Let's do the hardest further maths question in a level! What's the hardest question you have ever seen? Thanks for watching :) Subscribe: / @judekennedyatcl My Instagram: / judeekennedy
it is quite hard but it is fairly straightforward if you have seen a hyperbolic substitution before why is it 15 marks? 7-9 marks seems more appropriate
not really i just completed the question and lots of the time your second-guessing yourself if everything is going to work out and if things are going to cancel down etc. etc. its just kind of nerve-wracking. There's no hint that your tactic is even heading in the right direction until the very end.
This is a difficult question in the sense that it can be easy to mess up in your algebra, but you’re given the answer so you can easily correct it. If you can recognise to make a hyperbolic substitution then I don’t think it’s really that bad after that. There are a lot of harder questions that this in Further maths, but that’s just me being bad at other topics :)
With practice you get used to it issue mechanics, the mechanics section is just twisted and never makes sense is always annoying and for some reason covers good ton of topics from A2 physics considering you study it in first year makes it worse.
It's perfectly valid just to differentiate the right hand side. This bypasses any need to use hyperbolic trig function - and it just becomes a single maths chain rule/product rule question.
My thoughts exactly. If there are NO restrictions explicitly stated on how to approach the question. The student should assume any valid method to prove he assertion is available.
My thoughts precisely...it simply stated to prove the integral of the expression is equal to the stated result, but didn't mention how to go about it. But in a Further Maths paper, couple of things: 1) This would not be 15 marks (at least for Edexcel). Max about 7-8 marks. 2) They would never give the result unless it's a definite integral.
@anonymousms2005 Yeah, looking back, there are a couple of cases where I remember that they gave the result of the integral, but it's not very common, as you say. After coming out of the exam, I wasn't really confident because I finished the paper on the dot just as the invigilator told us to put our pens down. I had a very very slow start, but having spoken to my friends to ask what they got, they generally got the same answers as me so I'm more confident now but there are bits and pieces from that paper, which I'm still slightly nervous about. I just hope I smash the other papers in the next few weeks. What about you? How did you find it?
@anonymousms2005 Nice! I wish you the best of luck for the remaining papers. I do FM1 and FS1. I'm not too bad with FM1 but I'm not great at Impulse so need to work on that. FS1, Idk. Because of the decimal answers, I get super paranoid that I've got the wrong answer. Where are you going to go if you meet your requirements?
@anonymousms2005 Nice! If I get A*AAA (A* in Maths) and then grade 2 in STEP II, I'll be going to Imperial for Computing. Otherwise if I get 3 A*s, I'll be going to Edinburgh for Computing. I got rejected by Durham and Cambridge. I might see you in London if all goes to plan 😂.
All these questions are probably from OCR since it's the shittest exam board and they just want to screw their students over. I recognise it from the formatting of the question I think
I haven't had time to watch this yet, so probably won't apply to this horrific thing, but if your substitution can force the integrand into either the form f'(x)/f(x) or u/u, it's a good one.
In a situation where you will have a difficult substitution (ones containing inverse functions), there will tend to only be 3 different substitutions that can be made, arcsin(x/a), arcosh(x/a) or arsinh(x/a). Thankfully, arccos(x/a) is just negative of the differential of arcsin(x/a) therefore you won't need to know it. There could potentially be (1/a)arctan(x/a) however questions that require it can often be done using partial fractions. You can use the differential of each of the inverse functions to find which substitution you need (if you are doing Edexcel they are in a formula booklet on page 12). Essentially: If question contains anything of the form root(a^2 - x^2), you will need a substitution of u = arcsin(x/a) If question contains anything of the form root(x^2 - a^2), you will need a substitution of u = arcosh(x/a) If question contains anything of the form root(a^2 + x^2), you will need a substitution of u = arsinh(x/a) Obviously, each of these can be rearranged, for example u = arcsinh(x/a) is rearranged to a*sinh(u) = x (which I believe this video jumps straight to) where you can substitute and derive from there as shown.
Omw enjoy!!! Honestly I absolutely loved it and you learn so much more than you will in maths, problem-solving-wise. You'll get there if you put in the work consistently from the start!
@@JudeKennedyATCL thankyouu, I feel like further maths is a scary one before u start it, it looks impossible aha, but I’m good at maths and willing to put the work in to achieve my goals so thank you for letting me know it’s doable 😅👌
@@samstiles7053 yep!!? Trust me I looked at the past papers before starting and was terrified yet excited (or aufgeregt in German for a single word feeling) but now when I look back, I know how to do everything! It's such a strange feeling aha
Dw....looks bad but isn't bad. Personally, I don't like polar coordinates. Anything with graph sketching, I'm awful at but polar coordinates is even more funky.
X+2 = 3tanu is much cleaner. Ends up w/ 9 int(sec^3u), which is very standard and nice to remember bc it is (secx derivative + anti derivative)/2 [or by parts if you can’t recall this]. From there isolate theta and find sec and tan and plug back in
Question: I am expecting a comfortable 9 for GCSE Maths and I'm considering further maths a level. I'm not sure what I want to do with my career so do you think that maths, further maths and physics is a good option?
not true you can do FM, M, and physics as a trio if you want and all three arent too bad if you have a very good understanding of maths. i do chem phy maths and fm and u can balance it out as alot the maths a level is covered in fm year 1
This is far from the hardest a level further maths question. It may long and tedious and easy to mess up, but if you know your hyperbolic substitutions and hyperbolic identities then this should be a piece of cake as long as you are careful not to make any silly mistakes. Also, since the correct answer is already given, you'll know if you have made any mistakes or not when you've finished the question and can go back and correct your working if necessary.
Watch MIT integration bee. You'll see some quick integration there with some tricks. This was relatively easy after substituting, that being said I done my further maths a level 6 years ago
@@Username-ww2cd in my exam board we only have AS Further Pure (2hrs) and A2 Further Pure (2hrs 15) and then the mechanics, statistics and discreet and division mathematics modules, so we didn't have just core modules
wow whats that trick you used where you let the integral be "I" and then found an expression for it in terms of "I". That was really cool, I hope I get to learn about integration techniques like that in uni because I don't think they teach us that in maths or further maths. Everything else I agree with too.
This is impressive and everything, but its just not really useful at all. barely teaches anything and just kinda gives the answer to a question that is unlikely to pop up
