Transcript for:
AdMat Paper 1 Preparation Guide

all right people so we here to do a little admat paper one crash course please share everywhere um this is free obviously you seen it online so um what we're really going to do is focus on some sample papers um do some questions and let's see if we can get at least three sets of 45 questions done this is going to be really nice for you because I'm going to show you all the tips and tricks um that you can use in an ADM mats exam right so I know ADM mats when I do admat this is the live with the least amount of students online because admat not much people not many people doing ADM mats people who do admat have probably go to do pure mats engineering that kind so share it up with your admat crew let me come let me see if you know anything in admat here bios food very nice somebody El as ER in one of the bio questions I hope not um how much time do you have for the exam I guess you seen since it's 45 questions I think is less time now it's the same amount of time but the questions take longer to do in Adat it was good nice nice nice so let press like on it now let me let we get down into business let me get down into business so there'll be a lot of people who would rewatch as well so shout out to all your rewatchers people who watching in the future I always like to make sure I put this number here for those of you all who would be looking for online lessons at the student Hub you can WhatsApp this number + 1868 310 1306 you want to get hit up this number on WhatsApp to register for lessons in the student oh you're not see my screen my screen so plus 868 31 01306 that is what you want to do right so bu was a letter repeat same as it very nice well we hoping for um ATM for so let we go so these sessions off then these um multiple Chic sessions doing well the expression xus 2 is a factor of well we know we need to substitute positive two right according to the factor term in all of these so best bet is to just use your calculator to quickly put positive two in all of these so it'll be like four um and I'm going to put two in this two to the^ four 4 by 2^ 4 is [Music] 16us 2 by 2 power of two is four yall understand what I'm doing minus 56 and I get zero one time so a is indeed the answer so anytime you have a question like this where you have to check the the the factor in the questions put a little Aster on the question paper but you already found that a is the answer right you understand what I'm saying you don't need to go check the rest yet save your time go and do the others when you finish people you'll come back and just verify that all of these not giving you zero that's okay important little tips that could save you some time in the exam and admat paper one could actually um actually be a scene where you want to save the time AB plus 3 C minus 3B minus a what happens with this in admat this grouping question is that they're not in order so you want to rearrange them so I'll probably put AB minus AC plus no no no no no B is has a negative so I'll put minus 3B plus 3 C so this came across so I'm going to factorize out a out of this right so I'll factorize out a out of this I'll get B minus C then I take this B minus C and put it back here that's how this works and what I could factorize out of this to make everything right with the will definitely a negative3 you'll see that and you'll end up with a minus 3 by B minus C well done well done well done 868 Shalia C ID so this one is D all right we grinding for a little while here I don't know how long this may take two hours 3 hours uh which of the following graphs best represent F ofx Well we we need to examine the roots that's what we looking at so we have a root at X is equal to Z CU if if you equate this equal to Z you get a that meaning the roots here now these things we need to see which root they're looking at we also have a root at 1 minus x equal to 0 this ISX is equal to1 or X is equal to 1 so this can't work because this is netive 1 this one may work we'll come back to him this one may also work this can't work because it's negative one so which one is it we getting Roots at X is z and X is one the only thing left to see is to determine whether the Curve will give you a maximum point or minimum point and from this we can deduce that the Curve will actually give us a maximum Point how do we know that well if we expand this out we'll get X if you expand the X by we get x^2 this means the coefficient of X2 is negative so since the coefficient of X2 is negative we expect curve that looks like this the answer is B number of visas VX issued by Embassy annually is given by this this is a very repeated question least number of visas issued in a particular year X is so they want the minimum point of this quadratic so one of the fastest things you could do I'll be showing you lots of tricks in this uh thing right is is whether you have a Shar or a Casio I know one or two exam centers stop students from using their CIO which was which is Absol press mode press equation go on three and quickly put in the coefficients because what I'm looking for is the minimum point I'm seeing that it doesn't even cross the x-axis because there's imagin Roots so the minimum value of x is three but that's not what I want three is not even here that's the x value I want the Y value at the minimum point it's nine so the answer is B how is that so in other words I want the K when I complete the square and K is 4 a c minus b^ 2 over 4 a so if you substitute this a b c being these numbers a being 7 and B being NE 42 and C being this you would um you would be able to get the the value here this will work out to be equal 9 yes another way to do it is you can find H H is B on 2 a and you will get H to be -3 when you put B and 2 a yes yes however you want to substitute positive version of this cu the x is 8 so you want to substitute minus B on 2 a so this -3 into this so you'll put -3 into this and this as the X and it will also give you nine so there are three ways to do this question um I showed you the fastest ways to use your calculator um and then you can put the atic on it so you could come back and use a a calculation method just to double check nobody's watching your work when you're watching the answers right the roots of an equation are once again I could verify this on my calculator very easy I still in um quadratic mode so I could just put in the five the six I'm showing you all the tricks that people is G keep with the calculator showing you all of it yeah my class and the student would know all the different calculator how best you can use the calculator to solve all these you would see you'll begin to become almost terrified with the power if this is the first time I'm you seeing this by the time we do these three 45 questions um and I show you all the different ways you can use your calculator there's no way you get you're getting under 40 out of 45 in this multiple choice anyhow so you seeing what happening there we saw negative this turned to this was positive and it turned negative it means the roots are real and distinct real and distinct C is the answer so that's the calculator how do you work this out well you use something called the the terminant so you want the b^2 minus 4 a c you want to watch this number and see what happens so b s that's 6 2 - 4 by 5 by or the discriminant sorry um by minus 2 um so this is 36 uh 4 4 by 10 40 36 plus 40 so this gives me 76 now you really care about the number to be honest you just care about what whether the number is positive negative or zero so if the number is positive it's real and distinct if the number is negative it's not real that's all it's it's not real um it's it's also distinct but it's not real so imaginary this is real and distinct um and if this is zero then it's real and equal or repeated in some cases they'll put repeated so zero is the only exception where would the roots would not be distinct The Roots always distinct distinct just means two different Roots all right so that's enough knowledge on that I showed you the calculator way and I show you the how to calculate it using the this is called the discriminant discriminant this is the part in the quadratic formula that is under the square root side that's why it's so important it depends on whether this is negative or positive whether we can figure out the The Roots you understand or how we figure out the roots the sets of values of X for which all right so this is an inequality so you're going to bring across the we going to bring across the 10x bring across the seven now I'm not too sure how many people understand what I'm doing here I'm doing that crash course level um words of work I might not even keep it up after the exam X is greater than four hold up I get distracted talking me so I'm doing a crash course level work of worth a work of worth of work so we're going to be doing three 45 sets of questions three sets of 45 questions W I can't talk but anyhow um and by the time you finish this going through this going over this this is going to leave you in a really nice place for the admat exam I might even do an additional sample right before the admat exam if I get the chance right so what happened here the thing is yes I was following the rules of linear equations bringing stuff across solving as I go along but um I had to bring across the five and it's negative the rules is anytime you divide or or multiply yep by a negative number the sign was switch Direction like this so it's actually X is less than four C is the answer that we are going for um what's another way you know I'm trying to show you all different ways to solve because when you finish your multiple choice you want to go back to using different methods to solve it another way is to substitute so this one is saying X is greater than four this one is saying X is less than four fine if this is saying X is less than four let's substitute a number like three into this and see if it works 5 by 3 is 15 + 7 is 15 + 7 greater than 10 by 3 is 30 - 13 30 - 13 15 + 7 30 - 13 yes 15 + 7 is greater than 1 minus 13 this works now that's not full that's not a fullprof method me it so you don't start off with that that's just a way to verify if your answer is correct all right all right like keep pumping by the way your calculator can also solve this um calor can also solve this all right I could solve the linear equation part of let me leave it alone excuse me kind of here that's still coughing and thing um it yeah some calculator vide for the sh up Cur spring and Sh but not too deep for admat student um the calculator could solve it if it was a equal sign here so you could figure out X is equal to four but you still need to know which direction the range of values of X for Which F 5x + 6 is less than or equal to X2 right so your calculator could definitely solve this one so this is a quadratic inequality right so bring everything across or bring everything across on this side you get zero is so a lot of people would do this but this is a little weird to have the inequality sign here and if you had to bring it across there could get loss in transmission so let we do be afraid of the negative sign let's bring the the neg the X um squared across and face the music we have this we watching this ladies and gentlemen so what I'm saying is yes your calculator could very quickly so that you press mode you press in equality so I went down actually right I went down and I press inequalities I'm going to choose quadratic I'm going to choose what I'm seeing here I'm seeing less than or equal to so that's the fourth option number four everybody is seeing and understanding I told you I'm going to show you every trick in the book uh -1 5 and six no no one shows you how to use your calculator like this I'm showing you everything right so X is less than or equal to one um it's two separate situations so I'm not I don't want this or this I want two separate situations notice how there's a comma here I want my X be less than or equal to1 or my X to be more than notice how the open spot is facing the X more than or equal to you still need to know how to read the notation right and that's B all right so how do we do this otherwise well you solve it so this is -6 we want two numbers I will add to give me five but multiply to give me -6 so that is plus 6 x and - One X right + 6 is less than equal to Z and then you factorize you have X into x + 6 and you havex + 6 um we just need a 1 x we just need we just need a one + one so we have x + 1 and we havex + 6 or or 6 - x some of you all may have is less than or equal to Z so the roots for this would be x equal to1 or UMX plus 6 equal to Z so you're seeing what that means right uh that means X is equal to 6 so we have these two roots and then what you're supposed to do is draw the curve and you know the Curve will look like this because this is negative so it's a maximum curve so after you've drawn the curve you need to put in two points so one is negative 1 one is six so I put it in in this order negative will go left positive will go right and I deduce when this is I want it to be less than zero this is the xaxis right everything below this axis is less than zero everything above is more than zero I want it less than zero so less than zero notice the line down here is less than zero so what I what I've told my class to call this is the wings right this is the wings when it's in between we call it the sandwich so this is the wing so you know you're dealing with two situations you're dealing with a situation where X is less than or equal to negative 1 all X's more than or equal to 6 which is also B so that's the long way I show you the calculator way let me keep pumping um if you all understand that type I understand so far so good see know to solve these things some of youall is revision some of you all from my class because I know I send the link to my class some of you all fall asleep or you just done bu and um it you need to sleep but um you going be watching this in the future up if if F ofx isal 3x - 4 and fgx I leaving this out should I they removed functions from adms now let me just do it for for kicks right because it help the maths multiple choice anyway so f ofx is this fgx is that then G of X is what so how do you solve this kind of question this is like a compound this is like a compound um function composite function and then we have one of the functions but we need to get this function so have a few ways we could do we could solve this F G of x isal to x f ofx isal to 3x - 4 so there's a substitution method that we can use and there are other methods what method do you do you suggest now G of X means the G came first we did g of X then we substituted it into F and we got we got X so when you substitute G of X into X we supposed to get X well I think probably the fastest method is the substitution method where you just substitute the answer I already could visualize substituting this if G if this is G of X substituting it into F ofx I could already see this not going to help the X going to end up underneath this looks really promising so I'm going to try this one so I'm going to say three by x + 4 over 3 minus 4 oh there's a little problem here the three cancel oh yes it does work so I get x + 4 - 4 and I get my X so that is here that's the fastest way so the fastest way to do this question is just substituting the answer instead of doing the algebra behind it so you just look at the answers and you this I want G of x g of X is the first one g ofx into F ofx makes FG ofx so I'll check which one of these substituted into F ofx will just make the x that I want all right you all understand the tables below show the ordered pairs for two functions f and g okay the value of G inverse of f of3 so you need to do this bit by bit so you need to do F of3 so let's do f of3 f of3 means substitute three and then find F ofx so that's going this way right so F of3 if x is three f of3 is equal to two y understand what they're telling you there yes class and then so this is two now so anywh so I'm seeing this I just need to see two two right um I want G inverse of two so obviously I'm not going to pick this one and go like that that's wrong why because it's inverse I need to go backwards I need to use this one you understand the trick in this question so G inverse of two means I'll be going backwards like this so um five this used to be a really tricky question everybody used to get this question wrong if function H is defined by h of x equal to 5x + 2 Express in terms of a h of 2 a + 3 fine h of 2 a + 3 just means that I need to put 2 a + 3 in place of X so now I'm seeing 10 a um + 15 + 2 10 a + 17 the answer is c a function f real functions is defined by f ofx is = to 2x - 1 the function f 2 is defined as well this just means substitute F ofx into itself so this is f f ofx that's what this is so this means put the 2x minus one back in where I'm seeing the X you understand so now I'll have 4x - 2 - 1 so this is 4X -3 that's him there so they remove functions from the syllabus um but certain ways algebra can overlap with function so I would still advise um handling your functions questions when you're doing your past papers by the way knowledge all right so we out that let's do this question the root of 3us 27 m is equal to what the end root so they want you to simplify this well it's clear to me that they I want you to put this as as three as well um so this is 3 * 3 to the^ of three by m so far so good everybody now I need to group this up but before I group this up this is really 3 * 3 to the^ 3M this is a power to a power when you going power to power you multiply right and now this is multiply same base so we add so this is 3 to the^ 3 m + 1 so far so far so good and then there's a square root sign square root means fractional power well actually it's not square root it's ENT root still fractional power but the denominator of the fraction will be n so this is really 3 to the^ 3 m + 1 and the fraction is n the end power so the answer is a is there a way to figure this out if you you um forget how to do this in the exam you forget IND thees and you're not too sure and you're panicking yes there's a way to do it um there's a way called there's two things substitute in the answer I call that SATA um where you substitute the answer into the question and you can do it and then they substitute in a number um instead so that's like I I teach my class like two ways to look at this meaning here's what I mean so like you forgot how to do the indices you forgot how to do powers pick a number for m&n and pick numbers that are simple so like pick numbers like n will be two let's say the square root and M would be let's say one now I have the square root of 3 * 27 the^ of 1 work that out in your calculator the square root go back into normal mode Square < TK of 3 * 27 to the^ 1 so that's just 3 * 27 is nine and now I'm going to yall understand what I'm doing now I'm going to check the answers with n is two and M is one and see which one gives me nine so if n is two here this is two yep so if n is two here and M is one here this is 3 + 1 this is 3 squ this will end up being 3 squ which is nine so that one works now if I put n as two here and M as one I will get three to the power of five or some kind of thing this does not work once again if I put squar here and one here this is a really big number this doesn't work this doesn't work so you can substitute in numbers to verify showed you another way how to do the question please make note of these little techniques because sometime it might save your neck in the exam right um 8 plus you want to get everything correct in the paper one you know eight plus Square cuz if you get correct people in my class get 8 plus theun 5 2 minus theun 5 can be expressed as well all right so we need to multiply 8 by 2 so we get 16 8 by5 minus 8 by the < TK 5are < TK of 5 by two you'll have 2 plus the root of 5 and root of 5 by the root of 5 that's Just5 um can your calculator do this of course it can so the C can literally type this in and it will give you the answer so 8 + < TK 5 2 - < TK 5 11 - 6un 5 the answer is a 16 - 5 is 11 and -8 + 2 you could think of the root five as like a x you don't interfere with it right it's like a almost think of it like a little variable that we not interfering with so this is my - 6un 5 in the end there so long way short way I show you two ways to get the answer it don't get easier than that the value of 2 to the power of Z where Z is equal to 5 + log 23 is so they want 2 to the^ 5+ log base 2 three once again your calculator is just going to mash up this because your calculator could do logs in different bases the Shar there is a long way to do it on the Shar so 2 to the^ 5+ cuz a lot of the shops don't have multiple bases on the logs three and they telling me that the answer is 96 so you literally plug this into your CIO and walk away with the answer all right but if you couldn't what would you do well this is 2 to the^ 5 multiplied by 2 to the^ log 2 3 now when you see 2 to the^ of log base 2 that's like you're going up and you're coming down you can just cancel it these two things and right three right and 2 to the^ 5 is to the two could double check 2 by two by two by two by two and then you need to multiply this by three you get 96 three will just fall all right is there any other way now I'll show you the two easy ways to do it calculator and actually do it out the expression simplified once again your CIO is just going to mash this up you may need to watch the factorization to SP fig out which one is which < TK 5 - 1 all over 1 +un 5 equals so this is 3 - root 5/ 2 in other words half half of 3 - tk5 half of 3us root 5D is the answer so how do you how are you supposed to do this then well you have to rationalize doing it the long way so you do the calculator way and you go to the next question and then you come back and you double check with the LW method so you you multiply by the conjugate of the denominator so F yeah it just going to get worse bro let me tell you one time it just going to get worse it's just going to get worse when you see the amount of different things I the shop could do something but the the method to do the sh real and anything so anyhow root 5 by 1 that's rooot 5un 5 by its by another root five that's like5 -1 by 1 that's 1 And1 byg root 5 that's like positive TK five all right okay and this is one well this is like difference of two squar so you end up with 1 - 5 so you're going to end up with two 2un 5 - 6 over -4 so I could pull out I could firstly say two into everything right um that's a you decision Zara that's a you decision the Casio is a real big help for the exam it's a massive help but I didn't know if could get it in time for the exam when is it adms I telling to get it so long if you come on my channel so long I say to get this um so I could pull out the half but I still have a negative so strongly signs and make this positive and make this one negative so there's a little there's a little um tough arithmetic here for some students to see how to manipulate the negative sign to get it to look like one the answers so this is where CIO would come in really handy you would get real a real nice help in seeing that 2 to the power negative one um I just see my register zav see everything good by Good by was them exam 2^1 over 8 to 13 simplifies as it well once again your CIO just rip through that get better for Nonio users Nonio users going and watch your stream and be very angry 8 to the power of a fractional power not a problem 8 to the power of fraction one2 yeah you're doing normal normal things you get a quarter right um but still if you're really good in adms is not a problem you'll be able to do the question so 2 to the^ of1 is really let's SE divided 8 to the that means the cubic the cube root of 8 which is really two we know that's two so this is 2 to^ netive 1 that means 1/ two divided by cube root of 8 is really two so this is a half multipli by flip it around which is a quarter so not bad um if you if you are boss in ADM mats you could figure it out without having a CIO anything but um having the CIO really does help and give you a nice added comfort that you know two ways to get the answer in a geometric progression each of whose term is positive the fifth term is 45 and the seventh term is five the sixth term is all right so if the fifth term is 45 and the seventh term is five is a GP and we using stuff like common ratio so the fifth term a r to the^ 4 right CU a r n minus one TN and the Seven term a r to the^ 6 so what we saying a r to the a r to the^ 4 is 45 and a r to the^ 6 is five so it going down so we expect a common ratio that's a fraction right and they what they want they give us the fifth they give us the seventh by the way I can do this by just elimination I could do this by just guessing 45 divided by three I could do this by just guessing I could watch this and guess because they give us the fifth term you understand and the seventh term and know they asking me about the sixth term and the fifth term is 45 and the next term is five it can't be 40 it can't be went to 40 then it just jump all the way to five remember this need to go down by a common ratio something divide it then or multiply and I see like it multiplying by by 1/3 and I get 15 and then I multiply by 1/3 again and I get five so that the fastest way to do this question just watch the fifth term stay now you realize fifth seven they already the in between us it easy to just watch the answer and pick out the correct answer so what's the long way to do it then well what you're supposed to do is a kind of division Vibe so you're supposed to say okay um call this equation one equation two excuse me and say equation oneid equation 2 so think about it 45 divided five which is n and when you divide these two the A's will cancel and you'll get um I said one over two my bad I should have said two over one but fine you'll get R to negative2 if I divide the other way around I hope I could survive my voice two ID by one I get five over 45 get one n is equal r to^ two some people will see positive like this now um the other one I'll get negative two which still get the answer anyhow so the r has to be the the square root of one 19 so R is 1/3 and I'll only use the positive since that's the only one that works so R is 1/3 and once I know R is 1/3 I can just divide this by one3 to get to the sixth term so either way understanding how GPS work would help you to really go through this question really fast some of the odd numbers 10 to 50 this is always work out to be uh 600 and so if we working odd numbers 10 to 50 there are 40 numbers here um odd numbers there'll be 20 of them we'll be starting on 11 and going all the way to 4 9 so the first term is a the common difference is two so a is 11 D is two and you find the sum um the excuse me sorry for cing I just trying to live here I just trying to live find the Su to the 20th term what is the formula for S of S and S of n again why somebody's always G me this this formula in class sum of a it is AP um n / 2 to a plus n minus1 d n minus one into D so yeah you just hit them that shot and you roll out you roll out this is the longest way you could do it there's a first and last method that's a little better um so what we want it's 20 terms just remember it's half the terms so it's really 20 / 2 2 by 2 by 11 is the first term plus nus 1 so this is 19 by two and hopefully that give us 600 hopefully we are nice looking 600 there 10 by 2 by 11 is 22 plus 19 * 2 19 * two um 600 right so what the faster way to do this um hold on my just stor the room all right yeah we back again so was your short way to do this what I was saying right um the first and last them add them up uh so we have 11 and 49 so 11 + 49 and how many pairs of these we'll get cuz you'll have 11 plus 49 in other words we doing is 11 + 49 the next one will be 13 + 47 you understand and this pairing situation will go on until they meet the middle um so if there are 20 numbers there are 10 pairs there are 10 pairs so it's 10 times that and as simple as that you'll get the answer and all these pairs add up to the same thing right 60 60 so 10 * 60 is 600 so yeah so that's the fast way to do it when you have the first and the last in the ter now it was wasn't 10 and 58 you know to be 11 and 49 but same same thing um can you use summation and the calculator we really want some of a series we are some of yeah I guess you could probably set up a summation but the first four terms of convergent geometric Ser progression is given by 500 um right Su to Infinity um Su to Infinity is again um s Infinity 1us R something Infinity Again by e 1 minus r e 1 minus r we have a fraction right this is the 500 the first four terms is 500 so we working at 5 500 and 500 over so 200 over 500 is two fths so the two fth yep so is 1 minus 2 fths and that's our final answer there 500 over 1 - 2 fths 500 over 1 - 25ths so 1 - 2 fths is just 3 fths um so the E the way to go the long distance Runner runs the first kilometer of a Race So once again we AP land a lot of these things is just AP and GPS um progression series something finds that his speed drops steadily so that each kilometer is taking him 12 more seconds time taken to cover so we had to change it to seconds and then change it back to minutes and seconds fine that's the the mean task in this question why making this so long so 3 minutes um so 180 180 + 45 is five and two and two 2 to five minutes is the e that's your e and your common difference is 12 seconds and you want the time for the first 12 to terms so in other words you want the sum to the first 12 terms so it's 12/ 2 by what it is 2 a 2 by 225 + N - 1 so n -1 11 * 12 so we found the sum of an AP each kilometer is taking him 12 more seconds each kilometer is 12 more seconds so I'm adding 12 to every one time taken to cover the first 12 kilometers you could use the A and L but you had to find the L so best you just putting this whole Jing so simplify this is 6 by two by that is what 2 by that is 450 plus one to the two and there's still going to be some conversion there's a way to convert from seconds to minutes to to um uh minutes and seconds and the C you know I just forget how to do it it's pretty quick as well 34 3492 I Casio here watch it on the physical Casio and I might figure it a little faster it might help you in the future let me see if you could just figure it out not finding it way boy is it this one it's somebody it's some it's some it's some there's a way to there's a way to do it I used to know how to do it I probably do it on a YouTube video already go and find it I forget any this is easy to do we just this is this is the answer we got we want to divide this by 60 and when we divide by 60 you could get it like this and just do 58 point2 so 58 and a fifth so 58 12 there's another way to do a division on the Casio I'm just showing you some quick things that might um help you all in the future let's just go back up you could you could remain The Divide so you could Alpha divide by shs I think up in the wrong number by 60 I think the wrong number is in the answer so what would happen was the was the number that we had from before 34 3492 3492 Alpha this and divide by 60 so it will give you 58 remainder 12 you understand so 58 minutes 12 seconds might help you future um all right I enough for that question the line 7X - 4 y + 25 so the first first Pap go a little slower the second paper go faster and the third paper go fast 7X - 4 y + 25 is = 0 3x - y - 5 isal 0 intersect at the point P um fastest way to do this question might be to substitute substitute five and 10 in and see if it you know now substitute each point in and see if it satisfies each one so if I subtitute five and 10 in here substituting the answer well done SAA I'll get 35 uh minus 40 plus 25 that just makes no sense that does not give me zero you can see that not going to give me zero try negative one so I'll get -7 uh - 32 + 25 still I'm not getting zero here understand this is the fastest way to do it rather than having to solve the simultaneous equation um the student H I think we sold loud to so might have to borrow one for real a lot of math students have the CIO so if you have a math Regin who not doing adms you could probably borrow it and practice it and make sure you're now to reset those of you who going to buy last minute make sure now to reset the c or you switch it to now mode and you don't know what to do press shift and nine and then follow the instructions clear all yes reset everything so yeah practice using it and go with both the calculators just in case you get stuck with the Casio because people I know people can get stuck with it mode when you're going some mode some people don't how to come out the mode so you're in a mode here and you just day and you don't know what to do and you're struggling with your life here well you're supposed to just press mode and press one so practice it make sure you have know understand how the D the ma sometime you lost the the setup which supposed to be on one mat IO let give you this um let give you the setup that I use all right where was I so 97 by9 um them numbers too big Bo 63 uh -32 4 by what I'm putting in32 is that going to work that that something like that two abstract I get have big positive number n n n this a working so the answer be D hopefully so we have 7 by9 is 63 minus 88 cuz that's is four + 25 yes sir there's the one so this is the only one that work with the first equation and I had to work with both equations so the is the answer substitute N9 in here 3 by 9 is 27 - 22 - 5 is also equal to zero so D works for both of them that's the fastest way to do it and I take some time because I was talking to you and but you could very quickly just substitute and go through these kind of questions so yes this is a classic case of using SAA substitute in the answer uh one of the most deceptive things in a multiple choice that some people take for granted is the answer is in front of you you ever sto to think how ridiculous that is the answer is there the answer is in front of you so if the answer is in front of you one out of these four things you I mean the line true points P K2 and Q D D is parallel to the line or the value of K so they asking you to find the gradient in other words uh so if I rearrange this I would be able to pick out the gradient if this is rearranged the understand that the when the 3x comes across it will turn negative so the 21 will switch but we're not really interested in that this is what we're interested in this is the gradient and they said it's parallel so it means -3 must be equal to if we find the gradient of this in other words it must be equal to 8 - 2 over 6 - K which is 6 and if I bring across the 6 minus K to meet the -3 -3 by 6 minus K you understand I equated the gradient y 2us y1 X2 - X1 nobody need to see in multiple choice B all working and right nobody watching there um so what this gives us K to be boy K needs to be something like eight cuz if I oh I did a little bit of CA there guys so I was watching the answers and see which one pluging in here will give me six and if you're good in arithmetic this really helps like I'm throwing the eight here and I see 6 minus 8 is -2 -2 by -3 6 6 eight is the way to go instead of me having to multiply out all of these things I know the answer is in front of me you could always plug in the answer to get it the point 23 is at one end of the dam of the circle whose equation is blah blah blah the coordinates of the other end of the diameter is um what how we do this again by I could I could plug in the answers so what they telling me is I have this I have the center all right I have a few ways to do it I have the plug the answer using the center um and the radius yeah just using the center actually so I know the okay so the tell me this is 2 three but I know the center of the circle is from this what -51 how many of you all understand that 51 so I kind of draw this bad cuz the two Tre should really be here two three so I next side cuz it going backwards so it gone back a good bit and it need to go back even more yall understand how we going to find this you understand if this is two the same distance here must be the same distance here you know to the center so it went from 2 to5 so you need to go back by a seven again so it going to -12 so I sure about -12 and it's three here and it go one so going down two so you need to go down two some more again so you go down to negative one the answer is B yeah the center is hold on did I mess up this oh my gosh I mess up this so bad thanks by um pledge this is why you need to have two ways to get to the answer this is the center 5 negative one so was I was did I draw this three right way then 51 this is 51 I forget to flip the sign earlier forget to switch the sign 23 would be about here so two three so yeah so I need to and it's it's so interesting it's so interesting that they had the wrong answer waiting for me wow that was scary yeah ad on is really repeat so we doing the same thing but we doing it in reverse so it went from two to three so it need to go up another three so it'll go to eight and it went from three all the way to negative one that means it dropped four so you need to drop another four so you go to5 so 85 is the answer wow and the next thing you want to do which would have saved me with the next with the next part of this question is said take this and substitute it back in there so take eight and so make a little so it might take some time to substitute and make sure that it equal to zero so when it's equal to zero you know yeah for sure okay that is indeed a point on the circumference of the circle the vector a is given by that a unit Vector parallel so I want the square root 5^ S 25 um 144 so you want to divide by the magnitude the magnitude is the square root of 169 which is 13 you all understand what I did just just there I got the of X2 + y^2 so and I need to divide by this so This Is The Answer here that one is a given that that that the vector AB so this is AB is equal this is straight up the triangle OB minus O A so this is -7 oh wait 45 45 my bad my bad so this is 45 minus -7 25 so I'm seeing it has to be positive yeah so D is the answer there straight up triangle position vectors the angle so the angle is the dot product so I want O A do o over the magnitude o a and o um and the cost of the angle is equal to that so the angle is equal to the COS inverse of when I dot product this what happens 2x3 is 6 + 5 by -5 so this is 1 1 all over why looking like a is just the answer all right let me double check in case a negative sign or something I pop up um magnitude magnitude is what working out now so this is square < TK of 4 + 25 multiply theare root of 9 + 1 so you understand I squar 1 time you had to square them right the square root of 29 by theare root of 10 which is the same asot of 290 which is a so these questions this is the first time we put on the CIO for a little bit three four questions are no shortcut really to this you have to know the rules surrounding vectors and um um circles and coordinate geometry to do these things properly right if s of theta is equal to 513 so Theta is obtuse so meaning unit circle Theta is on this side this is Theta it's obtuse um but the sign is equal to 5 over 13 so I have this here being five and this here being 13 so opposite this is the alpha opposite over hypotenuse you should you had to no um trigonometry to understand this fully and this is a 52 triangle based off of your Pythagorean triples so then we want to find the tan of theta the tan would be well this is actually negative since it went backwards so the tan of theta is opposite over adjacent so I'm looking at 5 over -12 answer is B so that's the that's the quick way to do this you need to understand your unit circles all right COS of a plus b plus COS of a minus B what we looking at here COS of a plus b is really cos a COS B minus sin a sin B um plus cos a COS B and this correct I think so plus sin a sin 9 B so this gone this gone this and this will merge up so I get two of this I will get d as the answer all right so we start to reach back into a spot where you could actually verify your answer again you could use back your CIO to verify answer in case you forget how to use trigonometric identities you could choose two angles so A and B you could say let a be 10 let B be 20 and you could find the cost of 10 + 20 plus the cost of 10 - 20 figure out what that is and then double check each one of these and see if it works out to give you the same answer you get here understand is a form OFA so um I'll just do the I'll just do the answer so you can see what I mean so like if I have the cost of 10 + 20 is 30 minus H sorry plus the cost of 10 minus 20 so this is the cost of -10 so I get 1.85 1.85 so now I can just do two my cost of what it what it is is 10 10 by cost of 20 1.85 so I know I know my thing working understand I substitute values for A and B some random values that I just picked and it's supposed to work the others will give you one St W answers that is not 1.85 it pays to be able to know how to do those things the graph of y is equal to sin 2x is so sin 2x so this means it's seeing ahead in other words all right if I give you the graph of sin x sinx does this this is 2 pi this is pi um you know what let me show you it on decimals so you can know it once and for all now y equal sin x this is the graph of sinx guys now I want you to pay attention what happens when I do um I wish I could put this in terms of Pi I wish I could turn this in pi but this is pi and this is 2 pi right yall understand they telling me that right so what pays pay attention what will happen if I put the two here notice how it double up so now this is pi and this is 2 pi you get two versions then pay attention what will happen if I put the two here notice how it get bigger now it going up but it keep the same size so that's the two main things to test you at this level at Pat they could go a little they could go a little further you could visualize what will happen if you use a fraction it will go half the it will go half so this is 2 pi so in other words to get the whole thing you had to go quite to four pi seeing it if you understand type I understand so if I put three here you'll expect to get three of them before P reach well yeah one two three before two Pi reach yeah um so if I put the two here double up uh what else boy um oh like if I add one to it it shifts like if I add 60 oh let's let's let's use let's use Pi so if I add pi to it it shifts or let's say I add Pi on two this is what this one really shows up in um in pure mats more than anything but notice how this looks like C this is this is cost 2 pi up there this is cost right is in it so I shift it by adding I shift the phase all right enough talk on that so just make sure match up that question when it come in the exam so 2x are looking for it to double up which is this cuz watch if I continue out with this I'll get two by the time I reach the 2 pi yeah formula sheets the smallest positive angle for sin Theta minus cost Theta to be equal to Z for this is um we could substitute and check we can literally substitute and check by so I could say sign of put this Sol Radian you get say sign of you can substitute in the answer for this one real sick I just taking my little why to type it because I using my mouse Minus cost not most but quite a few questions you could substitute in the answer and you be real happy that you know about a little trip five on six all right this doesn't give me Z so what kind of foolishness is that um let's before here zero pi and four is there anything smaller here than pi and four this is not smaller than pi and four and this is not smaller than p and four so pi and four is the answer all you think about that what your thoughts on that people so is there another way to do this question yeah there's another way to do this question you could Solve IT divide everything by cost so you get tan Theta minus 1 is equal to Z or oh yeah equal to Z So Tan Theta is equal to 1 so Theta is the tan inverse of one and you just find the tan inverse of one quarter Pi a quar Pi Pi and four so you get the answer there as well well maybe it wasn't seeing to do that another way people might approaches is bring across the cost so you get sin Theta equal to cos Theta uh when is sin Theta equal to cos Theta so this is the next thing you just know it's F and four sin Theta is like this cos thet is like this this here is fire un for so there's a graphic approaches substitute the answer approach solve the equation approach ra ways you do this reals 45 pi and 4 is 45° yeah so s of sin Alpha plus 45 is equal to so once again you could substitute for this you could choose our Alpha then so we can choose like Alpha is 30 there and find the sign of 30 + 45 and put in 30 here 30 here see if that works yeah know 30 here 30 here see if see which see if they give you the same answer um I feeling tired so I ain't healing to do that so what's the method they want you to do well they want you to use the compound angle formula here most likely so how this works is that you'll have the sign of Alpha by the COS of 45 plus the COS of alpha by the S of 45 but the thing is the sign and C of 45 is the same thing we just show that actually the question before show that so the cost of 45 is iron radian mode don't mess up your life like that root2 and two root2 and two is the same as 1 over the tk2 please memorize this < tk2 and 2 is the same as 1/ < tk2 cuz if I multiply this by < tk2 < tk2 I will get < tk2 and two so anyhow so yeah so remember this is the same as 1 / < tk2 so I could factorize this out 1/ < tk2 by sin Alpha by plus cos Alpha and L and behold that is the answer there that the answer here a physics physics I'll be doing physics tomorrow starting from 12 you doing a physics crash course free again three things convert 4 pi over 5 radians into degrees well your calcul I could do that um but understand that Pi radians is 180 so it really what ask need to find four fths of 118 and think about it four fths multip by 180 and that the answer 144 and that the only answer here that makes sense anyhow is C be this it be that no way 4 is that so you know the answer the exact value of T 1501 again your calculator just going to give you this you see when these questions are mean people didn't know how to use the calculator now to see YouTube this is negative root3 and three which one you think is is is it negative root and three remember your calculator is um rationalize the denominator so get that root three back in the denominator and you will realize what going on this is the same as negative 1 over3 is the answer so people didn't know how to use the calculator good so it was it was stressing this is like a question that could stress out people but easy thing easy thing so how do you do this question by how we supposed to do this question wa oh yes Father you have a few ways um 150 what is 150 Bo 150 is 30 less so this is really 30 150 is 30 less than um 80 so uh I want to say by so yeah so this is like using the unit circle this is what I expected it to do you know you should know that the sign of 30 what the sign of 30 gives H sorry not sign tan you should know what the tan of 30 is uh once again I don't have this memorized perfectly again I I kind of lost my memory of it but I can work it out um for 30 40 60 90 you should know all the the signs the cosiness and the tan of that but as I said the CIO just have that on have that day it just have that day for you waited ready and ready and waited so the tan of 30 is root 3 and three or 1/ root3 so the T of 30 is supposed to be 1 over root3 so you know that right but the IDE is a c you're supposed to say Well since it's in this quadrant it's negative so I want1 over and that's how you're supposed to do this question understand but once again you you C could just handle that for you just don't forget if you see root three on three that the same as one over root3 if you see root2 on two that's the same as one over Ro tk2 right both of them both of them are the same thing oh wait so they have this you have your identity in the multiple choice but it is a difference of squares identity so when I multiply this by this I get 1us cos 2 x check it out and see and then this will go into this 1 + cos x time so I'll get sin x 1 + cos x and then I'll get the sin x multiplying by 1 - cos x but I know 1 - cos s x is actually sin 2 x since sin s X+ cos s x is 1 so all I have on top now is sin x and then I have sin X cos x but then I have a next sinx and then I have minus sinx cos x so these will cancel and I'll end up with two sinx this is the most popular um one of the sign will cancel so I end up with two over signx this is the most popular identity in CC mats this here is the most popular identity C CC adms most popular you almost guaranteed to do that in one in adance exam then paper two the paper one so Y is = 5 - 2x^ 5 then dydx is what oh the way to differentiate so to differentiate this all right differentiation people so to differentiate this and I'll show you how to do differentiation on your calculator um if you know um if you there's a way to do definite integration and definite differentiation on the so and I'll show you what I mean just now anyhow so to differentiate this you'll have to send this down by one multiply by the differential in the brackets so differentiate inside the brackets five if I differentiate inside the brackets I get -2 right and then also multiply by the original here so you'll get10 by 5 - 2x to the^ 4 so the answer is a um what's the other way to do this the way to do this on your calc actually longer than if you could just differentiate so to differentiate press shift on that you see differentiation here in your calculator you could actually type it in 5 - 2 alpha x and we want everything to the power of five so let me go back and just enclose this in our bracket here so I don't end up in problems so yes so we yeah so we use the chain rule to differentiate this but I use it automatically and X is equal to I just pick a random X let's say x is equal to 1 so it will give me an answer -1 810 and all I need to do is check all of these with one and see if I get Negative 81 0 and only one of them will give me 8810 so that's um definite differentiation where I I pick an X so I differentiate this when X is equal to 1 once again not much people know how to do that so that's the next little trick you got add there tricks b day the gradient at X is this and the curve is that oh oh okay okay okay okay so we want to differentiate so Dy DX is equal to cos x so this is the um differential equation here first differential so this is AK the gradient equation and then I substitute the value of x in this so I really want to find cost of Pi and six make sure my calculator is indeed in radians so you have to change your calculator between radians and degrees a couple times in the exam your first thing in your check over should be did I mess up any degrees or radians stuff shift pi over 6 um P / 6 < tk3 on 2K3 and 2 6 as like 180 ID 6 6 goes into that 30 times that's like 30° ro3 and to the answer wait somebody said the wrong thing did I do the wrong thing differentiate this you get cost p and six is ret to DDD are you get this one wrong yeah D so the equation of a curve is that the gradient function is what once again you can do the definite differentiation style and substitute a number and check the same number in all the answers and see if you get it oh let's plug in next just so so um what's next but we can differentiate this using the product rule so the product rule says udb yeah plus [Music] v DV D DX sorry um so U is this is on little annoy x^2 + 2 dvdx X is 3 i x - 1 and Ne 2 plus since this one an KN using the implicits using the um definite differentiation here might actually be nice know am I do the writing I Want dvdx I Want U dvdx and then I want V um DX so differentiate that I will end up with just 2x this is really X2 + 2 so I just up with 2X and then I need to simplify this so I have -3 here that3 was a little was that supposed to be negative3 no sorry that was supposed to be positive three so when I differentiate this is x - 1 to the^ three so it drops here the three drops there one joins the three and this goes to two so it's just three all right so everything looking like everything there so we just quickly move along this is x -1 2 x -1 Cub from both of them I could take out a x -1 2 and this leaves me back with a x^2 + 2 all multip 3 plus uh I'll have a x - 1 here multiply by a 2X this leaves me to xus 1 to b^ 2 so I'm seeing that it's not going to be that I'll have 3x^2 + 6 this is the longest question we do so far and I have 2x^2 - 2x and I had to go through the whole question to get that it's going to be C so xus 1 to b^ 2 3x2 + 2x2 will be 5 x^2 have the - 2x + 6 that question was the longest question because they forc me to do working they forc me to do it earlier I wasn't too interested in doing this I hate this question what going on there um was there F away boy as I said you could use the differenti on your calculator but you still need to substitute in all these numbers here so it's still kind of annoying anyway you're B to get Anno with that question one way or the other given Y is equal to but not hard just you had to work out some stuff Y is equal to 5 sin 2x then Dy DX [Music] is um so we differentiate this we get cos 2X and then you multiply by the two CU then you differentiate the 2X and you also have the five there was mining human own business so this is 10 cos 2x D all right we keep it pumping every everybody good so far the curve C is given by equation that the second derivative is given by so we want to differentiate this twice differentiating it once yes you can use your calculator in paper one for admx this is really 16 to xus one right so this is negative 16 x - 2 and differentiate this again we get two switch back to positive 32 x - 3 so who gain me this here you you you gain me this so this is 2 + to2 over X the pos2 so there we go um 40 we coming up to the end of the first paper the value of a for which the root how long we like our 9 minut root a0 x^2 - 5 DX 50 over 3 is I mean you could use your calculator for this why are we switching signs uh um because this was this I was differentiating 16 x to the1 when I differentiate this the negative one will come down here and match up my positive sign so I get 16 and this will go down again -2 and when I differentiate it again one more time so this one was this one was Dy DX and this one was D2 ydx I differentiated again the negative sign come back and mash up the dance and turn it back to positive like that but we come at two this time so the value of a um yeah so this one you're definitely going to use the calculator for this one and just do it really quick integrate x² minus 5 and we just going to plug in the answers so this is zero and this one was let's try five five works just so you're plug in the answer for this one right um so what was the way to do this for without your calculator I would take a bit longer so definitely doar a calculator and move on um sure shout outs shout outs get pass here I mean what that shout out shout out Heidi um yeah but so we need to integrate this we get X Cub over 3 - 5x between 0 so 0 and something a so what we really trying to say is when we substitute a into this a cub over 3 - 5 a We supposed to get 50 over 3 and even when you reach here you would still kind of just use some substitutions to help your mats work out faster I mean you could do it another way to factorize the a get the a s yeah just just fast to fastest to integrate this so they just want to integrate this nice so to integrate this what we're going to do this time is ADD so you're going to add to the power so it goes up to five and well you know the thing is go you know the thing is good right so like if if I was differentiating this right if why is that and I differentiating it it would have come down here the four would have come down here five this would have dropped to three and i' still multiply by the differential inside the bracket so to multip by but since I integrating this in coming down here this dividing not multiplying anymore and you're dividing by the new power so it's dividing by the five you all understand so I'm integrating here now I'm going back up and also I need to divide by the differential inside the brackets so I also training the Tre here so the answer for this is 3x - 5 to the^ 5 5 over 15 that's the short way to do it we for get the constant of integration so the answer is c um the region Heidi is starting to over going on ID you could get block and for them kind of behavior what is that the region in the first quadrant includes Y is equal to that some that was your first and final chance right make go some kind of something about yourself so the region in the first quadrant blah blah blah blah blah the volume so we to integrate y s with respect to X and then hit the multiply by pi that's find the volume between the limits Z and two so the it's it's important that we find the really ask this question the next waste of time question Heidi Heidi I done give you a shout out already Heidi what really going on with you heid you make you're causing me to lose my temper than you Heidi come on man I'm not feeling good Heidi I'm not in a Heidi I don't have the patience of this yeah so what we supposed to do is square this between 0 to two and you multiply by pi and um how you sing this way looking like a a nasty question to do boy is rotated yes squaring this looking like no piece so definitely do this one another calculator cuz who going and square that so we integrating and we're going to put the X's here I'm aor cator like oh God give a chance now all these integration calator you will work when I say to work all right so yeah hi see how spoil my calculator alpha x minus Alpha um minus uh sorry we do alpha here we want 1 / 2 and now we want Alpha x² yes so you're suppos to squar is but squ looking like too much work I just put in calculator good luck you could square that up and thing and then hit him a little between 0 and two 0 and two and and then drop a little pie on the outside to make sure you watching the scene a little pie right here shift by bang 415 spy C see is the answer so with your calculator you could do this in like 10 15 seconds but without your calculator you're going another Square I see way see other way you're going have x- a half x² you're going another a square and that is not pretty you're going to end up with you understand got to get the expansion there you get some for powers and all kind of thing yuck why is this question here the region in the first quadrant X enclosed by the thing I sorry for people with no calculator is this just going to waste the time what is there a fast way to do this that I'm missing have a fast way to do this boy there a full paper two for four Max all right whatever yes luk what going on bu long time so the region R is inclosed by the x-axis here so once again calculator this time you don't need to square cuz you're finding area for some reason myor want to move around and as fast as my X is so off bring him back up again resurrector resurrect yeah while you was up exam after exam I need close you off you just up the you probably needed a resurrect so boom so yeah so we want to integrate this Alpha x² + 2 alpha x - one between the lines two and what two and three two and three so this is just a simple integration to the 1 over 3 B yeah so this one is area so this one you just integrate y between the limits so I I just substitute and integrate between this one is volume so if it's volume you have to use this formula you have to integrate between the limits but you need to square the function first then put it in then integrate between the and also multiply by P in the ending mean how you your cator so you watch me put this in my calculator two three times and now still asking me how isting calator you know you can just pull back this thing you know that righto you get Miss some hiy Behavior here so so you just press integration look at right look at so this what integration now it must be um definite you must know the limit to integrated between and then you put Alpha to get the X's alpha x square plus 2 Alpha do it the first time you do it is feel kind of feel kind of feel kind of good but you feel kind of good anday two and three type it in feel the power to the one / two last two questions so we integrating sin x + 2 cos x well integral of sinx is cos x integral of cos x is positive sinx so who gain me this here Bo you you plus C right given that we differentiate this um and we get that oh so they're telling you if I differentiate this it will go to this meaning integrate this you'll get that so therefore but they helping you out here but my calculator don't help me out already I don't need your help brother man 1 x 1 x so if you integrate this what you're basically telling you is putting between 0 and two in X over 1 + x understand and and so you'll end up with something like two over 3us 0 2 2 T yeah actually yeah it was faster to just use the little tip all right and that's the end of that how you feel about them 45 questions next sample paper we'll be going through faster this took us an hour and a half next one we want to try and doing an hour and I feeling kind of sad but I wanted to do three so let me do our next one one time like break canting here so this expression is this is a repeat I'm not doing nobody repeats right um 1 /x + 3 A Sign Express as a single fraction so this is x + 3 by x^2 - 9 for the repeat is still sticking what the answer was um yeah so x^2 - 9 x + 3 this into that is X2 - 9 come up on to here and this into that you get 3 x + 9 a message from the Dark Side there want to factorize something here what kind of wickedness is this so I one time x + 3x+ hold on let make sure do the right thing here x² plus is xus 9 xus 9 was getting a little scary was getting little scary day so right and then this is so I see see a little future here I see future here people so what I saying is that you could factorize out X you get X+ 3 going and cancel out with this x + 3 here so you get X x^2 - 9 so the answer is B you get B yeah sweet given that f ofx is this um then F ofx can be expressed in the form what how they want me to complete this Square oh they take a little while to see that there slowing down so they they want they want me to complete the square so it have a few ways to complete the square whereever flat your boat you could even use your calculator to complete the square take all the two you get x^2 - 2x + 1 half of that square it you get x2 - 2x + 1 - 2 + 1 you're adding 1 you need to take back out that but really subtract so you really need to add back in two so we get in the end you get x minus half of that is 1 2 b² - 2 + 3 so who gave me this u u c is the answer C is the answer so you can complete this Square in your calculator is this is in the form a x + H to b^2 + K the calculator will give you negative this because it will give you um the X coordinate of the minimum or maximum point and it will give you this so um so very quickly you to complete the sare go on mode you go on equation you plug in you press three and you plug in your coefficients it's -2 is the a don't get -2 not one then -4 then one then you press equal give you the minimum value X is negative 1 so I know that this has to be positive one oh shocks we a little pickle here somehow I select the right answer but I had the wrong thing here this should be positive cuz remember I take out the negative to so this is positive positive I'm take the negative to right so positive I got a little double checked here so this is negative one so that means it's positive because remember x equal to minus H now and then this gives me the K value which is true so verified sweet right and they just give me it in a rearrange format here if you understand type I understand so this is that look the way to complete the square here again most completing the square so it's like a party then is a papy show now so we're going to put one day and we're going to put negative six here so anybody else hungry oh God the after exam hunger uh again you again um imaginary numbers here bro for the roots but we don't care about the roots three so I know is I know um this has been negative3 since I get three on the calculator and then K is four okay just read off that value there so H is -3 4 a is a remains one B is the answer you all understand of course I could complete the square the Long Way pull out the the a half of that and square it half of six is 3 -3 2 is 9 so I've created a perfect square of course you could do the formula method if you know only know how to do the formula method then you get half of that so that's three again put that square there but I added in nine so I need to take out nine um if I take out nine I will end up with just four here so that's the answer boom B so let me keep it pumping number five quadratic equation is such that the sum of its roots is oh by the way oh yeah I did mention this already this is the number to WhatsApp for the student Hub if youall want the best you could get in online lessons pure maths ad maths physics wherever it is you're going do your WhatsApp that number and organize yourself for the next cycle um you have find out the secrets long time and you had the right calculator long time the quadratic equation is such that the sum of it Roots is this and the product of it Roots is that the quadratic equation is well the sum of the roots had to go here so let me reconstruct this now this is x s sum of the roots will go here but you'll switch the sign 2/3 x and the product of the roots will you go here but you keep the sign and you notice how we have three and four here we going to multiply by the LCM of the denominators we're going to multiply by 12 I say hungry and a loss and see anybody hungry and 20 people in the live live one time any so 12 x you go to E 12 by this the three will cancel you end up with four so you end up with 8 X 12 by this the four will cancel end up with three so you end up with 39 So This Is The Answer here which is this one is this one yeah this is sum and product of roots this is the alpha beta thing you have to know the theory to understand I just do here the sum of the roots is equal to negative B or minus b and a then and the product of the roots is equal to C or C and A then if a is the one you know and this is ADM the set of values of X for which 3x + 2 is greater than x - 2 did I do this already bring this across get 3x - x bring this across you get -2 - 2 so you get -4 3x - x is 2X x is greater than -2 we didn't switch any law so we just keep it like this we didn't mess up anything so you don't need to switch anything h no you cannot spam the values of X for which 3x - 2 2x + 1 so if I multiply this by If I multiply the whole inequality by 2x + 1 to b ^ 2 I will get 2x + 1 by 3x - 2 is less than or equal to Z you'll notice I pick up the piece right so you'll get either 2x + 1 is equal to 0 the root of 3x - 2 is equal to Z so X going to be equal to a half or X is going to be equal to 2/3 so that's the two points of interest for us um this is clearly a minimum point because the a is positive X by 3x 6 X2 so I'm going to put my negative a half here and my 2/3 here and then I'm going to examine this I want it less than zero so I want the sangu situation I want it between negative a half and 2/3 half and 2 brother this man didn't just type AFK all right Heidi enjoy that food away from gboard oh gosh by Heidi Bo oh gosh Heidi this is not League of Legends oh you get mistake on IDI I thought you was on Twitch for a second Heidi how much accounts you really have boy he all the accounts X pronounces pronounce and the2 9x Cu uh what we looking for this is f ofx then what in the world is going on here oh H well it is an interesting one this is a polom and these kind of polom is do this and they were the range of values between -3 and three well let me try something here because sometimes you could be wrong in it now sometimes you think you get and you did not get the range okay fine let me substitute -3 into this and see what happen if I substitute -3 into this- 2 9 by -3 to the power of three you get C bless -3 right at is -27 bang bang and nine I'm going into that three times so we ending up with here positive six a positive six right boom okay then three going into this what we going to end up with we going with positive 27 2 9ths 9 going into that three times and end up with a -6 so the range is I could go down to6 and come up to posi 6 you use now I'm put this in in um and let me show you the danger I was talking about with this kind of graph minus 2 9s X Cube oh oh I don't have a don't have a X squ or anything so you're safe you're safe you're safe right right right right right um right we safe we safe we safe so the one between -3 so we seeing here that negative3 goes up all the way to six and um positive3 will go down toga -6 so that that the full range of values from that to that from here to there that we'll see so yeah we we we good to go we good to go the the problem I saying is like some of these graphs if you have like plus x s like if you try to take a range between like let me say one and four or one and this number here you might think you get through when you say the ranges from here to there but lo and behold in between that went up and come down and it could do all kind of things in between the numbers sometimes but since there was no X squ term there was just this x Cube you safe yes safe safe out here function the value of F inverse of one substitute the one to be equal to this to solve this kind of question um so x + 1 is equal to 1 x is equal to Z is the answer is the answer here if I put zero in this I will get one nine functions blah blah blah didn't we just do something similar to this this is f ofx no this is G x g f ofx take F ofx and put it in G of X so I'll have 4 + 3 / 2x - 5 could make everybody come over the 2x - 5 so this is 4X 2x - 5 + 3 so this is 8 x - 20 + 3 over 2x - 5 20 + 3 will give me that so I'll end up with this x cannot be equal to 5 or two I'll end up divide them by zero which one of these graph you pick a function this is a function passes the vertical line test this is not a function it doesn't pass the vertical line test does not pass the vertical line test this is a vertical line so it does not pass the vertical line test it have um there'll be more than one point that will cut this has infinite points along this line so no so a is the function the expression when simplified is this a repeat was it was it B this is a repeat so I'm not doing this one repeat those of you who just jump in I could go back and check that this is also I repeat was this 96 Pete which of the following mathematical statements are true um just now this could be a little confusing no this not true you're supposed to add so this is not true if you divide you subtract same base so this one is true um if you have the power you could bring it down so the B could come down so this is true so two and three two and three C is true that's pure Theory this is a repeat again was it a quarter this was I repeat so this is three in a kind of way 3 by 3^ 3 2x = 9x no this is not a repeat we didn't do this yet well it is a repeated question but we didn't do it yet um what I trying to say with this question Bo what is I trying to really do on this question I'm trying to form a little I could subtitute aners I'm trying to form a little kind of hidden quadratic something something here cuz this is really also three squar so I have the 2 x there have the three right the 2x here all to the power of three 3 so I can let equal y wait I thinking this question I shut I shut I could solve it that way too but I feel like there's a faster way um I could like a same situation working out here a same situation and equ think question look quadratic and kind of so what I could do is like do 3 by 3 to the power of three 3 to^ 3 is 27 right and you notice how that TR up in multiple choice 3^ 2 x bring up that three so I get three three by that is 6X and the three come up there too so I have 6X by a next three which is like how how much of X that is this is 3^ 2x so um 3x 6 is just now take let going take my time with that I 18 also this working out nice and getting scary things happening here 3 6 3 3 Q 2x 3x 2x is 6X bring up the three 3 by whatever yes so yeah so at the end of the day 6X by3 which is 18x is = to 2X so I figured how to do math so um want to see 9x is equal to x n what is happening so this is 3 to the^ one multip by three oh shocks I think in logs all you was doing shipping this three I apologize for shutting down there this is three two x I was doing logs and bringing up the power I was doing logs and bringing up the power so so this is 36x 3 to^ 1 is equal to 3 2x right so this is 36x Plus one multiplying so add so why I was doing as in log mod short in bringing up this so my bad my bad and is equal to 3 to^ 2x so 6 x + 1 is = to 2x um nice this is it 4X = to 1-1 X = to A4 that's the answer there now you can always substitute in the answer you could do a CA for this so you could put in negative one here hold on make sure I do this correct 6X + 1 is 2x bring across the 2x you get 4X bring across the one you get negative I get negative I I negative well again anyhow so we could we could do the so let me show you so like we could say three times 3 * 207 to the power of 2 * and we get a quart qu so that is really a half right 1 over a half let's put that negative that whatever that is and then we want 9 0.577 9 to the power of and since it work out to be the same thing we know we dealing with the correct answer is so the sum of the first n terms in a GP is given by that for the series the common ratio all let me see if I can catch back myself here because that's kind of you know much times I do this question in life like May 400 times for some reason I was thinking l so so the sum of the first nend terms of a geometric series is SN 400 times like about 10 times or so SN is equal to that for this series the common ratio is1 okay so let me substitute now S1 is = to 4^ 1 minus 1 so that's three S2 is = to 4^ 2 - 1 so that is 15 S3 is = 4^ 3 minus 1 so that is whatever that is 60 60 something 63 maybe maybe I I I don't know I don't really care so 315 common ratio is netive one so the common ratio the sum of the first n terms of a geometric series is that okay let me just double check this again so this is the sum sum so sum so it's summations right so this is the Ser the the sequence would be three then 12 then 15 - 3 is 12 63 somebody asking doing no no no I'm finding the um okay so S1 will be 4 to^ 1 minus one so three so the first term is three the second term the summation is 4^ 2 minus 1 so this is 16 - 1 is 15 but if I subtract the term will be 15 - 3 is 12 and the next one one is [Music] um 63 but 63 minus 15 is 48 but I don't want 63 - 15 I want 63 - 15 + 3 so I wondering if they make an error in the question well oh that man in the future that man that man in the past um when you see this Mao refresh your stream right now you're watching old things refresh your stream come up to me now going on you understand I now see your comments popping up here so um yeah so I saying by the common ratio is not negative one so something wrong with this question I think they want you to think is this but I think they forget to minus three this should be correct so three should be correct s2n is two 4 nus One um if I put 2 N here I get four squ I could rearrange this I could put two squ yeah so this is correct this works I can rearrange this if I substitute 2 N here this is the same as 4 to^ 2N is the same as 2 to the^ 4N that's fine so this works I think they wanted you to pick two and three but the the problem is there's a there's a error with this this part here there's a error with that part so it have an error in this question error in question the only one that works is actually three but they want you to pick two and three but there unless I seen something 35 63 63 minus 15 is 48 but it's supposed to be 63 - 15 + 3 and or is it 62 minus 15 sum of this is the sum of the first term Su of the first oh yes this is the sum of the first two terms I I thinking it this is the sum of the first two terms so subtract yeah so the answer is C answer is C answer is C so this is this is um cumulative so this is first term this is this is term one this is term one + two included in the 15 here already yes yes yes yes yes so subtract okay wow so once again this is sum of 3 K is equal to oh K is equal to one I was not understanding How It Was Written here one over K right so you could work this out so you can get 1 over 1 + 1 over 2 + 1 over 3 and they solve that really fast you could also put it in your calculator so I know it's going to be number bigger than one so it most likely is D CU I have one and then I have add a half and a third so a half and a third is what 5 six 56 and 66 so 116 the common ratio of the geometric Series so I want 12 divided by 8 and then 18 divided by 12 should give the same thing four into this three four into this two 3 over two D is the answer we starting to speed back up the sum while we do this already is 600 the coordinates of the center of a circle so the radius is six the center will have to be 1 and -3 C wow they some speed questions here boy points of intersection of the line here and the circle there all right so we want to substitute points with the maybe the line not the circle because three and one squared will always be 10 so we want to use the line to see which one will work out three so we're going to see this question 3 - 1 - 2 3 - 1 2 - 2 is 0 this works a -1 - 3 minus n this this not working this not working all right so we know this one working three and one working three -1 - 2 that so don't TR that one that one we why why they want me to tr that one all right let me try this 3 And1 minus1 minus 2 this don't work this starting to look a little scary boy answer is D [Music] um three all right this is one and3 all right yeah let do all right so this works so the answer is D let's try this last one negative 1 - -3 - 2 yesal Z so this works this is a popular question yeah yeah um H2 thanks I switched up the X and the Y it's supposed to be y supposed to be X and Y here so this one don't work either so all of these don't work the D works so D is the answer the line Y is equal to this and the line that intersect at the point so once again just double check the and see which one works 4 by make sure any writing so 8 minus yes so this one is working with that but let's see if it works here 4 + 3 by one this one works a Works 8 [Music] 26 8 to 16 this one doesn't work 10 this doesn't work zero this one works here but does it work here zero plus no it doesn't work there it this one works in the first one but not the second one so the answer is a so SAA really working out really strong for these kind of questions with the intersection point of intersection point of intersection it just working out real fast rather than having to solve the simultaneous equation vectors I and G represent 1 kilometer East and North respectively so that is I that is j a man SS a boat such that is minus I there's a current of 3i so I need to add 3i to this so it's 2 I + 2J easy things easy things well I do a Math's paper one yesterday and I'll do our next one I ain't settled the DAT night I doing a physics tomorrow from 12: I a sett the date on the mats yet I didn't do it either Monday or Tuesday after Wednesday I may not be able to do anything except comment two vectors are equal if the same magnitude same direction nice nice is that any errors in the bio paper the position vector of two points A and B relative to origin o boom and bang the modulus of ab and the angle AB makes with the x axis respectively somebody keep I know some people keep saying that had a error in the bio question find the answer to this let me just check check up on something here e I a see nobody talking too much about the errors yesterday we talk about so the modulus of a and the angle two position vectors so we need to find AB we need to find AB there's no doubt about it so AB is OB minus o you find this one out yet minus O A so this is 85 - 3 0 so this is 5 five so that angle of 45° and the modulus of that would be the square root of 5 squ 5qu square root of 25 + 25 50 so C is the answer if it's 55 that mean it going up like this with angle of 45 degrees trigonometric expression sinx we do this already what turn out to be now we do one similar to this you're going to end up with 1 minus cos squ x here tell is the most popular and no we do this D we get D I think we get D the sinx them cancel out we get as I repeat the figure m n below shows the quarter Circle the perimeter radius is four four so we to add eight and we to add this here um the perimeter of a circle they're using they look like they're using normal things so the perimeter of a circle is you could use a couple ideas to find the the AR length here but this is p on two and it's r Theta right so R is four by pi and two 2 two so you get 2 pi so this is 2 pi in terms of its length so this is 2 pi plus the 8 or 2 into Pi + 4 could work as well so the answer is D this is the AR length so 2 pi and add 44 um repeat so this will double up or they bring it a different way but you see it doubles up like this I went show you this this most remember I show you the graph smallest positive angle in radians whichin the range blah blah blah to satisfy this oh this one a little different once again you could see this question I'm man you can p multiple choice um you could see this you could substitute the answers and see which one work um what they were to do here excuse me so I don't think they were to expand this back out because then you factorize again so it's either cos Theta is equal to positive a half or cos Theta is equal to two so this one is invalid anyway CU When I equ to zero now I remember solving these trigonometric equations what happens iner to so want the C inverse of a half and whatever that is yeah is my answer P Tre P Tre P Tre is the smallest M anyhow I can double check if p and three would work in this by substituting it back the exact value of well you could put on your calculator to be honest C of five and I show you all how to do the long way already five Pi on 12 make sure I calculator in radians isun 6us < tk2 a qu of it B um in radians so one 60 so this is what 20° so this is 20 over 180 by pi so this is 1 9 pi pi over 9 so B um if sin x is equal to S then cos 2x so this is a very interesting question so you could do this question uh using a triangle idea watch so you could call this x mature and I might have to make a little move s so s call this one you understand like this is s over one the hypotenuse is one so sin x is s over one so this here my boy over here is really what he is really 90 - x right agre or or instead we canot that um uh could work out what this guy is here so this is remember one squ has to be equal to s² plus whatever that is squ they call it X so X is really 1 - s s so this is really 1 - s s via Pythagoras theem everybody following so far I going a little fast I use Pythagoras ter to find the adjacent why I doing that because cos 2x is really um have a couple ways to find COS 2x what is the double angle formula so we have sin 2x we have cos 2x I could even use the sorry for the there um Let me show this now where I could put this so I could I can use anyone so cos 2x is really cos x sin x or 1 - 2 sin x my goodness I could have use 1 - 2 sin s x I didn't need to go go through a last stress so cos 2x is 1 - 2 sin 2 x so cos 2x is 1 - 2 sin 2 x so I could just say 1 - 2 and sin x is s so this is s s so I could just jump down to C real fast um I could use the other stuff as well with this one minus s s here and work out this this real neat but this question is a cool question you could do a lot of proofs using this idea all right let me keep pumping s Alpha did I do this on already Al - 45 I think I did you know think I did me um oh this one is minus this one is plus so in this one we got positive so this one is minus so what we do with this we get S Alpha cos 45 minus cos Alpha sin 45 but the same thing the sign and COS of 45 is the same guy this one so this time you'll use the minor sign so it still look out to be a all right keep it pumping if f ofx is equal to sin 3x minus cos x then so we want to we want to differentiate twice reach into the differentiation style so differentiating this we will get so we'll get for first derivative we'll you get cos 3x and then we need to multiply by the 3 minus 4 um uh it will change the positive because it switches the sign when you're differentiating C 4X right so it switches the sign like that and when you go down the sign will switch again this will be -9 cos 3x this one will remain so you'll get 4 by 4 is 16 and it goes to cos 4X so we need to fin this which is not here wait did it did I switch I didn't switch I didn't switch I didn't switch it to sign I didn't switch it to sign I didn't switch it to sign did I say sign on right C remember I had to switch right so is D all right so 36 the curve C has equation f of x c has a station Point minus this is how I end up on memes and Tik Tok and oh go oh go minus 2 5 if the F Prime X is equal to this then okay I I don't know what I do I need to read this over the curve C has this um has a stationary point at -25 oh so they give you the second derivative and they give you the point so you're to substitute to find the nature of the type of point so when I substitute X is -2 I get -2 to the^ 4 - 16 negative - 15 sorry so this is 16 - 15 so this is positive and since it's positive we can expect a minimum point so C why say d -2 going in here you get 16 minus 15 if it's positive you a minimum if it's negative it's a maximum so C are get c c is the answer verify so we want to differentiate this this is a quotient so U is 2x - 1 V is 5 - x and if I differentiate this DX I will get two DV DX I will get1 so what I want to do that's not seen if there's a faster way all right so v^2 VD DX minus U dvdx I just want to substitute and hope for the best here okay all right so I end up at 5 - x d DX is 2 minus U my dvdx is-1 so -1 by dvdx by U is 2x - 1/ V ^ 2 5 - x to v^ 2 this will simplify to give me 10us x + um 2x - 1 I see a kind of 9 situation Happening Here positive 9 and oh did I leave out a two here positive 9 and the X's cancel positive 9 and the x is cancel the answer is e so I'll end up with 9 9 over 5 - x to b^ 2 so real signs you real watch these signs when you're doing this question and if you could come back and double check it using the method that I show you this is the method where you put shift differentiate and you put in the whole thing and you just substitute that value for for um X now minus one and then you put five minus X and let X be like X is three or something or two let say two so we get one so now you want to substitute two into this and make sure you get one so you get 9 5 - 2 to b^ 2 is indeed 1 9 over 9 is one one so it works out so you know that that way sh and in case you make a mistake with the sign you'll be like oh shs it working out so you know to go back and check and you might realize you leave out a negative sign or some kind of you point P11 on the curve blah blah blah the the value of the gradient there you use this the value of the gradient right so this is a case where you could use direct you could directly use this because you see you know what x is X is one and you have the Y so instead of having to differentiate a whole quotient rule again you could do this you could watch it again doing this from the start shift that fraction Tre Alpha is how you get to the x - 2 all over 2 alpha x - 1 put X is equal to one press equal and you get the answer one the gradient is one good stuff right and I can differentiate it and do do the long way to find out for sure given Y is equal to 2x^2 + 3 sinx then Dy DX is what so we going to differentiate this so you get 4X plus 3 cosx sign those switch for this one so they real testing on Trigon trigonometry um there are some questions here that I didn't do and I'll try to do some maybe maybe if I I'll try to squeeze in one more admat session where I'll do like some of the new style of questions that they bringing in the multiple choice they're bringing some kinematics questions now um I'll try to do like a couple of them but other than that we a lot of questions today um integrate this and we got six so if you integrate this and you multiply by four and add five well that's literally multiplying it by four and then add five outside of that so you multiply this by four 6 4 are 24 + 5 is so the answer is 29 so this just testing to see if you understand how integration works the region enclosed by the x-axis the curve blah blah blah is this a repeat I think it's a repeat but let's just do it nevertheless so this is integrating [Music] between I'm going to put negative use this sign for negative don't use the minus here always use this for negative squar + 2 um 0 2 one uh 5 over3 b is the answer keep it pumping I think this is a repeat as well so this goes up to four you divide by the four but also 4 by two is 8 plus K you also need to divide by the differential of what's in the brackets so this answer is B and for the tree is the region bounded by the curve Y is equal to 2 sin x the xaxis and the lines X is equal to 0 and x equal to Pi is revolved about the x-axis to form a solid of resolution the volume so we need to square this so that'll be 4 sin 2 x cu the two will Square as well we'll integrate this between the zero and the pi and we'll also multiply by pi so who is giving me that you are so that question didn't ask you to work out anything just see if you know the format not this one cuz we need to square it as well hold up Am I Wrong 4 sin 2 x no look the part two here and four there this wrong this wrong see no this is wrong as well you understand why I get this right I Square this so when I Square this this is 2 sinx by 2 sin x which is 4 sin 2 x I need to integrate this between the zero and the pi and then I need to multiply by pi so if there anything I could get four pi 0 Pi sin 2 x but that not here so is either this or this so the answer is a If This Then integrate that we so they want us to integrate so we're going to get 3x^ of 3 and divide by 3 now plus integrate cos x you get sin x 3 will cancel so it's xb+ sin x + C right so that's B so really easy questions coming down here bu the integral of cos x - 2 sin x so integrating cos x you get sin x again integrating sin x you get ne the sign will switch so this will switch to cos x so you get sin x + 2 cos x plus C D so how you feeling we know how much people here in the admat session you know admat is kind of Li amount of people are you ready to go on Sample three or you good day hit them next one we have been going for like about 2 and a half hours 2 hours 20 minutes good day go and practice the Rest by yourself go back to number 42 so yeah you get to see all the calculator tricks 2x - 4 to the so add one divide so if there's anything feeling to take a break I feeling tired I feel your answer is D for this one let me just double check oh eight sorry about that sorry about that sorry about that um can get the documents search online bro now I can't tell you more than search online see if you can find it on see you know IX on my back now so what else boy um yeah so I could probably come back in another time so tomorrow I coming in to hit them some Physics tomorrow I'll be coming in from 12: p.m. from mday we're going to do some Physics I want to probably do maths I will probably do mats on Sunday maybe mats a long session of mats maybe I might start like around 300 p.m. or something um your calculator supposed to be safe so they not supposed to play mad and take away a calculator they do that in a couple schools um and then maybe on Tuesday Monday or Tuesday I could swing back I want to do some chem I want to do some Physics again I want to do some maths ad mats again and some more mats so everything has to happen before Wednesday so so Monday Tuesday I coming back in with two more sessions so we get side um all right people love and blessings so I see tomorrow we can pick back up with some more physics if I get some energy I don't know if I come back into night self with some stuff what we can see love and blessings so we have sample three to go all right good