Oxford University Mathematician takes American AP Calculus BC Math Exam 

Please make video on JEE advanced solve (India)Math section 2016 exam .

Inflection is when gradient changes from decreasing to increasing. Remember 2nd deriv is the "gradient of the gradient" so when the "gradient" has either a min or a max you have inflection. Gradient does not need to ever be zero.

Hello Sir, u made an misact at #1:53 its indeed continuous. Cheers

Hi Tom, at what level of education did you reach when being hired at Oxford? PhD? Double PhD? Thank you for your work.

he fixed it

Isn’t ap multivariable calculus a thing

@@VoGnos no multi is pretty much exclusively a college/dual enrollment class for hs

So what was the point of that

@@VoGnos Multivariate calculus was the fourth semester in my undergraduate school. This covers the first three semesters.

I didn't actually take the material in the third semester of Calculus it covers... I did it independent study. The former calculus teacher, who had been promoted to vice principal, really understood Calculus and he helped me with that work. My high school was little more than a prison for the students unfortunate enough to be assigned to it. Without that VP, I would have been expelled.

Nice work getting a 5.

A 5 is a good attempt especially on your first try, don’t beat yourself up too much. You can always retake and reach for that perfect 10!

@@marving8907 I believe 5 is the maximum score:)

@@mathsunmasked56 yeaa I’m just messing with yea lol

nicely done

Whaat you wrote it?

Same here. I didn’t find it difficult except for the last one, but I think that I (probably) got it right

@@8ball708 i think he means thats the one he took

@@stuv12 Ohh that makes more sense

Bro u evil

I'm taking ap chem right now and I hate it lol

@@bb4251 the exam was brutal 💀I took calc BC today and it was moderate

😂😂

bro ts is easy asf ur finished

It just proves that the way we teach calculus to high schoolers is a bit backwards. Students who are able to perform well on these exams typically just study these problem-specific methods of answering a question. This man is a doctor in his field and is relying purely on knowledge of mathematical concepts to complete the exam. I guarantee that the first problem has some "simple" method that students are taught to rote memorize, when in reality this type of learning is unhelpful for most mathematicians.

​@@635atomword

Maybe 20 years ago lmao

@@krissv3ctor512 he did stay stylish, rather than fashionable.

Not at all? He looks like a younger version of every math professor I ever had, dresses exactly the same

@@AnthonyLauder fair enough

Agreed

Agreed, in my experience the best professors generally weren't always the ones who had maths come super easy to them, it's through their struggles and perseverance with mathematics that they are able to break things down in a simple intuitive process. Richard Feynman is a perfect example of this.

Same

Me dreading and excited for the exam as a junior in high school 😢

I don't think there's much of a point in being pedantic about timings because he spent so much time explaining what he was doing in reality if he was doing this in a test he wouldn't run out of time

they still use the 1-5 scale today

In a real exam he would have been told to leave the exam hall for constantly talking and giving away answers to other students. So 0/36 if we are being realistic.

you do realize he did this with absolutely 0 preparation while also spending much time to explain his decisions/thought process, obviously if he was taking this as a real exam he wouldn't be tight on time and he obviously would've got a 5, your clearly not the brightest individual....

"Quadrature" is a historical term that just referred to a geometrical method used to approximate an integral/area. Some mathematicians would actually consider a Riemann sum to be a (very simple) type of "quadrature" for estimating an integral. Usually, however, numerical methods classes would start with something a little more sophisticated to estimate area as a "quadrature" method. He mentions the trapezium/trapezoidal rule, which is sometimes taught in American intro calculus classes, where you draw a trapezoid and find its area for each Riemann sum interval, rather than using a rectangle. (That is, the two endpoints of the interval on the function are used to construct a trapezoid for each interval -- you'd sum the area of those trapezoids.) Tom also mentioned Simpson's rule, which basically would use a quadratic function (parabola shape) to approximate the shape of the function in each interval (rather than a rectangle or trapezoid). You'd find the area under all of these parabolic segments and sum them to approximate overall integral. Quadrature methods have other more advanced approximations for numerical integration too that focus on optimizing the calculations using increasingly better approximations to the functions within the intervals. There are whole classes of approximation functions designed for this sort of thing. The word "quadrature" itself, as you guessed, does have something to do with "four," as one of the first geometrical problems these approximation methods were applied to was trying to "square the circle" in ancient Greek mathematics. That is, to construct a square (a quadrilateral, hence quadrature) that would have the exact same area as a given circle. Numerical integration methods begin with using other quadrilaterals like rectangles and trapezoids to approximate the area under a given curve, so that's the etymological root of the term. However, as I mentioned above, in modern usage "quadrature" often just refers to any numerical approximation method used to find an area under a curve (i.e., an integral), whether it uses quadrilaterals or more sophisticated shapes.

iPad

不可能，因为高考好难呀😂

43:20 Your “MEH” here is amazing. I will suggest you’re able to have that attitude since you presumably know most (if not all) of this info already) and this is a test “for fun.” For those of us that had to take a test like this, this was traumatic in a way!

so x=6 technically isn’t a solution because f’’ goes from 1 to -1 but never any value inbetween. simply because the function is piecewise

There is a calculator and no section. Calculator is not required but it makes calculations faster.

there's 2 sections. AP Chemistry allows calculator now too but they added a bunch of question and topics that require calculations

I think he gets a bit of a break because he's talking to the camera and pausing to explain things to us while taking the test.

3 a btw

It’s called ‘Paper’ on iOS

@@TomRocksMaths the man the myth the legend himself, ty man.

Because xe^(x/5) is already the area (not the length or width), so it only needs to be multiplied by the thickness dx to get the volume element, and then we sum all those volume elements using an integral.

Yes! It is where the acceleration flips signs +/-, giving it a changing concave up and down shape

Yes. True indeed. Bessel, not to be mistaken with Brussel...

3, 4 if high ability. 5 and up are allowed but very rare. There's one girl taking over 30 this year though!

Most top us students take like 15 of these ap classes lol, some take 29

​@@blabbla-jp2snTaking more than 9-10 AP classes requires self studying and finding a school in the area that even offers the other AP exams. Plenty of top students take every AP they can fit into their schedule and no more, I took 8 and ended up with a merit scholarship to a top school without needing to take every ap exam.

Same

practice

its the exact equivalent to the current A-Levels.

This is an ironically uneducated post, filled with misconceptions, assumptions, arrogance and bitterness. Did an American girl break your heart? Were you rejected by an elite American university? @Andalusian_

@Andalusian_ have you taken any US high school courses

​@Andalusian_ you're whole rant is idiotic. The US system allows people of all abilities to get a broad based education. So, even if someone wanted to be a bricklayer they get a taste of some more advanced biology if the wanted or at least explore concepts. Furthermore, high school courses come in remedial, standard abd honors level. Then there is the AP exams fir those for are on the fast track to college (in combination with honors). So, an honors student taking AP exams is on par with their A Level counterparts. In fact, the AP system makes makes them a bit more advanced.

they made questions easier for 2021/2022/2023 due to decreased scores from quarantine. they're making it harder again - but it still may be easier than a levels.

​​@@bb4251it's on par with or more advanced than A levels. The stats exam is more rigorous than the ALevel module counterpart.

a quant would never say something like that