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Noticed a couple of minor typos that I’m correcting here :) In 1b, I picked up a negative when calculating the derivative. This was then cancelled later when simplifying. 16:55 - when equating the coefficients akbk. It should be 4 + 8 + 10 - 20 = 2. Everything else remains correct. 33:46 - when solving for the perpendicular here, we should have -R_b * tan(gamma). So there should be a negative instead of a positive. I did this in the next line, just missed the negative to begin with. Everything else remains correct. :)
In 1b, I picked up a negative when calculating the derivative. This was then cancelled later when simplifying. The negative doesn't cancel the answer is -ln|xcosx-sinx| + c.
A bit of history: the Cambridge entrance exam was abolished in 1986. STEP was introduced in 1987 in a number of subjects though it now only remains for mathematics. STEP I was not typically used for entry to Cambridge Maths (STEP I was based on the content of the A-level maths syllabus, and by design was graded one grade higher than STEP II and STEP III - by which I mean that an 1 in STEP I roughly translates to a 2 in STEP II or II etc). Since the adoption a number of years ago of the requirement of Further Maths A-level (or an international equivalent) for entry to the Maths tripos there was no reason to set STEP I as part of any offer. STEP papers II and III are very comparable in level of difficulty and marking. Directors of Studies get plots of candidates performance on STEP II and STEP III and these show no sign of a systematic difference in marks attained in either paper. Whether the average performance is higher in paper II or paper III will vary from year-to-year. Technically STEP is not an entrance exam. It can be taken by students who have not applied to Cambridge (and have no intention of doing so). Also, a good performance in the exam does not guarantee admittance to the course for those who have applied. If a candidate has taken STEP a year early their results will be available to Directors of Studies and Admissions Tutors. However, if they do not perform well at interview a college may decide not to make them offer (which would have to be unconditional, or nearly so since they already have their STEP results). Currently, such students are automatically put into the winter pool (there is no pool for mature applications in the March admissions round). The pool is the mechanism whereby colleges that are over-subscribed with candidates can make them available to other colleges looking for more applicants. Applicants that are compulsory-pooled seem to be less successful than those put in the pool because admissions tutors think they would be of interest to other colleges.
Matriculated in 1975 - got a conditional offer for the Maths tripos based on my Maths A-Level result in Lower Sixth form, predicted grades, and interview; not asked to take the entrance exam at all. Based on your video and subsequently having a look at a couple of the STEP papers I would say they are definitely some way above Maths A-Level (at least, as I remember it), and span the challenges between what, at the time, were the *_two_* further maths A-Levels that I took (Pure Maths and Applied Maths - yes, I took three Maths A-Levels, all WJEC!!) and the S-Level Maths paper. The subject matter of 'S' levels was identical to the 'A 'level syllabus, but the questions considerably harder. 'S' levels principally aimed to test candidates confronted with unfamiliar situations and show their reasoning. Special papers were last set in 2001 and then superseded by the Advanced Extension Awards and to some extent by Sixth Term Examination Papers. A-Level physics completed the set. Based on my undoubted preference for applied maths and physics I switched to Natural Sciences before going up, second best decision I ever made. I love maths, but I learned I didn't have what it would take to succeed at it professionally.
I did my math degree about 20 years ago and did well, earning a 1st class degree from Imperial. I then worked in investment banking as a commodity trader but my actual theoretical mathematics from undergrad days have forgotten so much. No idea how my young brain coped with all of that. Problem with mathematics if you are not using it frequently then you forget. Just like with the gym. The good thing, like the gym with muscle memory, the knowledge is still in the brain and just requires active recall with some refresh
I thought step was hard, then I saw what the actual Cambridge maths exam papers looked like (then I left immediately. Absolutely no way I was putting myself through that).
Hi Ellie. Thanks for the video which cast me back to 1993 when I took STEP II and III. Very challenging exams and I only just scraped through to get a place on the Maths Tripos. I had to work damn hard during the degree too, realising within the first couple of weeks that my dream of doing maths research would certainly be out of my reach. I did manage though to get a good result in my final year even if it was beyond what my average ability deserved. Just goes to show that exams are generally not a great indicator of talent or understanding! Just a few thoughts on the questions covered in the video... (1) In Q.1 I did the trig rearranging before making the substitutions with the benefit of making it easier to guess the correct substitution for the later integrals. For the first, multiplying top and bottom of the integrand by cos(x) yields x.cos(x)/(x.sin(x)+cos(x)). Also noting that du=x.cos(x).dx, this shows why the given substitution makes sense. For the second integral, this time multiplying top and bottom by sin(x), one gets a denominator of x.cos(x)-sin(x) making it obvious what the correct substitution should be. (2) For that second integral, you missed a minus sign in du/dx ie one should get: du = - x.sin(x).dx As a result the final answer should also have a minus sign out front. (3) For a bit of fun, an alternative approach to the induction step in the first part of Q.8 is to use matrices: Let v[n]^t = (a[n] b[n]) be the transpose of column vector v[n] and M be the 2x2 matrix with rows (1 2) and (2 5). Then the recursion gives: v[n+1] = M.v[n] Let q[n] = a[n]^2 + 2a[n]b[n] - b[n]^2 = a[n](a[n]+b[n]) + b[n](a[n]-b[n]) = v[n]^t.N.v[n] where N is the 2x2 matrix with rows (1 1) and (1 -1). q[n+1] = v[n+1]^t.N.v[n+1] = v[n]^t.M^t.N.M.v[n] It is easy to show that M^t.N.M = N and so: q[n+1] = v[n]^t.N.v[n] = q[n]
Hi! There’s an argument to say that STEP II is harder than STEP III since the content examined in the second paper is less so they increase the difficulty of the questions to compensate
@@sidnath7336 I’ve done a fair bit of both and I usually find that most questions in step 2 take me more time to understand what is going on. Step 3 has harder content but the questions feel more straightforward to me. A lot of other people also find step 2 harder than step3 but I guess it’s also preference
Yeah they’re meant to be around the same difficulty and it holds, most people tend to get around the same mark in both (I got 55 in STEP 2 and 58 in STEP 3 last year, around the same difficulty I’d say)
I studied math in Bonn, which is the leading math faculty in germany and also internationally recognized quite a lot. but you can still enroll with the worst possible highschool degree possible . i think this is because at bonn nobody gives a shit whether you get a job (except professor). many super talented math graduates end up unemployed or just do simple data science, accounting jobs.
@@leolacic9442 yeah, it is pretty much the same in economics. Bonn is quite demanding and really good in research, but jobs go to all the rich kids from private business school...
Some really nice problems here. I could probably manage the proof by induction and could see myself getting in a mess with the mechanics, care is required to get the balance of forces correct, and I don't have the trig identities stored in my head. It is enjoyable watching workthoughs of difficult problems which I wouldn't know how to start but when an expert proceeds through it all slots into place.
I'd say the hardest maths exams for students aged 17-18 was the mock exam I had to take for CSYS Maths Paper II (Pure Maths) in Scotland in 1998. The top mark was 51%. I got 34%. Our teacher said, "I already know you can do the easy questions, you already know you can do the easy questions, so there's no point in me testing you on them". The actual final exam (generally considered the hardest high school exam in Scotland at the time) felt easy by comparison. I got an A in the final.
My SYS prelims in 1986 were similar. The Paper I prelim was far too easy and the Paper II prelim was far too difficult. In retrospect this was down to the inability of the teachers at my school to create test papers of the appropriate standard.
At 17:00 in question #2, I believe the expansion of the middle term will yield 4(a(k))^2 + 18a(k)b(k) + 20(b(k))^2, which for the ab term does come to 4+18-20=2.
I occasionally do a STEP paper for fun and to keep my hand in. I'm very glad I didn't have to do anything similar aged 18 and applying to university (A-levels were nerve-racking enough).
@@johnholmes912 Nonsense. STEP is far in advance of A-level maths. Download some sample papers. And think about it: if STEP were easier than A-levels there'd be no point in Cambridge making applicants take it.
Congratulations on your genius Ellie, this mechanics question is insane 😅😅, a long time ago I solved all the questions in a high school level mathematics book, about finite induction, they don't even come close to the complexity of this question, they were very direct. It's always a pleasure to admire your intelligence Ellie. 😊
I had to do STEP II this year for my Imperial JMC offer, this years paper was so much better than past years and one of the questions on there was a classic example of invariance that I had done many times while preparing for the BMO. I think I did better than on past papers but too bad I missed my IB grades offer so no imperial rip
Three hours for (at least) six questions, that’s 30 min per question. As someone who took part in various maths competitions (national olympiads, IMO qualifiers, Middle European Math Olympiad) that is reassuringly little time. You know it gets hard at 90 mins per problem…
Nice video, I believe there is one harder math paper for high-school students and that is the International Math Olympiad, this year it took place in Bath, and the problems were really nice!
I just knew it was STEP from recognising the questions in the thumbnail, I didnt do very well at STEP lol Anyway, Im gonna be doing part III in a couple months, and I did watch your videos on guidance for part III so thank you Ellie!
Hello, I really enjoyed this video and your walkthroughs on some of the hardest math tests! Just a quick question- at 7:56, wouldn't du/dx be -x*sin(x), causing the answer to have an additional negative sign? Thank you
Already have a couple of videos going through maths in them but will make a separate dedicated video to add to my series on the hardest maths exams in the world 👀
@@EllieSleightholmThanks for sharing Ellie. Hope you can respond to my.old comment about balancing work /life balance and if you get paid well enough to travel a lot when you can. And how do yo not get bored and tired and FED UP with such a long exam?? Hope to hear from you. Thanks for sharing.
I suppose technically, the olympiad is a a challenge not an exam. But I do agree. I had the pleasure of been tutored by the late Andrew Jobbings for my step and for ukmt and olympiad 20something years ago and have to agree that the Olympiad questions, for a teenager, were more challenging than those in the step papers back then.
@@CKLewper Yes, although I myself had as much chance of being selected for the England cricket team as I did for the Maths Olympiad team so shouoldn;t really comment :) What makes the Olympiad questions different, as far as I've seen of them, is that there's usually no obvious "route" into them; you have to work out how to tackle them completely from scratch and with no help from the questions themselves. This isn't an ability everyone has, not even those who are good at mathematics.
ive always found the typical BMO2 easier than STEP 2. you may be misattributing the difficulty because the bmo gives more time per question, and the STEP's questions are often very fragmented.
Really? I wonder when that started. All Imperial wanted out of me mathematics-wise was an A-level (and a B grade at that). The interviews were given a lot more importance relative to exams than today, I suppose. Having said that, this was back in 1988, when dinosaurs still roamed the earth.
@@davidgillies620 Interesting, Imperial doesn't even interview for their maths undergraduate course anymore! They also don't require STEP for maths, I had to do MAT instead (but they do require STEP for computer science oddly enough...)
Hi Ellie, If I remember rightly, STEP is aimed at the top 5% of students entering for Maths A level, so it's more or less "baked in" that 95% of even A level students are going to fail it.
I am a bit confused here. In the mechanics problem, shouldn’t the coefficient of friction be static? Then, the force of friction is no longer simply proportional to the normal force. Instead, it should be whatever is necessary for static equilibrium. Then it suffices to write out the dynamical equations and set the forces and torques to 0. I got tan(alpha)=-tan(beta). Did I misunderstand the question? Why should we use the kinetic definition of friction here? Also, I am obstinate enough to spend two hours on doing questions from as opposed studying for my exams. Alas, it’s all good fun. Thanks Ellie for the wonderful video as always.
Mathematics students aged 17-18 here in the UK don't learn about the difference between static and kinetic friction - only physics students are taught that.
@@Treviscoe Correct. No matter how much mechanics you choose to do for your applied options in A-Level Mathematics or Further Mathematics, you'll always only use a single "coefficient of friction". As I said, the difference between static and kinetic friction is only covered in A-Level Physics. This perhaps reflects the fact that in the British educational tradition, "mechanics" within maths is still rather focused on the abstract side of the topic, as a vehicle for demonstrating the use of pure mathematics techniques. The 'practical' side of the topic is seen as more appropriately left to the physicists - so this is also why, for instance, A-Level Physics students are taught about things like sources of error, calculating uncertainties/error bars, giving answers to an appropriate number of significant figures, etc., whereas for mechanics within A-Level Mathematics, all of these issues are completely ignored - since we're dealing with abstract, idealised problems, all numbers are treated as exact and all non-exact answers are given to 3 significant figures (an arbitrary convention).
Hi at 34:20 I think when resolving perpendicular it should be negative R_b * tan(gamma) but in the next line it’s correct when you equate Wsin(alpha)cos(alpha). Also do you have any insight into how these questions are even made? I always wonder how they make the questions so elegant and cancel down to a nice answer.
@@EllieSleightholm no probs! I love watching ur vids, im starting my maths degree this year so really excited. Luckily didnt have to do STEP as i did well in another entrance exam my uni accepts.
I studied Mathematics at University in my Engineering Degree.I feel sorry for students who take Physics as their Degree.In Physics you have Quantum Mechanics,Etc.,where the Mathematics is out of this World.
Great explanations. I used to love doing these in school, but people often asked me what was the use of it, i.e. where were they used? I have to say I spent four years at university (natural science) and never did come across the need for these kinds of problem-solving. Could you tell me where they are used then I can shut up, at least in my mind, the dissenters!
Mathematical problem solving is pretty much starting with a set of fundamentals and using logical steps to arrive at a potentially useful conclusion, so solving these kinds of problems is useful training in logical thinking, something that is very useful in life for minimising poor decision making.
Can you try an exam of the university of Bonn from germany (Peter Scholze is researching there)? It's one of the hardest universitys for math in europe.
Hi Ellie, thanks for your video. Please can I ask what you were using that allowed you to circle things on the screen in a way that the inked circle fades after you drew it?
Day 78462 of me requesting you to take a look at X/ENS Maths D, hardest maths exam in France, Alain Connes (fields medalist) sat it in 1966 and got a 0/20. Its part of a series of entrance exams to get into the best engineering school in France (X or Polytechnique) and Ens Ulm (the university with more Fields medalists in its alumni than every single european country and every single american university!), definitely worth a look.
@@EllieSleightholm Ive been looking for 15 minutes now and still nothing. Not sure ill be able to find an official version in english because this exam is exclusively for french students. However, i could take a couple papers from recent years and translate them through chatgpt 4o then send you the LaTeX renders by email? Ill make sure the translations are correct before rendering
sin, cos, tan, cot = essentially a for loop function, that when say calculation miles per hour and distance over time, a square root of 4+3+2+1. Pythagorean theorem. You want to travel 1 mile at 30 miles hr. Not from starting at a resting point, but if the traffic light runs from red to green, and the first batch of cars start from zero velocity at rest and increase their speed. The light must stay green , for the remainder of traffic catching up behind them from a distance, relativity theory outside observer. The next set of cars would be traveling at speeds of 30 miles hour, how many seconds will it take those cars or one of them to reach one mile exactly.
Its close too foobar, 4*4,16*16*256*256 matrix tensor determinant quantum gravity newtons law of body. Friction, innertia. Its that like googke maps on cellphone screen size and rotating map in different direction not parallel to actual road, at center pivot rotation. The riad lines will cut in different directions border by 4 sides of screen devices. Thats foobar, that computer keyboard, but without algorithm for decrypting that, them mind stays locked in a 2 dimensional frame, not a spherical holistic view like that of birds in flight. Stone age.
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Noticed a couple of minor typos that I’m correcting here :)
In 1b, I picked up a negative when calculating the derivative. This was then cancelled later when simplifying.
16:55 - when equating the coefficients akbk. It should be 4 + 8 + 10 - 20 = 2. Everything else remains correct.
33:46 - when solving for the perpendicular here, we should have -R_b * tan(gamma). So there should be a negative instead of a positive. I did this in the next line, just missed the negative to begin with. Everything else remains correct.
:)
In 1b, I picked up a negative when calculating the derivative. This was then cancelled later when simplifying.
The negative doesn't cancel the answer is -ln|xcosx-sinx| + c.
www.cmi.ac.in/admissions/sample-qp/ugmath2023.pdf Try CMI entrance exam once :)
A bit of history: the Cambridge entrance exam was abolished in 1986. STEP was introduced in 1987 in a number of subjects though it now only remains for mathematics. STEP I was not typically used for entry to Cambridge Maths (STEP I was based on the content of the A-level maths syllabus, and by design was graded one grade higher than STEP II and STEP III - by which I mean that an 1 in STEP I roughly translates to a 2 in STEP II or II etc). Since the adoption a number of years ago of the requirement of Further Maths A-level (or an international equivalent) for entry to the Maths tripos there was no reason to set STEP I as part of any offer.
STEP papers II and III are very comparable in level of difficulty and marking. Directors of Studies get plots of candidates performance on STEP II and STEP III and these show no sign of a systematic difference in marks attained in either paper. Whether the average performance is higher in paper II or paper III will vary from year-to-year.
Technically STEP is not an entrance exam. It can be taken by students who have not applied to Cambridge (and have no intention of doing so). Also, a good performance in the exam does not guarantee admittance to the course for those who have applied. If a candidate has taken STEP a year early their results will be available to Directors of Studies and Admissions Tutors. However, if they do not perform well at interview a college may decide not to make them offer (which would have to be unconditional, or nearly so since they already have their STEP results). Currently, such students are automatically put into the winter pool (there is no pool for mature applications in the March admissions round). The pool is the mechanism whereby colleges that are over-subscribed with candidates can make them available to other colleges looking for more applicants. Applicants that are compulsory-pooled seem to be less successful than those put in the pool because admissions tutors think they would be of interest to other colleges.
Matriculated in 1975 - got a conditional offer for the Maths tripos based on my Maths A-Level result in Lower Sixth form, predicted grades, and interview; not asked to take the entrance exam at all.
Based on your video and subsequently having a look at a couple of the STEP papers I would say they are definitely some way above Maths A-Level (at least, as I remember it), and span the challenges between what, at the time, were the *_two_* further maths A-Levels that I took (Pure Maths and Applied Maths - yes, I took three Maths A-Levels, all WJEC!!) and the S-Level Maths paper. The subject matter of 'S' levels was identical to the 'A 'level syllabus, but the questions considerably harder. 'S' levels principally aimed to test candidates confronted with unfamiliar situations and show their reasoning. Special papers were last set in 2001 and then superseded by the Advanced Extension Awards and to some extent by Sixth Term Examination Papers.
A-Level physics completed the set.
Based on my undoubted preference for applied maths and physics I switched to Natural Sciences before going up, second best decision I ever made. I love maths, but I learned I didn't have what it would take to succeed at it professionally.
I did my math degree about 20 years ago and did well, earning a 1st class degree from Imperial. I then worked in investment banking as a commodity trader but my actual theoretical mathematics from undergrad days have forgotten so much. No idea how my young brain coped with all of that. Problem with mathematics if you are not using it frequently then you forget. Just like with the gym. The good thing, like the gym with muscle memory, the knowledge is still in the brain and just requires active recall with some refresh
That's a good analogy! Congrats on your first from Imperial - I also got in there (Electrical Engineering) but sadly didn't manage to graduate.
I thought step was hard, then I saw what the actual Cambridge maths exam papers looked like (then I left immediately. Absolutely no way I was putting myself through that).
Hi Ellie. Thanks for the video which cast me back to 1993 when I took STEP II and III. Very challenging exams and I only just scraped through to get a place on the Maths Tripos. I had to work damn hard during the degree too, realising within the first couple of weeks that my dream of doing maths research would certainly be out of my reach. I did manage though to get a good result in my final year even if it was beyond what my average ability deserved. Just goes to show that exams are generally not a great indicator of talent or understanding!
Just a few thoughts on the questions covered in the video...
(1) In Q.1 I did the trig rearranging before making the substitutions with the benefit of making it easier to guess the correct substitution for the later integrals. For the first, multiplying top and bottom of the integrand by cos(x) yields x.cos(x)/(x.sin(x)+cos(x)). Also noting that du=x.cos(x).dx, this shows why the given substitution makes sense. For the second integral, this time multiplying top and bottom by sin(x), one gets a denominator of x.cos(x)-sin(x) making it obvious what the correct substitution should be.
(2) For that second integral, you missed a minus sign in du/dx ie one should get:
du = - x.sin(x).dx
As a result the final answer should also have a minus sign out front.
(3) For a bit of fun, an alternative approach to the induction step in the first part of Q.8 is to use matrices:
Let v[n]^t = (a[n] b[n]) be the transpose of column vector v[n] and M be the 2x2 matrix with rows (1 2) and (2 5). Then the recursion gives:
v[n+1] = M.v[n]
Let q[n] = a[n]^2 + 2a[n]b[n] - b[n]^2
= a[n](a[n]+b[n]) + b[n](a[n]-b[n])
= v[n]^t.N.v[n]
where N is the 2x2 matrix with rows (1 1) and (1 -1).
q[n+1] = v[n+1]^t.N.v[n+1]
= v[n]^t.M^t.N.M.v[n]
It is easy to show that M^t.N.M = N and so:
q[n+1] = v[n]^t.N.v[n] = q[n]
I don't know what category these exams have to fall under but if you want to also look at competition papers, BMO2 is the hardest paper for UK.
Hi! There’s an argument to say that STEP II is harder than STEP III since the content examined in the second paper is less so they increase the difficulty of the questions to compensate
From experience, I think it’s highly dependant on the year - when I say it, STEP III was easier than STEP II but in other years it was not.
@@sidnath7336 I’ve done a fair bit of both and I usually find that most questions in step 2 take me more time to understand what is going on. Step 3 has harder content but the questions feel more straightforward to me. A lot of other people also find step 2 harder than step3 but I guess it’s also preference
@@sidnath7336 also the level of difficulty of recent years (2019 onwards) of step 2 has massively increased so that may be a factor too
Yeah they’re meant to be around the same difficulty and it holds, most people tend to get around the same mark in both (I got 55 in STEP 2 and 58 in STEP 3 last year, around the same difficulty I’d say)
I studied math in Bonn, which is the leading math faculty in germany and also internationally recognized quite a lot. but you can still enroll with the worst possible highschool degree possible . i think this is because at bonn nobody gives a shit whether you get a job (except professor). many super talented math graduates end up unemployed or just do simple data science, accounting jobs.
ha ha ha :(
@@leolacic9442 yeah, it is pretty much the same in economics. Bonn is quite demanding and really good in research, but jobs go to all the rich kids from private business school...
Some really nice problems here. I could probably manage the proof by induction and could see myself getting in a mess with the mechanics, care is required to get the balance of forces correct, and I don't have the trig identities stored in my head. It is enjoyable watching workthoughs of difficult problems which I wouldn't know how to start but when an expert proceeds through it all slots into place.
I'd say the hardest maths exams for students aged 17-18 was the mock exam I had to take for CSYS Maths Paper II (Pure Maths) in Scotland in 1998. The top mark was 51%. I got 34%. Our teacher said, "I already know you can do the easy questions, you already know you can do the easy questions, so there's no point in me testing you on them". The actual final exam (generally considered the hardest high school exam in Scotland at the time) felt easy by comparison. I got an A in the final.
My SYS prelims in 1986 were similar. The Paper I prelim was far too easy and the Paper II prelim was far too difficult. In retrospect this was down to the inability of the teachers at my school to create test papers of the appropriate standard.
At 17:00 in question #2, I believe the expansion of the middle term will yield 4(a(k))^2 + 18a(k)b(k) + 20(b(k))^2, which for the ab term does come to 4+18-20=2.
Out of line but I get where you are coming from
Very good explanations. So glad I opted to study biomedical engineering instead!
Is the math in biomed engineering easier than that in the video?😂
Why donyou say that??
Question 8 has a nice way via X^2-2Y^2=1 having solutions X=a(n)+ b(n), Y=b(n) by Pell
I occasionally do a STEP paper for fun and to keep my hand in. I'm very glad I didn't have to do anything similar aged 18 and applying to university (A-levels were nerve-racking enough).
It's much easier than my A-levels, and nowhere near the special papers I took
@@johnholmes912 Nonsense. STEP is far in advance of A-level maths. Download some sample papers. And think about it: if STEP were easier than A-levels there'd be no point in Cambridge making applicants take it.
Tbh, 23:40 prove of c_n convergence is required. And limit of 1/b_n^2 is not enough to assume c_n is convergent)
Congratulations on your genius Ellie, this mechanics question is insane 😅😅, a long time ago I solved all the questions in a high school level mathematics book, about finite induction, they don't even come close to the complexity of this question, they were very direct. It's always a pleasure to admire your intelligence Ellie. 😊
I had to do STEP II this year for my Imperial JMC offer, this years paper was so much better than past years and one of the questions on there was a classic example of invariance that I had done many times while preparing for the BMO. I think I did better than on past papers but too bad I missed my IB grades offer so no imperial rip
Three hours for (at least) six questions, that’s 30 min per question. As someone who took part in various maths competitions (national olympiads, IMO qualifiers, Middle European Math Olympiad) that is reassuringly little time. You know it gets hard at 90 mins per problem…
Ah the good old STEP examinations, I sat STEP 1, and yeah they were beyond crazy!!! Great video through Ellie))
STEP are not particularly challenging. That isn't their intent - they aren't meant to be easy but they are nowhere near Olympiad level.
@@ngc-fo5te bro called step easy
@@legend_legend_legend Who called it easy? But it isn't that difficult either.
Please, at 10:26 "multiply UP and Donw for 1/cos^4" . How did you find that term? Thank you.
I expected this video to be bad because of how much I hate step, but your explanations are surprisingly easy to understand, thank you 👏
Nice video, I believe there is one harder math paper for high-school students and that is the International Math Olympiad, this year it took place in Bath, and the problems were really nice!
I just knew it was STEP from recognising the questions in the thumbnail, I didnt do very well at STEP lol
Anyway, Im gonna be doing part III in a couple months, and I did watch your videos on guidance for part III so thank you Ellie!
I swear U THIS the BEST MATH UA-cam CHANNEL
What a very bright young woman !
Hello, I really enjoyed this video and your walkthroughs on some of the hardest math tests! Just a quick question- at 7:56, wouldn't du/dx be -x*sin(x), causing the answer to have an additional negative sign?
Thank you
Madam, True one (thing that won't have substructure) - Model
Nearing completion on 4 foot rock
I'd say the 2nd round of the British Mathematical Olympiad (BMO2) is harder. Also, you should do a video on the International Mathematical Olympiad :)
Already have a couple of videos going through maths in them but will make a separate dedicated video to add to my series on the hardest maths exams in the world 👀
@@EllieSleightholmThanks for sharing Ellie. Hope you can respond to my.old comment about balancing work /life balance and if you get paid well enough to travel a lot when you can. And how do yo not get bored and tired and FED UP with such a long exam?? Hope to hear from you. Thanks for sharing.
I suppose technically, the olympiad is a a challenge not an exam. But I do agree.
I had the pleasure of been tutored by the late Andrew Jobbings for my step and for ukmt and olympiad 20something years ago and have to agree that the Olympiad questions, for a teenager, were more challenging than those in the step papers back then.
@@CKLewper Yes, although I myself had as much chance of being selected for the England cricket team as I did for the Maths Olympiad team so shouoldn;t really comment :)
What makes the Olympiad questions different, as far as I've seen of them, is that there's usually no obvious "route" into them; you have to work out how to tackle them completely from scratch and with no help from the questions themselves. This isn't an ability everyone has, not even those who are good at mathematics.
ive always found the typical BMO2 easier than STEP 2. you may be misattributing the difficulty because the bmo gives more time per question, and the STEP's questions are often very fragmented.
Please do the math D of ENS exam to get into ens Ulm, its difficulty is legendary in france
How are you considering an entrance exam which requires a level knowledge only to be harder than any 3rd/4th year uni exam ??
Had to do STEP 2 for Imperial, just praying for even a 3 😅
You got this! 🔥
Really? I wonder when that started. All Imperial wanted out of me mathematics-wise was an A-level (and a B grade at that). The interviews were given a lot more importance relative to exams than today, I suppose. Having said that, this was back in 1988, when dinosaurs still roamed the earth.
@@davidgillies620 Interesting, Imperial doesn't even interview for their maths undergraduate course anymore! They also don't require STEP for maths, I had to do MAT instead (but they do require STEP for computer science oddly enough...)
your videos are so fun Ellie :)
Hi Ellie,
If I remember rightly, STEP is aimed at the top 5% of students entering for Maths A level, so it's more or less "baked in" that 95% of even A level students are going to fail it.
omg i just sat both step papers last month and results are coming out soon, hoping for a 1,1 🙏
I am a bit confused here. In the mechanics problem, shouldn’t the coefficient of friction be static? Then, the force of friction is no longer simply proportional to the normal force. Instead, it should be whatever is necessary for static equilibrium. Then it suffices to write out the dynamical equations and set the forces and torques to 0. I got tan(alpha)=-tan(beta). Did I misunderstand the question? Why should we use the kinetic definition of friction here? Also, I am obstinate enough to spend two hours on doing questions from as opposed studying for my exams. Alas, it’s all good fun. Thanks Ellie for the wonderful video as always.
Mathematics students aged 17-18 here in the UK don't learn about the difference between static and kinetic friction - only physics students are taught that.
@@amritlohia8240 Not even at applied A level?
@@Treviscoe Correct. No matter how much mechanics you choose to do for your applied options in A-Level Mathematics or Further Mathematics, you'll always only use a single "coefficient of friction". As I said, the difference between static and kinetic friction is only covered in A-Level Physics. This perhaps reflects the fact that in the British educational tradition, "mechanics" within maths is still rather focused on the abstract side of the topic, as a vehicle for demonstrating the use of pure mathematics techniques. The 'practical' side of the topic is seen as more appropriately left to the physicists - so this is also why, for instance, A-Level Physics students are taught about things like sources of error, calculating uncertainties/error bars, giving answers to an appropriate number of significant figures, etc., whereas for mechanics within A-Level Mathematics, all of these issues are completely ignored - since we're dealing with abstract, idealised problems, all numbers are treated as exact and all non-exact answers are given to 3 significant figures (an arbitrary convention).
That is so easy. They should make the candidate find their own substitution
Good work Sleightholm.
Hi at 34:20 I think when resolving perpendicular it should be negative R_b * tan(gamma) but in the next line it’s correct when you equate Wsin(alpha)cos(alpha).
Also do you have any insight into how these questions are even made? I always wonder how they make the questions so elegant and cancel down to a nice answer.
Just added a comment with this correction-thanks for spotting! The joys of being a mathematician always involves forgetting negative signs 😂
@@EllieSleightholm no probs! I love watching ur vids, im starting my maths degree this year so really excited. Luckily didnt have to do STEP as i did well in another entrance exam my uni accepts.
I studied Mathematics at University in my Engineering Degree.I feel
sorry for students who take Physics as their Degree.In Physics
you have Quantum Mechanics,Etc.,where the Mathematics is
out of this World.
You’re just great ❤
Purfect thumbnail ba d way🔥🤟
Great work and nice explanation Ellie, much appreciated!
I’m wondering if I can get a copy of the whole exam pdf?
Please attempt the HSC Mathematics Extension 2 paper next! It's Australia's hardest mathematics exam.
7:33 : wouldn't it be -xsin(x) ?
For q8, why did you introduce’k’? Why not just compute for n+1.
Great explanations. I used to love doing these in school, but people often asked me what was the use of it, i.e. where were they used? I have to say I spent four years at university (natural science) and never did come across the need for these kinds of problem-solving. Could you tell me where they are used then I can shut up, at least in my mind, the dissenters!
Pure mathematics isn't necessarily useful in applications.. but a large part of mathematics are essential for engineering and computer science
Mathematical problem solving is pretty much starting with a set of fundamentals and using logical steps to arrive at a potentially useful conclusion, so solving these kinds of problems is useful training in logical thinking, something that is very useful in life for minimising poor decision making.
Not in the UK? No A-levels in Scotland
I wonder who will spot a small mistake in question 8.
You should try ISI entrance test(UGA+UGB) for undergrad students from India which is held every year for the prestigious Indian statistical institutes
Very GIFTED☺
Where can we send you exams that we have found on the internet?
GREAT! Liked and subscribed ❤
How do you spot these kinds of substitution 9:34
Can you try an exam of the university of Bonn from germany (Peter Scholze is researching there)? It's one of the hardest universitys for math in europe.
Please provide pdf to download papers you are solving
You'll find a link to the paper in the description! :)
Does it pain you that not everyone understands mathematics? I think it is amazing too. I don't understand it that much.
ua-cam.com/video/_dhrqnDS_oU/v-deo.htmlsi=HoxkJ0AGGFEgftts
This is great!
I did these a few weeks ago, results day in < a month 😅
Hi Ellie, thanks for your video. Please can I ask what you were using that allowed you to circle things on the screen in a way that the inked circle fades after you drew it?
Bro in my countrie that's exam is just testing Ur self if I can go to exam national of Morocco
Thank you
try ENS ulm mp france
Is there a video on books recommendations?
Math is my world
How you DO everythings in Best way
I want video on best Oxford math textbook plz
I feel good to see your videos 💖 ellie
thank you so much 🤩
@@EllieSleightholm
ua-cam.com/video/tF-1dF0eBts/v-deo.htmlsi=m3CDsRiwsKLdig3J
(Basic state of the cosmos)
I enjoy UR BRITISH ACCENT too😘
Praying I haven’t failed step this year 🙏
i have to take this and the PAT and the ESAT ourghhh
What degree course is that exam?
There is a problem with twitter link
Just fixed! My username is elsleightholm :)
@@EllieSleightholm thanks😊
I am just going to say it, has it been hard in your profession? Have you ever lost friends or colleagues as as result of math?
CMI entrance exam is harder than this :) maybe check once and make a video...
Were your parents academics?
smart! am 14 years old and I wish to be like you
fun x maths ❤
Day 78462 of me requesting you to take a look at X/ENS Maths D, hardest maths exam in France, Alain Connes (fields medalist) sat it in 1966 and got a 0/20. Its part of a series of entrance exams to get into the best engineering school in France (X or Polytechnique) and Ens Ulm (the university with more Fields medalists in its alumni than every single european country and every single american university!), definitely worth a look.
Not sure if you'll be able to find an english version though, if you're interested let me know and i'll help find one
Would love an English version if you could find one!!
@@EllieSleightholm Ive been looking for 15 minutes now and still nothing. Not sure ill be able to find an official version in english because this exam is exclusively for french students. However, i could take a couple papers from recent years and translate them through chatgpt 4o then send you the LaTeX renders by email? Ill make sure the translations are correct before rendering
@@EllieSleightholm Sent you an email!
Beauty with brain amazing and incredible 🙏❤
Can someone in late 30s eligible to study Maths in cambridge
sin, cos, tan, cot = essentially a for loop function, that when say calculation miles per hour and distance over time, a square root of 4+3+2+1. Pythagorean theorem. You want to travel 1 mile at 30 miles hr. Not from starting at a resting point, but if the traffic light runs from red to green, and the first batch of cars start from zero velocity at rest and increase their speed. The light must stay green , for the remainder of traffic catching up behind them from a distance, relativity theory outside observer. The next set of cars would be traveling at speeds of 30 miles hour, how many seconds will it take those cars or one of them to reach one mile exactly.
These questions are quite easy for Indians as they faced very tough questions of mathematics in early age 😅
Mind. Blown. I think what makes this so hard is spotting the trick to unlock the question. Great explanations and thank you so much!
Definitely! Thank you so much!
It's the easiest exam just taught badly like robots counting in binary so boring. My maths students excell
Do STEP 3 I dare you.
Do Romania , we have some hard ones
i can see why
Its close too foobar, 4*4,16*16*256*256 matrix tensor determinant quantum gravity newtons law of body. Friction, innertia. Its that like googke maps on cellphone screen size and rotating map in different direction not parallel to actual road, at center pivot rotation. The riad lines will cut in different directions border by 4 sides of screen devices. Thats foobar, that computer keyboard, but without algorithm for decrypting that, them mind stays locked in a 2 dimensional frame, not a spherical holistic view like that of birds in flight. Stone age.
Hey Ellie try ISI Examination paper of India
Solve ISI math question paper
Indian boy 🇮🇳
Wonderful
I can apply. I can study in UK
You so clever and pretty 🤩
First things first she is cute ❤
indian exam is more harder than uk
How's it possible that the "UK's hardest" maths exam is an entry exam? Because clickbait?
Ok hardest high school exam
normal exam at asia 😀
this is elemntary in india.......who gives hints guys
I checked Indian exams, it’s quite easy tho
No-one cares