good video tho

Yes nice!!

Many other lists agree / also feature some of these questions. Clickbait but also true :) Some people have said in the comments there are harder questions but this is very subjective and no one has emailed me any questions that are actually harder.

@@arithmeticauk Okay thank you very much!! Great video btw :)

🫡

This is a UK exam and it's the not the hardest course for that age group. Further maths A-level is considerably harder.

Yep it could. We just used Rcos because that's what we chose, all other forms work them same

nope, this would have the maximum but it would not pass through the point specified

@@arithmeticauk excuse me, sin(π/3)=√3/2. 4sin(π/3)=2√3. It will pass the point. Maybe the mistake is the difference of how it does.

@@Bruh-bk6yo yes that it is true but i meant the origin. We see on the graph it does not pass through the origin, whereas 4sinx would.

@@arithmeticauk damn these graphs...

@@arithmeticauk why does using Rsin(x+a) not give the same result?

You can zoom in on KZbin by squeezing your screen. In future videos I'll try to make the font bigger

Appreciate the support :) Any topic(s) that you would like a video for?

Proofs, integration, differentiation, (although they might be hard to do in one video haha)

@@arithmeticaukmate please please do binomial Pd and binomial Cd harder questions

If you find one you think is harder then email it to me: [email protected]

@@arithmeticauk mm sure 👌🏻

@@arithmeticauk would you accept prelim questions, rather than questions in the a level paper itself?

@@asherang7 yeah sure, but I've made the video based on the hardest that have actually appeared in exams, I've got questions that are much harder than this from textbooks and other sources.

Infamous maths course 🔥 Will definitely make a video in the future on this!

Yes

What course did you take?

@@arithmeticauk The course to me doesn’t really matter. I mean I’ve taken AP Calc BC but I’d be a liar if I said that class was difficult for me. My goal is to possibly get to IMO however I don’t know if I’ll reach it.

Pure maths is obviously going to be easy. Just by the content alone, FP3 Vectors has been the only real trouble (for me). But I would argue that getting a 5 in BC pretty easy compared to an A* in Further Maths. Just the amount of content you have to master over pure maths, stats, mechanics, and decision maths as well as the high grade boundaries gives it an edge. But its all nothing to IMO. Even if you are a peerless genius, prepare to sell your soul to failure.

@@66sec65How old are you? I assume Calc BC is a later high school thing, albeit i could be wrong since i don’t live in America. IMO max age is 18 too correct?

@@jasimkunhi1543 Im not British but I’d say both are pretty easy at least in my opinion. I can at least certainly say getting a 5 in Calc BC is. Also I doubt I’d actually reach IMO, but the training is infinitely more important to me because it helps me learn how to apply maths that isn’t very direct. But hey if I’m one of the six people in America to reach IMO then I’d be very happy!

These are all A* questions, but this is the standard maths course. If you want harder questions then look at A-level further maths.

Sorry I didn't mean to be rude but ig my wording was rude due to other factors , i just wanted to know what grade students in America do these problems like I am not from America so I am not familiar with the A level etc stuff so I just wanted to know what grade are they from ?!

It's fine, didn't think you were rude don't worry. This is a UK course, 16 to 18 years old study this course.

@@arithmeticauk oh ok 👍🏻

Yes will make a video on these!

@@arithmeticauk if u could make one on rlly hard functions that would be class

@@rayzino3338 ayooooo

No lol

It is planned, just need to find the hardest problems, which requires doing most of the problems from all the past papers from all the exam boards!

@@unexpectediteminbaggingare8074whats your issue lmao

@@teodoraraducanu4 No problem

Some new videos coming soon. Will do a mechanics/proof version of this.

@@arithmeticauk bruh there are harder questions?

@@satya4577 this is just Pure... arguably mechanics can be harder!

how did you do overall

@@Dev-zn3yo Two A*s, in Maths and Further Maths, two As in Physics and Chemistry

@@TheDarkSide11891any tips? :(

​@@sun-do3tgTo be honest, it's just do the past papers, do the past papers, do the past papers. And when you think you're done, do the past papers. A lot of people get caught up on reading notes, but in my experience at least the best way to get ready for an exam is to just sit exams. I'd start with looking over your notes then pick a paper. Answer as much of it as you can without your notes, then when you're done use your notes to fill in the questions you couldn't do. Then do another paper the same way. You'll start catching on to how they ask questions, what type of questions they ask, and how to answer them. Eventually, you'll be able to go through all of the papers without your notes. Importantly, give yourself time and take plenty of breaks. Doing 5 papers in a row isn't going to help you. Do one a day, with a little bit of reading over notes in between. I also would personally sit and read the answer keys to help me. Sometimes inspecting their method will teach you something you didn't know. I always found that reverse engineering the answers helped me a bunch

@@sun-do3tg And if you can, try and avoid too many distractions. Don't get me wrong, I'm ABSOLUTELY not the person to be saying don't play games, look at your phone, etc at all leading up to the exams. Being miserable isn't going to help you study better. But for the 2-3 hours you're revising a day, try and find a quiet space, get rid of anything that you know is going to distract you and just try to focus on the work. Unless you're timing yourself, you should get up every half an hour or so and walk about for 5 minutes. I find that those short breaks from looking at the paper are often the time when you realise how to do a difficult question.

From a mix of exam papers. I can't remember the specific papers but they were from the post 2017 set and all AQA /Edexcel / OCR A / OCR MEI

What course?

Engineering first year

That's very nice!

Thanks!

I use Miro whiteboard

Indeed most likely they are but no one knows for sure, at least we know 3 of them have to be

Arctan identity - learned Idea behind decreasing x - learned Using arctan to decrease x - learned This particular xn - invented However I'd assume I'm not the first because it's a very popular topic and using a trick similar to this is not old... Euler used a similar one to approximate pi.

Thanks for the feedback. 😊 Difficult question to answer exactly. Let's say we want k digits of accuracy. Firstly note our xn will approach 0 as n goes to infinity but we should measure how fast it goes to 0 in log10. Let's measure this as v. Say we do m steps in our xn sequence ( with infinite precision ). Then in our power series we need to go up to the k/(2mv) term in the power series. mv is the number of decimal 0's we will have in our xn after m clicks. Our power series for arctan goes up in 2 hence the 2. Any term after this will have more than k 0's so for our calculation it will be irrelevant. If you're looking for whether it's an efficient calculation for a computer unfortunately I have say it's not... the use of the square root makes it really inefficient, especially if we want higher accuracy. Check out Ramanujans algorithm if you want a super efficient algorithm.

Must've been fate

Appreciate the support as always, anything you'd like to see? Proof that the sum of the reciprocal cubes is irrational?

haha thank you

Glad you enjoyed the video!

Thanks

Hello!