How to Do Well in the MAT Admission Test | Cambridge Students Advice
42:03

How to Do Well in the MAT Admission Test | Cambridge Students Advice

Ray Amjad 03.10.2023 2 977 просмотров 79 лайков обн. 18.02.2026
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📷 Follow Me on Instagram: https://www.instagram.com/theramjad/ Link to Ali's Course: https://docs.google.com/forms/d/e/1FAIpQLSf62t3bv5jY4GtTXuBl0Pb6U7zlENvGyER2qxGQivY74VBbQA/viewform Vishal's STEP Video: https://www.youtube.com/watch?v=tmsVyncYOxM === Links Mentioned === - Vishal's Website: http://vg354.user.srcf.net/ - STEP Foundation Modules: https://maths.org/step/assignments - Imperial FAQ: https://www.imperial.ac.uk/mathematics/undergraduate/degree-courses-and-admissions/faqs/ - Old MAT papers: http://www.mathshelper.co.uk/oxb.htm - STEP Database: https://ukmt.org.uk/senior-challenges/senior-mathematical-challenge - Senior Problems Book: https://ukmt.org.uk/textbooks/senior-problems - TMUA Past papers: https://www.admissionstesting.org/for-test-takers/test-of-mathematics-for-university-admission/preparation/ === Timestamps === 00:00 - Introduction 01:49 - What is the MAT 03:57 - Timeline for Preparing 05:48 - Old Past Papers 07:03 - Structure of the MAT 07:39 - Multiple Choice Preparation 10:01 - Section A 22:53 - Section B 25:51 - Question 2 27:20 - Question 3 29:58 - Question 4 31:02 - Question 5 33:55 - Question 6 35:38 - General Advice 39:02 - Ali's Course

Оглавление (15 сегментов)

  1. 0:00 Introduction 424 сл.
  2. 1:49 What is the MAT 379 сл.
  3. 3:57 Timeline for Preparing 288 сл.
  4. 5:48 Old Past Papers 217 сл.
  5. 7:03 Structure of the MAT 138 сл.
  6. 7:39 Multiple Choice Preparation 503 сл.
  7. 10:01 Section A 2517 сл.
  8. 22:53 Section B 599 сл.
  9. 25:51 Question 2 246 сл.
  10. 27:20 Question 3 594 сл.
  11. 29:58 Question 4 238 сл.
  12. 31:02 Question 5 502 сл.
  13. 33:55 Question 6 276 сл.
  14. 35:38 General Advice 627 сл.
  15. 39:02 Ali's Course 694 сл.
0:00

Introduction

hey everyone welcome back to another video so in this one we're going to be talking about the mat which is a maths admission exam and I'm joined by V and Ali V was in a previous video where we talked about the step exam also like a math admission exam and he decided to come back on and share some more uh tips and like tricks with his friend Ali in this video we're going to be talking about what mat is why you should do it tips for the exam overall and then tips for individual questions it touches upon some of the things that Ali covers in the course that he and his teamm so if you want to go into much more detail you should check that out um Ali do you have anything else to share about the course yeah so I'll give you guys a quick summ of what the course is and if you stick to the end of the video you'll have a more detailed breakdown of what the course includes so as Ry said my team and I pr mat course over the last few months that covers all the tricks and ideas you will need and so we cover all the tricks and topics for each topic individually and then you get a problem sheet which contains 100 to 150 questions per sheet so overall this course um will teach you all the tricks and ideas even for stuff that's outside the curriculum but is useful to know for instance uh some stuff about inequalities functional equations um stuff to do with integrals um Flor function so on so this is a comprehensive course that will cover um all the tricks problem solving strategies and ideas you will need to know for every of the 10 main Topics in mat as well as problem sheets um that contain questions from many sources to give you a wealthy Bank of problems to increase your problem solving and prepare your well for the awesome and there's a link to sign up in the description um and the link will be like updated over time as well and just bear in mind this video is sort of good to be long it should be treated as like a reference so I personally suggest you should watch it now um in full and then also come back to it in the future after you've like attempt a few more mat papers so I guess let's get straight to
1:49

What is the MAT

it so I guess to start off with is uh V can you say what the mat is so the mat is the well it stands for the mathematics admissions test and it's the admission test which you need to take if you're applying to Oxford for either maths or maths and computer science or computer science and philosophy so like maths CS or any of their joint degrees and it's also used at other universities such as Imperial maths uh War math and like many other universities use them to reduce their offers in Durham the standard offer is two-way Stars than a but if you get like a good enough score in the mat then you reduce your offer to a star AA instead well for Imperial it's like really recommended that you should take the me because sometimes they like they've been known to reject people who apply without it hoping like because sometimes if you apply without it they'll ask you for a step offer instead but sometimes they reject you for like so you kind of run some risk if you don't take the mat while for Warick the standard offer is two a STS and an A and then either a grade two in Step 64 in M or 6 6. 5 in tmua so yeah it's like it's a very good idea to take it and um it's taken generally in like the middle of October to like the end sometimes it can be early November and even if you're uh not applying to Oxford or even not applying to Imperial War or anything like that then it's still like but you're applying to Cambridge it's still a good idea to take the exam because it's it tests like more original mathematical thinking than you would see in like typical like a level papers and more advanced problem solving which can be good preparation for the like the interview which you do later on if you're applying to Cambridge like an easy example is some like some questions in the mat revolve around having to identify graphs based on a couple of given sketches that but those sorts of questions will be good for building your intuition when you practice your graph
3:57

Timeline for Preparing

sketching skills later for the interview a reasonable timeline to start the preparation for the mat is around like August or September because there's only past papers available on the website from 2007 so about like about 15 also like papers right now and there's also two specimen tests uh A and B and you can get through those like fairly quickly I also recommend you start with the early papers like the early papers and the specimen papers because the specimen papers were written back in like 2007 because the difficulty increase is like fairly gradual like it's mostly linear but like there's a couple of jumps so for example in 2013 and 2015 um you can see by the like if you go on the website you can see for each paper they have these mu1 mew2 and mu3 scores and for like for the years 2013 and 2015 for example they're much lower than the ones which are around them so like those years were like particularly hard but other than those two bumps um the difficulty increase was fairly gradual until about 2018 I think the still like the specification changed and um then from there the difficulty became a lot more consistent um with the exception of 20120 which happened to be a lot easier and um the syllabus changed so um like to reflect the changes in the a level syllabus and um just like with step if you like prepare earlier on like the rate at which you improve will be quicker than the rate at which these papers get difficult so you'll be well prepared if you have done like a vast majority of the papers by the time the
5:48

Old Past Papers

actual exam comes oh another thing to mention is there are also old mat papers from 1996 to 2006 but following with the difficulty trend from before they're actually a lot easier than the current papers so they're not like they're not really essential to do I remember I found out about these papers maybe a week or so before my exam and I became really worried that like oh there's another 10 years of papers which I now need to suddenly do but it turned out like these papers aren't really that useful preparation like you can do them for completion sake if you'd like but they since they're so old they don't really reflect like the current papers as much this is probably why um they're not even mentioned on the website and the only like the main Merit I think in these papers are the question fives because question five is a bit more unique as we'll talk about more later on in the video and maybe you could prepare some of the question fives from the old papers like I like having a look through them I found that 1998 2002 2003 2004 and 2006 question fives are generally like the most relevant ones uh to the modern style of question five so
7:03

Structure of the MAT

the m is into two sections there are multiple choice questions 10 of them so that contributes 40 marks and then there are four long questions that you could do so there are long questions that are numbered from two to five and it's also question six now from this year onwards there'll be no more question seven which I think in the past was used for philosophy degrees and other joint degrees of philosophy question six is usually for computer science related degrees so if you're applying for computer science at Oxford or a join comp science degree you'll do question six if you're applying for math you'll do two to five um but if you're doing computer science or as I said computer science joint degrees you'll do question six the multiple choice questions um in
7:39

Multiple Choice Preparation

my opinion they're very similar in fact they overlap with many of the questions to the T multiple choice questions so a good bank of questions to do if you're praying for the multiple choice part is to solve the T papers I believe there are seven of them um and it's SP to two papers paper one are 10 questions and paper two is also 10 questions paper two focuses more on logic which is not extremely relevant in the math although could be useful to understand logical thinking and you know the difference between Contra positives if and only if and so on but it's not as relevant whereas the paper ones are very similar to the m mcqs so if you want to practice mcqs I would also recommend doing the TM papers another bank of questions you could do to improve your problem solving is to work through SMC papers so I would recommend uh this book it's called senior Problems by Andrew jings uh and it contains 500 questions from SMC papers I work through this book in year 12 year 11 and also some of it in year 13 and I think it's really good for increasing your general problem solving so that book will contain questions on number Theory counting algebra and so on a lot of the tricks um overlap with some of the ma questions so for instance if you've done some of these questions you might have a better understanding of how to count um and how to count stuff properly in maths so like double counting combinations perations and there'll be lots of questions and number Theory as well um some of which are very similar to some mac questions so for example solving dant equations which are equations involving integers that has been the focus of quite a few long questions in the mat um and in general working through that book when increase problem solving so I would recommend doing that book um not necessarily only for the mat although it will help a lot but also to increase the general Mass ability and it will help you a lot with the interview so perhaps working through that book in year 12 or so could put you on a Good Foundations um the source of problems you could look at while you're in year 12 like for example in the summer holidays of year 12 are the SE Foundation modules which like I mentioned in my setep video are also really good preparation for step one and like uh leading on to step two and three uh because these problems like they also test like a very similar like sort of like syllabus and they um also are there to like stretch your problem solving abilities and are designed to get you from having just study a level maths in school um to like this more like involved types of problem solving so yeah I would also recommend the SE
10:01

Section A

Foundation modules so the first section of the mat as Ali's mentioned is the multiple choice there's 10 questions which are multiple choice and each in each question you have five choices each one's worth four marks and there's a decent deal of exam technique which is involved in doing these for example you could if you like if you are like strongly with time you could set like a dedicated amount of time to work on the multiple choice and then a certain amount time to work on each long question to make sure you actually get around to everything for example you could spend 40 minutes on the multiple choice so it's like four minutes per question but I personally prefer to have much more of a like I prefer to attempt to each question and then perhaps like some questions will take a bit like will be a bit shorter while some longer and if I feel like I'm spending too long on a question then I prefer to like kind of have like use my good feeling of whether I should like move on or not like a good feeling of whether I feel like I'm going to make progress anytime soon um and this also applies to the long questions so I feel like strict timing is not necessarily like a good thing or at least for me it's not a good thing because I feel like if I try to stick to strict timings and then I ended up falling behind for or something for example then I'd be really stressed about whether I'd actually be able to do any of the other problems in time so you can try out these like various approaches to in your time in the exam like practice them with some mock papers and things like that try to find out what works for you but personally I prefer to just attempt the questions and hope like kind of time the questions according to how I feel how much progress I feel like I'm going to make also there's a lot of very specific tricks which can come up in the multiple choice because lots of the questions are like over the past 15 years of mat there's lots of like repeated like sorts of ideas for example one of the major tricks is to like which can save a lot of time and which can um actually help you get things more um right more often than not is by eliminating cases so a good example of a question where we can eliminate choices is 2014 like question one B so this is a second multiple choice question and we're looking at the graph of y = log 10 x^2 - 2x + 2 so we can just substitute specific values of X for example like we could look at x = 1 and then we get log 10 of 1 - 2 + 2 so that's just log 10 of one so then we know that when xal 1 we get log one which is equal to zero and turns out there's only one function which matches that so instead of having to sketch the graph we just immediately eliminate all the other options and that took me about like 20 seconds I think and if you're allocating like for example 40 minutes for the multiple choice um that would be four minutes per question so now I've freed up about three minutes to work on other things another great example is this question where we can look at very specific choices of M and eliminate like various options until we left with the only reasonable ones yeah and here's another good example of um a question which is not too easy to work out but you can think of about very like specific cases and eliminate options which don't make any sense like for example immediately you can see that if any equals 1 then we just get 1 plus x y + y^2 and then we end up with like no coefficient of x cubed y to the five because we've got powers are just too small but then we immediately now have lost options A and B because they're too small no they're too big sorry so even if you like in this question we kind actually substitute specific values to find what the actual answer is but sometimes if you're running low on time for example you could just quickly eliminate options like this and then choose um like just randomly choose one of the options because now we've increased our chance of like we've increased our respective value of marks by just randomly guessing on this question by a decent amount another relevant idea for multiple choice but also later question three is uh the idea of trying to B integrals and considering where the integral is like positive and negative and things like that like mat uh and this is a common theme with like all these like admissions tests a lot of the time in a level you come across like an idea such as like integrals which represent area and now like what that topic really does is you've got this idea of areas under the graph which is a completely geometric thing and then there's integrals which uh like something you interact with algebraically so you can do like the algebra you can work out the integral or you can um think about this area geometrically and a lot of the time me questions like you to be really fluent with like switching between these two ideas so sometimes like because some points of view will work more nicely with um different points of view on what the integral is so for example if I was asking you I I've got a graph and I reflected it uh what's the area under the curve under this region or something and it's then you can just immediately say Reflections preserve the area so you can like it's exactly the same as before while in the integral you would have to justify that by doing some sort of substitution to show that there's like a symmetry and things like that which is a lot more complicated while when it comes to actually calculating for example thinking about in terms of an integral with like an algebraic object is much more like is much uh is like the right approach to take because now you can actually calculate so um another like an idea along those sorts of lines is bounding integrals so a really common thing is if you have a graph like f ofx or something then um and this is integrated between A and B then you know that the integral is this part and an easy way to bound this integral is by just taking the maximum value of f of x and you can see that this creates a rectangle of length B minus a and the maximum value is the like the height is the maximum value of f ofx so we quite easily bound the integral as this minus a the max another thing to think about is like positive and negative areas so sometimes there will be questions which ask you about what's the sign of this integral without calculating it is it integral bigger than this one and you can just think about like and those questions usually end up being like one integral like you have some positive area you have some negative area things like that and similarly this question uh you can use this sort of idea like to bound the integral by using this sort of rectangular geometric argument to then compare all these integrals without actually having to calculate them because for example okay part C is quite challenging to calculate especially with just like the tools you have when you're taking this exam but if you then like if you think about like this bounding sorts of arguments and like the like and the area in terms of like geometric points of view then you can quite easily see like what sort of like value you expect for this integral without actually having to calculate it and that's what this question is trying to test and there's like lots and lots of questions in Amat which test these sorts of ideas so in the mat you'll also get lots of questions gra sketching so in the multiple choice all the long questions and in general there are some useful tips you can think about when you're sketching graphs so first of all you can think about ASM tootes are there any horizontal or vertical ASM tootes in your function knowing how to calculate them is useful even if you know you're doing a multiple choice question there's options but knowing how to calculate them is useful for the long questions uh second you can think about um transformation so sometimes in the mat there'll be some short questions or long questions ask you to transform functions um and this can be quite difficult if you have successive transformation to figure out what the order is so for instance if you have um you know the graph of y FX and the graph of yals say Min - 3 F of 3x -2 and plus 2 um knowing the specific order is something that lots of students will struggle with u but understanding that will be useful to doing lots of math questions um also another thing you can think about is symmetries in graphs so you can think about you know is this graph symmetric about the y- Axis or the xaxis does it have symmetry about the line yal X and after knowing these symmetries will be useful for identifying the graphs in the short questions but also in the long questions as well lastly as V mentioned thinking about graphs is a good way to investigate intercours and areas um especially when you have questions to do with um PE wise functions which we'll talk by in a second so as I said knowing how to transform graphs and successive transformation is really important so here's an example from 2014 1 I so they give you a function to x s and you have to figure out what successive Transformations give you this new graph um so practicing this is really important so the trick on how to do these questions is to figure out how the new equation is Rel to the old one so in this question we have a graph of y x- y + 3 and if you complete this Square you can see so you get x - 2 um all 2 minus one so we can now figure out what the relationship is between the old one and the new one by writing this and splitting up the powers using indices we can write this as 2^ x - 2^ 2 times by 2 power for half and we can do that because we can use prop of indices to do that um and we can see therefore the answer must be B which is a translation par to the xaxis um as well as a stretch because you multiply by a half so that's a trick on how to do these types of questions figure out how the new one is related to the old one and then figure out what the successive Transformations are um that take you from one graph to the other um now another type of question that is quite common in multiple choice as V mentioned before um with the example about reflecting a point in a line is knowing how to reflect points and functions in particular lines so knowing how to reflect a function in a vertical or horizontal line or even other lines um is quite useful trick um you can figure out using geometric arguments but I think that's something you should definitely work on if you're trying to set this exam it has been asked quite a few times reflecting points or reflecting lines or in this case reflecting a function so it's quite a common Skilling to know and symmetries and reflections of functions also comes up in the long section of the mat so this is you know a quite common theme that comes up and how to deal with symmetries and reflections of functions another type of question which is really common in the mat are questions involving trigonometric functions like sign and cosine for these questions knowing how to find the general Solutions is U of trig equation is really important like some examples like sin xal a half sinal cos Y and things like that and identities such as Sin Pi 2 - x = cos x cos Pi 2 - xal sin x these are also quite useful identities to solve these questions as well as drawing graphs to investigate the number of solutions you could also use bounding arguments because um sin x and cosine X their absolute value is always less than one which is um another fairly useful fact when it comes to these questions right another type of function to be aware of is pwi functions that's come up quite a few times in the multiple choice and also in the long question section too um so a p function is just a function that has a different definition depending on the region effects that you in so for examples of that include the absolute value function as well as the floor function and other ones for example the ceiling function or even the square root function so knowing how to deal with absolute value equations and integrals as well as other pewi functions is really important U there's an example of that in 2013 question 1j which ask you to integrate a FLW function a Flor function has come up quite a few times in mat and it's quite popular for interview questions and other admission tests because it's quite interesting and outside the a curriculum however there is a common trick and there's a systematic way of dealing with pce functions in general um of which include absolute value functions floor functions ceiling functions and so on so if you think about it geometrically that's one way to do but there is a systematic algebraic way to deal with them as well um and you might be expected to know how to solve equations involving P functions for example let's say absolute value xal 10 or some other combination or um equations involving other PSE functions for example Flor functions or ceiling functions so knowing how to solve equations with them knowing how to sketch those graphs and knowing how to do calculus with them is really important and as I said there's a systematic way of dealing with them the
22:53

Section B

next section of the mat and the bulk of the marks is the long questions so that's questions 2 three four and five or um for the math students and for the computer science students it's questions two three five and six you might notice that there's question seven as well in the past papers but from 2023 onwards question seven has been removed uh another important change for 2023 is the marks available for each part of the question have now been given so you might like to um like if you're R low on time you could take a look at like some earlier parts of questions which you haven't attempted for example and just like quickly write out some small stuff to get a small number of marks it also helps you plan like how much time you could spend on each part or whether it's worth to continue going on a certain part of the question another thing you could do is if like you're stuck on one part for example you can likely use that part in a later part of the question and try to collect some of the marks there the marking is linear in general and um the first few marks are usually much easier to get than the later ones so I really recommend if you're running low on time to just pick up a couple of easy marks from the from any long questions you haven't done another like General exams um tip is uh thinking about the marks per minute can be quite useful because if you ever see a mark which you can get in like a minute then since the exam is two and a half hours long if you're going at the rate of a mark a minute then that's like easily full marks so if you can ever get a mark in a minute then you should just take it another important thing about the long question says that the questions come in specific topics which will go into more specifics uh of as we look at each question and like this is quite important because if we if you know the topic which a question you're struggling on is then you could take a look at questions of similar sorts of exams like you could take a look at step papers and use the step database and look up that topic practice a couple of questions come back and maybe you've picked up some new ideas which will make the mat questions doable also it means that you can focus your preparation on areas which you're weaker on for example if like I was weak at graph sketching then I could just do lots and lots of like the questions which focus on graph sketching and then um come back and maybe I'm better at the graph sketching questions now also it means that uh when you go into the exam you can have a set question order in mind based on your strengths for example you might not be so great at geometry uh which question four is so you might like to set that towards the end so you can if you have time you can just come to it and then have a couple of like quick gos at it or you might like to go for um you might be good at graph sketching so you might like to go for question three first that sort of thing so looking at the mat by question uh question two is
25:51

Question 2

normally about some sort of like algebra algebraic manipulation with often with sequences involved for example 2022 is with sequences and 2019 has like pols and lots of like heavy arge break manipulation looking at the sequences of coefficients like generally like this question generally tests like fluency with algebra and like sequence recognition and things like that so when it comes to dealing with sequences and this is quite useful in a couple of the multiple choice questions as well trying a couple of small values is a good way to check uh if you've got like the right like to try and spot patterns to calculate a couple of things and maybe you can prove things by induction as well um because once you have like a good guess of what the sequence is like induction is really helpful for uh proving that form is actually correct with these with question two though it's fairly General and you should generally be improving at these sorts of things another type of question which is often asked in question two is about like repeated applications of functions for example 2016 and um even some multiple choice questions so these ones are also fairly like heavy on like algebraic manipulation and just like a good understanding of like function notation uh composition of functions and things like that make sure you're strong uh like those sorts of areas for question two so for question three it's usually
27:20

Question 3

about graphs and integrals um and so for example 2013 question is a good example of how to think geometrically so as we said before in the multiple choice part A lot of the tricks for the multiple choice are for the long question so everything I mentioned for the multiple choice also the long ones so for instance for graphs sketching graphs and knowing the symmetries ASM toes thinking of behavior X go to plus infinity or behavior in the undefined points is a good way to draw graphs also using graphs and geometric arguments to deduce areas and integrals as V said previously is a good way to relate integrals to areas as you said for example if you reflect a function the transformation of Reflections preserve the a areas so that's quite a big topic theme in some of the questions as well as said think about when an integral is negative and relating propos of the function is the graph above the x-axis is a not do the part above the x-axis cancel out the part under the xaxis and therefore concluding when integral positive or not is an important skill to have this has been the focus of quite a few long questions in the past now SP alert if you've not done the 2022 paper so please don't watch the next few seconds but that has been the focus TR to question three which is thinking about when an integrate is positive or negative and relating it to you know how you could tell um that there's no values of the upper limit that the overall interal zero and again that just is just thinking about when the integral is positive or negative and relating into the function so to summarize question three us about graphs and integrals you should remember how to calculate asmt toes vertical and horizontal turning points um Roots y intercepts thinking about Behavior new X's plus minus infinity new asmt as well or other undefined points thinking about graph Transformations maybe you can relate it to a previous graph as well as think about symmetry so in some questions you might be asked to State some symmetries of a graph for instance does have reflective symmetry about xal a y equals P or something like that or other types of symetry as well um so that's so for instance all those things I mentioned about graphs you can also apply to integrals so for instance if you transform a function think about what happens to the area if you reflect it or translate it think about what happens to the area as well so that's been the focus of many question 3es in the past for the mat so again if you've not been doing many questions of those sorts you can do similar questions other resources for instance you can do graph questions or integral questions from Step One the relevant ones at least or as I said before you can work through some problems from this book so there are some good questions here on graph sketching and relating goph to areas for example finding the area um enclosed by like mod X plus mod Y is that's to three or something like that so you could do some questions from here or also from Step One um Step One uses the whole math but there are some relevant questions which don't use that much material so those could be perfect for practicing question three for the mat moving on to
29:58

Question 4

question four is usually graph sketching coordinate geometry or just straight up Geometry so everything I mentioned before for graph sketching will apply to this question but also some stuff to think about for coordinate geometry so for coordinate geometry usually do stuff for like equations of lines and circles intersections tangents and so on um and for this type of question as well as some multiple choice questions as I said before it would be useful to know for example how to find the shortest distance between a point and a line point and a function the shortest distance between circles short distance between parallel lines and so on and the general idea of drawing perpendicular and finding perpendicular distance in general also you should figure out how to reflect points reflect functions and so on um as that could be useful in some long questions as well so to summarize for the geometry part you should be aware of the GCC andal geometry you've learned Circle theorem similar triangles um congruent triangles Pythagoras and so on as well as sign and Coin and the proofs of those things for CA geometry should be aware of you know the equations of all those things circles lines tangents and all the things I discussed earlier and graph sketching um everything we've discussed up to now for graph sketching is also over for question the last question for the
31:02

Question 5

students who are applying for math is question five and these questions generally tend to be on things which aren't really taught in school such as um Counting arguments and combinatorics uh recurrent relations and using these to build like using like counting arguments to build recurrent relations and things like that uh these questions are also useful when it comes to interview prep later on so if you're thinking about the interview after the mat and there's any question fives you haven't done I'd recommend doing them sometimes you get given rules um in like some new scenario to construct things such as 2014's question or you can be given question like recursive functions like in 2019 which can then give you recurrent solution um usually there's like standard arguments to find like to build these recurr stations you can uh think about the problem combinatorially and then like break down the problem into cases like 2014's question five guides you through that process this technique is also used in like coms in general something called double counting where you try to count things in two different ways to show like two different like to then prove an identity because you've now shown that two different things are equal like for example uh the sum of binormal coefficients like the sum across a row of Pascal's triangle is equal to two to the end proved using that often um to find recurrent relations just like sequences it can be useful to work out some specific cases and then maybe you can spot what the recurrent relation should be an example of this like U building recurrence relations and testing out a couple of values in the first place to see what the sequence looks like is fibonacci's uh problem with the with rabbits where just like an me question he introduces a couple of rules so here it's you start with a newborn pair of rabbits once they're adults then they can give birth to like new rabbits each pair of rabbits gives birth to one new pair every month and then you just continue doing this every um every month and try to understand what the population of rabbits is after end months and if you work through this you find that the number of pairs is one 2 3 58 which is the Fibonacci Sequence where the next term is generated by taking the sum of the previous two and then once you've spotted this pattern now you can use a general argument to prove it which you can do by thinking about the number of rabbits which are able to give birth in a given month and then the number of rabbits which will be able to give birth in the next month and things like that so these sorts like these sorts of like this sort of way of thinking is what question five wants you to do most of the time the question six this one's
33:55

Question 6

taken by the people who do computer science and in the past there used to be a pattern for this uh which was mainly like logic style questions for example in 2013 so the tmua which Ali mentioned before the section two questions on logic were quite relevant but since like recent years there's not really as much of a pattern to these questions they generally test algorithmic types of thinking so recursive application of things and generally mathematical thinking which is more useful in computer science or at least is emphasized in computer science which is why they're being tested but it's the questions are fairly unique among um like math admissions tests since for example step doesn't test any computer science so it's quite hard to prepare for these like in isolation over them doing the question sixes themselves there's a couple of Step Foundation module questions as well which involve logic but particularly the warm Downs because they're structured to be like warm-ups to build up to the step question then a warm down which is like a fun puzzle these can be quite like algorithmic or like these can sometimes involve like logic style arguments but they like other than that like question six is fairly isolated like it's often about some sort of like procedure or algorithm and introduces Concepts which they want you to like they're testing how you can interact with this New Concept I guess just kind of like question five uh they first want you to work on some simpler cases and then it becomes more and more general or proves more General things later on some
35:38

General Advice

more general advice when it comes to these types of math admissions tests is just like for the mat tmua step and even applicable to the interview this is the first time which you're like for many people you'll be taking an exam which really tests your mathematical thinking in like timed pressured conditions um so there's a decent chance that you're going to be satting the exam Hall uh just sat there thinking not making any progress on the current problem not having any idea when you might make progress and in general just feeling like you're not able to do anything which could be quite stressful because you're sat there while the clock is just ticking and you don't know whether you're actually going to make it during my mat I remember this actually got to me um I ended up sitting down looking at question five which is normally pretty decent for me and I just couldn't form the recurrency relation properly I couldn't prove the things they were wanting to do and I kept trying to go over it but I kept making the same mistake again and then I end up wasting a lot of time just like worrying about how much time I'm wasting which is like a really bad spiral to end up in that situation it helped me to change questions to like complete like to clear my mind about the thing I was thinking about and like refocus and then later on I could come back to question five and have another go and uh do well on it um and in the end like this was good enough to make me do pretty well overall I man to get my Imperial offer and I think this experience is pretty helpful actually because it helps me understand like why I struggled in that moment in the mat and to then avoid it when it comes to steps which since I played to Cambridge was much more important for me and I think to avoid things like this uh you could like you should do some timed papers to see what the exam conditions are like and to see how you do like as if it was a real paper because then you could understand what it feels like to be in this like pressured situation and to get used to what the actual exam is like I would recommend though um if you're struggling to finish questions at all or if you're struggling with certain topics then it's probably better for you to sit down and do the questions in untimed conditions to really make sure that you understand the problem you get through it you understand the ideas so that later on when you're you become comfortable with all the techniques you can then start to do time problems another idea you could do is um make a spreadsheet to keep track of the um questions you did um well on the questions you did poorly on and like the things which you need to go over to do well or to have actually got to have gotten that question right because then once you do that you end up just with a list of the misunderstandings you have which you can then go over make sure you understand them and now you've like covered most of the like you've ground you need to in the mat since there's quite a lot of papers so a lot of the tricks which they could ask probably have already been asked and a lot of the ideas uh will be similar to in the next paper will be similar to something which you would have seen before in your
39:02

Ali's Course

would you would have seen before in your previous paper all right thank you for sharing all that information about the mat um is there anything else you'd like to add yeah so I would just like to add um that um a course an exciting course that my team and I have developed for the last few months and we've actually delivered it to 10 students recently so my team and I have prepared a syllabus that cover the mat so in this course I think it's one of the only courses in the world that is of this nature um so it's a very exciting project we've been working on so essentially what we've done is for every um mat topic of which are 10 main topics we've created a list of tricks for each one that covers all the possible tricks and ideas you'll need to know so for instance for trigonometry we've included a list of 30 tricks as well as examples of problem solving strategies that you need to know for that and we've done that for all of the topics the way we acquire the tricks is one obviously we've done all the papers ourselves so we've done maim in step and so we you know compile tricks from all of them but also in general from our experience solving math questions from competitions or you know doing our degree we've picked up quite a lot of knowledge um that we've uh put into this course so this is a quite comprehensive course that will maximize the score in the mat um because as we said before for all of the different topics you have a lesson which teaches you the tricks directly instead of you having to pick up yourself B papers and then for every topic you'll get a problem sheet they'll have a total of about 150 questions so overall this course um will provide you about 1. 5k questions the questions are taken from past m T way papers well step questions or m style as well as questions we've equated ourselves originally so my team and I have sat down uh for many hours to create those questions as well as questions that have been taken from competition maths that are relevant as well so the point of this is to give you a wealthy Bank of problems so that you will increase your problem solving as well and be familiar with many types of questions because sometimes in mat there might ask questions that they have not asked in previous papers and so being able to have experience um solving many types of question questions in different styles well put you in a good platform for that um as I said that this course will cover everything that you will need for the mat all the tricks even stuff that um is outside of the quickin but could be useful to know say as we said FL functions you know integration tricks um functional equations stuff like that this course will cover most of the things you'll ever need for the mat um and it's a very exciting project as I said that we've worked on we've delivered this course to 10 students and they've all loved it and made substantial progress um and be launching um it again soon so if you're interested there'll be a Google form in the description below of which you can sign up interest for um and I'm hoping that this could possibly help you if you're interested okay well that sounds awesome Ellie so I guess all we can say is like good luck for the m and any more words yeah hopefully the video was useful and good luck for the exam especially the one which is coming up soon yeah and again please make sure you try your best at the end of the day it's an Master exam so hopefully if you're app for a master degree or find a fun enjoy the process enjoy the challenge and I hope that many of you get into Dre inv that you want to

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