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Sure I'd be happy to, where can I find these papers?

​@@JonNichollsALevelMathsHelp, looks like we cant post links here. These can be found on mathshelper website under oxbridge section. That would be awesome if you could try them, really like your explanations.

​@@JonNichollsALevelMathsHelp, if you search for "mathshelper Oxbridge"

No problem, if you have any requests for solutions to particular questions, let me know.

I'll send you the original video through email and hopefully that will sort out the sound issues for the last bit! I also happen to agree with you regarding the contentious nature of (ii) - If Cesare is not telling the truth, and in fact Dita said nothing at all (rather than Dita spoke falsely), then Cesare must be a different species to Dita (since Cesare was speaking about Dita), but as you point point out, I'm not sure that we can say anything more than that. I've read through the question several times and I really do think that unless we can be certain that Dita actually spoke those words, we can't actually say for sure that Cesare is a vampire. Its an excellent point from what I can tell.

@@JonNichollsALevelMathsHelp Thank you ever so much Jon. Your students are so lucky to have a great teacher like yourself. You explain things amazingly well and always go out of your way to help. Thank you :) I don't think I could have done part (iv) under exam conditions, but I think it's a great question nonetheless. lol I can tell you enjoyed it :)

Cheers for the remark, its been a long time since I looked at this question so I'd have to have another look at it again and work through the entire thing to properly understand your point. Apologies, I'm sure you're right though, its clearly a question where you could take a lot of different approaches! Recently I've been working through the TMUA papers as that exam has really taken off this year in terms of the number of students at my school needing to sit the exam. I haven't bothered producing video solutions since R2Drew2 does a very respectable job of that. I'd like to improve my Olympiad skills as well, and the channel 'Prime Newtons' seems excellent for this purpose. Sorry I'm waffling. Best of luck if you are taking an entrance test, or best of luck if you're helping others to sit the exam instead.

​@@JonNichollsALevelMathsHelp Thank you for the response, this year I am taking the TMUA and MAT and I really like your explanations as they are very digestible when reviewing questions. Idk why but for some reason whenever I attempt TMUA papers I seem to make the stupidest mistakes that I typically don't encounter with the MAT or other style of questions, would you have any advice?

@@ArhysTheorem Ahhh you're a student, fantastic and best of luck in both those exams. I watched one of your videos and was very impressed with your solution, so I reckon you have a great chance. Careless slip ups happen to us all sadly, but I know what you mean. The time pressure in the TMUA is harsh and if you don't find the most straightforward approach in a question, then you're more likely to make an error in the extra work. Its tough though, because its not easy to spot the most straight forward approach. A few of my students have recently asked similar questions regarding 'getting quicker' in the TMUA - my only advice is to try to spot elegant solutions, because elegant solutions always involve less hard work and so less likely to produce a mistake in the working out. Easier said than done though!

@@JonNichollsALevelMathsHelp Thank you so much, appreciate the advice

Fantastic score Unaisa, really really pleased for you. Best of luck in the future!!!

No Problem Liam, I've not really popped much up online recently as I've been busy with a few other bits n bobs - but I will get back into the swing of it, come September when I start teaching again, which I'm really looking forward to. If you're doing the TMUA, I'm currently working through those papers. Let me know if you need any videos posted.

no problem, I've been doing loads of TMUA papers recently (practice papers, 2017, 2018 and I'll keep completing them) so let me know if you need some solutions. Alternatively, use R2Drew2's channel which is very good.

@@JonNichollsALevelMathsHelp actually i have a few questions about tmua. If I finished all the past papers, what resources should I have a look at. And besides, do you have any advices for improving the grades :). Tysm

@@huyanhnguyen9745 If you've finished the TMUA papers, I would suggest completing Q1 A-G from the MAT papers, as they are similar and multiple choice. Also maths challenge papers, particularly kangaroo and even maybe some olympiad questions. They will all help you to grow as a mathematician. With regards to improving your grade in the TMUA, I'd point out that most of the time, the last five questions are significantly more difficult than the first five. So if you need say 30/40 in the TMUA (which seems to translate to roughly a score of 7), don't waste lots of time on a really tough question at the end when there are easier questions at the start. Best of luck!

@@JonNichollsALevelMathsHelp thanks a lot for your advice. I will try my best for my imperial's preparation. You deserve million subscribers!

Great question. I massively prefer their answer, which is much more convincing. The more I think about my approach, the more I think its DEFINITELY WRONG. We're being asked if THERE EXISTS a k for which the polynomial expression is a cube number, whereas if we could factorise it into (stuff about k)^3 then that would prove that FOR ALL k it would be a cube number. For example, if we have k^3+26, that can't be factorised, but it is a cube when k=1. Do you see what I mean? As always, I'm wrong. hehehe.

Yep, well spotted! Typical me, naffing up the y intercept!

cool, thanks for that, I didn't know that. Really need to take a look at FP2 as I heard it had a few other interesting ideas too.

No its from Downing College's suggested questions to look at before interview. Although you'll also find it in this book here as Q1: archive.org/details/200puzzlingphysicsproblems/page/70/mode/2up and the solution is on page 68. A good question for interview practice.

@@JonNichollsALevelMathsHelp Hi sir, do you mind uploading a solution to MAT 2014 question 5? I'm finding it tough to understand the markscheme and theres only one other solution video online which is really wishy washy in my opinion. Thanks!!

@@OliverGoodman-todd Sure I'll take a look at it and have a go at writing a solution either this evening or tomorrow. Remember though, the MAT is changing this year and the short multiple choice questions will be worth 70% with the two big questions worth only 15% each. So the shorter questions are probably what you want to focus on (so complete all the short ones on the MAT page and then try TMUA questions, particularly from paper 1 starting from about Q5-Q20)

@@JonNichollsALevelMathsHelp Thank you very much, I'm hoping the two long questions aren't question 5 style haha but I'm preparing just incase. I will keep what you said in mind and definitely make use of the TMUA. Thanks again.

No problem, best of luck in the exam.

Appreciate the kind words. Let me know if you want a solution to a past paper question.

Sure will do, just going to an Italian Restaurant, will do it after.

Sure Edward and I appreciate the kind words. If you suggest a question from the past papers I'll happy work through a solution for you. You can find lots of collisions questions on the old M4 past papers from the old syllabus. I'll see if I can find one as well and pop a video up this evening.

@@JonNichollsALevelMathsHelp i dont think my comment sent but its q5 from the A2 further mechanics 1 specimen paper

@@sunnyxf2 no problem, will pop up a solution before the weekend. All the best.

@@sunnyxf2 No problem, will have a go at it and provided I can find a solution, I'll pop a video up with it on :)

@@sunnyxf2 Here you are Edward. ruclips.net/video/WueiWcDlgXs/видео.html Also, you might find this video useful, which I did ages ago. ruclips.net/video/jEn69um5Hic/видео.html

Sure I'll pop a video up on the various methods you can use for division - long division, grid method, equating coefficients, etc etc. Sorry its taken me a while to reply, I've been slightly distracted recently and haven't devoted much time to supporting students. Apologies!

@@JonNichollsALevelMathsHelp thank you very much

@shaehazellock6092 Sure np Shae, tell me where the question is from (page of textbook or which past paper etc) - or describe it - and I'll have a go at it :)

Really interesting question Ash. Just done a video solution but left it unlisted so you'll have to use this link to find the video: ruclips.net/video/vfURzUdDC6Y/видео.html Do let me know if my solution is correct or incorrect if you have access to the answer. I'm pretty sure we know at least 35 passed the test on the easier questions.

Thanks for the comment - I'm no expert when it comes to these papers but I'm happy to have a go. I figure if I start with the Q1's, which tend to be easier, then we can slowly build up to the tougher questions.

You're welcome Ronak, best of luck with UCAS and your A levels.

Best of luck Zeinab

Best of luck Seth!

No problem and in answer to your question about Q21, you absolutely can do it that way and it is a very speedy approach so really well done. Great spot, particularly for a paper like this where time is extremely limited. Best of luck in the real thing!

nah word. 1 hour left and i'm only watching this now 😂😂😂

No problem and best of luck in the test!

Yeah same bro

@@arthurfeld Best of luck in the test!

Yeah I don't know. I was shown it by a colleague many years back and I've always liked it for doing casual division. Can we call it that? Casual algebraic division? Try doing it instead of long division and see if you like it. It has its merits.

Yes its weird and I appreciate your thoughts. Now though, I'm thinking about it again and I think they aren't quite identical. The first one (B) still gives an answer when a is negative but the answer (C) wouldn't give you an answer since you can't natural log a negative number. So I'm leaning towards me being wrong in the video and you need to rule out (C) to ensure that the integral allows for answers when a is negative. If I'd used a modulus sign after integrating, it would have been more obvious perhaps. Quite subtle, no doubt about it.

I think you're right. Easy way to rule out answer choice D too! Thanks for this mini-series, there isn't a lot of information for this test online. I've got my exam tomorrow morning.@@JonNichollsALevelMathsHelp

@@Wolf-bt8lq best of luck in the exam, hope it goes really well for you!

@@JonNichollsALevelMathsHelphonestly it’s ridiclous it’s 1 mark and it requires all that integration and thought

Just because I knew that 3 was true (its to the right of the x coordinate of the stationary point and so its definitely convex (concave upwards) at that point, and their selection of answers implied that 2 and 3 couldn't be true at the same time. I'm guessing that if you plug x=4/3 into the equation y=2x^3-8x^2-2x=8 then you DONT get 112/27. Would you mind checking this claim for me? Because x=4/3 certainly appears to be a Point of Inflection. I think just the y ordinate is wrong.

Yes it doesnt work, i can see why its wrong now, thanks

@@My-fb5td Thanks for checking and pleased it helped.

sec^2 not sec. square root undoes the square.

Oh sorry i don't know how i didn't see that haha

Look at the roots. What is -2 closer to? -1 or -4? Symmetry.

Is it a geometric sequence? The sum to infinity formula only works if the common ratio is constant. But that is not the case here sadly.

Ah ok, and its not a geometric sequence as well right?

Because its being rotated around the x axis. If it was rotated around the y axis then 4 would be the height and 8/5 the radius.

Nothing mega useful, other than to say this test is all about how you handle being under extreme time pressure. Look for ways of ruling out answers quickly. And obviously keep practising using MAT questions (the short ones) and TMUA questions (not the logic ones from paper 2 as they don't seem to pop up).

No problem. I wrote solutions as some students at my school were doing the exam. The questions are tricky and the time allowed is ridiculous!

@@JonNichollsALevelMathsHelp where did you find the paper?

@@MillanMirchandani I used the internet wayback machine to find the old sample papers before they were changed. If you look at the comments section for my videos on the new sample papers, I provide a link to them there. Hope that helps.

because 2>4/3 and the curve is concave downwards only from -infinity up to 4/3.

Yeah great question. I reckon I could do probably roughly 25 properly within the time limit, maybe fewer, with reasonable (but not perfect) assurance that I've got the answer right. Its tough to say actually as the first sample papers released (the old sample papers) had more A2 Further Maths and that would have been tougher in the time limit. Obviously I probably would guess on some of the others. Note there is some negative marking (25% loss) but that is exactly flat in terms of expectation and therefore if you can rule out at least one answer, its worth a guess. I definitely wouldn't do the paper in order. I'd be attacking the questions worth two marks first, because often they don't seem to take longer than the one markers. If a one marker looks easier, then get it done obviously. Any of the questions which involve picking the correct identity, just plug in values to rule out answers as its quicker. Same goes for solving equations. According to a FOI request to Imperial, the scores in both 2021 and 2022 were not that high - in 2022/23 the median score of an applicant invited to interview was 35%, the highest score was 77% and the lowest score was negative 4% Source: www.imperial.ac.uk/admin-services/secretariat/information-governance/freedom-of-information/disclosure-log/student-information/student-information-admissions--withdrawals/ To my mind, that would imply that a score of 50% or higher is pretty good! Hope that helps. Just do your best :)

Thank you so much

y + 99 terms = 100 terms :) Incidentally, its a weird question because I can't figure out why that is worth 2 marks, when other questions which take longer are worth one mark. Strange.

@@JonNichollsALevelMathsHelp Thank you for the clarification! I really love your content, keep it up! :)

No, e = 1+1+1/2!+1/3! etc... I think you're missing the 2 1's at the start of the power series for e. Basically it starts at 0! (=1) so it goes 1/0!+1/1!+1/2!+1/3! .......etc. Hope that makes sense.

Hmmm. Wait a moment. Are you suggesting that the floor function can be applied 'term by term'? So that floor(a+b+c+d)=floor(a)+floor(b)+floor(c)+floor(d). I think I have a counterexample to prove that claim incorrect....... e.g floor(1.9+1.9)=3 But floor(1.9)+floor(1.9)=2 Have I understood you correctly? I think your method may be invalid, but led to the correct answer quite fortunately.

So for your first question, you're absolutely right. Its only because the answers were quite different that I was able to use the quick and easy approach. Otherwise you would need to use the formula for the angle between two vectors |a||b|cos(theta)=a.b which used to be taught in single maths but now is only found in double maths (although your teacher may well have taught you it anyway - I certainly do!). For your second question, once again I agree, the 'method' I use could easily 'fail' in a sense and leave you with two possible answers. But this is a test with extremely limited time, and so thats the reason why I think this is the best approach. Your choice of zero was probably quite 'predictable' for the examiner, so try and be more inventive with your choices. By the way, the method doesn't prove an identity (B and D are not correct - rather A and C are definitely wrong). The method can only show you which answers definitely aren't correct. Hope that makes sense! Best of luck in the exam.

@@JonNichollsALevelMathsHelp Great, thanks very much. I'm actually in Scotland so I'm doing Advanced Highers, and the angle between two vectors is in my course (not sure why I didn't think of that before!). In terms of choosing a value for theta that makes a lot of sense, 0 would be too easy for them to give us! I'll try to pick more obscure exact values. Was wondering if you have any advice on how I can familiarise myself with questions more A-level style? A lot of these questions are on content I have covered, just being asked in ways I'm not used to. Thanks for your help!

Glad you like it!

The quick answer is that 7C3 and 7C4 are both either side of the 'middle' of pascals triangle and that pascals triangle is symmetrical down the middle. To prove this algebraically is much easier than we might imagine. Here goes. nCr = n!/(r!(n-r)!). Ok so for nC(n-r) we need to replace all instances of r with n-r and note that n-(n-r) is simply r. So we have nC(n-r)=n!/((n-r)!r!) which is of course equal to nCr. Hence nCr=nC(n-r) always. Hope that helps.

Ah i see now, thanks, also any last min tips? exams in 9 days!

Thanks, and best of luck in the exam!