's 16 years ago that I had to solve such long calculation sheets myself. I am so glad that afterwards I could do proofs, reasoning and also some fun ideas in maths exams. Mathematics in school was very uninspiring but in the university is was fun like hell. :)

@user-tc7fp1nu6t

Жыл бұрын

It's really interesting how math gets so much more fun in university, despite being significantly more difficult. I hated math before university, now in university it is my favorite topic, especially the many types of differential equations.

@addygreen8919

11 ай бұрын

It is probably the opposite for a lot of people. :D

@Nelson-uj9cv

11 ай бұрын

hell isn't fun bro

@ymiros0953

11 ай бұрын

For me maths in university was just making little sheets of all the different proofs so I could recite them in my sleep cuz I had to know all of them in the exam. I didn't exactly find that to be very inspiring

@justaperson4242

11 ай бұрын

I think it is so intrresting to see everyone say how much better university will be! I myself am still in 10th grade (Germany) and I am looking forward to it!

Finally the appropriate target group for the German math exams..even too hard for a math prof..totally insane 😂..passed it myself with a bad grade..university exams were easier than this

@fritzx735

11 ай бұрын

BS even in Bavaria its way too easy.

@itsjustcarina5326

11 ай бұрын

Saaaaame, passed it with 4p😂i can still remember many students going wild because the Abitur was so hard. Since then i feel like there is a petition after every Abitur year

@alwayssomewhereelse8215

11 ай бұрын

me too haha i had 1 point in my abitur and now that i study biology, every math exam was a B 😂😂😂

@Warwipf

10 ай бұрын

What kinda uni did you go to? Uni math examns took me like 2 months of studying 6-12 hours a day to pass, for Abitur (BaWü) looking at a couple of exercises every day for 2-3 hours for a week was enough to pass with 13 points.

@Amphibax

10 ай бұрын

You can argue if its hard or not but for most students its unnecessarily hard and complicated Most people I know never had to deal with any math even nearly that complicated

Great video! If you choose to work through the (tougher) Part B (or an Abitur exam from another state in germany, maybe where they have Grundkurse (basic level) and Leistungskurse (advanced level)) and want it translated beforehand, I would be happy to translate it for you!

@TomRocksMaths

11 ай бұрын

Thanks for the suggestion - added to my list :)

@katyajohanna

10 ай бұрын

​@@StrawberryStar7In Bavaria there are no Lks and Gks. We have to do Maths and German in the Abitur and then a third subject (most do English) and then two oral exams in certain subjects (you can choose them from a short list). I did music and religion.

@honigkuchen5

10 ай бұрын

​​​@@StrawberryStar7kommt auch auf die Schulart an. Ich war in Baden - Württemberg auf einem wirtschafts Gymnasium und da gabs auch keine GK & LK's.

That’s a pretty tough test for high schoolers- German high school math classes must be pretty intense. I’m very impressed.

@Astromath

Жыл бұрын

It's the hardest one in Germany because it's the Bavarian Abitur The Abitur in most of the other states is much easier

@lensenstark9819

Жыл бұрын

@@AstromathWouldn’t say it’s much easier, but is easier.

@tiagomoraes1510

Жыл бұрын

@@lensenstark9819 cope

@idemobre3527

Жыл бұрын

It’s OK difficultly when u are used to the long questions

@belabiehler1477

Жыл бұрын

Well we also usually go up to 13th grade and I think this is a math exam for people who took math as a leistungskurs which means they have especially many math lessons during schooltime I think if you take that into consideration its not that bad😅

I wrote this exact exam 4 years ago😂 so this gave me some not so nice flashbacks. But you should also try part B I struggled with that much more

@Zoe_EK

11 ай бұрын

Exactly! I solved the first part in 30 min and struggled with the 3 other parts more😂

@Zoe_EK

11 ай бұрын

It’s been 7 years but I still remember all exercises from part B but none of part A😂

You are so cool :D I am a German/Bavarian and I did exactly this maths "Abitur" in 2019. I sticked true to Mathematics (even though I did poorly in this particular exam) and recently this year wrote my bachelor thesis in Theoretical Chemistry, particularly Density Functional Theory (DFT), where I elaborated on the quantum mechanical math behind it 😊

@k.m.8190

Жыл бұрын

Fellow 2019 Bavarian Abiturientin here :D To be fair, that particular exam is considered comparatively harder than prior ones so I hope you weren't too disappointed. It's so great to hear that you weren't discouraged but stuck with Maths - your research sounds so fascinating :)

@agiyx8591

11 ай бұрын

@@k.m.8190 Its always considered harder from year to year. In fact it gets easier to easier per year.

@IndependendtransgenderdollRex9

11 ай бұрын

Ach du heilige Scheiße Respekt am dich

@hopejohnson6347

10 ай бұрын

@@agiyx8591 no, it doesn't. I did my Abitur in 2004 and it was way easier than this one. I did my bachelor thesis in physical chemistry later on, btw so *wink* to OP :)

@larsmenken2679

10 ай бұрын

Seems to be the way. Math LK and then chemistry as well. I wanted to go into spectroscopy but the new prof we got was an electrode guy so I did molecular modelling instead. I did DFT around 2000/01 when we did it on a Pentium 2, but if we got lucky we got shared time on a Cray supercomputer with 8 cores ;-)

First of all, props to you for also showing how you struggle with a quesation. That's really genuine content. As a math teacher myself, it is always interesting to see people who are trained on far more complex problems sometimes try to pull out the nuke instead of remembering that it's a high school exam and therefore a simpler way must exist. Anyway, very entertaining video. I actually showed it to my students because of how nicely you narrate your thought process.

at 44:30 the vertical lines are used in Germany, because we use the comma for decimals. So the English (1.2, 2.6, 9.2) would be (1,2 | 2,6 | 9,2) in German. If we didn't use the vertical line, it would cause confusion: (1,2, 2,6, 9,2)

@mrocto329

11 ай бұрын

I believe (1,2 ; 2,6 ; 9,2) is also used when using comma, so why something so different?

@marsultor6131

11 ай бұрын

@@mrocto329I guess because in handwritten form ; could easily look like :, would just add more confusion.

@m.h.6470

11 ай бұрын

@@mrocto329 I have never seen it with ; I only know the | form. In my school years, it was always |

@TomRocksMaths

11 ай бұрын

Ah that makes sense - thanks!

Almost 45 years after my Bavarian Abitur those videos are so much fun to watch! To rediscover the bits and pieces of knowledge, securely tucked away in remote parts of the brain, under a layer of dust, and to put them back together and see them work again... keep those brain cells busy, folks! Add a second level of of satisfaction if those videos are made by a foreigner. Seeing again and again that the language of science and math is indeed universal! Thanks, Professor!

i had 6 points in this exam and im proud of every single one

I completely failed the math Abitur exam with a F+ and it didn’t stop me from studying civil engineering

44:58 The sphere question is a lot easier than you might think, if you just treat it as a vector question, and don't bother finding the plane equation. The midpoint of centers of the spheres is the center of the circle. Then you can find the distance from the center of a sphere to the center of the circle, and do pythagoras for the circle's radius.

I took this exam. And I remember some of my struggles and i feel so stupid now. Lol. I was pretty good at maths but I didn’t do that well on the exam itself. It’s so cool to see you solve it.

I have dyscalculia and ADHD and somehow managed to teach myself enough math in my final year of school to get 9 points on my math Abitur (for Americans that’s basically a C). I was very proud of myself and haven’t done any math ever since. It’s been a full decade and I literally use a calculator if I have to do simple additions. 😅 School was fucking painful and I refuse to suffer ever again.

@freya4679

10 ай бұрын

Omg du kannst so stolz auf dich sein! Ich hab auch ADHS (aber keine Dyskalkulie) und hab im mündlichen Mathe Abi in Baden Württemberg 2023 auch nur 9 Punkte geschafft 😅 Mathe hat mich aber auch noch nie interessiert

@Sternburg

8 ай бұрын

Mündliches Mathe Abi? Du Verrückter@@freya4679

Thanks a lot. I'm a maths teacher myself and know how it feels like to make little mistakes or to be stuck and not seeing the way out. It's a relief! Like Heidegger put it: teachers are the more-learners. As to the circle thing: as the bowls have both the same radius, the centre of the circle is exactly in the middle between M1 and M2 (-1, 0, 2). And: you almost found the distance between the two centres, squareroot of 36 (not 34, small calculating mistake) equals six, that's 3 in each bowl. As 3 square plus r square equals 5 square (Pythagoras) you get r=4. Reading through the other comments, that's nothing new here... Anyway, thanks alot.

I'm getting PTSD-like flashbacks to my own Abitur. That exam was brutal and I threw up three times afterwards.

I really enjoy these videos sir! Keep these up! I love making maths videos!! Keep up the amazing job sir!

I had straight As in my Bavarian Abitur, but almost failed Maths. At our prom, our Maths teacher took me aside and apologized that he had to vote for the option we ended up taking, being aware that it was only tasks I struggled with. He said the other version had mostly text questions and then he would have had everyone but me failing. He was such a darling. I'm not sure if he actually felt bad enough that he just pretended I had passed 😂

@jkraemo

10 ай бұрын

Doesn’t the Abitur get graded by external teachers in bavaria? In NRW different schools exchange their Abitur exams to get graded so there is no favouritism.

@jkraemo

10 ай бұрын

@@StrawberryStar7 Der letzte Satz hört sich stark danach an als hätte der Lehrer sie benotet und sie aus ihrer Perspektive aus Mitleid durchgewunken

@jkraemo

10 ай бұрын

@@StrawberryStar7 Das impliziert aber weiterhin, dass der Lehrer benotet hat, warum sonst sollte er denn so tun als ob sie bestanden hätte? Der letzte Satz ist auch einfach nicht besonders präzise geschrieben, also komm du mal lieber von deinem hohen Ross runter.

@jkraemo

10 ай бұрын

@@StrawberryStar7 Da interpetierst du jetzt aber wahnsinnig viel rein was so gar nicht gesagt wurde, aber klar so kann es kann natürlich auch sein. Impliziert heißt ja nicht dass es so sein muss. Weißt du was eine Implikation ist?

@viola8119

10 ай бұрын

@@jkraemoich hab 2021 in Bayern mein Abi gemacht und an meiner Schule (bzw. wie ich aus Erzählungen weiß allgemein im Umkreis) hat zuerst der jeweilige Lehrer korrigiert und dann gab es eine zweite Korrektur durch einen Lehrer der anderen Mathekurse

Most importantly part in German math exams: Underline the result twice. Might not count otherwise 😅

Oh man, this brings back a lit of memories. This was more entertaining to watch than expected, especially with the added handicap of questions being lost in translation. Btw, "Abitur" would be pronounced roughly like "AH-BE-TOUR"

Please try part B, cause it’s soooo much harder than A. In Germany we always say, that A has to be B good, cause it’s easy B and C are brutal some times. I had like 96% in A but like 60%-70% in B…

In the German/Bavarian Maths Abitur there is an A part (easier, without calculator) and a B part (harder, with calculator). For each part, there are two different groups of tasks that are very similar. But you are only allowed to work on one of these task parts, i.e. either 1 or 2. The teachers decide before the examination which task groups are presented to the students. You have only done part A, can you please do the more difficult part B?

@DumblyDorr

Жыл бұрын

Seconded :)

@swityfx6383

Жыл бұрын

Not only Bavaria and Bavaria was the easiest Abitur I have practiced.

@joku3151

Жыл бұрын

It would be cool, if he would take on an advanced math exam (Leistungskurs Mathematik Abitur). There is also a version of the advanced math exam in which you can use a CAS calculator.

@daredevil7846

11 ай бұрын

@@swityfx6383 It's actually considered to be the hardest

@maximilon927

11 ай бұрын

​@@daredevil7846 By Bavarians, lol

The thing with task group / Aufgabengruppe, 31:20 The exam in Bavaria is provided centrally and the teacher doesn’t know until the day of the test how the exam will look and what topics it covers. This means the teacher has to prepare the class in the best possible way in order to be ready for any topic that is part of the syllabus, they can’t just say: ”oh, this topic is not so important, we will skip it and I promise it will not be part of the test”. This ensures that all students in Bavaria have the same difficulty and the same prerequisites in the exam and it doesn’t matter what school you went to and reaching a certain number of points is comparable across all schools. But because it can always happen that there are questions that the teacher might find very difficult because they didn’t really practice that type of question or maybe they know it would catch the students off guard, there are different groups of the test and the teacher can choose what group is the most appropriate for their class. I remember in Physics there were a number of topic areas and the teacher told us we could shorten or almost ignore one of them and focus more on the others and they would then not choose the group of the test where this topic appeared, which was cheating a bit and also a bit of a risk because then they have less choice and could be forced to choose a group with a difficult question beacuse the other group would cover a topic we hadn’t practiced. Am I making sense here?

@flowerdolphin5648

11 ай бұрын

That is interesting for sure. In Austria we don't have this for math, it's the same exam for everyone across all Gymnasiums. The only one where you yourself as a student can choose your exam is German, where there are three groups. And a lot of teachers will choose to not teach poetry analysis because they think students should not need to deal with that because it's too difficult for us. I rebelled and chose that exam anyway lol.

@thomasgabler3476

11 ай бұрын

I am a Bavarian Maths Highs School teacher and yes, you are making perfect sense. On the day of the exam we come in very early in the morning and solve all the parts ourselves, then we discuss which ones we choose. My biigest fear every time is that i might have forgotten to teach something that ist part of the exam...

@ymiros0953

11 ай бұрын

Isn't this here just that there's an A exam and a B exam where the tasks are the exact same, but the numbers get tweaked and every second person gets A and every other gets B so that when you copy from your neighbour your numbers are all wrong? At least that's how they did it in all the exams in my school. Well looking at it again the tasks later on differ more, so maybe not.

@pmas1

11 ай бұрын

@@ymiros0953 No, definitely not like that in Bavaria. The tasks are distinct (but supposed to be equally hard of course) and the teachers decide in the morning, when they see the exam for the first time, which group their students will solve.

@thomasgabler3476

11 ай бұрын

@@ymiros0953 No, those are totally different tasks. Our exams take place in the school's gym with tables spaced 1-2 meters apart and 3 teachers watching all the time.

Love it man. ❤ You just triggered a time travel in my memory. It has been almost 20 years since I have done my Mathe Abi.

It would really interesting if you would do the „Part II“ portion to give a real assessment of the German Abitur. Love your content!

my math examens in university (MBA) werent as difficult as the Math Abitur and I was just basic-level Maths for the Abitur, not advanced level! Kudos to all students passing this one - you know more about maths than you will ever need in your entire life!

@user-nm2cl3xh7q

10 ай бұрын

Yeah, that was actually the exact Abitur I had to do 😂 Everything about it was awful

@MiauZi69

10 ай бұрын

wtf? i think this was quite manageable .......

@peterlustig6888

10 ай бұрын

MBA in what?

so basically, you got part A to be done without any tools and part B, where you are allowed to use a calculator and a predefined formularsheet. in Part A you can choose between groupe A or B again, depending on what does look easier to you and finish these tasks in 90 minutes. afterwards you will go for Part B of the exam, again choosing between Group A or B and solve these questions in 180 mins i guess.(not sure abnout the exact timelimits here). both togethrer will give you up to 120 points

Awesome! Very interesting how the exams differ in different countries!

Wanna know something crazy: I never understood math in school. Watching videos like yours teach me a lot more than most teachers could in school. And I know a lot of folks who learned math at university because the school system didnt teach it properly.

@wfefeefhh

8 ай бұрын

I actually never got math in school i got 6 points out of 15 at my abitur examen and even had to repeat one year because of math. I also had an average grade of 3.5 not gpa but german grade! After that i did my bachelors in business administration with an average grade of 2.1 and currently iam doing my masters in statistics and my average grade is 1.8 just shows how bad the german school system actually is

You placed that right Abitur is the German A-Levels. The German GCSE is called ZAP (Zentrale Abschlussprüfung) and is taken about 2 to 3 years before the Abitur with students using that dagree to get into job training and might not go on longer to get into University.

Love the challenge! I think the circle-question could just be solved with triangles and pythagoras, and as both radii are equal the center is trivial. Then again, it has been a few years since I wrote my Abitur😂

Awesome video! imo the australian HSC Maths Extension 2, Q16 and Q15's (the whole exam is 3 hours, maybe a little too much time for you on video) are usually the most creative and hardest high school math problems i've ever encountered and I would love to see you try them!

54:00 they only ask for the center and radius of the intersection circle, not for the full equation. So you can do it on a 2d projection, i.e. the center of the circle is the midpoint between m1 and m2, and the radius can be done via pythagoras (half the distance between m1 and m2, the radius of the circle, and the radius of the sphere, 5, are the three sides of a pythagorean triangle)

@Fishpizza1212

11 ай бұрын

The half distance between m1 and m2 is the sqrt(34)/2, the r = 5, so the hypotenuse is 5, side a is sqrt(34)/2, and side b is what we are calculating. Then b = sqrt(5^2 - (sqrt(34)/2)^2). Then b = sqrt(25 - 34/4) then b = sqrt(16.5). However, at 57:30, Dr Tom calculates that radius as 4 in Maple, not sqrt(16.5) which may be an error.

@ymiros0953

11 ай бұрын

@@Fishpizza1212 Well 48:50 2^2 is 4 and not 2, so it's 36 and not 34 (which also makes more sense cuz it's easy to take the square root in your head in case the student didn't think of squaring the 10) Also even if the 2 radii were different I'd still use relatively simple triangle geometry rather than what he did here

@leonardofacchin1452

11 ай бұрын

Yes, in my opinion the solution was meant to leverage the symmetry of the system, which was guaranteed by the spheres having the same exact radius. These kinds of tests are meant to be completed in a pretty limited timeframe, so they tend to present "computationally tamed" problems that do not require too many complex computations. Another way to find the center of the circle would have been to find the intersection between the plane of intersection of the two spheres (that Tom had already computed) and the line passing through the centers of the spheres.

As someone who is going to take a test like this (Abitur but not in Bavaria) in 2024, I'm quite delighted that I understand many of these questions despite having a terrible grade. This motivates me to keep my head up and learn more maths, as despite unerstanding the questions, I don't have a clue on how to answer them, except for if they're about derivatives.

@maggy756

10 ай бұрын

du schaffst das schon

@mfchd3315

10 ай бұрын

Solange du im Unterricht aufpasst und das meiste so halbwegs verstehst schaffst du es definitiv mit entspannten lernen vor dem Abi.

@bombe0074

10 ай бұрын

Welches Bundesland, hab auch 2024 Abi, in Hessen

@marvin2678

9 ай бұрын

und wie läufts ?

@niismo.

8 ай бұрын

@@mfchd3315 Ja darin lag das Problem. Im Unterricht kann man nicht aufpassen, weil der Lehrer uns stumpf Seitenzahlen nennt und nichts selbst erklärt. Wenn man nach Erklärungen fragt, bekommt ein Minus auf die mündliche Note. So kam es dass ich als guter Mathe-Schüler den Mathe LK gewählt hatte und dann komplett zurückgelassen wurde. Ich bin jetzt seit dem neuen Schuljahr bei einer Mathe Nachhilfe, welche enorm hilft. Somit sollte ich das Abitur schaffen, Mathe-Abi ist glaube ich nächstes Jahr irgendwann im März.

Gives me flashbacks to my Abitur preparations... I was using this exact Abitur exam (and some more obviously) for practice

As far as I remember from my Abitur, the student has 150% of the time that a math teacher needs for it so you were very well on time :D

For the intersection of balls one can IMO simply use the half of the distance of the centers (3), the radius (5) and Pythagorian theorem which seems to give the Pythagorian triple (3, 4, 5) resp. 4 as the final answer.

@magemage5659

11 ай бұрын

was also my approach - the spheres have the same radius so they intersect at equal distance, which is 3 from either middle point. Also one shouldn't forget that you were supposed to calculate the center of the circle which is just the mid point of the 2 centers.

you got all the translations right. that's worth an extra point.

Great job! You finished the first half of the 2-part exam!

For someone who is bad at maths, it was still a pleasure to watch the video and see how people make brilliant math i myself could never do. Really enjoyed it!

Actually you only got the first part. The first part is always quite straight forward and there are no pitfalls, it's the second part where most students struggle, because it leaves a lot more room for finding the solution. My exam was 19 years ago, but I still remember one of the problems we were given. For the problem a piramid-shaped tent was given. The tent had a rectangular door on one side. One of the problems then was this: Imagine a point lamp hanging inside the tent down from the highest point in the middle. How far down would it have to hang in order for the lit area in front of the door outside the tent to be exactly 1 m²? It was quite a cool exam imho. It was the one from Baden-Württemberg in 2004.

the center of the intersecting circle is trivially on the line through the centers of the spheres. So a possible final few steps of that particular question are: 1. intersecting the line through the centers with the plane of intersection. 2. determining an equation for the intersection circle of either of the spheres and the plane of intersection 3. and then determining the distance of the center point to any of the points on the actual intersection There is a shortcut here where you can argue that given the radii of the spheres are equal, the center of the intersection must be in the middle between the centers of the sphere, but the general solution has been set up beautifully already, so that argument is not necessary

Had flashbacks watching this. I did the exam two years after 2019 but typically you do old exams as preparation and I calculated my way through the 2019 exams multiple times as well as the five previous years.

nice to see you managed the "warm up part" of this excam.

Pls do also the Part B of the Abitur exam. You've done "only" Part A for which you're not allowed to use a claculator and you have 90 minutes of time. Afterwards that Part there is another Part (= Part B) for which you're allowed to use the calculator. That part is even bigger (more tasks) and more difficult than this one. I believe you've 3 hours of time for that 2nd Part.

@Karikato

10 ай бұрын

I believe you confuse something. Part A and B are the variants, that you usually get as far as I understand. So you can't spy the results from your neighbour and write them down.

@Yadc

10 ай бұрын

​​@@Karikatothose exist aswell that you get A or B exams so you can not copy your neighbours solutions. Where I live in Germany we get a first part(without calculator), you get that sheet at the start of an exam and need to finish it in an certain amount of time(time varies depending on which grade you on). The second part is usually the complex part where you also allowed to use your calculator. I think the concept of first and second part starts in 10th grade.

@sweets3rialk1ller

8 ай бұрын

@@Karikatono💀 there’s always Part A and then Part B.

Very interesting video and I find your way of explaining your thought process extremely entertaining and helpful! If you choose to do part B as well (I'm sure you're aware of it by now, since so many have pointed it out) - I'd be more than happy to help with translating it in advance. (German from bavaria with english speaking relatives here).

very nice, as a bavarian wo also went to a boarding school in england i can tell you, i think you absolutely nailed the difficulty, its supposed to something like a-levels, yet not as hard as FM is suppose so that was nice. Generally speaking, the length of the exam with both parts defo adds to the difficulty as well. Here in munich at the University (Lmu) we barely have exams this long, so its acutally very confortable in comparisson to those from the Abitur.

I sat my Abitur decades ago and I still sometimes dream I forgot to take the exam and need to address that asap.

I took my math exam nearly 20 years ago (Thuringia, Leistungskurs) after our teacher worked on Bavarian exams with us; and up to today I wonder how I achieved a top grade. In the meantime, I'm not understanding a single word of it anymore! 🤣

There are also three different topics in the exam. In the aide free part you have to do everything and in the part wich allows the calculator you can choose in between analytical geometry and stochastic.

@albadorado6280

11 ай бұрын

The analysis (algebra) part is mandatory

Thanks for the cool and sincere session. At school Math was my favorite class but at University in Germany it was quite disappointing sitting there with 350 students in Audimax and Prof. was only reading from the script. What incredible loss of time..

The intersecting sphere question was just Pythagoras. As the two spheres have the same radius the circle of intersection centre is just the mid point of the two sphere centres. The radius of the circle then follows.

I suffered through the Bavarian Abitur about 10 years ago, so at one point of my live, I was able to do all of that, but I've basically forgotten everything, so it was like you were speaking in tongues. The American tests you did were way easier, I was actually able to solve most of them correctly, whereas here I read the questions and was blanking so hard. It kind of triggered some mild PTSD in the process.

@calistafalcontail

Жыл бұрын

To this day I dont understand why something most people never need again in life ever, is a "must manage to solve" to get a certain degree. It can ruin talented, smart peoples plans in life. I would rather pick between learning an additional language or math. Most people know after grade 10, that they dont wanna be rocket scientists anyway. The ones who love math can run with this and the ones who dont should take another challenge, cause they wont study anything in uni that requires higher math anyway.

@marcosrodriguez2496

Жыл бұрын

@@calistafalcontail This isn't even real math. It's just testing whether you can follow simple receipe to solve these questions. Nothing to do with being a rocket scientist. And I would argue you do need this all the time once you know how to do it. It's like knowing how to use the internet. Sure if you don't know about the internet, you also think you don't need it.

Regarding the Task Group thing - from how it looked to me basically there are 2 types for the same exam and you will either get Task Group 1 or Task Group 2, basically by chance and it is just so if people should sit too close to each other that they can't cheat off of the neighbours sheets. At the end it doesn't matter much since the tasks are made to be similar but different enough, but yeah technically you wouldn't have been allowed to switch, considering that you would only be presented with one or the other. Many have also already mentioned it but yeah the Math Abitur is split into 2 parts Part A and Part B, part A being without any extra tools (calculator, collection of formulas) and part B with those tools. What kind of calculator is allowed is also different from state to state because some allow with graphic function some don't. But yeah Part A is usually 90 minutes and Part B 180, for a total of 4.5 hours. Usually you can start working on Part B before the time for Part A is over but you are not allowed to use your tools until those 90 minutes are actually done. Again might be slightly different from state to state, for example where I wrote it I think the total time is 5 hours with the B Part being 30 minutes longer but yeah those are some details, though it is said that some states have harder exams than others which I can't really judge since I only know the ones from the state I was in.

Since the two spheres have equal radius, the center of the circle would be exactly between the two sphere centers. So the center point has to be (-1, 0, 2). Can be calculated using the vector between M1 and M2, dividing in half and adding it back to one of the centers, or just take the arithmetic mean. ((1,2,3) + (-3,-2,1))/2 == (-1,0,2) Since the distance between the two spheres is 6 (we pretty much calculated that in part "a" which gave a squared distance of 36), half of that is the length from one of the sphere centers to the center of the intersection circle. Together with the radius of one of the spheres we can construct a right triangle between M1, C and any point on the intersection circle. This is a 3,4,5 triangle (5 is the radius, 3 is the cosine*R and 4 the sine*R). So 4 is our circle radius. Of course this trick only works because the spheres have the same radius. In the german tests they usually like to construct questions where you may be able to use the results of the previous parts. Not a hard rule, but that's often the case. To better understand question 2, b we can think of it like this: Points where all 3 components are the same, lie on the diagonal that goes through the origin. So essentially on the vector (1,1,1). Any plane who's normal vector is perpendicular to this line and does not contain this line / the origin is parallel to this line and therefore has no intersection. Any other plane would intersect that line at some point. So we essentially calculated the dot product between (1,1,1) and (a,b,c) and it must be 0 so the two vectors are perpendicular. That's what that (a+b+c) == 0 actually means geometrically. Of course an important detail is that "d" must not be 0. ps: The "ur" in "Abitur" is similar to the "ur" in "your". Though of course finding equivalents in other languages is always difficult as even in english people are pronouncing things quite different ^^. And I don't just mean AE vs BE,... all the dialects :) I could have said similar to how you would say "Uhh", but even that is not the same everywhere ... Ahh maybe compare the "tur" with "tour". So it's abi-tour

@TomRocksMaths

11 ай бұрын

Yes the mid-point trick is exactly what is used in the accompanying worksheet which goes through a correct solution.

@skayt35

11 ай бұрын

​@@TomRocksMaths yes, and it makes use of the "easiest" Pythagoras: 3² + 4² = 5². Geometry in German schools is very much about visual constructions in a plane which the ancient Greeks performed (some of which then drove them nuts because they could really draw lines resembling numbers like pi or sqrt(2) which they couldn't calculate as fractions).

🇩🇪🇬🇧🇺🇸🇪🇺 *Most unique* video I've seen in years, as a German veeery interesting to watch! I was more curious than ever having someone compare it to other systems, cause this is one thing I will never know. Ive never seen an english maths class, how it develops over the years or how hard the exam is at last. Theres no way I could compare, so your reaction was something ive always wondered for!

"Begründen" does not mean prove in this context. It better translates to "argue why"

You have to keep in mind that this is part 1 from the exam, the part without a calculator, afterwards you'll get another or in some states even 2 parts with even harder questions

Nostalgie! I did my BaWü Abitur back in 2010. nice to see this 🥰

49:05 The center of the intersection circle of two spheres of equal radius is the middle between the two center points of the spheres, and the middle between (1/2/3) and (-3/-2/1) is the middle of each component separately, so that's (-1/0/2). The radius of the intersection circle is the square root of the sphere radius squared minus half of the distance between the two center points squared (I would make a 2d drawing to prove that, but it should not be too hard to figure it out). The distance between the two centers is sqrt((1 - -3) ^2 + (2 - -2) ^2 + (3-1) ^2), which is sqrt(16 + 16 + 4) = 6. Half of that is 3, so the radius is sqrt(5^2 - 3^2) = 4.

Strangely I really enjoyed watching you solving this part of bavarian Abitur. It feels like every year, at least on of our 16 states fails in creating the math Abitur. Mostly, it's to hard or some tasks aren't solvable. You'll probably find one of these pretty fast. Maybe you can do one of these :D I highly recommend deepl for translating. Its AI-driven and is really good for translating stuff in a scientific context. It's used by our university, too.

In Germany we say: „die Aufgabe war geschenkt“

CAS stands for computer algebra system. You can decide if you would like to use a normal calculator or a CAS in the exam and then you pick your exercise depending on which option you have chosen

It´s Friday 1am, I do have a bachelor degree in tourism marketing, being from Germany and watching this video. Great choices of life.

Part A was quite nice for me because the tasks aren't not so convoluted. As someone who didn't practice enough part b was quite annoying. I probably got most problems right bit it took me forever since I wasn't as used to solving problems as I should be as a leistungskursler. Apart from the time factor it was doable id say. Did it last year in Sachsen which is usually one of the hardest as well

I had mostly the same approaches as you - with the exception of the intersecting spheres. I wonder if mine is valid, too. I thought: the spheres have the same radius, so it's exactly analogous to drawing two intersecting circles of equal radius at the ends of a line-segment. Connecting their points of intersection will exactly bisect the line. Thus, the center of the circle of intersection must be exactly the mid-point between the two centers of the spheres, since they have equal radius and intersect. (For dimension 3, the circle of intersection between 2-spheres defines a plane, each point of which must be equidistant to the centers, and thus must be the unique plane bisecting the line-segment.) This gives us the center of the circle. To get the radius, we can then use trigonometry - the mid-point on the line-segment connecting the centers of the spheres together with any of the centers and any point on the circle of intersection forms a right triangle. We know both the radius of the sphere and the distance from a center to the midpoint - so we have the hypothenuse and the adjacent and can solve for the opposite using Pythagoras - this will be our radius. (I reasoned "visually" - imagining two intersecting spheres of equal radius, a line-segment between the centers, and a right triangle between the mid-point, a sphere-center, and a point on the intersection. Rotating it gives us the circle of intersection - so the opposite of the right triangle must be the radius) This seems a much simpler approach than the analytic one - but I'm not sure if I'm missing anything.

@glowredman

Жыл бұрын

I would've done it like you described aswell.

@paulkopold6364

Жыл бұрын

I am very sure your approach works, since I am from Bavaria, did my Abitur in 2019 and followed the same approach and it was not marked as wrong. Also the argument makes sense, had the same thoughts during the exam

@Supremebubble

Жыл бұрын

I don't think "trigonometry" is the right word but yes, this is most definitely the intended solution. In part a) it askes us to prove that the spheres intersect. This is easily solved by calculating the distance between the center points which you can do in your head (it's 6) and see that 6 < 2*5. Now the calculation of the radius in part b) is much easier too, because the distance to the midpoint is 3, the hypotenuse is 5 and we see that the radius must be 4. It's a pretty neat problem actually.

@DumblyDorr

Жыл бұрын

​@@Supremebubble It is a pretty neat problem, I agree :) But I do need to ask: Why wouldn't "trigonometry" be correct? I mean... "metron" := "measure", "trigon" := "triangle" => "trigonometry" := "measurement of the triangle" Trigonometry is more than just the trig functions, and arguably Pythagoras is its core and foundation. After all - sin theta = length of opposite / length of hypothenuse. It's just that using Pythagoras directly is a lot easier than using trig functions here.

@klaus-udokloppstedt6257

Жыл бұрын

that was exactly the way I did calculate it. first: circle center is the half of each coordinate pair second: calculate the radius via the circle-inner triangle going to the center distance

3 b) in Geometry is kind of easy to solve actually. Since both spheres are of equal size, you can simply take the center of the line connecting both centers which is (-1,0,2). For the radius you can actually reduce the problem to 2D. What I mean is that you have not two spheres, but two circles with r=5, intersecting each other. You want to know half of the distance between the two intersecting points. You can easily calculate the distance between the two given centers to sqrt(36)=6 [you forgot to square the 2 so you'd get 36 instead of 34]. Half of that is 3, using the Pythagorean theorem you get sqrt(5^2 - 3^2) = 4 as a final result.

@u.s.navy_pete4111

5 ай бұрын

Good solution! Only the center of the line connecting both centers is at (-1,0,2), not (2,0,2).

@Lorenzo_der_Ritter

5 ай бұрын

@@u.s.navy_pete4111 thanks for pointing it out, you're right of course

@u.s.navy_pete4111

5 ай бұрын

@@Lorenzo_der_Ritter You are welcome!

I completed The math Abitur this year. For the last question you do not need to delve that complicated, Simply constructing a triangle in the cross section of the sphere with sides r=5 for the hypotenuse and 3= ( the distance between both center of spheres /2). By Pythagoras our last side is the sqrt of 16 which is 4. For the distance I just subtracted k1 from k2 and took the distance which is 6.

@black_panda5988

8 ай бұрын

Dachte schon ich bin der einzige der die Aufgabe gelöst kriegt

On question 4b) I think they want you to argue that they intersect at a point that lies on y=x, not solve for the exact point. I read the original question in german and that is how I would interpret it. Also at our school in Bavaria our teachers selected one of the two task groups for us to take. Part A and B additionally need to match task groups, so if you take task group 1 for part A you should take task group 1 for part B as well. Very interesting video👍🏼

It's funny that Tom struggled with the two problems that are using discrete probabilities and 3D geometry. I don't know about other people's experience but when I was in high school these were the 2 topics that a lot of math teachers avoided or explained poorly. I don't know if it is because they are difficult to teach/explain or because they require a different way of thinking but I find it interesting.

@thomasgabler3476

11 ай бұрын

I can't speak for all maths teachers, but when I studied maths, we could choose to leave out one of those two. Discrete probabilites are sometimes very tricky, especially choice with/without repetition and/or order of sequence. I often think "yes, your solutioon seems to make perfect sense, but the result is wrong - why?!!" I think you are correct - they require a different way of thinking. A lot of students who are rather bad at "normal" maths suddenly excel at probabilities, because you need very little algebra knowledge.

@milanprolix2511

11 ай бұрын

@@thomasgabler3476 "your solution seems to make perfect sense, but the result is wrong - why?!!" I have been on both sides of that one! (as a student and a teacher) I think it is the scary side of probabilities: In most domains of math at High School / College level, either you are right or not and you can usually tell, but with probabilities, you can have complete confidence in a totally wrong result. For 3D geometry, I think it is more: either you see it or you don't. I personally did not! I just solved everything with coordinate algebra or, as my teacher said: "using a pneumatic drill to kill a fly"! 😅

@juliab3326

10 ай бұрын

These topics were the only ones I could remotely get behind in school. I was always bad at Maths but these exercises probably helped me not to fail this exam (speaking about Abitur)👌

@steven_003

6 ай бұрын

⁠@@milanprolix2511As my professor says: „Everything that isn’t wrong is allowed.“ or how I like to say: „to just brute force it“. 😂

I just discovered this channel. You seem to make maths fun! I wish you could've been my teacher but I guess we've been to school around the same time xD

Yes, you did it right. You're able to decide if you want to do task 1 or task 2 for Analysis & Stochastik

48:35 interesting how 2^2 equals 2 😂 Btw the German notation if a point in geometry (with the vertical lines between the numbers) is to not clear any confusion of whether something is a number with decimals (and the line a comma) or two separate coordinates. Don’t know if you do it the same way but for us in Germany bigger numbers have dots to separate every three numbers: 100.000 is a hundred thousand, while 1,01 is one point zero one. Hope you understand what I mean 😅

Man I still remember when I took this exam a few years ago. Can honestly say, I don't understand like 70% of this, even though it was my best mark back then.

11 years since sitting in front of this and haven’t used any of this since…no clue how you showed up on my timeline but glad to see you struggle also😅

Omg, this is the exact exam I did in school. I finished school in 2019 in Bavaria and the Maths Abitur that year was notoriously difficult.

@petermayer9292

10 ай бұрын

Irgendwie ist doch jedes Jahr außergewöhnlich kompliziert und sogar unfair kompliziert

That was my exam. :) As someone who's written this exact exam in Bavaria in 2019 I can tell there was a huge revolt, almost a demonstration, against the difficulty of this exam as it was seen as too hard. Edit: Also this was not the whole exam. The exam contains Analysis Part A & B, Geometry Part A & B and Stochastik Part A & B. While Part B can be solved with a calculator its use is strictly forbidden in Part A. Part B was way more difficult.

@thisorthat629

11 ай бұрын

As is tradition, every year is the hardest and easiest simultaniously, and barvaria over overeything... get a new spiel

@Amphibax

10 ай бұрын

​@@thisorthat629the problem is the difficulty fluctuates over the years sometimes harder and sometimes easier. I would consider this a problem in a exam which should be the same difficulty for everyone.

@epox_

10 ай бұрын

I was mad that we didn't get probability calculations😢 it would have been my strong suit

@Alexseya

8 ай бұрын

​@@AmphibaxIt doesn't really. If you look at the big picture, it's all relatively similar. If you prepare properly, this wouldn't be too hard for you. (The key is to take all the exams of the years before, because the vast majority of questions, especially the difficult ones, repeat every other year.

I actually finished my oral "Abitur" in maths just a couple weeks ago and got a perfect score. However i graduated in Nordrheinwestfalen (another state in germany) whose Abitur is generally considered a bit easier than Bavarias and i only did the basic course. Still very interesting to see an expert of the subject just crushing through the stuff that i struggled with sometimes. Still, Maths has always been one of my favorite subjects in school just because of how precise and free from interpretation it was. You're either right or wrong and i loved that.

@TomRocksMaths

11 ай бұрын

Congrats!!

Watching him do the first part in a different language made me realise that this is more calming than doing it in a german classroom. Its been twoo years for me, I dont have Abi but MSA and im also not from bavaria. Im from Mecklenburg-Vorpommern, oir exams are "easier" but that also deoends on the teaching style from your teachers and apparently that didnt work with our teachers. How the hell do I understand everything he does in this video when I completely failed math from grade 5 to 10.. Over five years I felt like I have missed ALL the memos, suddenly they only soeak elvish or something and now I get everything..

Thank you for the video. I would like to comment on the geometry task that you didn‘t finish: I do not have the solution sheet for the Bavarian Abitur since I teach Math in Hamburg. But I am pretty certain that the expected solution was to cut the plain (that you had already calculated) with the straight line which contains the two centers of the spheres. The solution is the center of the circle.

This is the Abitur I took when I tool my final exams in school!! Apparently I knew circles better when I was 18 than you now..I think you just have too many tools at hand when you're a math professor. We did not learn about rotations in school at all, so never thought about anything complicated. The middle point of the intersecting circle just has to be in the middle between the middle points of the spheres, to get its radius, just use the pythogarean theorem.

@jroemling

11 ай бұрын

How do you get to the middle point? My first thought would be vector math, calculating the length of the vector between them and then going half distance from one of them. I remember vectors and matrices were a big part in 1997 when I took my test.

I have been watching your videos of taking various mathematics examinations and enjoy them. Are you willing to solve complex computational problems in higher mathematics using only a "slide rule", even though it is an outmoded tool?

at 57:50 you can reuse the vector between the center of the two spheres M2 and M1 which is v = (4,4,2) with length 6 as we already know. Then you just can go half way of that: v/2 = (2,2,1) which results in M3 = M2 + v/2 = (-3,-2,1) + (2,2,1) = (-1,0,2)

I did my Abitur now about 18 years ago in Bavaria with a so-called 'Einserschnitt' (most preferable average grade), but to my shame - or that of the Bavarian Abitur, depending on how you want to look at it - I only got that great final average grade because... I literally learned the Maths exam by heart. Yup, you read right. When I took the Abitur we had to give exams in only 4 subjects, 2 major and 2 minor ones. I was able to take both French and English as major, which gave me a guaranteed 15 points (or straight A), History as one of the minors, which only requires some cramming, so no issues there either, and Maths as a second minor. All throughout school I was average at Maths, usually getting a mark of 2, 3 or an occasional 4 (or B-D for the Americans), depending on how complex the topic was or plainly depending on in how much of a mood I was to practice at home or not. Most of the time I was in no mood. So I knew Maths would most likely be the subject that would pull my final average down. So I went and bought those books which contained all the exams of the last 5-something years, and I crammed those. Plain and simple. Well, originally I bought them to actually practice until I realized that the pattern of the questions was very repetitive, and more or less only changing number values and the wording around a bit (for probability sometimes it's light bulbs, sometimes it's flower bulbs, but the basic task always stays the same). They're just not going to reinvent the wheel for every new Abitur. Once I realized that, figuring there was no way I'm going to gain any real deeper understanding for the subject matter before my exams, I decided to do what had never been much effort to me, I learned the questions and the corresponding solution parts by heart. And it worked perfectly. There was only one question in my actual abitur that deviated from the question patterns I had studied, but because I didn't have to waste much time on the other questions, I could basically dedicate more than half of my time to solving that one unknown question and by some lucky epiphany somehow came up with the right solution. I'll never forget how after the results were out my Maths teacher who literally knew me for 2 years as a 'Sorgenkind' (a bit of a problem case) came running up to me in the hallway beaming going "You did so so well! It's amazing! You HAVE to look at your exam sheet! I am SO proud!' I never had the heart to tell him my understanding for Maths was not an iota better than before XD

I would love to see you trying the Austrian maths exam (Matura). Especially as there is an English translation available and you can check your marks afterwards. Probably pretty similar to the German one, although there are only two parts and you're allowed to use a calculator throughout the whole thing. Total time available 4 hours 30 minutes. (5 hours and 30 minutes since covid)

@McDonaldsCalifornia

8 ай бұрын

That one is easier I think

@byjynydjshsnny2430

8 ай бұрын

@@McDonaldsCalifornia no its way more theoretical

@steven_003

6 ай бұрын

@@byjynydjshsnny2430I found the one I had to take way easier than the one in the video.

You have to try the part b of the advanced course with calculus, stochastics and linear algebra.

In Austria, its the same math test for all the states. But there are two different version, depending on which math classes you got in your school career.

You should give the Austrian "Matura" math exam a shot. They also provide an English version. :)

@TomRocksMaths

11 ай бұрын

Thanks for the suggestion - added to my list :)

@kimlee7763

11 ай бұрын

Yess would be super cool to see you take the ahs matura