what maths today I'm going to go through exam technique with you with a new paper for you National five maths essential skills 2024 this is paper one I'll do paper two later today and this is cut of Mr Ry so the whole point of this video is I'm going to try and do it as live as I possibly can so really not much editing not editing out all the mistakes that I make or not EDI all the pauses and try to do it like fresh without me sting looking at Solutions or anything like that to get an idea of how I would do an exam and hopeful that will help you for tomorrow so I see that this is 40 marks it's a about an hour and I've not to use a calculator and the first thing I check is the formula sheet and just get myself familiar with this is the quadratic one if it mentions roots or finding the roots I use that and notice also the BET under the square root signs called the discriminant which can help me as well and then I've got my sign and cosine rule for angles are sides and triangles area of a triangle all my volume ones I always take a not of them and especially the fact that if you've got a f here in front of a cone if I get rid of that F I get a cylinder H and then the last one standard deviation you've got this one and this one and I always use the top one so I just kind of know the bottom one let's start so when I'm starting I kind of go through the paper scroll through it or you know you would kind of open the paper up and just kind of have a look to see what's in it how I feel about it and feel I can start it when I'm ready and I always think to myself look good Ru I'm if I can work it a bit a marker a minute that seems reasonable doesn't it a mark a minute for a question obviously a little bit over a minute you get but it's a good rir if you're taking too long the question you can't want to move on okay just checking what's St recording because something does messes me up so two and a fifth * 1 and a 7th so I know I need to do times so I'll change it to fractions 2 f is 10 and 1 is 11 over 5 1 * 8 is 8 + 7 is 15 over 5 and I remember that I've made made a mistake already of course it's not five it's eight I don't know why I wrote five but I know it's eight and that's where you would double check 2 5 is 10 + 1 is 11 over 5 1 * 8 is 8 + 7 is 15 over 8 right that's fine I'm good now I can times that directly or I remember that you can actually just simplify by dividing the top and bottom by any the same number any two numbers would work only works for times doesn't work for add so dividing by five I get three and dividing by five I get one just make sure I'm happy with that yep 11 * 3 is 33 and 1 * 8 is 8 now I might not be sure if that's simplified or not so I could just do 8 and 33 is 4 with one left over 4 an eight is definitely simplified so I'm done there if I check the official answer yep 33 over8 so I'm happy find the equation of the line shown below we let me just copy this onto our new page so that we've got plenty of space to work on this you obvious have lots of space in your answer book but I don't so I've got an iPad so there we are equation of a straight line so if you're working on equation 3 n i remember that we need two things a gradient so I'll immediately try and remember that formula and write it down so it's setting there for me and then I use the y - B = MX - A some people might use y = mx plus C so then I start I want my gradient so I need an X1 and a y1 and an X2 and a Y2 so I'll put that's the ones I'm going to use just to help me 6-- 3 now make sure you check your minuses here 6 minus in the formula then minus 3 good 1 minus and then minus 2 in the sum good so 6 - - 3 is 9 1 - - 2 is 3 9 / 3 is 3 quite happy with that so then I Need A or B so I'll just pick a and b I'll use the positive numbers cuz I think they're easy to work with Y minus b y - 6 = 3 x - a - 1 good y - 6 = 3x quite happy with that - 3 quite happy with that plus 6 to both sides so y = 3x 6 - 3 is 3 so + 3 double check I'm happy with everything I've done and I feel like I am so we'll move on change the subject over formula D = 4 P2 over 5 to P so I need to change it to p and that's sitting on the top of a fraction so the first thing I can do I think is times so that gives me 5D = 4 p^2 thinking about like that that's over one if you want to think of fractions we need divide by 4 cuz it's p^ s I'll need to get to oops I've written 4D see how easy it is to make mistakes I do that over time by the way so you'll be seeing all the mistakes that I normally make 4 d 5D over 4 = p^2 so then square root so P = Square < TK 5D / 4 you probably fine with that answer but I can see that four can be square rooted so I would maybe then go P = otk 5D over the 4 is 2 I've got a feeling you would get the mark stopping here but if you go too far most of the time even if you make a mistake after you've got the right answer you won't get penalized so feel free to go too far but just watch out yeah we would have stopped at that point the diagram shows a circle Center zero um it gives me lots of information I hate these questions but I'll look to see if information's in the diagram that one's there yep that one's there yep and I see a tangent I have to find this Angle now I don't know how to get to that angle and you probably don't either but I do know some rules tangent and a radius me at 90 I know that if I've got a diameter making a triangle I get 90 and I know that if I've got iSeries in other words I remember it's two radius make this I get iSeries so let's I we usually go through my list I look for tangents first cuz they're outside this the thing the circle so I've got a tangent here meeting a radius make sure you pick the radius so I've got my 90° either side now I put that in because I'm using pen there's my 90° there so I can do 90 - 58 68 78 88 makes 32 put it in there and 90 minus 34 well that is 44 54 64 74 84 56 so I can put 56 h here because we make 0 might not need that one but it doesn't matter but I've used that rule diameter triangle 90° so let's see if I've got a diameter and does it make a triangle yes at the circumference as long as it's at the circumference that's 90 it does the same that side so I can just shove 90 in these places and go thank you two radiuses making a triangle well I've got two radiuses side side but we don't make a triangle anywhere so that's not really doing anything what I mean by that is it should be something like this making a triangle and that would beos well that's not part of this so I'm just not using that so it's fine now angles on a triangle up to 180 so I've got two sides of this I can see that joins there should be a line there 90 + 34 so let's just write that 90 + 34 is 124 so I can do 180- 124 which is 56 so I get 56 down here doing the same on the other side 90 + 32 is 122 so I can do 180 minus 122 which is 32 42 52 62 72 58 i' got 58 down there so I've now got two angles that make this little shape 56 + 58 well that's 58 108 114° double lines make sure I'm quite happy that I've done my sums right no silly mistakes if I do scroll it out and do it again make sure if you do make a mistake and you don't want it marked you don't leave it there CU they'll Mark both I me it'll give you sometimes the lowest Mark of two so score out what you don't want to be marked if you go have to go to this end of exam paper because you gone into space just make sure see end of the exam paper scroll it out and just do it again at the end question five the graph of a function of the form y was ax2 + BX plus C right the vales of B2 - 4 a c well that's called a discriminant b^2 - 4 a c can be either greater than zero for two I'm not going to write it two re and distinct Roots it can be equal to Z for two real and equal roots or one real in equal root and less than zero for no real Roots now I would don't think you'll get asked it in this way to be honest with you usually you're asked you're given the numbers a b and c like 3x2 + 4x + 5 and they ask for the nature of the roots and you just sub b^ s minus 4 a c and if you get a positive number you say two re and distinct Roots if you get a number equal to zero you say two real and equal roots and if you get a negative number you see no real roots but in this case you have to identify that where our rout is where it cuts the x-axis it's only cutting it in one place where the turning point is so one place means it's equal to zero because there's only one roote or two and equal Roots which is the same as one roote question six part of a graph of y = a sin BX is shown Bel all find the values of A and B have a good look at this first and see what the numbers go up to so I can see it goes 2 minus two exactly the same that's a high and low point so that's my a I'm happy with that and immediately I think to myself for B it's two but they probably try to trick me so I make sure I count one wave two wave oh but stopped at 180 so there'll be another one two so it's actually Four tricky tricky B = 4 and we're done there question seven the monthly energy B for average two bedroom house Dro by 20% to 176 what was a monthly bill before the drop see a lot of people think we do 20% 176 but it's not that at all it's dropped by 20% so that means that 80% equals 176 and it's a reverse percentage question now if this was a calculator paper at this stage I divide by 0.8 and just get my answer but I'm on a own calculator so I Som need to get up to 10 100% good R from is if if if you can get down to 10% then you can go back up to 100 so divide by eight I think I could divide that by eight 176 8 1's are 8 8 2's are 16 and 8 2's are 16 22 yeah I'm quite happy with that so 10% 22 so 100% which means I'm going to divide by times by 10 10 * 100 must be 220 now a question I guess I will double check my answer so I've done 8 into 17 8 1's are 82 is are 16 plus 1 is 17 so carry 1 8 2 is 16 22 220 yeah I'm happy with that let's you're Mark by way you get Mark just for writing that down so it's worth reverse percentages if there's no time it's usual reverse percentage question eight the diagram D in the diagram dcde represent vectors M and N AB = 2dc deal EB find DB in terms of M and N quite tricky sometimes these questions uh try and put in much information as you can let's use this statement AB is 2dc there's DC there so that's two of that so let me just write that on the diagram don't be scared to write on the diagram fine that paper it says de equals EB where's de you don't need to write that because you don't know what that is but you can see there it go there's little dashes there so I've go go DB so I need to go from here to here but I don't know how it go that way so you just go the gr that you can use the letters on so I can go this way and this way and + 2 m that looks good to me happy with that and express be in terms of M and N well I need to go from B to e but I can't I already know how it go from D to B I go this way which is the same if I've went that way it's the same as going that way so that's that Vector there so I know that D to b equals MN so I could actually since I want to go backwards b to D it would be the reverse of that so Min - n - 2 m but it's a half cuz I'm going to go half away so that's how I'm thinking of that so b equals a half of - n - 2 N you can expand that or not but I won't expand itus a half n minus I think you should expand it a half of two is 1 so minus M and we're done there yeah stop the video there just to start it again because if I something gets too big or it messes up I always check this is still recording sometimes because if I don't check that then what happens is it's actually I'm sitting here talking to myself you you wouldn't believe how many times I've done questions I'm sitting here talking to myself it's crazy so here we go let's start this one simplifying 2D remain is two c okay a lot of people make mistakes of me so I'm going to make sure I try not to um I've got a rule which is power power means times the power so starting with a d - 2 * 3 is - 6 that's good now a lot of people just like two here but actually if it's in the bracket it that's to be cubed as well so I need to do 2 cubed 2 2 is 4 * 2 is 8 so 8 D six and read the question I'm not finished it says positive power so the other rule is a negative power can be a positive power by making a fraction and the thing with a negative power goes underneath it just turns positive but I've still got the eight hanging around so the eight still sitting at the top because that's not moved I think I'm happy with that I think that' be three marks in the real exam as well question 10 the diagram shows triangle STV St is 12 SV is 14 sin s is 3/4 find the area I'm see area I'm checking my examp paper it's probably area of a triangle so back up I go and copy it area of a triangle is a half AB sign C so I check that and I immediately going and write it down so I don't forget it so you need to understand this formula but basically A and B have to be either side of an angle you know so usually you would know this angle but you don't go on calculator but what you do know is the whole of s s that's just sin C so that means that that is the three quarters if it was a calculator paper it would say something like s is 60 and you like sin 60 but it's not sin 3/4 CU you can't do that you not got a calculator so it's just 34s so I've a half * a let's just call that A and B uh 12 * 14 * 34 now you can do this in any order you want but a simp handy way to do this if if a half goes into 12 half 12 6 I'll just take that to 6 * 14 * 3/4 now none of these numbers four goes into but that's okay I can do six I'll just divide 14 by 4 the side 4 8 12 2 left over so 0 carry 2 4 5 is 20 so that's 3.5 and then I can do 3.5 I've divided by 4 so I'm going to times that by three so that's 33 are 9 No 3 f is 15 33 are 9 + 1 is 10 that's 10.5 so 6 * 10.5 6 10 are 60 we start it we actually 6 f is 30 six nothings is nothing so put a three 6 1's is 6 63.0 or 63 and my units centim squared pretty sure I'm quite happy with that yep let's move on question bear on the background question 11 a function f of x is the find is FX = 7X - 2 find F of -1 so here we go f of -1 if it's in the brackets it means I'm substituting so 7 * -1 -2 that's - 7 - 2 I think I'm happy that's - 9 so let's move on F of P = -3 so if it says equals I'm now making the whole thing equal but it's not X it's p so I just change it to p no big deal add two to both sides watching out -3 + 2 is -28 divide by 7 I'll WR that there 74 is 28 and it's just one minus so it's minus 4 I think I'm happy with that question 12 solve an equation x + 4 3 is less than or = 2x - 5 / 2 so I'll put these in brackets I think and since it's like an equals here I can just do top times bottom so 2x + 4 same sign top * bottom 3 2x - 5 so I expand my brackets that's 2x 2 fours is 8 3 2s is 6 x 3 5's is 15 I like to keep my X is positive especially when equalities so I'll move the 2x over so that's positive so it becomes negative on the other side so Min - 2x that's 4x - 15 move the 15 then so I'm going to add 15 so I get 15 23 on this side is less than equal to 4X divide by four I can but I can leave it as a fraction is less than equal to X just is can I simplify that nope no numbers going to 4 and 23 you can leave it like that or you can change it but wouldn't to the other side and it would be greater than or equal to you flap it now if you made your x negative as well if you kept it on the left all the way through You' be divided by negative at the end which means you would have to flip it as well if you divide by negative you C just check that 23 four yep okay question 13 bubble tea is sold in small and large cups they are similar the large cup has a volum of 540 let's just take a note of that and has a height of 12 let's just put that there and the small one has 160 and we to find uh height well we're starting with volume so if you're starting with you've got two things of the same volume and volume so that gives you a volume scale factor if you've got area and area gives you area got length and length it gives you a length so I can only get the volume scale factor vsf the volume scale factor is I'm going to get into the small one so I start with a small one over a big one now but I want to try and find the height I always go back to the linear scale factor if I've not got that so to go back to the linear scale factor from one you've already got you do the opposite of what you would normally do so I usually Cube to get the volume so I'll cube root now this looks really hard but we check if we can simplify that to see if we can do that so we can divide by zero and 16 32 48 49 50 51 2 3 4 pretty sure that goes in three times 16 goes into 54 3 times does it 16 3248 so it's a cub of a f just double shck got so I've got 16 over 54 so can I divide that by let's just divide that by two and two that gives me 8 over 2 2s is 4 2 7 is 14 oh 8 over 27 I must have made a mistake when I counted that so there we go see you can see how you need to think think and the reason I was getting confused with f is I'm knew I couldn't cube root three so but I can cube root 8 2 2's is 4 * 2 is 8 and 3 3 is 9 * 3 is 27 quite a hard one this but usually there you go two fuds so that means that my height is just two fuds of 12 12 ID 3 is 4 * 2 is 8 8 cm and we're done there question 14 Express X2 - 4x -1 in the form p x + p s + Q so I always thank you half the middle term and don't worry it it says plus there it can be plus or minus and then immediately take away 2^ 2 so 2 2 is 4 - 4 I've got Min -1 still so that's x - 2^ 2 - 4 - 1 is - 5 you can check your answer by way X2 double that - 2x - 4x we just do 2 2 is 4 well 4 - 5 is - 1 so I'm happy with that it says the RO of the equation the RO of the equation oh my gosh I hav seen that start of exam paper yes it's the quadratic formula mentions The Roots so if I ask you to find the roots or solve the equation as a quadratic there it is there so you just going to copy it now this is non-calculator it does come up now again not often so I'm going to write x = minus B plus or minus < TK of b^ 2 - 4 a c/ 2 a and it says it's going to be expressed in form x = a plus orus root B the reason it's saying that is you cannot actually work out sometimes you leave it as a SD so if it comes out as a if it's non-calculator that's what you do if it's calculator you would actually work out using numbers so just Sub in your numbers well a is 1 one in front X2 B is - 4 C is -1 so you've got x = - b - - 4 plus or minus - 4^ 2 - 4 * 1 * -1 over 2 * 1 no is not anything in the fraction so it's going to be simplification involved so that's four plus or minus the square root always work this bit out first 16 4 * 1 * 1 is 4 but it's plus cuz a minus is a minus so 16 + 4 is 20 all over two now you cannot simplify yet because there's not a number here so I'm going to do otk 20 at the side as a third that's < 4un 5 gives me 2un 5 So my answer becomes x = 4 + or - 2un 5 over two and both of the numbers can be divided by two so I can just divide by two now four divid by two is two 2 / 2 is 1 so we 1 < TK 5 X plus 2 plus or- 1 < TK 5 I'm think I'm quite happy with that so I'm done here that's a big Master I've went through the national five maths 2024 essential skills people one hopefully you found that useful especially exam technique me actually going through it live me making mistakes me showing you what I would do in an exam as I'm going good luck with your revision today and I'll see you later on today with paper two take care stay safe and goodbye