Top 5 HARDEST A-level Maths Pure Exam Questions of all time! (90% of students couldn't even start!)

In this video we go through the Top 5 most difficult alevel maths problems of all time. These questions were from or resemble questions from WJEC, Edexcel, AQA, OCR A and OCR Mei.
We begin by looking at a problem on summations, specifically a geometric series. The second part then gets us to use telescoping combined with logarithm identities to evaluate the sum.
The second question is on additional angle trignonometry. In this question we use the Rcos form to exploit the information given to find our answer. This could also be attempted by differentiation but we show the easiest alternative to finding maximums ie. using transformed common functions
The third question is on a differential equation, we show there is only 1 intersection with the coordinate axis!
The fourth question is on vectors, despite not appearing much in the course this question still took alot of mark and was very tricky (poor students!). We go through in depth how to complete this, reversing key ideas on vectors such as parallel vectors.
Finally we meet a very trick coordinate problem. We use SOHCAHTOA, trigonometric identities, completing the square and the cosine rule to complete this problem.
These video lectures are taught by a highly experienced tutor. The content taught will be useful for many courses around the world including: A-level Further Mathematics, IB Math AA HL, AP Mathematics and University level.
If you'd like to learn maths fast and to a high standard then check out www.arithmeticatuition.com , this is a professional tutoring organisation specialising mathematics. We offer a Free Initial Assessment Lesson and some of the best tutors on the planet.

[@TheDarkSide11891]

I remember doing all of these for revision for my A Levels. Great questions for improving your advanced problem solving skills.

[@Dev-zn3yo]

how did you do overall

[@TheDarkSide11891]

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

[@sun-do3tg]

@@TheDarkSide11891any tips? :(

[@TheDarkSide11891]

​@@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

[@TheDarkSide11891]

@@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.

[@sirensoulegaming4158]

For the very first question you did here my method was to pull 20 outside of the summation (since every term is multiplied by 20, you can factor it out), then the sum is just adding powers of a half, starting with the 4th power. with r = 1 at a bottom this is a standard summation with a value of 1 (can observe very trivially that the limit as r -> infinity = 1), so we can get the value of r = 4 starting by doing 1 - (1/2 + 1/4 + 1/8) = 1/8 (1 being the value of the sum r = 1 to infinity, the bracketed bit being the first 3 terms of the same sum). Finally, 1/8 * 20 = 5/2.

[@sentheaS]

For the second part of the first question I instead saw that the numerator was 50 factorial, but missing 2x1, so was 50!/2, and the denominator was 49!, ‘missing’ x1, so the argument was (50!/2)/(49!/1) = 50!/(2x49!), which is 25. Of course doing the same thing but for me it was easier to think of it that way :)

[@arithmeticauk]

Yes nice!!

[@anishnicholas1967]

Can you do another video with even more of the harder questions asked? Or like hardest question asked per topic?

[@arithmeticauk]

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

[@satya4577]

@@arithmeticauk bruh there are harder questions?

[@arithmeticauk]

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

[@snasundertale8949]

apart from the last 2 which i can't judge on since i'm not a geometry person and the third which needs a bit of calculus albeit being simple, the first 2 are simple algebra 2 material at least in america

[@66sec65]

Haha I wish I had these more simpler questions. Nice questions though! I have buddies who told me that the A-Level Pure Maths exam was difficult but seeing this told me it's not that bad.

[@arithmeticauk]

What course did you take?

[@66sec65]

@@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.

[@jasimkunhi1543]

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.

[@shinnyii]

@@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?

[@66sec65]

@@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!

[@reyaancali8503]

i dont understand why you used the Rcos(x-theta) formula as i thought it was Rsin(x+theta) also could this come up in the exam without them giving the format?

[@arithmeticauk]

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

[@asherang7]

these peoblems seem pretty standard for a level to my knowledge

[@arithmeticauk]

If you find one you think is harder then email it to me: [e-mail]

[@asherang7]

@@arithmeticauk mm sure 👌🏻

[@asherang7]

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

[@arithmeticauk]

@@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.

[@sulamakamyon12345]

where are these questions from

[@arithmeticauk]

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

[@7yamkr]

Take a look on indian jee advanced paper also👍

[@arithmeticauk]

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

[@janakhannas3604]

Can you do as level alone please

[@unexpectediteminbaggingare8074]

No lol

[@arithmeticauk]

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!

[@teodoraraducanu4]

@@unexpectediteminbaggingare8074whats your issue lmao

[@unexpectediteminbaggingare8074]

@@teodoraraducanu4 No problem

[@Aditya_196]

😵‍💫 we need tougher what grade for which these questions are for

[@arithmeticauk]

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

[@Aditya_196]

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 ?!

[@arithmeticauk]

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.

[@Aditya_196]

@@arithmeticauk oh ok 👍🏻

[@pigeonlove]

Font is too small

[@arithmeticauk]

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

[@Bruh-bk6yo]

11:14 wait, what? Isn't a=4, b=0 also a solution?

[@arithmeticauk]

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

[@Bruh-bk6yo]

@@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.

[@arithmeticauk]

@@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.

[@Bruh-bk6yo]

@@arithmeticauk damn these graphs...

[@theunavailableyoutuber2199]

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

[@jaspercarran3432]

do you think these are actually the hardest a level questions of all time or was that just clickbait

[@arithmeticauk]

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.

[@jaspercarran3432]

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

[@shuraimabdulaziz]

Are all these questions from A2??

[@arithmeticauk]

Yes

[@samyak101]

these questions are so easy, i solved all the qs in my mind

[@jashung4905]

avg american hard questions lmao

[@arithmeticauk]

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