hello and welcome to all of you it doesn't matter if you're just a baby exelo that graduated from primary school trying to study a hit or a super senior Secondary School student that's sitting for their old level soon because axi the exelo is here to teach you all of the set one topics along with memes dreams and everything else in between so welcome to the One-Stop video series of the ultimate secondary school math guide putting a negative sign in front of a number is just like flipping a light switch let's say we have the number five and since it's positive it represents the light being on if we put a negative sign in front of the five it's just like flipping the light switch and turning it off if we put another negative sign in front of the neg5 it's kind of like flipping the light switch back on again and the two negative signs sort of cancel each other out and it becomes positive many times in math they want you to round off your answer to three significant figures which is kind of like taking the first three numbers of something but it's a little bit more complicated than that okay let's try to round off to three significant figures and I call this the cover up and Peak method what we're going to do is we're going to focus on the first three digits and cover up the rest like this then we're going to take a Peak at the next digit which is nine if this number is five or greater that means we have to round up if not we can just leave it as it is so 823 will become 824 the last step is to add in zeros to the back of 824 so that it has the same number of digits as 82395 so let's add in two zeros to the back of 824 to get the final answer of 8240 okay the next variation is the 0.00 something kind so these zeros in front are actually not counted as significant figures so let's write out the zeros in our answer first again we take the first three digits which is 485 and we take a Peak at the next digit which is is two since this number is less than five we don't need to round it up so we can leave it as 0.485 as our final answer let's try out this question where they want you to round off each of these individual numbers to one significant figure to estimate the final value for 60145 using the same method we take a look at the first number we take a Peak at the next number and since it's a zero we don't have to round up we fill in the zeros to get the answer of 60,000 so let's repeat this process for all the other numbers like this and you can get the final answer of 100 have you heard about primes the fastest growing sports drink in history no no no Logan you're not getting a sponsored segment in my video so a prime number is basically a number that can't be nicely divided by anything other than one and itself some of the prime numbers are 2 3 5 7 11 and so on and take take note that one is not a prime number these five numbers are going to be our best friends for this topic here the whole idea of prime factorization is to split up a number for example 280 into the prime numbers using something what I call the going down the letter method so let's start off with 280 and we're going to try to find a number from our prime numbers list that we can divide it nicely by since 280 is an even number let's try dividing it by 2 to get 140 and we can take 140 divided by two again to get 70 and then it will repeat this process and divide the number until it becomes one if we look to the left of our ladder method we can finally get our prime factorization of 280 equal to 2 * 2 * 2 * 5 * 7 now since we have two multipli by itself 3 times we can write the final answer as 280 = to 2 Cub * 5 * 7 if you are really insecure you can even press this in your calculator to make sure you get 280 back okay let's imagine the question gives us another number 550 is equals to 2 * 5 S * 11 and they want us to find the highest common factor and the lowest common multiple for these two numbers imagine you're at like a dinner table or a party the hcf is like the nice guy that never takes more than needed so between the two Cube and the two he'll always choose the one with the Lesser power so he takes two so we apply the same logic by comparing the fives now we run into a slight problem 280 has a 7 and 550 has an 11 over here in this case since he's such a nice guy because they don't share each other's number the hcf doesn't take anything from them so the final answer for the hcf is just equals to 2 * 5 equal to 10 on the other hand the the LCM is just like the greedy inconsiderate dude that seems to eat and take everything from the dinner table so comparing the twos he takes the one with the highest power which is 2 CU and he also takes five square when comparing the fives now when it comes to different terms he just doesn't care he just takes them all so he takes seven and he takes the 11 as well so the LCM is equal to 2 Cub * 5 S * 7 * 11 which is equal to 1540 whenever you see questions like this come out about finding some constant right I'm going to teach you how to use my Jenga method of stacking and removing blocks we refer to the prime factorization of 280 to draw out our Jenga diagram since it's two to the power of threee the Jenga stack of the number twos is three blocks tall and for five and seven they are both one block tall each since the question asked for a perfect square which means power two but the power can also be multip of two like 2 4 6 and so on because it's 280 * K we can only stack blocks on top of it and our goal is to make every stack either two or four or six blocks high so for the stack of twos by putting another block of two there it's now four blocks tall and for the number five and seven Stacks by adding just one block to each of them they are both now two blocks tall after all of that the value of K is just basically all the new blocks that we added so the value of K is equal to 2 * 5 * 7 which is equal to 70 now let's try something a little more difficult the first step is to prime factorize 360 which gives us 2 Cub * 3 2 * 5 because p and Q are prime numbers each of them are just like adding and removing one block since it's 360 * P divided by q p is basically adding one block and Q is basically removing one block the question asks for a perfect Cube so each stack needs to be like 3 6 9 and so on high if we look at our current stack the number two is already three blocks tall so we don't have to change anything there now the number three is only two blocks tall so we need to add another block to the stack to make it three blocks tall now we know that P is equals to three because it refers to this block over here to solve for Q since we can only remove one block let's remove this number five block which removes this stack entirely so we know that Q is equals to 5 if you're still feeling a little insecure about your answer you can always subit the values of p and Q into the original equation which will give you 216 if we try taking the cube root of 216 you can see that we get a nice number so we know that we're good the whole idea of simplifying is to combine the same terms together so for this question you can see that the equation is made up of some a terms and some B terms so let's shift all the a terms together to the left to get 3 a minus 2 a and shift all the B terms to the right to get plus 4 b + 5B now let's combine them together so this will give me 1 a and this will give me 9B and this is our final answer you know how at the start of the class the teacher always has to like distribute out worksheets to every student so that's basically how expanding Works in this question we want to distribute this number two out to the 3x and the -4 so let's multiply 2 and 3X together which will give us 6X and we can do the same 2 ultip by -4 which will give us Min - 8 okay let's try out something similar for this question we multiply -6x and -5x so remember that two negatives multiplied together gives us a positive so it's positive 30 x² and let's multiply the second term of -6x and 3 y together to get -8 XY whenever you want to combine two fractions together the goal is to always make the denominator the same thing so for this question since three and four have a common multiple of 12 let's try to turn both of them into 12 for the fraction on the left if we multiply three to the top and the bottom we can get 12 but remember whatever you multiply to the top you must also multiply it to the bottom and for the other fraction we multiply by four to the top and the bottom and let's expand out both of the numerators and we are ready to combine the fractions when combining remember that this negative sign here affects both this 8X and the 20 term so we have to put a bracket like this so now let's expand the negative to both of these terms and simplify our numerator and we can get the final answer of x - 32 / 12 factorizing is basically like your teacher collecting back that one homework assignment from everyone the the goal of factorization is to find out what common term can we take out from a few things we can see that these two terms here have a common factor of five and a common factor of X so we can split it up into 5x * 5 y over here and 5x * 8 Z over here since they both have 5x we can take them out and put them in front over here then we can just write whatever that's left which is 5 Yus 8 Z inside these brackets you can notice that factorization is just the opposite of expansion because if I expand this out I get back the original equation okay now let's try a more difficult example this type of question is a little bit tricky because we don't really know what to factorize here but do you notice that this 3 a minus 2 C here looks very similar to the 2 C minus 3 a okay so here's what we're going to do since this doesn't have a bracket we will try to make it look like 3 a - 2 C so let's try to factorize out the -1 from these two terms to get -2 C + 3 a which we can rewrite to 3 a minus 2 C now that these two terms are the same let's factorize both of these 3 a - 2 C's out of these two terms and whatever that's left inside of the bracket is 5 q minus 1 the reason why it's minus one is because there's kind of like an invisible one in front of this bracket and and that's our final factorization now for solving I'm going to teach you two ways to do it one is the legit textbook method and the other is kind of like my cheat method that I've been using since I was a small xelot to solve for x because it's stuck with the x + 3 over here so we're going to do minus three on both sides so this plus three and the minus three here will cancel each other off and we get x = 5 - 3 which gives us 2 so for my cheat method we kind of have to like move this three to the other side of the equal sign but very importantly we have to flip the sign so it becomes five - 3 which is equals to 2 next when the x is at the top of the fraction and we kind of want to get rid of this four at the bottom we multiply four on both sides and the four and the four here will cancel out and the other side is 7 * 4 which gives us 28 so for my cheat method anytime there is something at the bottom of the fraction we can kind of move it over to the other side side and it becomes a multiply so 4 * 7 also gives us 28 in this question you can see that the x is stuck at the bottom because we don't want to see fractions anymore we multiply both sides by xus 2 so these two things will cancel out and the right side will become 3 * x - 2 after expanding this and rearranging we get 3x = 12 and let's divide both sides by three to get the final answer of x equal to 4 now for my cheat method okay this one takes a little bit of imagination so imagine that this x - 2 is wearing a hat that says 6 now he transfers that hat over to his friend three on the other side so the fraction on the left side is gone and we get x - 2 equals the 6 / 3 which is 2 now we shift the -2 over to become plus two and we get the final answer of xal to 4 I'm going to teach you about this cross multiply trick and you can use it when you see the form of one fraction equals to another fraction without anything else now it kind of works like a x shap so on this diagonal this 2 and this x + 1 are multiplied together and let's put them here in an equal sign X - 1 and 3 are also multiply together so let's put them on the right side after expanding the terms and shifting all the X to one side and all the numbers to the other side we get our final answer of X is equals to 5 now imagine you traveled to the US and went up to a money exchanger to exchange 50 Singapore dollars and the guy gave you 36.67% 50 will give us an exchange rate of 1 SGD to 0.733 4 USD and we leave it to four significant figures Now using this exchange rate that we calculated now we want to convert our USD into the most valuable currency in the world Bitcoin ethereum nope I'm talking about Robux the exchange rate from the USD to Robux is 0.0125 USD is equals to one Robux and the question asks us to calculate the exchange rate of SGD to robu now the first thing to notice when we take a look at these two exchange rates is that the currency in common is USD since USD is in common our goal is to make the USD in both ratios equals to one for this ratio let's divide both sides by 0.733 4 because any number divided by itself will give you one and we get 1. 364 is to one now let's do the same for the other ratio dividing both sides by 0.0125 and it gives us 1 is to 80 since the USD in both of these ratios is equal to 1 we can finally compare SGD to Robux and it gives us 1364 SGD is equal to 80 robu our last step is to make it into the one is the something form so let's divide both sides by 1364 to get our final answer of 1 SGD is equals to 58.6 5 Robux okay let's say Matt can eat 17 hot dogs in 5 minutes and zerat can eat 14 hot dogs in 4 minutes how long does it take both of them to finish 100 hot dogs now the first step is to find out the individual Hot Dog Eating rate what we want to find out is how many hot dogs can they eat in one minute so mat's eating rate is 17 hot dogs divided by 5 minutes which is 3.4 hot dogs a minute for zerat 14 / 4 gives us 3.5 hot dogs per minute so since they are working together we can actually add up the two rates to get 6.9 hot dogs per minute now the question wants us to find 100 hot dogs so we kind of have to draw this rate triangle thing the rate always goes to the bottom left hand corner and now let's take a look at the units since it's hot dogs per minute hot dogs goes to the top and minutes goes to the bottom because the question wants us to find how long it takes in minutes using the triangle it's equal to the the number of hot dogs divided by the rate so let's put in the values 100 hot dogs divided by 6.9 will give us the answer of 14.5 minutes let's try to convert 72 km/ hour into m/s since it's 72 km we multiply by 1,000 to get 72,000 M now for the 1 hour we ask ourselves how many seconds are there in 1 hour so we know that 1 hour has 60 minutes and 1 minute there's 60 seconds so the denominator becomes 60 * 60 so 72,000 / by 3,600 gives us the final answer of 20 m/s using the same idea of the rate triangle just now distance speed time also has a triangle like this which I'm sure that you're all familiar with now this topic has a very underrated formula which is that the average speed for any journey is the total distance divided by the total time and take note for the total time we need to add up all the time values including when the car or whatever object is also resting let's try out this question where they ask you to find the average speed from a to c I know many students are tempted to just take the average of 60 and 70 but that's wrong we have to use the formula to find the total distance and the total time first to calculate the distance from A to B we take the speed of this portion which is 60 times the time taken which is two and it gives 120 we do the same with BC to get 2110 so the total distance is 120 + 21 0 which is equal to 330 kilm and the total time is 2 hours plus 3 hours which gives us 5 hours finally the average speed is just 330 km divided by 5 hours to get the final answer of 66 km per hour when I used to be a no life basement dweller of an exelo playing TF2 and all day I will always wait for the Steam summer sale where games would have huge discounts now imagine that the game is originally $20 and because of the sale it becomes $15 and we want to find the percentage reduction okay I know this looks a little bit crazy but here is the percentage change formula the original price is $20 and the final price is $15 so since it's final minus original over original it's 15us 20 over 20 multip by 100% an important thing is that you don't press this percentage sign in your calculator when doing this and it will give you an answer of -25% and since the percentage change is minus 25% the percentage reduction is just 25% for this question since a is 15% less than b we try to let the price of b equal to X number of dollars since a is 15% less 100 - 15% gives us 85% of X and we can write it as a is equals to 0.85 X because a + b is $74 we can put in the values and it becomes x + 0.85 X is equals to 74 so solving for x we get the value of x is equal to $40 and that's the price of B an installment plan is basically when you're too broke to buy something but you still want to buy anyways so the company that sells it to you goes like you can just pay me 20% of the cost first and then for the rest you can pay back in like 12 months and then they pray very hard that you don't go bankrupt so imagine you want to buy a TV that cost $1,000 under an installment plan the down payment is $200 which you have to pay up front and the rest is paid in eight equal monthly installments with an interest of 6% per anom which means per year so we take $11,000 minus $200 which gives us $800 so this $800 is what we need to pay in eight chunks with something called interest which is kind of like the extra that you need to pay the company the formula to calculate this interest is interest is equals to P RT so p is the amount that you have to pay off in this case it is $800 R is the rate which is 6% per year so let's put that inside okay the T value here is talking about the time frame and this is where it gets a little bit tricky since since the rate is per year the time frame needs to be in terms of years also so let's convert this 8 months into years which is 2 over three years now we put that into our formula and we can get an interest of $32 now to find the installment each month we can take the $800 plus the $32 divided by8 months to get $104 per month okay bonus trick question round I want you to imagine that you're a Wall Street stocks Trader so on day one you make a loss of 10% but on day two you make a profit of 10% so the question is are you STS or not STS to solve this question let's imagine you start trading with $100 on day one you lose 10% so we do $100 multipli by 90% so we left with $90 so on day two we make a profit of 10% so we do $90 time 110% and what do we get we get $99 wait didn't we start with $100 as you can see we actually lost $1 so the final answer is not STS have you ever wondered what a day in a life of a talking exelo is like man I'm just chilling at the bottom of the fish tank living my best life no homework assignments no responsibilities unlike all you humans since I'm such a hardworking exelo that's teaching you math all day why not sponsor me some food by hitting the like And subscribe button if I end up starving to death I hope that all of you fail your math exams let's try to find the general formula for a number pattern that goes like 11 13 15 17 and so on so this 11 here represents the first term so we call it n is equals to 1 and this is n equals to 2 and so on there's just two things that you need to take note of so the first is the first term of the sequence which is 11 over here and the next thing is the common difference which is how you get from one number to the next so that is positive2 so to calculate the general formula TN it is equals to the first term plus the common difference multipli by n minus one so the first term is 11 + pos2 * nus1 so we can expand this and we get our final answer of 9 + 2 N we can actually check if we are correct by substituting n is equal to 1 and seeing we actually get back the first term which is 11 and yes we do sometimes the question asks if let's say the number 136 is part of the sequence just now so the trick here is to equate the general formula TN is equals to 136 and we kind of try to solve for the value of n so let's try it out 9 + 2 N is equal to 136 so after trying to solve for n we get the value of n is equals to 63.5 we know that this doesn't really work out because there's no such thing as a 63 and a half term so we can write 136 is not part of the sequence since the nend term is not a positive integer okay sometimes the pattern in the number pattern is not super obvious like this example the first step is to look at the terms at the bottom of the fraction we can notice that the numbers are like all square numbers so if we write out n is equal to 1 n is equal to 2 and so on the answer is just n s for the bottom for the top we can see that it has a common difference of five so we can use the method that we used just now so TN for the top is the first term which is 1 plus POS 5 bracket n minus one and after expanding it and rearranging the terms it works out to be 5 nus 4 so the general term for the entire sequence is 5 nus 4 / n^ 2 have you ever played these 2D games like Geometry Dash this topic is all about representing points and lines using the X and Y AIS so imagine this is U and the x-axis is basically like moving left and right so if I'm standing at xal to 1 and I take one step forward I end up at x equal to 2 the y- axis is just like moving up and down so right now I'm at Y is equals to zero so what I'm going to do is I'm going to dig straight down just like in Minecraft by three blocks so I end up at Y is equal to 3 the position that we are at can be written in coordinates form in the XY form so our coordinates right now is 2 comma -3 an equation kind of works like a vending machine where you put something in and you get something out so for the equation Y is = 2x + 1 let's try to put in x = 1 so 2 * 1 + 1 will give us Y is equal 3 so what this means is that this equation actually passes through through this point where X isal to 1 and Y is equal to 3 okay now what if I wanted to draw this graph in order to draw a straight line we need to form this table of X and Y coordinates for us to plot onto the graph so let's use three points at three different x coordinates X is equals to 1 2 and 3 we put each of these individual X values into the equation to get the corresponding y values so if we put x equal to 1 we get the value of y is equal to 3 three and so on now we just plot all of these coordinates onto the graph and we draw a straight line through them okay now this is the most important formula that will carry you from set one all the way to set 4 a straight line equation can be written as our golden formula y isal to mx + C if we compare this to just now's formula of y isal 2x + 1 we can kind of see that the M value the gradient which is equals to two gradient just means how steep of the slope the line is positive gradient means going up and negative gradient means going down the C value means the Y intercept so it's the Y value at the point where the line cuts the Y AIS which in this case is one so C is equals to 1 okay now let's try to reverse the question a little imagine they give you a straight line graph passing through these two points how do I calculate the values of M and C just by looking at the graph okay the C value is quite easy because we can can just read it here so at the Y value of the Y intercept here is 1 so C is equals to 1 now for the gradient this actually this other formula where the triangle means the change in the Y value over the change in the x value so to get from this point to this point the x value has to go right by four units and the Y value has to go up by eight units so the change in y is 8 and the change in X is 4 so m is equals to 8 / 4 which is equals to 2 okay let's try out a more difficult question if you look closely do you notice that this question here doesn't really follow the Y is equal to MX plus C form so we have to manipulate a little bit first so let's shift the 5 y to one side and the 2x - 20 to the other side now let's divide the whole equation by five and now we finally get our Y is equals to mx + C form from comparing the two equations the M value is 2 over 5 and the C value is-4 so let's do a rough sketch of this graph first we label the C is equals to-4 here and since the gradient is positive that means it's going up and it should look something like this the coordinates of the Y intercept is 0 comma minus 4 since at this point the x value is zero okay now for the x intercept it's where the graph cuts the x-axis and at this point the Y value is equal to zero so let's sub y is equals to Z inside our equation and we get the value of x is equals to 10 so the coordinates of the x intercept is 10 comma 0 okay real talk I think this is probably everyone's most hated topic because of all the angle properties that you have to memorize let's first take a look at these two examples over here you can notice that these three angles here add up to 180° because they lie on a straight line so 2x + 90° + x equals to 180° and the reasoning that we write is adjacent angles on a straight line for the other example because these four angles here add up to 360° so 4x + 3x + x + 72 is equal to 360 and the reason is angles at a point from here we can solve for x in both examples okay pretty easy so far welcome back to the wonderful world of Sesame Street Boys and Girls today's segment is the letters of the day the first letter of the day is the x-shaped angle property and it can only work when these two lines here are straight we can see that these two angles here are equal and these two angles here are also equal so we call this property vertically opposite angles for the Z and the F shape it only works when there are two parallel lines so for the Z shape this angle and this angle here are the same and the property is called alternate angles for the the F shape we can see that this angle here is the same as this angle here and the property is called corresponding angles for any triangle you can think of the sum of these three angles here always add up to 180° for an isoceles triangle because the two sides are equal this angle and this angle are equal and for equilateral triangle since all three sides are the same each angle is 60° okay so let's try to put it all together the first thing is the highlight all the parallel lines in the diagram so here we can kind of see the z-shape coming out in order to find X we have to find this angle because we can use the alternate angles property later on this angle is just 180 minus 123 equals to 57° and the angle X is also 57° because of alternate angles let's update the diagram now that we found X and let's look at this triangle over here because this is a straight line This angle is 80us 110 which is 70° and we can find why since the sum of angles in this triangle here adds up to 180 so 180 - 70 - 57 gives us the final answer of 53° there's a few types of four-sided quadrilaterals the first is the parallelogram where these two sides are equal and parallel and the same for these two for a trapezium only this and this are parallel rhombus is kind of like communism everything is the same length and the opposite sides are parallel and lastly for a kite these two are the same length and these two are also the same length for this question using the communism property that all four sides are the same in a rhombus we can kind of see that this becomes a isoceles triangle so this angle is also 23° finally 180 minus 23 - 23 gives us X to be 134° polygons are B basically anything from a triangle onwards for a triangle the number of sides is three and the sum of angles is 180° for a square n is equals to 4 and the sum of angles is 360° you can kind of start to see a pattern here so let's try to find the sum of angles in a pentagon there's actually a formula that connects n to the sum of the angles where the sum of angles is nus 2 * 180° we can see that for the triangle n is equal to 3 so 3 - 2 * 180 gives us 180 each of the angles inside the polygon is called the interior angle and it's just the sum of angles divided by the number of sides now let's try to calculate the interior angle of this Pentagon that has five sides the sum of angles is 5 - 2 * 180 which gives us 540° to calculate the interior angle 540 / 5 gives us 108° there's something else called an exterior angle which is where we take any one of these lines and we extend it and this here is the exterior angle so the exterior angle here is 180 minus 108 which is equal to 72 but there's actually another important formula that can be used to calculate the exterior angle which is exterior angle equals to 360 / n so for this example since n is equal 5 360 / 5 can also give us 72 okay I know this is a pretty complicated looking question that wants us to find the number of sides for this polygon if we can find the exterior angle we can use just now's 360 ID n formula to find the value of n since this here is a pentagon this angle here is also 108 so we can take 360 - 108 - 96 to get 156 which is the interior angle of the polygon here and using the line extension method just now the exterior angle is just 180 minus 156 which gives us 24° so the final step is to use the formula of the exterior angle which is 360 / n and we can solve for n to be 15 sides do you know about a Pokémon called polygon which is made out of you guess it polygons okay but there's another type of polygon called a irregular polygon where the angles are not equal to each other so this over here is a five-sided irregular polygon so the only formula that we can use is the sum of angles for this kind of polygon is nus 2 * 180° okay I'm sure that all of you know how to use a protractor so I'm going to introduce you to this thing with one stabby n and one pencil nend called a compass so let's say this question asks you to construct some kind of triangle here such that this angle is 70° and this length here is 6 cm for the angle 70° we can actually use the protractor Mark 70° out and extend out a dotted line now we need to draw a line from this point to somewhere on this line which is exactly 6 cm so that's where we need to use our Compass okay we use a ruler to measure 6 cm between the ends of the compass and then next you got to stab your paper on this point here using the sharp n and draw a Arc like this using the pencil n so the point where the arc intersects the dotted line is actually the point Z and the last step is to finally construct our full triangle the most important thing for finding area is this thing called the perpendicular height I think we all know that the area of the triangle is half time base time height but this height has to be somewhere from the base so we extend out a line and we draw a line here that touches the top where it's 90° and this is called the perpendicular height for the area of the parallelogram it's just the base times the perpendicular height and you can imagine this part here gets moved over to form like a rectangle and finally for a trapesium you have to memorize the formula where it's half bracket a plus b * height where A and B are kind of like the floor and the ceiling of the trapezium and H is the perpendicular height okay I want you to imagine that we have a disc and a ring the area of the disc is p Pi R square and the ring has a circumference of 2 pi r but how do we convert the area and the circumference into the 3D wall if we keep stacking these discs you can see that it kind of forms like a cylinder and similarly if we keep stacking these Rings it forms a hollow cylinder if we stack the disc to a height of H we can actually derive the volume of the cylinder from the area and is equals to PK r² * h it's the same thing with the Rings and since we are stacking the circumference so the curved surface area of the cylinder is 2 pi r * H okay let's try to use the idea to find the volume and the total surface area of this toilet row here the first step is to divide by two to the outer and inner diameter to get the radius so now let's focus on the volume first I think the most intuitive way to find the volume is by taking the volume of the big cylinder minus the volume of the small cylinder CER okay but let me teach you another 200 IQ method so using the idea of stacking from just now another way is to find the area of this donut over here and multiply it upwards by H units so the area of the donut is the big circle < * 6 2 minus the small circle Pi * 2 2 then we multiply the height by 10 to get the volume of 105.3 CM cub in order to find the surface area it consists of the the curved surface area of the big cylinder the curved surface area of the small cylinder and the area of this dut thing at the top and at the bottom since the curved surface area is 2 pi r h the curve surface area of the big cylinder is 2 pi * 6 * 10 and we do the same for the small cylinder as well now because we already calculated the area of the donut and the top and the bottom is the same so we can just do 2 * 10053 now adding up all these areas together we can get our final answer of 70372 cm² now let's try to extend this idea of stacking to prisms so for this Toblerone chocolate looking prism over here we can find the area of this triangle and we can kind of Stack it out horizontally to get the volume and similarly with the surface area of these faces instead of calculating them individually we can actually take the perimeter of the triangle and just multiply it by the length so this idea can be applied to any shape with a uniform cross-sectional area where we calculate the area or the perimeter and we just stack it across imagine we go up to the streets and ask people who their favorite YouTuber is and we give them three choices dream Mr Beast and your favorite math aelo Juan Jordan from the results over here based on the category and the frequency we can actually plot something called a bar graph bar graphs are good to represent categorical data since the people can only choose from these three choices now let me open up my YouTube studio and check my analytics real quick from this data it shows how many subscribers I gain for each day and as you can see we can draw something called a line graph to plot this data because it's used to predict Trends and data that changes over time kind of like the stons meme now imagine that YouTube just released some data on how many total views each category of my videos got over the past year we want to represent this in a pie chart because it's used to represent the percentage of certain categories to make a pie chart we need to calculate a new column called the sector angle the first step is to calculate the total number of views so we can add up 360 + 700 + 100 + 280 equals to 1440 now if we want to calculate the sector angle for let's say the lifestyle category we just take 360 divid by the total 1440 multip by 360° because it's a circle and we get the sector angle of 90° so let's repeat this for all the different categories and to double check you can actually add all of these up to make sure it actually adds to 360° the last step is to use a protractor to measure the angle and draw out all the categories like this and that is it for all the set one topics I know I know most of them are pretty easy but there are a few difficult ones that even some of the SE for students struggle with like prime factorization and polygons the rest are mainly the foundation for topics that you will learn in set 2 set 3 and set 4 even if you're are like a genius ex like myself I would still recommend you to watch through the whole video to refresh your memory as always these videos take me ages to make so I hope it helps you get the A1 and thanks for watching Axel Auto out