Oxford University Mathematician sits Cambridge Entrance Exam (STEP Paper) PART 2

Oxford Mathematician Dr Tom Crawford completes the STEP Exam which is used by Cambridge University as part of the admissions process to study Undergraduate Mathematics. Part 1 is here: • Oxford University Math...
Marking begins from 1:06:28
The exam taken by Tom is the STEP Paper 2 from 2021. The exam forms part of the entrance requirements for admission to the University of Cambridge to study Undergraduate Maths.
You can download the test for yourself here: tomrocksmaths.files.wordpress...
And the mark scheme is here: tomrocksmaths.files.wordpress...
The exam is based on material covered in A-level Maths and AS-level Further Maths which are taken by 17-18 year old students in the UK as part of their high school education.
Produced by Dr Tom Crawford at the University of Oxford.
Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: www.seh.ox.ac.uk/people/tom-c...
For more maths content check out Tom's website tomrocksmaths.com/
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
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Get your Tom Rocks Maths merchandise here:
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[@TomRocksMaths]

Watch part 1 here: kzbin.info/www/bejne/h6TXmZ2sYr6apMk

[@JeffCottonBWFC]

The fact Tom didn't even check his answers for Q3 scares me, you're a braver man than me!

[@faisalmemon8818]

That's an amazing score on the STEP. I think it would place you somewhere in the top 3 students doing the exam and you never used up your total time allocation so could have gone back to checking your work and possibly fixing some of the missed solutions. When I did the STEP it had only been running for 3 years. You just had the exam papers. No internet; no solutions! These explanations, and the sharing of thinking process is so valuable. You remind me of other mathematicians I've met that were so approachable and down to earth whilst at the same time being such genius. A humbling experience for the rest of my life.

[@RC32Smiths01]

Enjoy these insights into exams and challenging questions. Each feels unique and simply a new world at times.

[@basicallyiamawesome7520]

I recently attended a Maths talk called “Maths Inspiration” which was located in Leeds, and when I arrived I couldn’t believe it but Tom was a speaker and was the first to give his speech. I felt really lucky to be in the crowd and listen to you speak about how maths can save the world as I am quite a big fan of your videos. Plus I’m not gonna lie it changed my perspective of maths and gave me a much better understanding of its broader uses in the world. Also just wanted to add on I’m pretty sure you can see me in the photo you took at the end of the speech, I’m waving in the middle row with my mates.

[@owenjordan5535]

I took these exams as a teenager (not this exact paper) and they were easily the hardest I did at school. Just following along was making me nostalgic for all the hours spent in the classroom at lunchtime! 🥰

[@alevelmathstutoruk]

Brilliant video, as always!

[@Benhutchie22386]

Love these videos Tom!

[@nicholasdavies6264]

Thanks Tom, another informative and well presented vlog 👍

[@horstschlaemmer4235]

Really kewl channel.Math makes fun. And you are the best example .

[@barrieshepherd7694]

I did not understand or follow any of that but watched the whole video. I'm sure that if you had been my maths teacher I would have stood a chance of at least knowing what on earth was going on! Brilliant and engaging video. 🤣

[@sachalucienmoserferreira2233]

I thougt my english unsterstand get a level up,because i dont need more legends to watching you. Thanks for this brilliant video Tom!

[@glennsaunders630]

Awesome!!!! Absolute genius!

[@oliversmith5919]

Gotta respect the bravery. The guy sat down for 3 hours knowing it should be calm all for our entertainment

[@wqltr1822]

Damn the graph sketching question is just a nice introduction to the lambert w function

[@mrawesome2704]

Could also do the one, which implies physics, because I want to undergraduate in engineering and I do not really know how to prepare properly and since I’m living in Germany and my math physics classes aren’t very astonishing, I would be quite happy if you go through it

[@hydroarx]

Question 4 is about the Lambert W function!! Blackpenredpen binging coming in clutch 😁

[@phenixorbitall3917]

Like a Champ! :) 👍

[@JamesThompson-pp8lp]

1:20:13 Might have to dock a mark on 4iiid as the statement about which root was larger was wrong. You said it was larger when you applied g, but missed the fact that your substitution flipped it round. Even so, well over 90% on a STEP paper is mind bogglingly good! 😊

[@user-ir8er1bh4q]

Should be noted, he never used all his time, while still explaining it for us and yet had such a good score. He also not realy went back and checked much. Deffinetly expected this from him, I guess is not easy to get an Math Professor :D Some I've seen here pointed out, this would be a top 3 students entry.

[@ragad3]

Agreed, and also 1:11:55 another mark on 5(i) because of the lack of the modulus within the log. He corrected it when he repeated it on top of the next page for (ii) onwards, but as an examiner marking the paper using the key, one mark should likely be deducted! So, 115/120. I also agree with ​​⁠​​⁠@user-ir8er1bh4q that he would likely have caught most of these mistakes if he had used his remaining time to go back and check his answers.

[@abz7800]

What a epic teacher

[@fcturner]

*an

[@abz7800]

@@fcturner not really big on grammar or punctuation when commenting online

[@rossg9361]

Studied math at a Canadian university, this is a very difficult university entrance paper. Very difficult!

[@meowpurrr]

will you ever do the MAT? (Qs for mathematics applicants)

[@mysteryman480]

I can (on a good day) do these exam tasks but not within the time limit; it would take me the whole day.

[@bumblebee9051]

Good Morning Tom, I have a question for you and I hope you'll be able to answer it. Do you believe that there are two types of people when it's comes to maths. For example, I am very fast at calculating, mental maths however I struggle when it comes to methods, I struggle remembering methods of algebra and fractions despite being taught step by step. What are your thoughts Tom? And any advice?

[@VenkataB123]

Not Tom, but I don't believe so. In fact, there are different stages people can be in. Some are in the stage of early learning, some in the stage of understanding and applying, and some are in the stage of knowing a concept and avoiding mistakes. Eventually, with the right amount of willpower, everyone can come to the third stage, though yes, surpassing it would be hard as that would mean you're perfect, which isn't a practical concept.

[@lamp2208]

I heard that the IB HL Mathematics is more difficult than H2 A level mathematics... do you have an opinion on this?

[@rav1617]

its true IB HL maths is about as hard as A level further maths, but a lot harder than regular A level maths

[@petersaccocia4510]

Very humbling to think that this is the exam you must pass to BEGIN studying math at Cambridge.

[@Beny123]

Exactly, the selection process is insane. I am hoping my children ace the test even though they decide not to study Maths at Oxbridge.

[@stevepowell6234]

In Q4 root e^{-g(-1/3)} you erroneously said this was the larger root. You lose another point 😊.

[@kennethreeves5068]

Tom, as "Kool" a math Prof as Kelvin cool can get.

[@antoniocicchella7574]

Great video! Can I ask you what notetaking app you’re using?

[@TomRocksMaths]

It's called "Paper"

[@user-pt7ss6cj2c]

I feel the school

[@isabah4401]

step 3 when 🥺

[@warlord1981nl]

Dude starts writing and 3.5 minutes into the video I am completely lost lol 8 minutes in and I have no clue what he did rofl, this video does an excellent job of making me feel stupid.

[@mickeyhead9770]

Don’t know why KZbin suggested I watch this video…I have no clue what he is talking about, I’m just fascinated by his hair. 😅

[@olayinkaanifowose5099]

Step is hard, jeez. For the first question, would it work by arguing that since Tn is largest when n is zero -> Tn=e -1, and then setting the n in e/n! to zero as well to get e/0! = e and saying e > e-1?

[@matthewbeasley2336]

T0 is e-1 but you want to prove the statement for ALL natural n, not just the special case n = 0

[@olayinkaanifowose5099]

@@matthewbeasley2336 Oh I see. What about showing that a the curve inside the integral is less than e/n! since t(1-t)^n is always less than one for all n since 0

[@squeezy8414]

@@olayinkaanifowose5099 yeah that’s pretty much what he did but I don’t imagine you need to actually sketch the curve

[@olayinkaanifowose5099]

@@squeezy8414 I was just looking for a way that doesn’t involve replacing the thing with one. It just seemed more intuitive to do it this way

[@user-pt7ss6cj2c]

I think alone is good

[@user-pt7ss6cj2c]

the school is good

[@drizym1037]

Can you pass the famous exam in France : ENS ULM 1966 thk

[@mehakchamoli3563]

Does he even look like a MATH Professor?! Well, anyways, excellent job! Tom

[@fcturner]

Since he is one, he looks like one 😊

[@charlesarthurs]

He is not remotely a professor. He's not even tenured, so far as I can tell. He helps out at Oxford and milks it for all it's worth.

[@tffury2007attack]

@@charlesarthurshe said he teaches undergraduate math at Oxford

[@tdhltzadvances]

Please solve Tokyo University math entrance examination🤲

[@wanyekivincent2883]

Too easy

[@rayanraahim6290]

Easy

[@thatomofolo452]

😲😯😮

[@Mackie17]

How do high school students do this if it's hard for a professor and Doctor of maths lol?

[@Beny123]

Hard work and a mathematical brain to begin with.

[@nullenski]

thought i was good at maths.

[@user-pt7ss6cj2c]

I feel no man

[@user-pt7ss6cj2c]

I like you help me

[@ronaldkasajja6793]

Champ

[@BarriosGroupie]

I find it frightening to think some teenage kids are able to do this.

[@312Lawliet]

I agree, it's quite tough for an entrance exame. I studied math in germany and some of these questions are harder than some of my homeworks :D.

[@ankursharma8709]

JEE ADVANCE NEXT PLEASE

[@theSSBguy]

Sir please solve the JEE advanced paper

[@lamp2208]

@Memes shorts y

[@Abc-vc4ml]

🤡

[@veerpatel6719]

@Memes shorts what do you expect, India population big

[@Benhutchie22386]

Shut up

[@ys92legand24]

jee advanced so easy i do in sleep

[@Baron-Ortega]

Ahh but does the test do enough to remind the entrant about slavery and how being white and British, especially male (not that there is a gender binary of course ), is the worst crime in history?