Oxford University Mathematician takes American SAT Exam

Oxford Mathematician Dr Tom Crawford completes the Math sections of the US SAT exam alongside fellow ‪@numberphile‬ presenter ‪@SparksMaths‬.
Watch Ben attempt the same paper here: • SAT Maths Paper Live -...
Watch Tom and Ben mark each others scripts and talk through the exam questions here: • SAT Math Exam Walkthro...
The paper taken by Tom and Ben is the SAT Practice Test 10. This is used as part of the admissions system for US universities/colleges. You can download the test for yourself here: tomrocksmaths.files.wordpress...
And the mark scheme is here: tomrocksmaths.files.wordpress...
More information on the SAT Exam (alongside more practice tests) can be found here: satsuite.collegeboard.org/sat...
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:
beautifulequations.net/collec...

[@alexjbriiones]

Appearances can deceive us all, but I never would have guessed in a thousand years that the punk guy is a math rock star. Well done professor, you're a great guy.

[@steinanderson9849]

he has navier stokes equation tattooed on him, fully committed to the math!

[@cuac5869]

Seeing math majors at college on a regular i think he fits the stereotype xd.

[@jeffburnham6611]

Don't feel bad, I thought Oxford had higher standards of decorum.

[@kathleentaylor8840]

Peerless as a punk is its own decorum.

[@elwood1029]

What I find odd is that I can't easily understand the apparently deliberate ornamentation of this person's appearance without just concluding that they want the way they appear to be *noticed*, perhaps as a part of their identity in some way. I find this odd because I can't see why wanting one's appearance to be noticed as part of one's identity contributes to videos aimed at accessible online maths education. Unless, of course, the reason for the ornamentation is to draw in and hold our attention for the sake of getting us to focus on the videos in the first place. But I suppose that's the oddness: using one's unexpected appearance (as a maths professor) to startle people into paying attention to your maths talk might work initially ("come for the quirky look, stay for the interesting maths"), but it also runs the risk of making viewers focus more on the way you appear than on what you're actually saying. If this person were to give these maths videos dressed as a giant purple dinosaur, for example, that too might work as a hook. But you can see how the more you actually cared about the maths itself, the more that hook-tactic could become irrelevant or possibly annoying. A pattern of choices about one's appearance that are intended to express rebellion only to be subtly coopted into a mere strategy for maximizing views in one's online career? Nowadays that's about as Punk as postage stamp.

[@carelvoltaire1654]

I'm 30 and I've completed two engineering degrees, I can't believe how fast I can solve these "problems" but in high school, I struggled very much with the SAT. I guess I did learn some maths along the way.

[@mastod0n1]

I'm the complete opposite. I'm about to turn 30 and I got a perfect score on the math part of the SAT and 12 years later I work as a line cook and have gotten so rusty at math. Some of these questions I could have answered almost immediately and intuitively back then but now I have to actually exercise my brain.

[@sanitary103]

@@mastod0n1 any reason you did not choose a profession mathematics related considering you were so strong in high school?

[@morbidgirl6808]

I'm doing software engineering as a undergrad student. I was tenaciously bad at physics and maths in the high school. Nowadays, I've been doing surprisingly well in applied physics classes, linear algebra, calculus, differential equations and even statistics. I don't know, but it suddenly became too easy and fun for me as compared to high school. I decided to practice it on daily basis. The more I do it, the easier it gets for me. When I look back, I realized how simple were physics and mathematics in the high school.

[@frankj9270]

Im 18 in my first year of engineering calculus sequence and i feel the same way. I dont know how i didn’t know all of this

[@anonymoushuman8443]

@@sanitary103 there are no professions related to math

[@jasonpatterson8091]

It was refreshing seeing a non-US tester take this without constantly commenting on the relative difficulty of the questions. The SAT isn't intended to do the same thing that GCSE or A-level or national certification tests around the world are intended to do. It's intended for any student who might attend college and in practice is given to all students in many states, whether that student intends to be a particle physicist or dig ditches. The questions are supposed to be approachable by any student who has had algebra and geometry. The difficulty comes from time constraints and a student's ability to apply what they're supposed to know to the various problems. When exchange students take the test, they do score higher than the average US student, but they're not average students - they're academically high achieving kids whose parents are able to afford to send them halfway around the world for a year. In other words, we don't get too many future French ditch diggers as exchange students... Exchange students typically do about as well as academically high achieving students from the US.

[@christiand.3348]

Sorry to say, I neither was a high performing student nor did my parents pay for my stay abroad. The only 2 advantages I have are first to live in a country, where tution fees for University are a fairytale and secondly that my parents taught me in my teen years that I can work in school holidays to earn money. This helped me to afford my one year stay in Canada. But at least my parents supported me psychologically. :) I simply do not see the reason to have such tests, if you may become a student who will not be exposed to any major math problem during studies. This should be basic knowledge in high school, not more not less.

[@rimun5235]

Another aspect is that international students study a crap ton for their exams. The sheer amount of time other students study for their exams around the world is a lot. The SAT is not an exam most American students spend years preparing for. Most people spend a month or two preparing for the SAT. However, in my home country, you start preparing for the national exam the moment you enter High School. You also do not get much of a vacation. Students not only study after school, they study on holidays and also have to go to school earlier for four years just to prepare for an exam. Of course, international students are going to find the SAT easier.

[@Julian-qs8xq]

@@christiand.3348your 1 specific personal case doesn’t change the fact that most exchange students come from fortunate families with higher opportunity.

[@christiand.3348]

@@Julian-qs8xq I know more then 10 persons from my classes, which did the same year abroad. Non of them got significant support from their families. You might be right in some cases, but is definitely not the majority. At least not in my country (Germany). There might be countries with a lower standard of living. If students from these countries stay in the US, often rich parents are supporting them. The average families there might not be in a financial position to send their sons and daughters over to the US.

[@Julian-qs8xq]

@@christiand.3348 it’s nice that you and people you know got to have a cool unique experience like that. I see where you are coming from, especially considering a country like Germany where opportunity is abundant. The truth is, most exchange students in the United States are sent from China, where many wouldn’t have the option.

[@spitfire4sergi]

Thank you for using your passion and talent to better our species!

[@adamlabnaki9216]

I always love how at the end of each question, Tom does a quick "whoo!" as if to say, "that was a relief, got through that one". Maths gives this unpredictable tension that can make you anxious because you just don't know what numbers you end up with but yet it's so addictively exhilarating and satisfying once a question has been solved!!!

[@pizza2668]

Um actually, i think he was saying "cool."

[@localmilfchaser6938]

It’s boring asf

[@kidwimpy7366]

Unless your bad so you stay anxious forever.

[@jmbs9833]

Or you write your name on the paper, put it on the teachers desk and tell him, that you can predict the outcome of that test... Math is so satisfying...

[@FordsTowel]

I love this too. Sometimes I physically pat myself on the back when I get a question done.

[@monismazhar6581]

This is like watching a level 100 boss completing level 1 side missions that was easy shit for you man

[@samayahone3497]

this could not be more true xD

[@abcdefg4570]

After taking a bit of calculus, this shit is easy.

[@yaslaan]

An average Turkish teenager would eat these in a breakfast dude. I wasn't a bright one and almost 7 years past since i graduated from highschool and this sh.t was even too easy for me. An average Turkish highschooler would finish first 20 questions in around 3 minutes whether they know english or not. And also probably without using a pen to calculate. F..king education system teaches us diffentials calculus integrals and all kinds of harvard level sh.t in highschool. I feel like i could conquer harvard in a year with tight discipline after watching this video. But here im working in a job that pays less than 300 dollars in a month.

[@Akamaikai0923]

Probably because the test is actually easy.

[@Jeffrey_Tyler]

Well, it IS a test for 16-17 year old kids and he's a mathematician and professor at one of the most prestigious universities in the world. I'd hope it would be easy for him or else that'd be worrying 😂

[@mrtoast244]

As someone in my 3rd year of electrical engineering I like to look at high school tests to remind me how far I've come. Sometimes I feel like I'm falling behind, even if my grades are average, but if you're learning then you're always getting better at these things even if it doesn't feel like it.

[@shuween706]

I always thought the SATs were a LOT harder than this! This is so much nicer than I imagined and it was actually quite fun to do it along. I wish our high school exams had been like this. I haven't had anything to do with math for the past 7 years, and I don't think I would be able to solve my high school exam papers anymore at all, but this was actually surprisingly simple and fun

[@bambi9609]

The point is for it to be easy and fun. It tests up to math concepts that you learn in your first year of high school. The hard part is the time limit. 25 mins no-calc, and 45 minutes calc. You get a bit over a minute per question. Once the minutes are up, you cannot revisit or otherwise do anything within the section (which includes the scantron - it’s either filled in or it’s not).

[@lotusflower8442]

The SATs aren't considered as finals in the US, but as something to help with getting into universities. They're bits and pieces of math we've learned from middle school all throughout the first half of high school, so I would think it's easy, but then again there's the reading portion so I'm definitely going to study for that😅

[@homeboi808]

I’ve proctored SATs, the actual SAT is a tad harder, they also have some “experimental” questions they trial that don’t count and they are noticeably more difficult.

[@Willy_Warmer]

I'm not that far into the video, but so far, as a freshman in Algebra 1, this shits pretty easy. It's weirding me out

[@echochamber1234]

​@@Willy_Warmer most of the questions are suppose to be easy. the main challenge is doing the problems quickly and reliably for hours on end. and then some of the harder questions do require good reasoning skills or having practiced so much that you recognize the correct procedure. but true that nowhere on the SAT will there be advanced math like calculus

[@jorggamingcr409]

As an engineer I now feel this kind of exercises are great for a weekend afternoon, not because they are easy (believe me, I struggled with math at high school and college but with a lot of practice I became better each day) but because it is really fun. When I was younger and even when I wanted to become an engineer (electronic) I tought math was boring and had no use in electronics, but math can be really fun and once you get the "feel" of it, you start seen its applications everywhere.

[@aaliaaslam3841]

hey, im a high schooler and I find maths quite interesting. not only SAT level, but calculus, tougher algebra, trigonometry, etc too! real/imaginary numbers etc, on the other hand is probably what I like least. i was wondering whether to take Maths in college and pursue Engineering. can you tell me if higher Maths leans towards algebra/trigino or if it delves deeper into abstract imaginary concepts?

[@priyadarshinisaikia1395]

@@aaliaaslam3841 i have the same question as you, engineering or a math major. I love math and maybe physics😅. It just comes naturally to me.

[@setsu2221]

I mean... this test was really easy though, even without preparation (as an engineer). Its relative level isn't easy, which is what I feel like you were hinting at. But if you cannot do this with ease as an engineer, then... oof?

[@wngmv]

@@aaliaaslam3841 I did mathematics and then statistics for PhD. Mathematics (basically linear algebra and calculus) are fundamental to anything STEM. imo, engineers don't get enough mathematics training. For a BS level degree and career, you don't necessarily need to study that much maths. But if you do want to pursue a PhD degree, then you get a huge headstart doing mathematics for undergrad. In fact, if you do Mathematica for undergrad, it is pretty easy to switch to EE, ME, CS, or stat for your PhD degree. Also, studying maths for undergrad is also very useful because you get a crazy amount of robust logic training. This is extremely useful not only for your future career, but also in your life because you approach your problems more logically.

[@wngmv]

@@aaliaaslam3841 also, college level maths is about rigorous proof, not numbers anymore. You enter a realm where everything is symbols and little numbers are involved. It starts with calculus (what we call analysis), and linear algebra. Then it branches out of real analysis (extension of calculus), geometry, complex analysis (where imaginary numbers are dealt with using algebra), and then functional analysis, topology, differential equations and other stuff. The things you like and you didn't like are all covered, and most of them are covered in a semester. Naturally there will be subjects you like and don't like. But they are just a single course, and you'll be taking 20-30 subjects on mathematics depending on the specific college and tracks you take.

[@felicityc]

38:00 I love him so much. He took a clearly easy question that you can just answer with no effort and took the time to write out the entire function and think it through. Can you imagine how many people would scoff at that? I have mad respect for that quality of teaching.

[@signature7336]

@@mohemeenahmed7560 It's a linear function, it's not exponential because you're doubling the people - not squaring

[@edenchung8661]

@sign ature the question says that you double each year, so 30, 60, 120, 240, 480, exponential, not linear

[@wakimura303]

good for content creating but bad for actually taking the test. time is money

[@henryposadas3309]

​​@@wakimura303 that's the point. Obviously he's creating content and teaching. He has an audience. Otherwise he wouldnt even be talking. Common sense.

[@sophocles1198]

Not sure why you fell in love with this explanation.

[@ap3xmath123]

Just recently found you and I can safely say! I feel so confident in being a super start and super smart!!!

[@mtkimbrell]

I commented on a video from @mathemaniac page but again; @Tomrocksmaths I love that you take on these challenges. It shows that the great math minds don't always just wave their wand and "poof" out a proof. You actually do have to take the time like anyone would with a puzzle to figure out the solution. The secret to being good at math is to break it down and take the time for details. I was a horrible math student in primary school but then something clicked and I had the drive and patience to work through it. I went on to successfully complete about every Math class I could take with a B.S. in Electrical Engineering and M.S. in Engineering. Thank you for not making it look like a magic trick!

[@blaight87]

As someone who thinks math lost me when letters got added I always appreciate raw enthusiasm in an expert field. I did my PhD in cellular neuroscience and would be similarly happy to explain neuroprohins on camera. Keep it up man. Best from Germany

[@bookcat123]

Math lost me when they added numbers… I get the logic as long as it’s in letters but can’t add to save my life somehow. Perhaps together we’d make a single competent mathematician!

[@Joshua-dc1bs]

Don't you need a lot of maths for neuroscience? Hodgkin Huxley Equation, Nernst Equation?

[@umberto488]

@@Joshua-dc1bs liars gonna lie

[@BboyKeny]

@@Joshua-dc1bs Maybe it depends on from which approach you take to neuroscience. If you're interested in the computational part, you need math. If you're interested in the cells then biology and chemistry will take you far. Although mathematics is beneficial in both biology and chemistry.

[@wyterabitt2149]

​@@BboyKenyMaths is more than beneficial, it's a core part of any chemistry and biology into degree level (or even lower levels depending on how the education system works in your country) understanding. It's not low level maths either, doing biomed I lived with an engineer who didn't think it was even remotely easy when they saw what I was doing at times.

[@Neil-ii3dp]

As a former SAT tutor (25 years ago), this was a ton of fun to watch. Next time, can we do mathematicians take the verbal section of the SAT?

[@ATLTraveler]

I got a 780 on math and a 610 on English LOLOLOL

[@faithk13]

They don't do the verbal portion anymore (thank god) unless they added it back from when I took it 3 years ago :)

[@ttt69420]

@@ATLTraveler Very respectable score for a highschooler.

[@ATLTraveler]

@@ttt69420 I know my mom was a high school math calc teacher when I was young and in high school so obviously she helped a lot but have always been good at math. My problem is I suck at English lol. I never really enjoyed reading and reading is very important to scoring well on SAT English portion. My class was one of the first couple years when they added writing as well, cant remember what I got on that section but I was a decent writer just sucked at English.

[@MacDaniboi]

I haven't studied maths in 10 years, but I found this to be not particularly challenging.

[@TheRealCptObvious1]

I’m pretty rusty with maths since finishing school a few years ago. I’m subscribed to this channel now to refresh my memory and probably learn a thing or two

[@constellations8572]

Small note on number 6: An even easier way to solve this is to factor out x^2-1 to (x+1)(x-1) and then divide out the x-1. This would leave you with x+1=-2 which is negative 3.

[@N.a.syed.]

If you're correct, well done!

[@subtopewdipie4159]

Yeah I was shocked he didn’t do this as a math teacher

[@mujtabaalam5907]

@@rottedpotato2028 Can you give an example where his method would cause you to miss an answer? Include your multiple answer choices too

[@BMAN4000]

@@rottedpotato2028 OP is referring to the difference of squares polynomial identity. a^2 - b^2 = (a + b)(a - b). in this case, we would get (x + 1)(x - 1) / (x - 1). you then cancel out (x - 1) since it is in the numerator and denominator, leading to a removable discontinuity or a hole on a graph. that means (x - 1) cannot part of the solution and you are left with (x + 1) = -2 which you then solve for x to get negative 3. referring back to the factoring method done by the teacher in the video, he gets (x + 3)(x - 1). when solving for x for those equations set to zero, you will plug x = 1 into the original equation to find that it does not exist, therefore x = 1 is an extraneous solution.

[@jurijaerts1086]

@@rottedpotato2028 false, you can always do this. There are no exceptions

[@nobbytho]

my sat being just 15 days away and i just started practicing, this was probably one of the most helpful video to get one doing questions, watching you solve and at certain points thinking how did you just deduce that (say in qn 9 first section, without finding the slope) helped me find the reasoning behind for myself. thank you so much!

[@kugelblitzingularity304]

He was speedrunning the test. I would suggest you do it with two points just to be safe.

[@Shadow-fb2ec]

@@kugelblitzingularity304 i would be slow as fuck bc I suck at maths

[@namename5336]

So now it is 6 days away?

[@namename5336]

@Maiahi Good luck to both of you 👍

[@yugiohlegend]

Good luck! You got this

[@tess5747]

I envy your maths knowledge. I struggled with maths at school and numbers scare me a bit. The ease in which you answer questions I’d be scratching my head over for hours is so impressive. If my maths teachers had been like you I would have engaged more.

[@chrispycryptic]

You need not find maths intimidating, I promise you that your experience in learning the subject is sadly closer to the rule rather than the exception. Problem solving is a skill that doesn't come naturally to most people, achieving a level of rigor in your understanding on maths is really quite difficult. Between you and me, I think it has a LOT to do with how the subject is taught. Particularly in gradeschool where it gets more of a "rote memorization of arithmetic" treatment rather than showing an appreciation for the underlying concepts early on.

[@______IV]

@@chrispycryptic: You are so right. It has SO MUCH to do with how it’s taught, and that goes for every subject. I was kicked out of my high school algebra class by a teacher who said I wasn’t smart enough to handle regular algebra, and transferred into a throwaway class with an even worse teacher. After high school I took algebra freshman year in college, had an amazing teacher, and not only got an A+ but was tutoring a few students on the side. My middle school and high school were filled with tenured teachers who hated teaching and despised young people yet couldn’t be forced to retire unless they did something illegal in class or just stopped showing up.

[@lonelysoul3704]

Your thumbnail just made me realize why last night I couldn't solve a math problem. YOUR THE BEST. THANKS

[@andrewmckiernan4361]

I really wish I had this video when I was taking the SAT last year, this is great!!!

[@RC32Smiths01]

Took the SAT a longggggg time ago. This stuff is something I'd definitely need a refresher on haha. I look forward to this perspective!

[@rorywhyte6722]

Terribly good, thank you!

[@kidd1941]

Love to have a rockstar professor like this 😭😭🔥🔥

[@andrewharmon5843]

If you're interested, the ACT (the other college admission test in America) is typically known to have harder questions, but being easier to improve on

[@stanleymyrick4068]

Yeah. Back in 1988 I scored 25 on the ACT out of 32. In October 1989, the ACT changed its tests and recentered the test scores, changing to 36 as a top score. The result of both the test change and the recentering change is that the middle 50 percentile rank changed from between 17 and 18 to between 20 and 21 and far more scored in the 30s than ever did before 1990. A 25 back when I took it probably is somewhere equivalent to 28 or so today. Thing is, I got lucky. I ran out of time on the physics/science part (my weakest subject probably) and started marking answers in. Wound up making 30 in physics, while getting 23 in math and probably around 18 in whatever else was there, reading or something. My true score would probably have been 20 give or take.

[@AlexK0708]

I took the ACT and SAT twice each in high school. Honestly thought the ACT was noticeably less difficult.

[@JJJRRRJJJ]

@@AlexK0708 I agree. Thought the ACT seemed way simpler, and felt like I nailed it. But I actually did much better on the SAT.

[@camy369]

@@AlexK0708 I’ve never taken the SAT, but based on this video I’d say the ACT was much easier as well. This practice exam had stuff I didn’t even learn about until my 2nd year of college like standard deviation. I remember my ACT was only basic things like area of different shapes, mean, median, and mode, etc.

[@patrickmcpartland1398]

​​@@camy369a basic Google search pulled up that basic statistics and Probability are indeed part kf what the ACT tests for, totally about 8 to 12% of the questions on the math portion.

[@mishkaatrawjee1271]

This was so fun to watch as an SAT tutor. I did the test with him. And it was great that he got all of them right. I’m half of the video in. I didn’t see it all yet. Hope he did get all right lol. I should make a video like this. Super clean. Great reactions 😂

[@pieTone]

Even tho I'm a 15 year old romanian kid who is not even in highschool I still find this video very enjoyable. ( and I am very excited to have solved some problems instantly with my current math knowledge :) )

[@frankj9270]

@Ray Lant bro.

[@Jomz31]

@@CharL2031homie get ur ged or start workin construction 😂😂

[@bb4251]

As a 15 year old American kid, most of the people in my classes know these problems lol. It goes in line with the on level curriculum for each grade, but a lot of people are advanced, accelerated or doing college math at their local universities right now. My school has 4 thousand people and about 100 people in my grade are doing multi variable calculus at a state university right now - one of the top 30 tech universities in the world. The on level curriculum is really easy, but taking on level classes looks pretty bad for your resume unless you’re content with going to an average university

[@Hoopsjvl]

I like what you did on Problem 15. My first thought was to multiply the first eq x2 and subtract to get an equation where x = a fraction and it was easy to see which solution caused a divsion by zero.

[@chriswork4785]

Another approach is to put them in slope intercept form and determine which a value gives them the same slope (without being identical equations). Two linear equations that never cross must be parallel and have the same slope.

[@sadathusain3787]

I've taken both the SAT and GRE exams and the math sections on these standardized tests are more a test of mental stamina than anything else.

[@rambler209]

When I was in high school, I took an SAT prep course that taught me that the time per question for the calculator section was significantly higher than for the section without the calculator. Therefore, if you can get the questions to a point where you can deduce the answer, it is a significant advantage over just finding the exact answer. Remember, all answers are multiple choice, and if you can take enough practice tests, you can usually find a similarity in the way that they give you the incorrect answers.

[@TrueFilter]

American tests are such a joke.

[@tpthpt5973]

Great video!

[@BenHawkinsvids]

This copy is an exam I taught somewhere around 100 times in my time as a test prep tutor. There are many problems I love on this test, but question 19 in the no calc section at 16:10 is my favorite. Too much focus on process would cause students to solve for x and y independently and then add up to 5x+5y. The ability to take a step back and actually realize the why behind what questions ask was the biggest key to properly approaching these tests.

[@sjsnnsndxdnendnndd5939]

I’ve lived in both us and the uk and have taken psat, sat, gcse and a level maths and the thing I’d say about the sat is the questions are quite straight forward but there’s so many of them that’s it’s easy to lose concentration and drop marks and as the grade bounds are so high in the sat, trying to not make mistakes is the hard part. (Exams are super long when you take into consideration the English sections too)

[@TomRocksMaths]

Yes the time was definitely more of an issue here than on any of the UK ones.

[@blackfalcon1324]

The thing is, it doesnt really matter how easy or strait forward it is, it is graded on a curve.

[@albertosimeoni7215]

With how many 0 the factorial of 2004 ends ?

[@carstenmeyer7786]

@@albertosimeoni7215 2004! has *400 + 80 + 16 + 3 = 499* factors of five and even more factors of two, so it ends in 499 zeroes.

[@albertosimeoni7215]

@@carstenmeyer7786 And the number of zeros limit tends to 1/4 of the original number...

[@leoduckworth6286]

Great video, A interesting exam to see the thought process behind would be step 3 since it’s more problem solving based compared to the others

[@TomRocksMaths]

I’ll get to university admissions exams eventually don’t worry!

[@ajsctech8249]

great channel. Please do an SHL or Saville Aptitude test. Great to see how a professional math guy tackles these types of tests that non-maths people often have to pass.

[@ORDEROFTHEKNIGHTSTEMPLAR13]

Exactly..

[@optimatus.]

bro doing these questions taught me more of the sat than anything else so far

[@YoSoyCristianoRonaldo]

Excellent

[@chrisi359]

I need this video as I will be taking the SAT in the near future 😅

[@drfpslegend4149]

I love videos like this, because it just shows how people actually do math. Like there's no magic going on or crazy computer-brain number crunching. Just a normal person who gets mad when there's lots of words to read, who has the right framework to approach each problem and think about it clearly.

[@navjotsingh2251]

When you get to advanced abstract algebra and algebraic topology, it’s all black magic from there. That is way different than anything you do in high school or undergrad 🥲

[@drfpslegend4149]

@@navjotsingh2251 Well I think there is something to be said of demystifying the mystical so to speak, which is what I think Dr. Crawford here is going for. Lots of people have this warped view that math is this alien field of study that only geniuses find their way into, which isn't true at all. Given the right education and support, normal people of average intelligence can be taught how to solve advanced math problems, and can even go on to become mathematicians. I'll agree that the types of problems change as one goes higher up the ladder of mathematics, but as a graduate student myself, I can tell you that I still get grumpy when I have to write out a long epsilon delta proof or something similar. The point is that I know how to write an epsilon delta proof in the first place, just like high schoolers can be taught trigonometry and calculus, and college students can learn number theory and abstract algebra. Not a lot of people get to the point where they can see this for themselves, so it's nice when professional mathematicians demystify what goes into solving what are probably some trivial problems for them, but will be seemingly unsolvable problems for many people.

[@georgegrubbs2966]

You are taking a long time to work these problems!

[@nathanbeer3338]

Tom is the only one who can talk about the physics of peregrine falcon while doing his SAT

[@TomRocksMaths]

I believe Ben did exactly the same thing

[@kevinralph5305]

I didn't understand or have a clue about his working outs, I was just fascinated by his speed and knowledge of maths. I'm afraid basic maths is my limit.

[@andrupribadi5989]

Yeah it will never get old. If you have brain you can have/be anything/anyone!💪🏽

[@enicolexx]

looking at this made my head hurt. idk how u make it look so easy but great job !!

[@CRFYS]

Can't wait for this. It'd been a few years since I took my maths gcses. I'm very curious to see what style of questions they have on the exam.

[@drgatsis]

Fun to watch the nostalgia :) I did the paper 2 question involving averages in 3 seconds in my head. I used 1600 as a reference (since it was the mean) and the 1200 and 2000 average out to 1600 anyway. 700 is 900 below 1600 so the the answer must be 900 above 1600. I use this approach to compute averages. For example, the average of the numbers 78, 80, 82 and 84 can be found by using the reference of 80. Then you have ( (-2)+(0)+(2)+(4) ) / 4 or 1 --> answer 81

[@joshuapoznick7762]

Damn man has put in work I remember when he was a student now hes a professor

[@anwerabdallah569]

may god bless you you are a very smart student

[@javerjimbau6309]

You should try Malaysian SPM additional mathematics. As a former British Colony, 17 year-olds in our country used to sit for GCSE O-levels before it was taken over by SPM. There are two mathematics subjects taken in SPM, mathematics and additional mathematics. The latter taken by science stream students and hence substantially more challenging. Would love to see how a mathematics professor would approach and review the syllabus.

[@PassionPno]

Additional Maths is also taken by arts stream students.

[@luthfeeghazale6206]

​​@@PassionPnoit differs based on the school and program...from where i lived in Malacca, there is a secondary school which they have an upper grade class (f4-f5) which offered economy and additional maths..where as in my school they dont add addmaths to the economy stream

[@loveaintfree1409]

Man I want to learn math from this professor.

[@TomRocksMaths]

[@ORDEROFTHEKNIGHTSTEMPLAR13]

Same I'm absolutely useless at it..

[@williamwu5798]

Great job professor, I think you should have a try on the Chinese college entrance exam math paper, which I think it's very challenging for everybody.

[@hassadhassan2610]

you feel it easy now because you work and u understand the math application in real lie. i struggle to this during school because i dont understand what it is use for especially additional math

[@Jeffrey_Tyler]

This was an interesting video. I think doing this is a great mental exercise. Also given that it IS a test for 16-17 year old kids, and he's a mathematician and professor at one of the most prestigious universities in the world, I'd hope it would be easy for him. If it wasn't then that'd be worrying 😂

[@elitefamilyparkour]

This dude has crazy patience. On most questions the answers were either obvious on first sight or after a few seconds of thinking and yet he took the time to write everything down 😅

[@cowprophet]

Gotta show your work

[@lkdub]

Would love to see you give either of the Irish Leaving Cert Higher papers a go!

[@murraycorradini6762]

If you're looking for another test eventually, would be interesting to see you give the Australian HSC for Standard 2, Advanced or Extension Mathematics a go!

[@TomRocksMaths]

I think this is on my list (some Australian ones are anyway!)

[@random19911004]

Australia 2Unit Advanced is a walk in the park (but are harder than this SAT by far). Australia 3Unit and 4Unit get some pretty tricky questions. You will not get 100% without specific revision of the content. You might not even get 50%.

[@mohamedmotaz5194]

@@random19911004 💀you are funny.

[@msbhv_jin]

I did hsc 3unit maths, was surprised at how easy the sat was, this is like 9th grade-10th grade content.

[@TheMiguelfbduarte]

I would love to watch you do the Portuguese Math exam.. Looks so much harder than any of these questions, or maybe it just looked much harder when I did it 😁

[@RobertMJohnson]

that must be why portugal has universities like MIT, Stanford, Princeton, CalTech and Berkeley, eh?

[@preyxd]

@@RobertMJohnson That literally means nothing...

[@RobertMJohnson]

@@preyxd your lack of understanding is your issue, not mine. grow a brain.

[@clytemnestra]

@@RobertMJohnson There a lot of things that contribute to US universities being the best in the world and the SAT is definitely not it lol - way to out yourself as knowing nothing about education or education policy

[@RobertMJohnson]

@@clytemnestra we have some of the greatest medical schools ON EARTH. and to those medical schools go the best performing students from, mostly, the best US undergraduates. to get into the best medical schools, the MCAT is REQUIRED, and the top programs have the highest average MCAT scores for their students. that's one of the KEY CRITERIA they use to make their admissions decisions. are you going to sit there and tell me that the MCAT has nothing to do with the caliber of students at the best medical schools? and are you going to sit their and tell us all that for decades, the SAT hasn't been used by college admissions officers in the US as a criterion for selecting the very best undergraduates to whom they offer admission? that's your position is it?

[@williamlee4617]

I would love to see you try the GMAT math section next time.

[@spaece420]

i gave my SAT exam like 2 years ago and i still get nightmares from it

[@marlena8492]

You should take an american IB math exam. It’s fairly similar to the GCSE but it’s fairly complicated calculus and the mark scheme is super strict.

[@haasfx]

When I was 12 to 15, math is hard asf. now I'm 18 and just watched a few math videos for a year, I can solve those math problems from back then. its like my brain decided to go upgrade itself when I reached 17-18

[@Rex-mj3hp]

I am 17 years old and I just stumbled upon this video .I have gotten a rough idea of the sat exam , some of the concepts and the questions are from grade 10 and 11 .I am in grade 11 and I had a fair idea on how to solve a good chunk of questions. it helps me a lot since I am in the Indian education system. Btw nice video :)

[@Golden.Chords]

This should be a cake walk for you don't worry 😂 .

[@TheSimCaptain]

I can't believe how simple these questions are compared to the 11 plus exam in the UK.

[@enigma7791]

It must be difficult not to "over engineer" getting the answer when your knowledge far exceeds what level the test is? That is something both Tom and Ben constantly have to remind themselves of.

[@highpath4776]

I went off to general tangent on pesticides as to what organic or other solutions would be better or what is the death rate of species beneficial from the use of any specific chemical / use of gen modified items

[@NoActuallyGo-KCUF-Yourself]

Yep, most questions on the SAT can be estimated or found by checking the answers much faster than formerly writing all the steps.

[@UnlikelyToRemember]

@@NoActuallyGo-KCUF-Yourself Problem 30 is a great example of this. Angle B is quite obviously 90 degrees plus some angle that has to be greater than 45 degrees (it is opposite of the longer side of a right triangle). 150 degrees is the only answer > 135 degrees. Problem solved. No need for any actual trig.

[@dakerbal]

Amazing! I'd love to see you try an IB math paper... tougher!

[@TomRocksMaths]

Unfortunately they won’t let us put it on KZbin :(

[@dakerbal]

@@TomRocksMaths That sucks! I would've loved to see a take on paper 3 especially... the IB be like that I guess..........

[@RobertMJohnson]

the point of the SAT isn't to be the toughest test in the world. the entire point is to stack rank US high school students in math during a given year applying to college. one year, you might get 44/50 questions correct and it puts you in the 94th percentile of students. another year you might get 44/50 and it puts you in the 97th percentile of your peers.

[@dakerbal]

@@RobertMJohnson indeed... when did I ever say anything else? of course the SAT has a completely different target audience, I was just saying that - especially for an Oxford mathematician - maybe IB would be interesting!

[@bibia9047]

Man, this is the exams I had in the first year of high school.

[@krin5506]

can't believe i watched this whole thing.

[@Kno_Buddy]

This is way easier than the SAT I took in high school. This was easier than a regular weekly quiz. Then in college I had a math class one hour a day four days a week at 8AM and we would go through an entire chapter of the book in an hour and the class the next day would always start with a quiz from the day before. We made it through the whole book before the middle of the quarter.

[@michaelcosta7235]

We had to dumb it down because teachers were looking bad at how few students could get through it.

[@Kno_Buddy]

@@michaelcosta7235 My SAT was honestly harder than my college entrance exams.

[@michaelcosta7235]

@@Kno_Buddy I believe that. However, this new SAT is such a joke compared to the one I took back in 2000.

[@Kno_Buddy]

@@michaelcosta7235 I took the SAT and ACT. My school also required the ASVAB (Armed Services Vocational Aptitude Battery Test). I scored some pretty decent marks on all of them. I scored high enough on the ASVAB to get any job in the military I want, but they won’t take me because I have anxiety and PTSD. My high school graduation test too I scored in the top 10 of the country.

[@timothytufts3093]

I agree. Took the ACT and SAT in 1972. But then my memory could be inaccurate.... and I've had 4 years of college math since then....

[@NoActuallyGo-KCUF-Yourself]

Tom's weakness here is overthinking the questions and being too diligent to compute exact answers. Estimation, approximation, and process of elimination quickly deal with 85% of the questions.

[@heika_206]

He's a mathematician, what do you expect? XD

[@bekanimal]

Thank youuu aghh I was pulling my hair out when he didn't use efficient test-taking strategies (e.g. on number 14), especially if his goal was to get as low of a time as possible. And to the other commenter .. I'm a mathematician, and I would expect another mathematician to prioritize efficiency in this particular setting !

[@heika_206]

@@bekanimal Yes, I was just joking. No offence :)

[@RobertMJohnson]

the ENTIRE point of the SAT math section is mdiem's comment. Europeans may think it's sort of "easy", but this is a TIMED test with ZERO REVIEW and it's 5-10 questions that separate the exceptional from the "good or great" students. and estimation and 'seeing the shortest path to solution' is key to acing the test within the given time. not impugning the professor's knowledge in the least. i'm sure he's f brilliant.

[@derrickoleary8908]

@@RobertMJohnson This raises my curiosity. All tests are timed and all tests are subject to strategic analysis by teachers who impart these strategies to their students. But should I infer that the time allowed is intended to create additional pressure and so be a differentiating factor that rewards strategy and estimation in addition to mathematical knowledge? Is the test also a test of deciphering the tests?

[@aldante7079]

you look like the coolest professor ever 🤘

[@TheFinalVenue]

I'd be interested in watching you take the GMaT math portion in a live demo

[@alaynamcdermott8222]

I work as a tutor and have probably done this exact test more times than I can count. I will say, you did take some pretty round about ways to some answers but it was always so interesting to see the problems solving! Oh and Q19 on the no-calc is way harder for many students who get zoned in and don’t pay attention to what the question asks!

[@jocxse]

18:40 made me spit out my drink 😂

[@Wandering_Chemist]

Dr. Tom still rockin that early 2000’s emo 🖤 look lol 😂 love it!

[@loftyradish6972]

I haven't done real maths in years, statistics and I are friends, but not real maths. I have a problem with my working memory which then caused terrible maths anxiety but this was just soothing and interesting to watch. Even if my brain can't hold and manipulate numbers, I can still understand the logic and theory behind it.

[@zaxtonhong3958]

Interesting (although it makes sense) that he seems to take the thorough route to these answers, despite the “quick ways” being much better to use on the SAT

[@UnlikelyToRemember]

Noticed this too. For example the means question: 1600 was the mean and you had 1600, 1200, 2000 which by themselves are also obviously 1600 mean, then 700 and x (700 is 900 under the mean, so x must be 900 more or 2500). And so on.

[@davidgould9431]

54:08 I'm probably missing something but, given (200 × 5280) ÷ 3600, I'd have been tempted to do a pile of cancelling before any multiplications: 200/3600 is 2/36 is 1/18; 5280 is divisible by 3 and 2, so 5280/18 is 880/3. Being a bear of little brain, I like to keep the numbers as small as possible, so divide and conquer is the policy. Your mileage may vary, as they say.

[@bambi9609]

It’s because of PEMDAS (order of operations). You do your Parenthesis (P) first, then Exponents (E), then Multiplication (M) and/or Division (D), then your Addition (A) and/or Subtraction (S). So… 1. P - yes Parenthesis - 200*5280 = 10560 2. E - no exponents 3. M/D, no M, yes D Division - 10560*3600=2.933 4. A/S - no addition, no subtraction I know my reply is a little redundant but if you had never done the PEMDAS way you could get lost among the acronym. TLDR - the SAT tests very basic middle school and early high school math which means the simplest way to target the problems are through elementary order of operations (PEMDAS).

[@davidgould9431]

@@bambi9609 Yes, quite. 50 years ago, when I was learning this stuff, we didn't bother with acronyms: they are just more to remember. Then you have to remember what they stand for, then you have to remember what to do with it. Tedious and error-prone. We just learnt the rules and did lots of practice. You might have pointed out that, in my example, the parentheses are redundant because we only have multiplication and division. That means you don't, in this case, have to evaluate the parentheses first. Understanding what's going on is so much more satisfying than learning an acronym and being limited to sticking to it.

[@thapliyal_jii]

Huh being a 9th students can do some of these questions feeling so nice after a long time

[@ullintalulna7066]

First of all, THANK YOU, since this is a very useful video. I am italian. This exam looks sooooo easy for me. I did the scientific address High School, and i think at my final year i could have done this fairly easy.. Did i acknowledged at that time that being a high ranked candidate to being admitted in the IVY league would have been so easy i would have migrated.. ;)

[@notnek12]

Small note on Q5 since it's a common misconception : the square root symbol shown is always the positive square root so it's not "plus or minus". Tom seems to say that since x is positive that's why the answer is 3x as opposed to -3x but that's not right. EDIT: Just starting watching the subsequent video and realised that this is discussed :) EDIT2: Actually what I've said about is not completely correct. See comments.

[@LewisMcS]

I'm not amazing at maths but what I believe him to be saying is that x (axis) is a positive number as he's not working with a negative graph (-1 on x axis would be said as negative for example so he is saying it's positive because of that coorelation). again not a pro, not even got A-Level maths yet so could be out of my depths with this

[@LewisMcS]

just realised I was completely wrong in answering because I was answering for the graph one ahha, it just so happens as i was listening to the video and reading this comment he said 3x but he was talking about the graph so when i scrolled up I had that in my head.. my bad lol

[@bekanimal]

Tom's reasoning is correct here. I didn't watch the other video you're referring to, so maybe it said what I'm about to say, but the given expression could actually be equivalent to -3x as well, specifically when x0, and so for that reason he could eliminate the -3x possibility.

[@notnek12]

@@bekanimal Yes you are right and it's something I missed. If x>0 wasn't specified then it could be +/- 3x even though the square root symbol means the positive square root.

[@hellnohavean9874]

As a JEE aspirant, i can say this paper was very very easy (just talking about the mathematics section)

[@pisky5067]

true

[@jellyd4889]

This is fun maths.

[@mbb1849]

In high school these seemed so difficult but now it seems easier 😂

[@TheAshutoshj]

Great video Next exam video can u go through an actual MAT exam?

[@TomRocksMaths]

I’ll get there eventually :)

[@camachojankowilderbeismar6167]

Is good greetings from Bolivia

[@TomRocksMaths]

Hello in Bolivia!

[@sumanverma4153]

I am a IIT JEE aspirant and it took just 18 min to solve the whole paper. We are taught all this in class VI.

[@leroydanny4072]

Not possible

[@juicesnap]

For question 6.... you could also just eliminate C and then plug in the other answers into the equation and it would be faster.

[@samaahithokkunda6930]

I can't stop thinking about the difference in difficulties between SAT math and Indian engineering college entrances.

[@ozuu07]

exactly dude..we are just basically overqualified for this

[@wbfaulk]

This is the base level exam for all college entrants, regardless of the field they're intending to study. So people who are going to college to study acting or literature or philosophy are taking this same test. There are other exams that test for advanced knowledge in particular subjects. They are called AP exams and, generally, universities accept them as proof that you can skip over entry-level courses in those subjects. Not all potential engineering students would take an AP Calculus exam, but certainly very many do. That said, they are going to skip you over maybe 1 year's worth of that subject.

[@wbfaulk]

Also, I feel like these questions are easier than the ones in the actual exam, but it's also been 30 years since I took it, so it might have changed. I'm pretty sure that there are far more questions, too. I think this sample test is more to give you an idea of how the test is structured and the general types of questions that will be asked rather than being directly representative of the difficulty of the real test.

[@avantikasingh01]

I think some of our high schoolers would be really happy to take this test rather than sit for their math board exam.

[@jacobdaniels3246]

@@avantikasingh01 That's because a math board exam is a MATH exam while the SAT is a college-readiness assessment. It has no meaning for colleges other than showing that you didn't sleep in class every day.

[@Orholam5]

I don't think I've ever yelled "JUST SUBSTITUTE" so many times. you took the hard brute force approach to some simple questions where you could just substitute and see which answers satisfy the equations. remember the SAT is a timed exam and bad answers are penalized so people need to always know the fastest way so they can have time on other questions

[@VeridicusX]

That's a good point. I think that he's also teaching though, (as well as entertaining the viewer.) Plus in British math exams there are usually "method marks". You score for showing your working - even if you give a bad answer.

[@bambi9609]

@@VeridicusX yeah, that’s different from the U.S. You either get it or you don’t. Even on free response questions for some exams it’s all or nothing.

[@pisky5067]

5:11 I cant believe he didnt saw that left side is x+1 and you get x=-3 immedietaly. It was painful to watch

[@wft15]

​@@pisky5067*see

[@TheAzharrrrr]

11:44 I was thinking of another way, where we can solve simultaneous equations using matrices, to confirm that there are no solutions, determinant ad-bc has to be 0. Not sure if this concept is covered under the SAT exams but thought this concept might help too. Either way, loving your video!!!

[@warcatfurever101writeroffanfic]

The irony I get this vid recommended after my Sat today and it’s the no calc section I did the night before

[@NoActuallyGo-KCUF-Yourself]

SAT mathematics is quite simple, so they make up for it with confusing wording in the questions. Once you see through the test writers' BS and know the usual tricks, it is all quite easy.

[@vegetableball]

I think the "high school math" ability of a person with "PhD in math" really depends on the actual math field the person major in. I feel that if the major is more related to algebra or number theory things, the "high school math" ability is higher. In Tom's case, it is fluid dynamic, that is related to analysis or computational things, I feel that Tom's "high school math" would be lower relatively.

[@SOPHOCLESIFY]

This should be elementary to anyone with a stem PhD regardless.

[@PeterGroen]

It probably differs per country, but in the Netherlands you should have this -basic- level just to start at university (for any bachelors degree). Probably most people already have this level halfway during high school (on the level preparing for university).

[@DepthAsscociation]

@@PeterGroen Yeah, of course. It’s a high school test. I got a perfect score on the math section in 9th grade - it’s not meant to be challenging. If you don’t know basic algebra by college you’re in big trouble.

[@bambi9609]

@@PeterGroen that’s the same way it is here. Unless you’re very bad at math, you’d have taken all of this math by age freshman year of high school, Sophomore at the latest. Even if you’re bad at math it should still be completed by Junior year. The SAT is a college-readiness test. The entire point is to verify the ability to do basic algebra, geometry, and stats because it shows universities there’s a solid math foundation to be built upon.

[@homanasiri843]

Sat nonsensical test good scores come only with coaching

[@firemonkey1015]

5:19 wow you did it with a quadratic I didn’t even think of that lol. I saw those difference of squares and immediately went for the cancel. X+1 = -2 -> x = -3. Love how many ways math can be done. I didn’t expect to get all these problems because only a year ago I couldn’t do math, managed to work my way up to calculus II in college as an adult. Soon to be calc 3.

[@shayanchamas60]

The horizontal tangent to the parabola problem can be solved by taking the first derivative and equating it to zero. Then just solving for x. Then substituting x into the c equation to find c. It's a 2 step process. I believe the idea here is that the only way a horizontal line can be a tangent to a curve is if its a max. or a min. Great work though!!

[@le09idas]

I feel that many people who could have scored high just didn't practice enough because these questions seem to requires 20% basic math and 80% problem solving mastery.

[@RobertMJohnson]

take the timed version and see if you could have aced it at 16 years old.

[@DepthAsscociation]

@@RobertMJohnson I aced it at 14 - you act like the SAT is the math Olympiad

[@vizender]

Hey. I wonder if you’d be interested in trying non-Anglo-Saxon tests ? Here in France the baccalauréat in mathematics is a 4 hour exam with no multiple choice questions. However I’d understand the language barrier can be quite the problem !

[@capitalb5889]

It is not actually an "Anglo-Saxon test" - it is an American test. The mathematics tests in other Anglophone countries is not multiple choice to my knowledge - certainly A-level Maths in the UK isn't.

[@footballdude54]

tom just did it

[@racquelsabesaje4562]

the function f is an increasingexponential function

[@bounchi8312]

Please attempt iit adv maths paper and explain how is it.????????( IIT JEE ADVANCED)

[@random19911004]

Looks like a perfect score to me. The only truly tricky question was Q35 @ 48:56 To pick the value of b such that the two sides were multiples of each other to get infinite solutions. I stumbled a bit there. You got it by adhoc way of choosing b = 2.5 'by inspection' (so the multiple was 'a'). I did not think of that. I would prefer a more systematic method.

[@pietromoroni3050]

The only way to have an infinite number of solutions for a single equation is if the equation is 0*x=0, so you just need to put the coefficient of x equal to 0 and the non-x part equal to 0 at the same time and you get 2 equations for a and b

[@random19911004]

@@pietromoroni3050 Yes (a-4)*x = 10-ab [ Compare with 0*x = 0 --> (a-4 =0 and 10-ab = 0. More systematic approach) ]

[@UnlikelyToRemember]

This one was solvable at a glance, a has to be 4 to give you 4x, and so to get 10, then b obviously must be 2.5 (10/4).