Bro try to solve JEE advanced math paper next !! Just writing Indian exam will attract a lot of Indians saying this cause I want your channel to grow xd
Agreed. I’ve always said “ Don’t judge the book by it’s cover” This guy chose his ability and all credit to him . Top notch brain and good luck to him 👍
@@geha9450 No, if you define "good" as genius. You can master nearly any subject in math with cheer effort and patience. Innovation, to create new math, that takes a genius. If you are ok with just learning, I think you can be a pretty good mathematician.
What a great idea! I often do “walking, talking mock exams” where students have a go at answering a question and then I go through the question myself, and have always found this incredibly useful, a video like this is super helpful for students to hear thoughts and discussion while seeing an exam paper for the first time! Keep up the great content Tom! 👏🏼👏🏼
Not pertinent to the subject of the video, but it's really cool seeing someone with what society would consider "alternative style" having a doctorate AND teaching at one of the most renowned universities in the world. That's so awesome.
I love Toms facial expressions when he looks at the next question. He's that little boy again sitting an exam and going "ohh gosh!" But then rationalising that he does know a way forward.
Maths teacher here, so glad I came across this and its explained so well! Not often I get to teach higher GCSE so seeing the content is always a treat. LOVE the tattoos.
I remember our physics teacher once accidentally gave us a GCSE exam for practice when we were in our A levels. They then left the room, so we couldn't let them know something was wrong (It didn't say GCSE on it, we just figured it out because it was so easy) until near the end of lesson. The best part is it meant they had given their GCSE students the A level exam we were supposed to be doing. SO they were literally handed a test they had no way of knowing how to do. I can only imagine the stress they must have felt.
@@nathand7334 GCSE maths is compulsory for ages 15/16 secondary education, A-Level Maths are optional ('A' stands for Advanced) at ages 16-19 typically taken by those who want to pursue STEM subjects at university - the difficult between GCSE and A-Level Maths is very steep.
My maths teacher were very harsh to me and my friends who didn't know how to solve math problems. One of my friends cried many times during math class. I wish math teachers were more calm and fun like Tom.
Hi Dr Crawford, it is Tom here. For Q.20 (a), ∠ACB=180-2x. You can use the alternate segment theorem (in any circle, the angle between a chord and a tangent through one of the endpoints of the chord is equal to the angle in the alternate segment). Then ∠ABC = ∠ACD. Thus ∠ACD=∠BAC=x. Alternate interior angles are equal on parallel lines, AB//CD. Which also helps with Q. 20 (b).
It fascinates me how I could do this at high school and now Im 30 and I probably could not solve any of those. But then again, I havent really needed any of these nor even remotely after I set foot out of the school doors.
For anyone who might want help remembering trig exact values like he used in Q27 Sin goes 0 | 30 | 45 | 60 | 90 √0/√4 | √1/√4 | √2/√4 | √3/√4 | √4/√4 See how the numerators are just the roots of 0 to 4, and the denominator is always √4 (=2). Cos goes 0 | 30 | 45 | 60 | 90 √4/√4 | √3/√4 | √2/√4 | √1/√4 | √0/√4 So Cos is the same as Sin, but the identities are just flipped around. Pretty simple Tan goes 0 | 30 | 45 | 60 | 90 √0/√1 |√1/√3 | √3/√3 |√3/√1 |√1/√0 Now Tan is a bit of a pain in the ass because there's not a clear pattern like the other two. Personally, I just remember 0113333110, and I just split those into pairs, root them, then divide.
I really love this type of video :D It teaches me more than I could think of. As a math enthusiast, I want to see more of these in the future. Thanks so much, Dr. Tom!
@FlyingMonkies325 hen they were young but 99.8% of us don't get that sadly, in a class of 15 only 1 or 2 people actually get more support. - thats because in England the lowest most illiterate child will get all the attention and the rest of the class have to be at his speed. If anyone is too smart they will be punished by having to do more work or help others or socially. Remember if you give any kids that are smart and help a decent parents help you are obviously a racist neo-Nazi.
@@TheRandomshite123I forgot a lot of things that I just use my calculator for. Decimal conversions for example. Calculus and beyond it got fuzzy for me. It was nice seeing this and taking a step back.
#20a - Angle ACB = 180 - 2x. If you bisect it, it creates two angles, both of which are 1/2 (180-2x), or 90-x, and it will cross line AB at point E. The remaining angle in this smaller triangle (ACE) is 180 - x - (90-x) = 90 degrees. So we have a right triangle ACE and an identical right triangle BCE. If you run a line perpendicular to any chord AB in a circle where it bisects AB, it will go through the center of the circle; so, because the line EC creates a 90 degree angle to line AB, and BE = AE, it goes through the center of the circle. By definition the line EC is also perpendicular to line CD (which is tangent to the circle) Therefore, since AB and CD are both perpendicular to EC, they are parallel to each other. #20b - Because point D can be anywhere on the line CD, the angle BAD can have multiple different measurements. Therefore we know the fixed line AC cannot always bisect angle BAD. So the other two have to be correct. Also, by using the answer from the previous question (20a) the line from C through the center of the circle (point F) bisects angle ACB. Because it's equilateral that means the angle BCF is 30 degrees. The angle DCF is 90 degrees so adding them together gives 120 degrees. The angle ACB is 60 degrees, so therefore the line AC bisects DCB #26 - your sign is backwards for b. It should be -24.
As someone who's 17 and studiyng trigonometry in school i can tell you it doesn't looks easy because it isn't. I've never felt dumber than during trig lessons, 2 months in and i'm still confused lol
Me, as a university teacher (not professor, not mathematician - engineering) was really pleased by: "I don't know, what standard form means" ... because practically no standard form is needed ... just the useful one ...
Oh man, my maths prof was pretty good, but also a bit scary. I wish there were more teachers like you to stop kids being afraid of math :) I had a lot of fun watching this video, thanks!
My maths teachers were terrifying! Always talking about how they wish they could bring back corporal punishment, slamming down on the desk and the board. Not to mention laughing and making fun of students who didn't know the answer or who had a brain freeze cus they panicked
@@Stettafire I grew up in Poland and in the early 90s I changed schools and found the most terrifying teacher - his nickname was Mustard and he would sometimes hit students across the head if they gave a wrong answer. I remember that many times I wanted to answer his questions, but was too afraid. Luckily in high school I had an amazing teacher who somehow managed to make me enjoy math lessons (on most occasions :D )
i havetn been to math in 7 years but i was answering adn doing the thought process as fast as him on most. thanks for the mental boost :) loved the vid
Q20) Alternate segment theorem! As a fellow educator who teaches maths at this level (which is pretty much lower than yours obviously 🤣🤣🤣), i like the fact that you checked your solutions just like we always remind our students to. Q7 is the perfect example! Love your vibrant vids dude! 💪🏻👊🏻
Don’t do the equation of the circle! The tangent is perpendicular and you can use geometric mean or similar triangles or point-slope form to get the intercepts
Tom, this is so entertaining. Obviously it’s been a long time since you did these calculations because you have moved on to more complicated Mathematical problems AND becoming a Professor of Mathematics! Brilliant !
Honestly my favorite moment is 3:27 when he intuitively notes 9.7e-4 but isn't sure so he uses the standard zero-counting technique but still isn't sure so wastes an awful longer than he had to manually imagining the 9.7 going back one decimal to see what is the power 10 should be elevated to, and even still isn't sure. Glad to see even mathematicians struggle with scientific notation.
I like the fact that no matter your math level, when you first approach a math problem your brain always goes "😬" before finding the solution. Then again, no matter your level, you make the same face after finding one because you could have made a mistake. There's no way out of that, so keep doing this "😬" without losing your self-confidence, and keep studying math, people!
I think I found the solution to Q20 (a): Let O be the center of the circle. We know that OC ⊥ CD because CD is tangent to the circle. Since A, B, C are points on the circle, AO = BO = CO (as radii). We therefore have another isosceles triangle, ABO with AO = BO. Because ABO and ABC are both isosceles and share the same base (AB), the bisector of ACB (angle) is a bisector of AOB (angle). Projecting CO onto AB, it intersects on point E, and OE is the perpendicular bisector of AB. Therefore: EC ⊥ AB and EC ⊥ DC. Therefore AB || DC Quite wordy, but it should go well with a little diagram :)
Im 293 but back in my day me and my laddies used to do the 0 levels and I would never have thought i was going to make it but look at the world today,a beatifiul concoction of smart people like you breaking the stigma the universe brings upon you and nourishing the young effervescent trees of this universe.THANK YOU SOLIDER FROM LITHUANIA/GAMBIA since im also gambian
Solution to 39:30 Draw O in the center and draw radii OC, OB, OA. We have now made two similar isosceles triangles (BOC and AOC) because all 3 sides are equal. This means the two angles BCO and ACO have to be equal. Thus, angle OCD is equal to (180-2X)/2 = 90-X Since the tangent line is perpendicular with the radii, angle DCA is complementary to OCD making DCA equal to X Now we have alternate interior angles equal, so AB and CD are parallel
Q20 solution: Let O be the center of the circle. Extend OC until it hits AB; they're perpendicular because ABC is isosceles. Meanwhile, OC is also perpendicular to CD because radii are perpendicular to tangents. Thus AB || CD.
@@PegasusTenma1 C,O and the intersection with AB are collinear *by construction* - that's what "Extend OC until it hits AB" means. It is a perfectly good solution, and probably the one intended.
@@PegasusTenma1 I spent ages trying to prove AC || AD, until I realised that D could be anywhere, so re-read the question and felt quite the fool. I think Tom had so much trouble visualising the solution because his diagram was *so* "not to scale" that he could not see what was actually going on.
Having just used this EXACT paper to teach my Higher Maths Students, and just having finished teaching Standard form to my Year 10s, this is hilarious to watch.
For 20(a) we can simply construct the line CO (where O is the centre of circle), so CO must be perpendicular to CD since CD is a tangent (tangent is perpendicular with the radius between O and point of “contact”), but CO is also perpendicular to AB since it bisects angle ACB, and AC=BC. So CO is perpendicular to both DC and AB, which implies DC is parallel to AB.
I loved taking my GCSE, A and AS level mathematics exams back in 1990 but crumbled on the Oxbridge exam. Got a place at Manchester Uni doing maths but couldn't handle the statistics and probability....switched to engineering and now much happier!
For question 15, I think that linear interpolation would be appropriate, as the line between the two appropriate points already reflects the increased slope (as compared to the left most part of the graph).
Q20 b): Since D can be anywhere at all on the tangent line, we have no information about BAD, so that eliminates the 3rd option and the other two _must_ be the two correct ones.
Q20: if you draw a isosceles triangle in a circle then the height of base AB will pass through the center of the circle. then it's easy to prove that the base AB is parellel to the tangent DC
Q20 add a line to bisect the triangle. Q25 product of gradients of perpendicular lines is -1 (provided one line is not horizontal) and gradient of OP is 2. Hidden in this question is the definition of tan.
The RUclips algorithm works in mysterious ways. As a child, I hated maths at school in Spain. And here I am now watching a one-hour-long video in English of an Oxford professor taking an exam. Amazing!
For anyone wanting to know the answer for Q20 at 37:08 here it is: the angle CAB is equal to ABC ( Angles opposite equal sides | AC = CB ) due to the isosceles triangle. That leaves angle ACB to equal 180-2x ( The sum of the Interior angles of the triangle ACB must be equal to 180 degrees ). Then the angle ACD is equal to angle ABC so both angles are equal to x ( Tangent chord theorem as CD is a tangent). The obtuse angle DCB is equal to angle ACB (180-2x) + angle ACD (x) which equals to 180-x. The sum of angle ABC (x) and DCB (180-x) is equal to 180 degrees which proves that these two angles are co-interior angles which proves that AB is parallel to DC.
Q20) (the bottom angle should have been 180 - 2x) then you could have used the alternate segment theorem to say angle ACD = x. Then you can show that ACD and BAC are also alternating angles, which is only true if AB is parallel to DC.
For question 14 you could have done 360-144 = 216 which = x+y and you know the ratio of x and y which is 1:3 so you can share 216 in the ratio 1:3 to get x and y which is x = 54 and y = 162
I'm from Germany and I always thought that most/all countries use the same symbols especially in maths. In this paper I found 2 deviations which gave me some problems for a little bit. 1. 22:00 angle description/name: We use greek small letters for the angles (α, β, γ ...). Latin small letters are used for lines. I was a bit confused because for me there were ratios for lines without possibility to calculate them. 2. 36:10 I did not recognize the sign of a period. We here use an overline/vinculum to mark a period. So I would have chosen the wrong answer. It is interesting to see that even maths can vary.
![I.N "HALLUCINATION" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/n5B5q1Hwt_U/mqdefault.jpg)
Watch Ben take the same exam here: ruclips.net/video/7FUY8eyYZR4/видео.html
Idea: For your next 'Professor Tries (XYZ) Exam Paper' video, livestream it
Professor you should also try jee advance maths exam you will love it
Bro try to solve JEE advanced math paper next !! Just writing Indian exam will attract a lot of Indians saying this cause I want your channel to grow xd
Can only practicing make me good at maths ? Please i need to know iam not that good at maths but i wanna improve
@@zzzzzz6152 main thing is visualisation and feeling on practice both of them improve and yes don't ignore theory as it helps in building our concepts
MGK's pretty good at maths.
AHAHA
@@skull5207 HAHAHA
Lool
😭😭
OMEGA LULULUL!!!!!!
He literally looks like the exact opposite of what I'd assume a math professor looks like let alone at a school like oxford
probably some sort of child prodigy. It can't be normal to be this young lol
That’s why he’s employed. To try and ‘modernise’ or something
@@Alex-si5te either that or hes a really good teacher
@@sejmyname I'm sure both
Agreed. I’ve always said “ Don’t judge the book by it’s cover” This guy chose his ability and all credit to him . Top notch brain and good luck to him 👍
When you fight the final boss after completing all the side quests.
Wait, surely you’re the final boss Andrew?
@@TomRocksMaths Maybe on easy mode.
Do I need to be a genius like on TV in order to become a good mathematician?
@@geha9450 No, if you define "good" as genius. You can master nearly any subject in math with cheer effort and patience. Innovation, to create new math, that takes a genius. If you are ok with just learning, I think you can be a pretty good mathematician.
When Harvard is side quest and school exam is boss fight🤣
Bruh he’s doing the exact same paper I did in my mocks. I love to see the ways to answer the questions I couldn’t do!
@@nlonal I had one single enterprise mock right at the end of Year 10, and that was it. But remember that your school might be different.
@@nlonal every school is different but I think they should at least do it once
@@nlonal in our skl our y10 mocks (as they were called) were just end of year exams.
@@nlonal We did but they were cancelled because of COVID :/
@@sp4uw in year 10 i had no mocks. did mine all in yr 11
What a great idea! I often do “walking, talking mock exams” where students have a go at answering a question and then I go through the question myself, and have always found this incredibly useful, a video like this is super helpful for students to hear thoughts and discussion while seeing an exam paper for the first time! Keep up the great content Tom! 👏🏼👏🏼
awesome thanks!
+1 to this, some of us need to see how to do stuff
Not pertinent to the subject of the video, but it's really cool seeing someone with what society would consider "alternative style" having a doctorate AND teaching at one of the most renowned universities in the world. That's so awesome.
Three imaginary numbers walk into a bar. The first one says to the barman, "Three beers please for I and my friends, Jay and Kay".
... hello Hamilton, is that you? 😂
This joke also works for unit vectors
@@AdolphHItler-rs1wi Dang, I missed that one.
Haha, jk.
I love Toms facial expressions when he looks at the next question. He's that little boy again sitting an exam and going "ohh gosh!" But then rationalising that he does know a way forward.
every time
Only difference is he looks like he's enjoying doing the exam paper this time.
Maths teacher here, so glad I came across this and its explained so well! Not often I get to teach higher GCSE so seeing the content is always a treat. LOVE the tattoos.
I remember our physics teacher once accidentally gave us a GCSE exam for practice when we were in our A levels.
They then left the room, so we couldn't let them know something was wrong (It didn't say GCSE on it, we just figured it out because it was so easy) until near the end of lesson.
The best part is it meant they had given their GCSE students the A level exam we were supposed to be doing. SO they were literally handed a test they had no way of knowing how to do. I can only imagine the stress they must have felt.
my anxiety
Haha let the GCSE kids solve integrals and differential equations 🤣
Is A level high, and do you mean the gcse is easy for you?
@@nathand7334 A level is the next part of school above GCSE so they would of found the GCSE exam easy for them.
@@nathand7334 GCSE maths is compulsory for ages 15/16 secondary education, A-Level Maths are optional ('A' stands for Advanced) at ages 16-19 typically taken by those who want to pursue STEM subjects at university - the difficult between GCSE and A-Level Maths is very steep.
My maths teacher were very harsh to me and my friends who didn't know how to solve math problems. One of my friends cried many times during math class. I wish math teachers were more calm and fun like Tom.
I hate doing tests, but somehow seeing someone smurf a test is great. Vicariously living through a math god
Tom, when you talk about maths, you sound like you're eating something delicious.
I'm dying at this comment what a random thing to say😭😭😭😭
@@finlayhutchinson7370 Ha! Ha!
Math is delicious
@@epicvideogamer7675 Most definitely!
lol
Hi Dr Crawford, it is Tom here. For Q.20 (a), ∠ACB=180-2x. You can use the alternate segment theorem (in any circle, the angle between a chord and a tangent through one of the endpoints of the chord is equal to the angle in the alternate segment). Then ∠ABC = ∠ACD. Thus ∠ACD=∠BAC=x. Alternate interior angles are equal on parallel lines, AB//CD. Which also helps with Q. 20 (b).
ABC, not ABE.
Shush
He’s not naturally smart , he has worked all his life for his achievements & let this incredible individual inspire you all!
It fascinates me how I could do this at high school and now Im 30 and I probably could not solve any of those. But then again, I havent really needed any of these nor even remotely after I set foot out of the school doors.
For anyone who might want help remembering trig exact values like he used in Q27
Sin goes 0 | 30 | 45 | 60 | 90
√0/√4 | √1/√4 | √2/√4 | √3/√4 | √4/√4
See how the numerators are just the roots of 0 to 4, and the denominator is always √4 (=2).
Cos goes 0 | 30 | 45 | 60 | 90
√4/√4 | √3/√4 | √2/√4 | √1/√4 | √0/√4
So Cos is the same as Sin, but the identities are just flipped around. Pretty simple
Tan goes 0 | 30 | 45 | 60 | 90
√0/√1 |√1/√3 | √3/√3 |√3/√1 |√1/√0
Now Tan is a bit of a pain in the ass because there's not a clear pattern like the other two. Personally, I just remember 0113333110, and I just split those into pairs, root them, then divide.
Holy shit....thank you, the way u descried it looks so simple.
Did you just explain a fucking chapter in a comment? Thank you mannnnnnnn
Tan is sin/cos
I really love this type of video :D
It teaches me more than I could think of.
As a math enthusiast, I want to see more of these in the future. Thanks so much, Dr. Tom!
As a current Year 12 further maths student I would LOVE to go back to the time I did GCSE maths it was so fun and free
My high school teachers: “Your professors won’t accept these types of behaviors”
These professors:
Spoiler alert, most professors are no where near as pedantic as teachers provided you make an effort and study
I know, right?!
@FlyingMonkies325 hen they were young but 99.8% of us don't get that sadly, in a class of 15 only 1 or 2 people actually get more support. - thats because in England the lowest most illiterate child will get all the attention and the rest of the class have to be at his speed. If anyone is too smart they will be punished by having to do more work or help others or socially. Remember if you give any kids that are smart and help a decent parents help you are obviously a racist neo-Nazi.
@FlyingMonkies325 Have you tried studying English? You most certainly need to.
@@Stettafire Hence the pedanticansm
It appears I have forgotten absolutely everything from my school days. Oh well, this was still entertaining watching you work everything out!
Could be worse, I'm in my second year of a chemistry degree and I'd definitely fail this exam
@@TheRandomshite123I forgot a lot of things that I just use my calculator for. Decimal conversions for example. Calculus and beyond it got fuzzy for me. It was nice seeing this and taking a step back.
@firemonkey1015 same, I'd still fail this exam and I've just graduated with a degree in chemistry
Deeply, deeply impressed that 2 professional mathematicians would do something so courageous as this.
#20a - Angle ACB = 180 - 2x. If you bisect it, it creates two angles, both of which are 1/2 (180-2x), or 90-x, and it will cross line AB at point E. The remaining angle in this smaller triangle (ACE) is 180 - x - (90-x) = 90 degrees. So we have a right triangle ACE and an identical right triangle BCE. If you run a line perpendicular to any chord AB in a circle where it bisects AB, it will go through the center of the circle; so, because the line EC creates a 90 degree angle to line AB, and BE = AE, it goes through the center of the circle. By definition the line EC is also perpendicular to line CD (which is tangent to the circle) Therefore, since AB and CD are both perpendicular to EC, they are parallel to each other.
#20b - Because point D can be anywhere on the line CD, the angle BAD can have multiple different measurements. Therefore we know the fixed line AC cannot always bisect angle BAD. So the other two have to be correct.
Also, by using the answer from the previous question (20a) the line from C through the center of the circle (point F) bisects angle ACB. Because it's equilateral that means the angle BCF is 30 degrees. The angle DCF is 90 degrees so adding them together gives 120 degrees. The angle ACB is 60 degrees, so therefore the line AC bisects DCB
#26 - your sign is backwards for b. It should be -24.
It's 2am and i'm watching a guy looks like a rock star doing math exam.
excellent choice
I haven’t studied maths since my A level in the 90s, but love watching you work ☺️. You make it all look so easy (apart from trig 😄)
روح حطو في طيرك
@@omartaha5558 طب ليه عملك ايه
As someone who's 17 and studiyng trigonometry in school i can tell you it doesn't looks easy because it isn't.
I've never felt dumber than during trig lessons, 2 months in and i'm still confused lol
@@-daigher-2549 Look up tutorials online, try not to learn trigonometry as just ratios but as functions.
@@-daigher-2549 trig is quite easy I’m 13 and can do right angle trig easily
Me, as a university teacher (not professor, not mathematician - engineering) was really pleased by: "I don't know, what standard form means" ... because practically no standard form is needed ... just the useful one ...
Oh man, my maths prof was pretty good, but also a bit scary. I wish there were more teachers like you to stop kids being afraid of math :) I had a lot of fun watching this video, thanks!
My maths teachers were terrifying! Always talking about how they wish they could bring back corporal punishment, slamming down on the desk and the board. Not to mention laughing and making fun of students who didn't know the answer or who had a brain freeze cus they panicked
@@Stettafire I grew up in Poland and in the early 90s I changed schools and found the most terrifying teacher - his nickname was Mustard and he would sometimes hit students across the head if they gave a wrong answer. I remember that many times I wanted to answer his questions, but was too afraid. Luckily in high school I had an amazing teacher who somehow managed to make me enjoy math lessons (on most occasions :D )
i havetn been to math in 7 years but i was answering adn doing the thought process as fast as him on most. thanks for the mental boost :) loved the vid
The AQA paper is so much easier than EDEXCEL omg
@@rungun6620 that’s complete bullshit I went to a state school lol that’s just not true
@@rungun6620 thats cap 🧢
Fully 1000% agree
christ the gcse appers are all incredably simple exam baord to exam board that this statement is not only flase but also incredibly inane
@@ajaykeshav2726 it’s not
The fact that he could probably do this whole paper in 10 minutes but made it seem like he didn’t know what he was doing
Q20) Alternate segment theorem!
As a fellow educator who teaches maths at this level (which is pretty much lower than yours obviously 🤣🤣🤣), i like the fact that you checked your solutions just like we always remind our students to. Q7 is the perfect example! Love your vibrant vids dude! 💪🏻👊🏻
Hey! I came to see your live talk the other day on maths! Just wanted to say thank you and congratulate you on having such a big community online :)
awesome - thanks!
Don’t do the equation of the circle! The tangent is perpendicular and you can use geometric mean or similar triangles or point-slope form to get the intercepts
Tom, this is so entertaining. Obviously it’s been a long time since you did these calculations because you have moved on to more complicated Mathematical problems AND becoming a Professor of Mathematics! Brilliant !
This was very fun to watch!
The fact that he had to check at 3:50 if he had the right exponent of ten makes me feel a little bit more confident in my math abilites :D
Had this exact paper last week for my mocks. It's nice seeing how to answer the questions I got wrong and couldn't do
You copied the comment, did you not?
Honestly my favorite moment is 3:27 when he intuitively notes 9.7e-4 but isn't sure so he uses the standard zero-counting technique but still isn't sure so wastes an awful longer than he had to manually imagining the 9.7 going back one decimal to see what is the power 10 should be elevated to, and even still isn't sure. Glad to see even mathematicians struggle with scientific notation.
I like the fact that no matter your math level, when you first approach a math problem your brain always goes "😬" before finding the solution.
Then again, no matter your level, you make the same face after finding one because you could have made a mistake.
There's no way out of that, so keep doing this "😬" without losing your self-confidence, and keep studying math, people!
i agree entirely
God do I wish I had someone go through our mock like this once we did it, would have helped so much when I was still studying maths
I think I am speaking for everyone when I say that Tom is the most spicy and good looking maths professor out there. Keep up the good spirits, Tom!
You mustn't have seen Professor Leonard.
When you complete the game and return to the first level
guilty
I think I found the solution to Q20 (a):
Let O be the center of the circle. We know that OC ⊥ CD because CD is tangent to the circle.
Since A, B, C are points on the circle, AO = BO = CO (as radii).
We therefore have another isosceles triangle, ABO with AO = BO.
Because ABO and ABC are both isosceles and share the same base (AB), the bisector of ACB (angle) is a bisector of AOB (angle).
Projecting CO onto AB, it intersects on point E, and OE is the perpendicular bisector of AB.
Therefore: EC ⊥ AB and EC ⊥ DC. Therefore AB || DC
Quite wordy, but it should go well with a little diagram :)
Im 293 but back in my day me and my laddies used to do the 0 levels and I would never have thought i was going to make it but look at the world today,a beatifiul concoction of smart people like you breaking the stigma the universe brings upon you and nourishing the young effervescent trees of this universe.THANK YOU SOLIDER FROM LITHUANIA/GAMBIA since im also gambian
I'm not trying to be rude but I couldn't fall asleep and this helped me. Interesting video, your brain works wonderfully!
Solution to 39:30
Draw O in the center and draw radii OC, OB, OA.
We have now made two similar isosceles triangles (BOC and AOC) because all 3 sides are equal.
This means the two angles BCO and ACO have to be equal.
Thus, angle OCD is equal to (180-2X)/2 = 90-X
Since the tangent line is perpendicular with the radii, angle DCA is complementary to OCD making DCA equal to X
Now we have alternate interior angles equal, so AB and CD are parallel
Q20 solution: Let O be the center of the circle. Extend OC until it hits AB; they're perpendicular because ABC is isosceles. Meanwhile, OC is also perpendicular to CD because radii are perpendicular to tangents. Thus AB || CD.
That’s not a good solution. You cannot assume that point O, C and the intersection of OC with AB, all three are collinear
@@PegasusTenma1 C,O and the intersection with AB are collinear *by construction* - that's what "Extend OC until it hits AB" means. It is a perfectly good solution, and probably the one intended.
@@davidgould9431 yes I missed the fact that ABC is isosceles so OC would be collinear and perpendicular to AB.
@@PegasusTenma1 I spent ages trying to prove AC || AD, until I realised that D could be anywhere, so re-read the question and felt quite the fool. I think Tom had so much trouble visualising the solution because his diagram was *so* "not to scale" that he could not see what was actually going on.
@@davidgould9431 It was a shame since otherwise I am very good at geometry problems, even tougher ones.
I love these exam videos. Thank you! :)
When someone so cool and comfortable with post doctorate mathematics happily admits Circle Theory is not ready to be pulled from memory…
Legend 💪
Did this test for my PPE’s today - not long until the real exams 😬
hope they went well!
@@TomRocksMaths thanks I felt decently ok during it
The AQA higher paper looks like its equivalent to Edexcels's Foundation paper lol.
Yep
AQA is also hard. See the 3rd calculator paper. I have seen in some cases AQA calculator paper is hardest.
plus you need more marks on aqa to get a good grade whereas in Edexcel you don't need nearly as much because the questions are slightly harder
@@HallowsK5 True. I did OCR and we needed 91% to get a 9 A* and it was a little difficult ngl
Wait till you see edexcel igcse further maths
Having just used this EXACT paper to teach my Higher Maths Students, and just having finished teaching Standard form to my Year 10s, this is hilarious to watch.
For 20(a) we can simply construct the line CO (where O is the centre of circle), so CO must be perpendicular to CD since CD is a tangent (tangent is perpendicular with the radius between O and point of “contact”), but CO is also perpendicular to AB since it bisects angle ACB, and AC=BC. So CO is perpendicular to both DC and AB, which implies DC is parallel to AB.
Wtf
I loved taking my GCSE, A and AS level mathematics exams back in 1990 but crumbled on the Oxbridge exam. Got a place at Manchester Uni doing maths but couldn't handle the statistics and probability....switched to engineering and now much happier!
This literally made me feel more confident for my mocks as some of these questions i would be able to get right
Good luck!
@@TomRocksMaths Thank you , hoping i atleast pass 😭🙌
I'm a high school mathematics teacher. And this video was very fascinating to watch.
glad you enjoyed it :)
would be fun to see you doing igcse additional mathematics too
Try and do the ukmt senior past paper
I tried and failed to be a mathematician - I am so jealous of this guy but at the same time I love him so much. Knock em dead Tom! :)
sending hugs
Man I really appreciated your work
For question 15, I think that linear interpolation would be appropriate, as the line between the two appropriate points already reflects the increased slope (as compared to the left most part of the graph).
Wouldn't step graph also be appropriate?
Alternate segment theorem for Q20
I can’t believe how many free marks are practically given away in this paper. This was way easier than my normal maths paper 8 years ago.
Which paper was yours ?
ok albort einsten
Q20 b): Since D can be anywhere at all on the tangent line, we have no information about BAD, so that eliminates the 3rd option and the other two _must_ be the two correct ones.
Man did all the DLC quests before starting the campaign
Can't wait Start the video already
This is the paper I sat for my final mock before covid cancelled all my GCSEs
Q20: if you draw a isosceles triangle in a circle then the height of base AB will pass through the center of the circle. then it's easy to prove that the base AB is parellel to the tangent DC
I'm 36 years old. Why did I just watch this?
Learning never ends.
you love burzum
Do more of these. We can follow along at home.
ikr?? no manipulation in mathematics
There is an easier way to solve q5 b you could subtract the exponents and get 3x10^2/4 which simplifies too 300/4 which simplifies to 75 as he said.
More of these would be great!!
coming in 2022!
I love how you make Maths less intimidating
don't know why i got this recommended, but this was so calming and i have no idea why
59:38 if 1 = 25 + b, shouldn’t you minus 25 to get -24 = b, meaning the turning point is (-2, -24)?
Yes he fd up
Q20 add a line to bisect the triangle. Q25 product of gradients of perpendicular lines is -1 (provided one line is not horizontal) and gradient of OP is 2. Hidden in this question is the definition of tan.
This is the math teacher we never had
thanks now i know what to focus on remebering for my upcoming gcse
Remember how to spell "remembering."
The RUclips algorithm works in mysterious ways. As a child, I hated maths at school in Spain. And here I am now watching a one-hour-long video in English of an Oxford professor taking an exam. Amazing!
as long as you had fun :)
For anyone wanting to know the answer for Q20 at 37:08 here it is: the angle CAB is equal to ABC ( Angles opposite equal sides | AC = CB ) due to the isosceles triangle. That leaves angle ACB to equal 180-2x ( The sum of the Interior angles of the triangle ACB must be equal to 180 degrees ). Then the angle ACD is equal to angle ABC so both angles are equal to x ( Tangent chord theorem as CD is a tangent). The obtuse angle DCB is equal to angle ACB (180-2x) + angle ACD (x) which equals to 180-x. The sum of angle ABC (x) and DCB (180-x) is equal to 180 degrees which proves that these two angles are co-interior angles which proves that AB is parallel to DC.
How fast is he gonna do this one then
This makes me smile. I can't wait to have kids and do math with them.
Didn't know MGK is so good in maths
Hello! Could you try out the UKMT Maths challenges? Would love to see you try out those maths problems!
this is genuinely helpful revision for my gcse exams, thanks!
Best of luck!
@@TomRocksMaths a bit late but thanks
STEM professors are either old and stodgy (in a sometimes endearing way), or absolutely cracked young lads like this one, no in between.
Yo tom i wonder if you could give the "HKDSE" test a try, that would be interesting!~~
ah yes, pain and suffering
as a hongkonger i can relate
Q20) (the bottom angle should have been 180 - 2x) then you could have used the alternate segment theorem to say angle ACD = x. Then you can show that ACD and BAC are also alternating angles, which is only true if AB is parallel to DC.
Haha I think this is the exam I took for my GCSE’s last year. This is interesting to watch
hey just started watching your videos, there are really cool !
awesome, thanks!
Every exam seems quite easy in front of you 😄
The exams are easy, stress and time constraints make it difficult. 🥲
The most entertaining video ever.
It’s nice seeing someone so happy doing math (even if it’s the equivalent of an MLB player playing tee ball)
i can't help but smile when solving maths problems :)
@@TomRocksMaths I'm an 8th grade can u solve papers and explains stuff all teachers in mys cool look strict u looks o friendlu
For question 14 you could have done 360-144 = 216 which = x+y and you know the ratio of x and y which is 1:3 so you can share 216 in the ratio 1:3 to get x and y which is x = 54 and y = 162
Have you tried attempting the JEE advance maths entrance test? I heard it’s pretty hard.
@Dnomyar Akunawik jee advanced maths is pretty average when compared to university math he would hv no problem
With this shirt, tom can become invisible to AR headsets. Good luck finding him in the future when everyone will be wearing one.
I’m going for my Master’s mathematic-economical exam in 5 days! Wish me luck 😊
Good luck!
@@TomRocksMaths Thanks!
gl mate!!!!
I passed 😊
@@alexanderkaiser89 gjjjjjjj
never seen a maths teacher have such a colourful style of attire
I'm from Germany and I always thought that most/all countries use the same symbols especially in maths. In this paper I found 2 deviations which gave me some problems for a little bit.
1. 22:00 angle description/name: We use greek small letters for the angles (α, β, γ ...). Latin small letters are used for lines. I was a bit confused because for me there were ratios for lines without possibility to calculate them.
2. 36:10 I did not recognize the sign of a period. We here use an overline/vinculum to mark a period. So I would have chosen the wrong answer.
It is interesting to see that even maths can vary.
When you move to studying maths at 16+ you start to see a lot more of the greek alphabet, and after that at uni it's mostly just the greek alphabet.
Super interesting. Growing up in the US we also used an overline to mark repeating pattern decimals.