0:00:02.030,0:00:07.574 A formula is a recipe or a rule[br]for doing something and it works 0:00:07.574,0:00:10.742 every time it gives the[br]relationship between different 0:00:10.742,0:00:15.014 quantities. Some formerly a[br]standard formally written down 0:00:15.014,0:00:19.766 by Mathematicians and scientists[br]to cover a wide range of the 0:00:19.766,0:00:21.062 relationships between different 0:00:21.062,0:00:26.403 quantities. Others can be made[br]up such as that for a washing 0:00:26.403,0:00:28.368 powder or a magician's memory 0:00:28.368,0:00:30.610 trick. More of that later. 0:00:31.530,0:00:36.300 Formally, usually use variables[br]and letters instead of numbers, 0:00:36.300,0:00:41.600 and that gives the relationship.[br]Let's have a look at. 0:00:43.550,0:00:49.622 The formula for the area[br]of a circle A equals π R 0:00:49.622,0:00:54.176 squared, where a is the[br]area of the circle. 0:00:57.640,0:01:00.328 And R is the radius of[br]the circle. 0:01:04.110,0:01:07.827 This formula works every time[br]and shows the relationship. 0:01:07.827,0:01:12.370 So we square the radius. We[br]multiplied by pie and it 0:01:12.370,0:01:16.087 gives us the area and it will[br]always work. 0:01:18.160,0:01:23.836 Imagine we have a circular lawn[br]where the radius is 3 meters. 0:01:24.920,0:01:29.509 And we want to know how much[br]turf in square meters that we 0:01:29.509,0:01:32.686 need to order so R is equal to 3 0:01:32.686,0:01:38.050 meters. So what we're going[br]to do instead of writing are 0:01:38.050,0:01:42.922 in our formula. We're going[br]to write the number 3, so A 0:01:42.922,0:01:47.388 is equal to Π * 3 squared.[br]Now, it's really important 0:01:47.388,0:01:50.636 that we put the[br]multiplication sign back in 0:01:50.636,0:01:54.696 as soon as we put numbers[br]back in our formula. 0:01:57.000,0:02:03.897 Π * 3 squared is π[br]* 9, giving us 28.3. 0:02:04.530,0:02:06.300 So the area of our. 0:02:07.310,0:02:12.880 Lawn is going to be 28.3[br]meters squared, so we're 0:02:12.880,0:02:18.450 going to need at least 29[br]meters squared of turf. 0:02:24.180,0:02:28.646 There are many formerly that[br]relates to the area of 2D 0:02:28.646,0:02:32.300 objects and also to the volume[br]of 3D solids. 0:02:33.120,0:02:36.242 Let's have a look at one. Now[br]let's say we want to find the 0:02:36.242,0:02:37.134 volume of a football. 0:02:39.870,0:02:45.980 Now football is a sphere, so we[br]want the formula for the volume 0:02:45.980,0:02:52.090 of a sphere and that's V equals[br]4 thirds of Π R cubed. 0:02:52.760,0:02:57.540 And let's say that the[br]radius of a sphere are 0:02:57.540,0:02:59.452 football is 10 centimeters. 0:03:00.930,0:03:07.242 So in our formula to workout the[br]volume instead of writing, are 0:03:07.242,0:03:12.502 we going to write 10[br]centimeters, so V equals 4 0:03:12.502,0:03:17.236 thirds π multiplied, again[br]remembering to put the multiply 0:03:17.236,0:03:23.548 symbol in and instead of are we[br]writing 10, so 10 cubed? 0:03:25.240,0:03:27.305 And if we calculate all of that. 0:03:27.880,0:03:35.120 We end up with the[br]volume equaling 4189, so the 0:03:35.120,0:03:42.360 volume of the football since[br]the radius was in centimeters 0:03:42.360,0:03:45.980 will be 4189 centimeters cubed. 0:03:54.690,0:03:58.466 There are many formerly relating[br]to scientific principles. 0:03:59.710,0:04:03.868 And we're going to have a look[br]at Newton's second law. 0:04:09.160,0:04:15.163 And that law relates force[br]with mass and acceleration. 0:04:16.340,0:04:22.240 And the formula is F equals[br]MA mass times acceleration. 0:04:23.830,0:04:28.246 Let's imagine a circus artist is[br]going to be fired from the 0:04:28.246,0:04:32.335 barrel. And he's going[br]to be fired horizontally 0:04:32.335,0:04:36.385 and the mass of a circus[br]artist is 60 kilograms. 0:04:37.810,0:04:42.573 And he's going to be fired[br]at an acceleration of 2.5 0:04:42.573,0:04:44.305 meters per second squared. 0:04:45.510,0:04:49.500 Our formula is F equals MA. 0:04:50.780,0:04:53.786 So instead of em, we're[br]going to write 60. 0:04:56.110,0:04:58.476 And instead of a, we're going to 0:04:58.476,0:05:02.226 put 2.5. But again, because[br]we're putting numbers in. 0:05:02.860,0:05:07.920 Instead of the letters, we must[br]remember to put the multiply 0:05:07.920,0:05:12.520 sign back in so it'll be 60[br]times by 2.5. 0:05:13.710,0:05:21.174 That gives us 150, so the[br]force on our circus artists is 0:05:21.174,0:05:25.476 150 newtons. And Newton is[br]a unit of force. 0:05:30.350,0:05:32.835 Let's look at an equation[br]of motion. 0:05:34.210,0:05:37.160 Z equals you plus 80. 0:05:38.920,0:05:41.928 Fee represents final speed. 0:05:45.120,0:05:47.010 You initial speed. 0:05:50.770,0:05:52.579 Hey, is acceleration. 0:05:56.000,0:05:57.458 Auntie is time. 0:05:59.520,0:06:03.270 And imagine that we've got some[br]values for you A&T. 0:06:04.030,0:06:05.040 So you. 0:06:06.640,0:06:07.699 Equal to 5. 0:06:09.110,0:06:12.872 A is equal to two and T[br]is equal to 3. 0:06:14.040,0:06:18.300 So to calculate V, the final[br]speed, we're going to 0:06:18.300,0:06:21.282 substitute these numbers[br]instead of these letters. 0:06:22.520,0:06:29.100 So instead of you, we write 5[br]instead of a. It's two, we must 0:06:29.100,0:06:33.330 write the multiply sign because[br]we're now putting numbers 0:06:33.330,0:06:34.740 instead of letters. 0:06:35.330,0:06:37.787 And instead of T we write 3. 0:06:38.750,0:06:42.530 Now we've got a good[br]opportunity here to look at 0:06:42.530,0:06:46.688 our order of operations. If[br]we were to start from the 0:06:46.688,0:06:51.224 left and work through to the[br]right, we would be in error 0:06:51.224,0:06:54.248 because we should do[br]multiplying before we do 0:06:54.248,0:06:57.650 addition. So a quick[br]reminder of our order of 0:06:57.650,0:06:59.162 operations with Bob Mass. 0:07:01.410,0:07:06.684 Where the B stands for brackets,[br]the apfa powers. 0:07:08.090,0:07:12.398 Steve for divide[br]and for multiply. 0:07:13.870,0:07:15.160 A for addition. 0:07:16.900,0:07:18.608 And S for subtraction. 0:07:22.010,0:07:26.620 So multiply comes before[br]addition, so we need to do 0:07:26.620,0:07:32.613 2 * 3 before we do the[br]addition, so it's 5 + 6, 0:07:32.613,0:07:35.379 giving us an answer of 11. 0:07:42.880,0:07:48.237 Let's look at another equation[br]of motion. This time V squared 0:07:48.237,0:07:51.159 equals U squared plus 2A S. 0:07:52.860,0:07:55.968 Again, the final speed. 0:07:59.360,0:08:01.169 You initial speed. 0:08:05.180,0:08:07.130 Hey Accelleration. 0:08:10.610,0:08:13.110 And S distance traveled. 0:08:15.360,0:08:18.096 And imagine we've got a Cliff. 0:08:20.150,0:08:24.695 And we throw a stone off the top[br]of the Cliff and we'd like to 0:08:24.695,0:08:27.725 know the speed with which it[br]hits the water below. 0:08:28.810,0:08:31.519 And the Cliff is[br]100 meters high. 0:08:33.350,0:08:37.046 So we know that you[br]are initial speed. 0:08:38.420,0:08:42.836 Is zero 'cause we're dropping[br]the stone from rest at the top? 0:08:45.080,0:08:49.202 Our acceleration is the[br]acceleration due to gravity, so 0:08:49.202,0:08:51.492 that's 9.8 meters per second 0:08:51.492,0:08:56.840 squared. And as the distance[br]that it falls is 100 meters. 0:08:58.550,0:09:02.060 So instead of the letters[br]in our formula, we 0:09:02.060,0:09:03.230 substitute the numbers. 0:09:04.470,0:09:06.110 UO 0:09:07.450,0:09:14.596 plus two times[br]a 9.8 times 0:09:14.596,0:09:16.978 S 100. 0:09:21.690,0:09:28.274 That works out at[br]1960. Sophie squared is 0:09:28.274,0:09:34.708 1960. So to calculate V,[br]the final speed when it 0:09:34.708,0:09:40.780 hits the water, we need to[br]square root 1960 and that 0:09:40.780,0:09:44.092 gives us an answer of 44. 0:09:46.040,0:09:46.940 And because. 0:09:48.730,0:09:53.130 Our units are meters per second[br]squared for acceleration in 0:09:53.130,0:09:57.970 meters for the distance that[br]it's fallen, the velocity is 44 0:09:57.970,0:09:59.290 meters per second. 0:10:05.750,0:10:12.026 Another equation of motion is S[br]equals UT plus a half 80 0:10:12.026,0:10:15.580 squared. What S is the distance? 0:10:18.380,0:10:20.850 You is the initial speed. 0:10:24.980,0:10:26.339 T is time. 0:10:28.240,0:10:30.030 A accelerations. 0:10:33.360,0:10:35.103 And the final to the same as 0:10:35.103,0:10:40.281 this one time. Not so much in[br]this time that we have a well. 0:10:42.870,0:10:46.511 And we want to find out[br]how deep the well is. 0:10:48.520,0:10:50.968 And what we do is we drop a[br]stone down the well. 0:10:57.280,0:11:01.780 Use the initial speed of the[br]stone is 0 because we dropped 0:11:01.780,0:11:03.655 it. It started at rest. 0:11:04.990,0:11:09.098 Let's say it takes 3 seconds for[br]the stone to hit the bottom. 0:11:10.660,0:11:16.684 And AR acceleration is that due[br]to gravity of 9.8 meters per 0:11:16.684,0:11:22.115 second squared. So instead of[br]writing you T&A in our formula, 0:11:22.115,0:11:25.580 we're going to substitute and[br]put these values in. 0:11:26.760,0:11:34.024 So S equals you[br]0 multiplied by T3. 0:11:34.990,0:11:40.570 Plus half multiplied[br]by 9.8. 0:11:41.680,0:11:44.188 Multiplied by T squared. 0:11:45.560,0:11:49.174 So we put all the figures in.[br]Now we can carry out the 0:11:49.174,0:11:56.840 calculation. 0 * 3 zero[br]plus half of 9.8 four point 0:11:56.840,0:12:00.830 9 * 3 squared is 9. 0:12:02.630,0:12:07.226 That gives an answer of 44 to[br]the nearest whole number. And 0:12:07.226,0:12:10.673 because our units are meters[br]per second squared and 0:12:10.673,0:12:14.503 seconds, the depth of the[br]world will be 44 meters. 0:12:20.130,0:12:23.970 Let's have a look at the formula[br]for kinetic energy. 0:12:26.070,0:12:29.860 Kinetic energy equals 1/2 MV 0:12:29.860,0:12:36.858 squared. Where M represents mass[br]and the is the speed that the 0:12:36.858,0:12:38.850 mass is traveling at. 0:12:39.530,0:12:44.997 The amount of work done, kinetic[br]energy. Let's compare a sprinter 0:12:44.997,0:12:50.464 running and the work that is[br]done by the sprinter running 0:12:50.464,0:12:56.428 with that of a truck. So the[br]sprinter is mass 70 kilos. 0:12:57.830,0:13:02.175 And the running at a speed of 10[br]meters per second. 0:13:03.520,0:13:04.680 Another truck 0:13:05.830,0:13:09.058 has a mass of 2000 kilos. 0:13:10.470,0:13:16.686 And that's going forward at a[br]speed of 20 meters per second. 0:13:17.600,0:13:21.870 So let's compare how much[br]work they're doing. So for 0:13:21.870,0:13:22.724 this printer. 0:13:25.080,0:13:31.668 The kinetic energy equals 1/2.[br]The mass is 70. 0:13:33.630,0:13:36.620 The velocity is 10 squared. 0:13:37.950,0:13:41.138 So we have 3500. 0:13:42.840,0:13:43.968 For the truck. 0:13:45.760,0:13:51.530 The kinetic energy again[br]is 1/2 instead of the M 0:13:51.530,0:13:53.261 we write 2000. 0:13:54.980,0:13:59.776 And instead of the V, we've got[br]20 to be squared. 0:14:01.010,0:14:04.646 And that works out at 400,000. 0:14:06.260,0:14:10.737 So the kinetic energy of[br]the truck is more than 100 0:14:10.737,0:14:13.586 times greater than that of[br]the sprinter. 0:14:14.800,0:14:18.470 I haven't written the units[br]down, but for kinetic energy 0:14:18.470,0:14:19.204 there jewels. 0:14:23.950,0:14:29.842 Let's look now at the formula[br]for the period of a pendulum 0:14:29.842,0:14:33.770 where T equals 2π root L over G. 0:14:34.720,0:14:37.544 What city is the period of[br]the pendulum? 0:14:43.990,0:14:47.302 And that means how long the 0:14:47.302,0:14:53.040 pendulum takes. To go from[br]one side of its motion to the 0:14:53.040,0:14:56.685 other and then back again. So[br]that's the period. 0:14:58.180,0:15:01.337 L is the length of the pendulum. 0:15:06.320,0:15:09.210 And she is the acceleration. 0:15:11.820,0:15:13.068 Due to gravity. 0:15:17.090,0:15:20.359 Which is 9.8 meters[br]per second squared. 0:15:21.780,0:15:25.320 Let's imagine we've got a[br]grand father Clock, and the 0:15:25.320,0:15:28.860 length of the pendulum L is[br]equal to 1 meter. 0:15:30.070,0:15:32.178 So in our formula. 0:15:33.720,0:15:41.376 Going to put 2π multiplied by[br]the square root L is 1 0:15:41.376,0:15:45.204 meter divided by G is 9.8. 0:15:48.050,0:15:55.274 And that gives us 2π. Now, if[br]we calculate 1 / 9.8 and then 0:15:55.274,0:15:57.338 square root the answer. 0:15:58.810,0:16:05.386 We get 0.319 *[br]2 and by pie 0:16:05.386,0:16:11.140 and we end up[br]with two .007. 0:16:11.820,0:16:18.442 So the period of the pendulum to[br]the nearest second is T equals 2 0:16:18.442,0:16:23.172 seconds because we've used the[br]units of meters per second 0:16:23.172,0:16:24.591 squared and meters. 0:16:29.160,0:16:33.263 That was a selection of standard[br]formerly now for the magicians 0:16:33.263,0:16:37.364 memory trick. I've got a[br]selection of 30 or so cards 0:16:37.364,0:16:40.796 here, each with eight digit[br]numbers on, and if I could have 0:16:40.796,0:16:42.798 a helper to select one at random 0:16:42.798,0:16:47.420 for me. Now, if you could[br]give me the two digit card 0:16:47.420,0:16:50.940 number which is on the top[br]left hand corner, I'll tell 0:16:50.940,0:16:54.460 you the 8 digit number on[br]the card number 14 #14. 0:16:55.750,0:17:02.166 OK, the[br]8 digit 0:17:02.166,0:17:05.374 number is 0:17:05.374,0:17:11.170 314-5943. 7, is that[br]right? That's correct, very 0:17:11.170,0:17:17.410 good. OK would like to try[br]another one, just to show that 0:17:17.410,0:17:24.170 it's not a fluke. Can you give[br]me the two digit number again 0:17:24.170,0:17:27.810 #13 #13? So the 8 digit number 0:17:27.810,0:17:33.685 is 29101. 123, is that correct?[br]That's correct, good thank you 0:17:33.685,0:17:37.870 very much. Well, I haven't[br]actually memorized all 30 0:17:37.870,0:17:43.915 numbers that are here. I'm using[br]a formula, so let's have a look 0:17:43.915,0:17:48.565 now at the numbers and show you[br]what I did. 0:17:51.060,0:17:54.960 Now the only information I was[br]given was the card number. This 0:17:54.960,0:17:56.910 number at the top left hand 0:17:56.910,0:18:02.744 corner. So I had to work out the[br]8 digit number from that card 0:18:02.744,0:18:09.670 number. Now the formula I[br]was using was 2 N at 0:18:09.670,0:18:13.440 three. What end represents[br]my card number? 0:18:17.130,0:18:21.726 So for example, the number 10 if[br]N is equal to 10. 0:18:22.830,0:18:30.089 Then I would do 2 times by 10 at[br]three, which gives Me 2 * 10 is 0:18:30.089,0:18:36.494 20 at 323, so that gives me my[br]first 2 digits of the number two 0:18:36.494,0:18:42.899 and three, and then what I do is[br]add the two digits to get the 0:18:42.899,0:18:45.461 third number. SO2AD3 gives me 5. 0:18:46.390,0:18:51.010 Then the next number comes from[br]adding the previous 2 digits. 0:18:51.010,0:18:53.530 Three at 5 gives me 8. 0:18:54.240,0:18:59.100 Five at 8 gives me 13, so I'm[br]going to take the 10 away and 0:18:59.100,0:19:00.720 just write down the three. 0:19:01.640,0:19:06.008 8 at three gives me 11. Again,[br]I'm going to take the 10 away. 0:19:06.620,0:19:12.275 And write down the one three add[br]one gives me four and one add 4 0:19:12.275,0:19:17.553 gives me 5, so there's my 8[br]digit number and all this I was 0:19:17.553,0:19:19.438 given was the card number. 0:19:20.650,0:19:26.357 OK, let's show you another one.[br]Let's take this one an is 6. 0:19:27.560,0:19:33.950 So 6 is going into my formula to[br]workout the first 2 digits, so 2 0:19:33.950,0:19:40.766 * 6 + 3 two 6 is a 12[br]add. Three gives me 15, so the 0:19:40.766,0:19:46.730 first 2 digits are one and five.[br]Then I add one and five that 0:19:46.730,0:19:53.120 gives me 6 for the 3rd digit I[br]add five and six. That gives me 0:19:53.120,0:19:58.232 11. I take away the 10 and one[br]is the next digit. 0:19:58.880,0:20:00.110 Six at one. 0:20:00.190,0:20:01.996 Gives Me 7 for the next one. 0:20:02.740,0:20:05.410 One at 7 gives me 8. 0:20:06.200,0:20:12.168 7 add 8 gives me 15. I take the[br]10 away, so I write down just 0:20:12.168,0:20:17.390 the Five and eight, add 5 gives[br]me 13 again. Take the 10 away 0:20:17.390,0:20:19.628 and I end up with three. 0:20:20.500,0:20:24.240 So there we have a magicians[br]memory trick. Now you can 0:20:24.240,0:20:28.320 obviously make it as easy as[br]complicated as you like for your 0:20:28.320,0:20:31.380 audience, so you can choose[br]whatever formula you want. 0:20:32.480,0:20:34.848 And delight your audience. 0:20:36.040,0:20:37.618 So to summarize. 0:20:38.230,0:20:39.859 Working with formerly. 0:20:40.520,0:20:45.070 What you do is substitute[br]numbers in instead of the 0:20:45.070,0:20:49.620 letters and do the calculation.[br]But remember the order of 0:20:49.620,0:20:54.170 operations so that you are[br]correct with your final answer. 0:20:54.920,0:20:55.880 And that's all you do.