Oxford University Mathematician Sits High School Maths Exam

Oxford Mathematician Dr Tom Crawford completes a high school (A-level) maths exam as quickly as possible... The paper taken is the Edexcel Pearson AS Pure Maths Paper from 2018.

Produced by Dr Tom Crawford at the University of Oxford.

You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.

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[TomRocksMaths]

I made a slight error in Q9 (c) (ii) where I said 2x=-2 means x=-4, when I clearly mean x=-1... what can I say - the pressure got to me.

[Alex-zwsr]

You know he's high up in mathematics when he easily reasons weird concepts, but takes several seconds to do -2 + 3

[gibran.zidane]

when you finish all the side quests and then you go back to the starting zone

[deltius]

imagine going to Oxford and thinking your professor is gonna be some old guy and this dude shows up

[thecakeisalie]

when someone's appearance doesn't feel like it matches their profession, you know there's some genius involved.

[owenjarvis]

Man said he ain’t been in a level for like 16 years. WHAT. MAN LOOKS ABOUT 21

[PanzerfaustBR]

I knew you're going to ace it when you got the + C at the end of the integral. Truly, this is the sign of pure mastery!

[konvoy]

Did i Just watch an hour long video of guy solving a maths paper without getting bored.

[landoncube]

I'm glad that jobs are being more open to hiring people that tattoo themselves and express themselves with an external look. Really wouldn't expect a rocker look with tattoos to be a math professor at Oxford

[Patrick-pudi]

love how you're talking yourself thru the problems. wish more teachers did that--it's really helpful to hear the thought process in real time

[jhfh]

Hi, A level Maths teacher here. I thought your video was really interesting, especially the cases where the you write maths is different to what would be expected of students in an A level exam. I thought you might be interested to know where an A level examiner would probably disagree with some of your (written) answers. I understand that you're well aware of all the details involved and you've just saved yourself a bit of time or considered the details to be trivial.

Q2a: Your sketch and solution alone would probably score 1 or 2 out of 3. You described the reasoning for what you were writing verbally, but on a reason question like this the justification would have to be included in writing. You'd also possibly need to explain it's always positive, not just non-zero (probably by finding at least one value of the function for some x).

Q2b: You score full marks, A level students would usually be trained to look for a counter-example alone and that would also score full marks.

Q6a: For both marks, since the question says 'explain', you would probably need to not only find the profit is negative but also interpret that in context, so you'd need to write down why a negative value for P is a bad idea, not just say that it is (anything written about negative profit is a loss would do).

Q6b: It's the S<=>D button (surd to decimal) you're looking for here, as Im sure someone has told you :p. Since you're asked for a selling price, this would probably need to be in sensible units in the context of the question (pounds and pence) to score full marks.

Q7: You've definately got full marks here, but I noticed you initially made the very common students' error of assuming the triangle was acute! You may also be interested to know that cosine rule used to be included in the formula booklet until 2017, and now students have to memorise it.

Q9c you noted in the description

Q11: Full marks, just some different methods. Since this is an AS (Year 12) paper, students would use a binomial expansion using coefficients generated by the choose function (nCr). The method you use is taught in year 13 now. Both formula are given in the formula book, though 'proper; taylor expnsion, involving derivatives, is only done in further maths.

Q12a: You are definitely skirting the line on the minimum needed for a 'show that' question with 4 marks! In particular I wouldn't advise a student to have an incomplete line like your 3rd line. I would think your answer would get full marks though.

Q12b: You forgot that since x is acute, 3x is up to 270 degrees, so there are multiple solutions (actually 3). This is a very common error. Also, students nowadays should solve the quadratic on a graphical calculator to save time.

Q13b: You weren't quite specific enough with q, it is not just a rate of increase over time, it represents a percentage increase of approximately 12.2% every year. Depending on the mark scheme you might not need the percentage form, but you definately would need the 'every year' part.

Q15: A definite integral like this could be done on a calculator too now!

Thanks very much for making your video. I found it absolutely fascinating how many ideas from a level a higher educator would use and find normal and which ones they might not. I hope you find my comment an interest too and not something to knock or criticise you in any way. Hope you make more videos in the future. All the best.

[louroth]

I’m just approaching the final exams of my mathematics degree and it’s been tough as “COVID teaching” has really sucked out the joy of learning the subject - feels like the perfect time to have discovered this channel and remind myself why I pursued maths at higher education in the first place! Thank you Tom!!

[nb]

Crazy as this isn’t the ‘typical’ professor look. Looks good 👍🏽

[evolutiagames]

Seeing you write "<0" instead of simplifying is making me rethink every exam I've ever taken. I love that technique!

[atticusjones]

"that'll be four across and five down"...the mere fact that that utterance stems from an Oxford mathematics professor gives me hope for my future in the subject.

[gsz]

You are the true definition of "never judge a book by its cover". You are very talented.

[danielc]

Dude Can't believe you came up on my recommended, I remember you talking about the 7 Millennium problems in the beginning of August 2018 at St John's College for the Inspire Programme which I found extremely interesting and even wrote about them in my Personal Statement, you ignited a spark for me to know more and more about maths, 3 years later and I am now in my 2nd Year of Maths at Exeter! Want to say thank you for being educative and entertaining, I remember you stood out the most, even showing us your all your math tattoos including the equation you modelled yourself as part of your PHD. All the best to you Tom and great content!

[alejandromontoya]

Man! I ended my engineering degree 5 years ago and now I am finishing med school, it's so relaxing/nostalgic watching you answering this problems. You sure are a great teacher, keep up the good work!

[mrpenelope]

All this shows is that if you put the effort to really learn something and you're passionate about it, it will show, even at lower levels.

This man truly loves this subject and it shows by the way he does the math and explains the process and outcome of each answer.

[domc]

14 years since you sat a levels! You've aged like fine wine sir