 You want a calculator out. If you don't have a calculator, you're going to have to just follow along, but you absolutely want one tomorrow because today is going to be very quickly a review of some of the handy math skills. Now, if some of this you're going, I'm a little lost on this, worry, but don't freak out. You're not going to be using all of this on Tuesday. This is me saying, here's stuff that's going to be handy during the year. But I always start out by answering this question, what is physics? I took physics in high school. I started teaching physics and my mom said to me one day, I know what math is. What the heck is physics? What are you teaching? And I had a physics prof who always told me that physics was the science of measurement. That's one definition. I don't know if it's the best definition, but he felt that it was a good definition because if you're measuring something, you were doing physics. If you weren't, you weren't. Well, fair enough. But it leads to the obvious question. What do we measure? Primarily here in high school, we measure three main things. We measure time. What are the units for time seconds? We measure length. What are the system internationality standard science units for length? Yep. And I'll spell it the proper Canadian way with the R-E instead of an E-R. Don't ask me why, but that's how they spell. By the way, my handwriting is atrocious. If you can't read something, feel free to ask. It has gotten better, believe it or not. It used to be worse. That's why I type almost everything. Physics 12, every lesson will be given to you like this. It's kind of a pre-type, let's fill in the stuff, also because it's way less frustrating for me. When I first started teaching physics 12, I would spend 10 minutes just sitting here watching kids copy out a question and just what a waste of time. So I pre-typed everything. And the third thing we measure is mass. Now, mass should technically be measured in grams, but a gram is so small, the standard measure of mass is actually the kilogram. I understand why they did that because otherwise you'd have all these extra zeroes on every single answer. It'd be a pain to write, but I don't like the fact that there's no prefix, there's no prefix, and suddenly there's a prefix. The units used are SI units, stands for System Internationale, it's French. And in fact, there are seven base quantities in physics. These seven quantities are what every other physics unit that we ever learn is based on. The first three I've already talked about, we have length in meters, time in seconds, and mass in kilograms. Does anybody know what do we measure electric current in? Not volts. Actually joules is a measure of energy and it's actually a Newton meter, which actually means it's a kilogram meter per second squared meter, based on the three up there. Ohm is a measure of resistance, Watts is a measure of power, Sean, amps, symbol, A. You won't define, and I just give, we will actually define an amp, but all the other units are based on that. We'll define it based on a unit that's actually part of defining. Temperature. What do we measure temperature in? We measure it in degrees, but we don't measure it in degrees Celsius or degrees Fahrenheit. You actually know what the System Internationale, the standard measure of temperature is? Degrees what? What? What? Degrees Kelvin, or a little degree symbol and a lowercase K next to it. Named after William Thompson, who was also Lord Kelvin, that was his British title. Good mathematician, knew a lot about heat, thought he knew a lot about electricity, but he was wrong, but very, very powerful. We figure he set back our discovery of electricity by about 25 years, because he was in charge and he believed it worked a certain way, and it didn't, and anybody who spoke against him, he ruined their career. He was very vindictive. However, until about three years ago, Google was great, because if you Googled the name Kelvin, my name, the first thing that came up was a web page that said in huge letters, Kelvin is God, right? Sadly Google redid their algorithm, that's not the case anymore. Although I don't know if you've tried Googling your name, there's a Kelvin Dewick who owns a resort in the Bahamas. I need to get in touch with that guy and see, free room. The amount of a substance, what do we measure the amount of a substance in? Those of you that came 11 should know this. Volume is a mathematical concept, it's actually not a unit measure. As soon as I say it, you'll know, but I'll see if it comes up with it. Mr. Prusa has that lovely little box cube hanging, you've seen one, you've seen a mole. This last one is my favorite unit, because the first six, you can't tell what they are until you see it. In other words, if you were from a foreign country and they never learned English, and I use the term meter to you, this does not pop into your mind. Or if I use the term second to you, this does not pop into your mind. I love this last one, because even though you've never actually seen this unit of measurement, as soon as I tell it to you, you'll know exactly how big one is. Does anybody know what we measure light intensity in? Physics 11 guys who have me last year, I told you last year, at the beginning of the year. Remember? It's a cool one. Candles, you all instantly right now know how big one candle is, don't you? To me, that's a great unit of measurement. The sun is like several trillion candles. What's one candle? That's a great example of what we measure light intensity in the first six years of the year. We don't look at temperature and heat in physics 12, although it's nearly cool, listen, cool stuff. Moles, you've done in chem 11, those of you that have done some chem, light intensity we don't look at at all. In fact, I know almost nothing about it. Then we also have all these turned the page, or next page over, I think I went two to a page for you guys. Wonderful prefixes. Yes, normally I fill those in, but for physics 12, I'm not gonna. In physics 11, we did an awful lot of unit conversion, and I hate unit conversion. My argument has always been why is give me the units and what I want. I wouldn't measure it if I was doing a physics experiment. I wouldn't measure it in hours. I would set my stopwatch to seconds, and I would just measure the stupid thing in seconds. So even though this chart is here, I'm going to leave it blank. I have a formula sheet, the official Provincial 12 formula sheet for you, but I have not photocopied it yet, because I always photocopied on color photocopy paper, so it stands out. It's what you're allowed to bring to tests. There was no color photocopy paper on Tuesday, yet we were out. So I'm going to photocopy it today after school. I'll have a few tomorrow, and one of the things, Katie, that it has on it is this chart filled in. In other words, you don't have to memorize it. Having said that, as the year progresses, there's gonna be, I think, three of these that I'm gonna tell you to memorize, just because if you're looking it up every time, you're gonna go crazy every once in a while. I'm gonna say, look, if you're lazy, memorize this stupid one here. So there's the prefix system. You did it in Physics 11, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah. During this course, we're gonna use models, often mathematical models, to help us understand a particular set of phenomena, to help us understand what's going on. Note, gotta be full of honest with you. The models will almost always be wrong. The coal, about 90% of what I teach you this year, is gonna be garbage. Because the math will get yucky if I want to be, get on to the real world. For example, math catch. And back, we'll look at projectiles, except we're gonna ignore air resistance, because you really need to count for this to be air resistance, and the math gets yucky. We're gonna look at circuits, except our wires will never get hot. Because when they get hot, the resistance of the wires actually changes, and that means your circuit changes, and that means the wires get hotter, and the resistance changes again, and we need to count them. Forget that, we're not gonna do that. But you know what? In that toss to math, as long as my projectile is reasonably aerodynamic, air resistance won't play that big a role. Anyways, if I tried to throw you a piece of paper, fair enough. Air resistance plays a huge role. But, we're gonna live in our magic, idealized, nice, clean physics world. If we're looking at two things being touched by a rope, the rope won't have any mass, cuz that would be yucky now. Or if we have a pulley, the pulley will be massless and frictionless, because to try and take that into account, we need calculus, and that's yucky now. Who's doing calculus here, by the way? So you'll have a huge advantage in Calc, because one of the first, by about November, when you're doing applications of derivatives. A lot of them are straight physics. And you'll be going, that's where that comes from. I know how to use it, I just didn't know where it came from. Turn the page. Now we're gonna get into the math stuff. Since our models will be mathematical, good math skills are a must. Here's a review of some of the basics. The first one is solving a quadratic equation, although that begs the question. What is a quadratic equation? What makes a quadratic a quadratic? How can I glance at an equation and instantly know this is a quadratic equation? And it's really easy, everybody know? I think you thought it right and said it wrong. Louder, Nicole? Square, yeah. It's got a square, it's a quadratic. It's got a cubed, it's a cubic, it's got a bigger exponent. But if it's got a squared, and no other wonky weird stuff, like no square root of x, or no something to the power of x, or no sine or cosine. It's nice, clean, squared is your biggest exponent, it's a quadratic. So here's the question, how do you solve a quadratic? What's the first thing that you always do? Math 11 review, time boys and girls. Make it equal to zero is what I'm gonna say. You said move everything to one side. I like to say make it equal to zero. And my philosophy for grade 12, I want to free you up. What I mean by that, I'm blank, what was your name again? Brett, I should have that. Okay it is, you were there before, just confused. Brett, what I mean by that is, I would much prefer you to be able to glance at A and without showing any work, rewrite it equal to zero in your head. In other words, I'm gonna do this. You can go plus two both sides and show all the work if you want. Go ahead, but if you don't need to, I'm really gonna push you to start doing some stuff in your head. Now, a lot of that was because the provincial exam used to be two hours and it was a sprint, and so anywhere I could save a kid 30 seconds if I could do that 30 times, that was like an extra 15 minutes of time. Now I just do it because I'm a nerd. So we've made it equal to zero. Now what, well you either factored or if it didn't factor, you pulled out the quadratic formula. This one I can glance at and I know it factors. Does anybody know how you can tell with these weird ones that have the coefficient in front? How can you tell that they factor just by glancing at them? You guys know the trick? Easy trick, okay? Here's how you know that it factors. It doesn't tell you how it factors. It just tells you you can factor it. Joel, what's five times two? Are there numbers that multiply to 10 and add to seven? Are there two, yes, then it factors. In fact, I could also have an 11 right there. Are there numbers that multiply to 10 and add to 11? That one would also factor. Any other number there? Well, it doesn't necessarily tell me how it factors. How does it factor? Well, there's about eight or nine different ways. There's something called factoring by grouping, not groping, but grouping. There's something called the, there's a method from India. It's the cheat-nuncheat method. There's something called the box method. I'll be honest. The best way to factor, this is what I always teach my kids in grade 10, is to cheat. Seriously. What I mean by that is, clue in that the teacher who wrote this question is not that smart and doesn't want to try and spend 30 minutes coming up with something with huge, ugly factors. They're often doing the math in their head because they're lazy, which means probably they're just imagining two brackets, foiling them in their head and writing that down as the quadratic. Yes, that's how we make up the questions. This is what I mean. Put your pencils down, look up. If I was factoring this, I would say, what's the first term? I got your last name, doesn't it help me at all? Neal. What's your name again? Strangely enough, oh, there it is, sorry, it's a hole punched. I was going, wait a minute. Trevor, thank you. Trevor, Trevor, what's the first number here? 5T squared. For that to be there, I know that if this factors into two brackets, it had to have been a 5T and a T. Nothing else works. Prime numbers. What's the last number? For that to work, there had to be a one there and a two there, or a two there and the one there. I imagine the one there and the two there. I'm gonna write it, don't you yet? And in my head, I foil it, see if I get a seven in the middle. I foil it out in your head. Do you get a seven T in the middle? One times T is what? One, five times two is what? So you get a 10T and a one T. Is that gonna give you a seven T? What's that gonna give you? I got the numbers in the wrong place. I want the plus two there and the plus one there. That sounded like a long explanation. When you get good, you can do it in five seconds. In fact, when I taught factoring these ugly, remember doing factoring these ugly ones? When I taught it to my grade 10 students, ah, I got a letter B. No, what's your name again? Brianna, okay, I had the B part. Brianna, what I would do is I would give them, I kid you not, a hundred of these, which sounds like a lot, but something magical would happen after around 30 questions or so. Somehow their brain would actually develop a circuit and they would write the first two numbers and their eyes would glaze and they would just see the answer. What are the roots? What are the roots? Come on, you just did math 11. What's the root of this bracket here? Negative one, right? What was the trick for these ones? You learned a great shortcut. What was it? Change the sign and divide by that. Negative two over five. Having said that, in physics, they will almost never factor because the numbers are gonna be decimals in yaki. They might KD factor if it's a GCF. You might get one where this is zero, in which case you could have factored out a T from both, and that's a lot easier. Usually they won't. So solve this one. What kind of an equation is this? It's a quadratic. How do I know? It's got a squared. By the way, I'm gonna be repeating it over and over, especially for those who do math 12, because in math 12, by the end of the year, you'll have like 10 equations. So you'll always hear me start out. What kind of an equation is this? And we'll decide what kind it is, and then we know our plan of attack. So what kind of an equation is it? It's a quadratic. How do I know? It's got a squared. What's the first thing I do? Make it equal to zero. I have a preference. I hate the quadratic term being negative, so I'm gonna minus this to this side. I don't like the squared term being negative because we never made you factor those anyways. So I'm gonna go like this. Zero equals 4.9 T squared minus 12 T. Now this factors how? What's the first thing that I always, always, always, always, always, always, always, always. I'm talking Mitchell every single time it's a habit. Always look for when someone says factor. You guys know? You always check for first. You thought it right and said it wrong. Not a common denominator, there's no denominator there. Greatest common factor, always, always. Who's math 12? Please remember that. I've just done you a huge favor and I'll do the same speech in math 12. Always check for a GCF first. I mean, factor out a greatest common factor. The rest of the numbers are all smaller, easier math. There is a GCF here. Yeah, there is. What? I heard it. What? Gee. This one does show up in physics fairly often. This is a projectile if your initial height is zero. In case you're wondering. What are the roots? You remember from last year when you had the variable all by itself in front of the bracket, what was the root for that one? Zero, right? Right? Oh yeah, I remember some of this stuff now. And then when you had a binomial, the pattern was change the sign of the constant, positive 12, divide by the coefficient. And can someone actually do that on their calculator, please? What is 12 over 4.9? 12 over 5 is gonna be 2.4. So it's gonna be a little more than 2.4. 2.43. In my head, pretty good. Is it 2.43? Yeah, rounded out properly. 2.45. 2.45 what? So 2.45 it is. SIG figs. How many of you loved SIG figs last year and just thought they were the best invention ever? None of you? Physics 12, I'm very pragmatic. On the provincial, they wanted every answer to two or three SIG figs. So the rule this year is I don't care. Give me every final answer to two or three SIG figs. There is your SIG fig lesson. Is that to two or three SIG figs? Yes? Is this, well, zero is kind of special. Zero, if you just give us that, we don't care. You could say 0.0 on it, fine, but it's zero. What kind of an equation is this? Emily, what kind of an equation is this? How do I know? So that's where, what's the first thing I'm gonna do? Okay, now the easiest would be to plus the 10 over here but I'm telling you, I hate the squared term to be negative. That's when I make dumb mistakes. So I'm actually gonna move both of these over in my head, that's gonna become positive. Yes, and that's gonna become negative. And can we just go 4.9 T squared minus 12 T minus 10 equals zero. This might factor if there was numbers that multiplied to 49, negative 49, you know what? It's got decimals, I'm not gonna try. So what did you learn last year when the equation didn't factor what was the magical, wonderful, useful thing that you learned last year? Quadratic formula. I haven't bought candies yet. I'm gonna go shopping this weekend but for a future candy, can anybody rattle off the quadratic formula for me? Thank you for playing. Click the consolation prize at the door. Have a nice day. Mitchell, too slow. And negative X, really? Come on, have a nice day. Zay, nah, you're out of luck, man. You had your shot. Zay, negative equals minus square over B squared minus four is the upgrade. Can anybody say it faster than that? Can you say it backwards? A2 overall, C, A, four minus square B, root square B, negative, no, minus plus B, negative equals X. Yes, I'm enough of a nerd. I memorized it backwards. I love the quadratic formula as a math nerd. My math twelves have heard this feature already but Mitchell, I say that the quadratic formula is like Shakespearean math. It's almost like Iambic pentameter because it's the only one of its kind. The quadratic formula has been known well over a thousand years. The Arabs had it a long time ago. They had a variation of it. And when people found that there was one formula that could solve every question that had a squared in it, for centuries, mathematicians were saying, hey, is there one formula that will solve every equation that has a, is there a cubic formula? Or is there a quartic formula? Or is there a quintic formula? For about six or 700 years, it was one of the holy grail big quests in math. Could you find one? And it was only around the 1880s that a mathematician proved, not only can't you find one, there is none. There's nothing in degree three or degree four or anything higher. There is no one size fits all formula. There is a cubic formula that works when you have an x cubed but no x squared. There is a cubic formula that works when you have an x cubed and an x squared but no x, like there's certain specific sub, but there's no one size fits all. So over here, we're going to write, that's also on the formula sheet that I'll be giving you tomorrow, so you don't have to memorize it. x equals negative b plus or minus square b squared minus four is okay. What did that mean? Based on this equation, what am I going to put wherever I see a b? Negative 12? What am I going to put wherever I see a? What am I going to put wherever I see a c? This is where those calculators are going to drive you crazy. Especially because in the quadratic, hopefully you clued in last year, if you had a good calculator, you could just backspace, change the minus to a plus and hit enter and get the second answer right away or change the plus to a minus because it's plus or minus. So get your calculators out. Oh, let's write it with the numbers in place once. Actually, I'm going to be fussy. You don't have to be, but I'm going to do this right. I shouldn't have written x. What's our variable here? I'll do, if you write x, I won't take marks off right now. I'm not that bad, but let's put it t equals negative b. What's negative negative 12? 12 plus or minus the square root of. Usually if I can, I do b squared in my head. Hopefully most of you have memorized most of the perfect squares. So I'm going to write 144, that's b squared. Save myself some typing. Minus four times 4.9 times negative 10. All over. And often I'll do the 2a in my head because my two times table, I'm pretty good at even with decimals. Two times 4.9 is 9.8. So if I want to do this in one line and as a math nerd, I do want to do this in one line. What's the first thing I'm going to type? I'll give you a hint, not 12. It's the very first thing I'm going to type. Why? Is there more than one thing on the top? Better put the whole thing in brackets. Is there more than one number in the bottom? So I can get it, that's why I multiplied by two in my head, otherwise I would have had two numbers in the bottom and I would have used brackets on the bottom too. Bracket, that's my open bracket on the top. 12 plus square root button. Now my calculator, when I hit the square root button, automatically does an open bracket, which is good because is there more than one number in the square root? Bracket, 144 minus 4 times 4.9 times negative 10. Close bracket for the square root. Close bracket for the top. Divided by 9.8, enter. The first root is 3.1 or 3.11, but not 3.106 because that's four sig figs. Don't need that anymore. Am I right? Is that the same thing? I think I'm right. Minus four times 4.9 times negative 10. Close bracket, close bracket. Yeah, I'm right, am I not? So one of the roots, T equals 3.1 or, and this is why, sorry, having a two line display calculator is so handy, I can now go second function, enter, backspace, or on your calculators, figure out how this works. Maybe it's just the backspace button. I changed that to a minus. You really use that calculator for all of last year? This is such a time saver for that whole quadratic unit because the other root is negative 0.657. Gonna pause here. You need to know how to solve a quadratic. Well, okay, I lied. You either need to know how to solve a quadratic or how to use your calculator's built-in quadratic solver. And if you use the built-in quadratic solver, all you need to do, Connor, is write down the quadratic equation as your work and I'll have to assume that you use the quadratic formula. I won't know that you use the technology. That's how they work on the provincial and I'm good with that. In fact, I have a quadratic solver and I use it all the time. So what's your homework? There's the magic ding, we're live. I can replace or erase the pause. So we've been looking at solving quadratics. Let's look at example D. What kind of an equation is question D? Quadratic, how do I know instantly? Got a squared. Those of you in math 12, I'm doing you a favor when you have about 10 other equations in your back pocket. It's nice to know right away what it is and what your strategy is. What is our strategy? What's the first thing we need to do to solve a quadratic? Make it equal to zero. Now the easiest way would be to plus the 19 over, but I have a personal preference. I hate the quadratic term being negative. That's when I make dumb mistakes. Did I do my mistake speech with you guys yesterday? So to me, I always make a joke. Blanking on the name, I got Brianna here, but back there, hang on a minute, I gotta check. Kayla, geez, I should have had that. Kayla, I used to always make the joke, I never make mistakes, I would say. What I mean by that, to me in math or in physics, a mistake is a dumb mistake that when you look at it later, you're like, what the heck was I doing? Here's the classic one. Two times three is five. Oh, they added instead of multiple. I see that all when people are in a rush. Who's in math 12? Okay, I've taught math 12 before. I guarantee if you're in my math 12 class, when we go through the tests, after each test, when we go through it, you're gonna be angry at yourself because about 80% of your errors are gonna be mistakes. Only about 20% are gonna be mistakes where you actually didn't know what to do. So I am big on whenever I try and learn something new, I wanna do it in the minimal amount of writing, I'm lazy, but with the maximum amount of getting rid of dumb mistakes and one of the things I do mistakes with is negatives. So even though the easiest would be to plus the 19 over, I hate the quadratic term being negative. I'm actually gonna plus both of those over to this side. I'm gonna rewrite this as positive 4.9 T squared plus 4.3 T minus 19 equals zero. Trust me, does that factor? I don't care, it's got decimals and I'm gonna try. It might with like decimals, but I don't know my decimal times tables, it doesn't. So I gotta pull out the quadratic formula. Well, not really. Who's got a graphing calculator here, a TI-83? Get it out. TI-83? Ooh, show me the cover, show me the front. Are you in math 12 as well? I didn't know. Are you in math 12 last year? Okay, the 86 is, that is legal. Okay, I'm okay with that. I don't know if you'll have this. Anybody have a TI-83 or 84? None of you, okay. Who has a Casio calculator? Look at your calculator. Top left, second button from the top. You have a count button. You have a built-in quadratic solver. Okay, so you have the same one, Kayla, or not? Okay, so ready? Get it ready. Press the mode button and keep pressing it until you see equa, which stands for equation. Ah, yes, equa, sorry. What number does that associate itself with? Press one. And then what does it say? Ah, so that's if you have, don't hit anything yet. That, remember last year when you had systems of equations, x's and y's? That's if you have two or three unknowns, but I think there's also an arrow sideways on the screen, is there not? Press arrow sideways on that little oval. What's it say there? Degree, question mark. What makes a quadratic a quadratic? Press the two. And you will see it asks you for A and B and C just like the quadratic formula. Type them in, equals to enter, type them in, equal. See if you can figure the rest out yourselves. Now the rest of you poor peons that didn't spend some money. You're gonna have to do this by hand or if you have a graphing calculator, I will give you the quadratic solver. If it's a TI-83, I don't have one for a TI-86. Check your manual, there might be one built in. I'm not familiar with that one there. The rest of us, normally I would write out the quadratic equation since I have it right here and it's on my page. I'm just gonna go straight to plugging in numbers. T equals negative 4.3 plus or minus the square root of. I always said yes, I said yesterday, if I can square the term in my head, I will. I don't know my 4.3 times table or my 43 times table, so I'm gonna write 4.3 squared. Minus 4 times 4.9 times negative 19, all over. I can do two A in my head, two times 4.9, two times five would be 10, two times 4.9 is 9.8. You got the roots all ready? By the way, if you use that on a test, I'll give you zero. Oh, no, no, actually sorry. Unless you write that as your work, if you write out the quadratic formula, I double check the provincial exam marking rules. The rules are I have to assume you use the quadratic formula. I'm not allowed to assume that you use the built-in solver. Work for you as well on me? The rest of you, I'm deliberately not going to my calculator right now because you need to learn how to type this in your cells. What's the very, very, very, very first thing you're gonna type? Bracket, more than one thing on top. Try typing this in. I'm gonna freeze the screen so you can't see what I'm typing on my calculator. Of course, the people at home, unfortunately, that means that they can get this. See if you can get the roots. I think for one of your roots, you're gonna get 1.58. Yes? Why would 1.579 be wrong? What did we say yesterday? What was my 30-second SIGFIG lesson for the entire year? What did I say? Every answer is gonna be what? Two or three SIGFIGs. There's your SIGFIG. Honestly, the reason I do that, by the way, unless you have equipment that has tolerance specs printed on it, SIGFIGs are only a concept. Those of you in university, when you're doing labs and each piece of equipment actually has an accuracy, then SIGFIGs are useful and important because then you know how accurate you can be with the equipment that you're using, but then they're in contact. Yes? You might have yours in a rounding up mode, so what you wanna do is flip your calculator over and press the reset button on the back with your pencil. Also why I like those ones. There is a reset button, yes? Yeah, I'll unfreeze the screen. I get T equals 1.58, and I think I did a big rant about a good calculator yesterday. With the graphic calculator, second function enter brings up your previous line. With a two-line display, usually back arrow brings up your previous line, but it's way nicer just to be able to change that plus to a minus and not have to retype everything. Negative 2.46. Emily, is that right? Because you have the built-in solver, so we know yours is right. We'll assume you could type in A, B, and C correctly, right? Did you know you had that last year? 2.46, did I read my calculator wrong? Am I, yeah, 2.46, thank you. Now, I talked about mistakes. I am the king of them, so here is the rule. Don't assume that because I wrote it down, I'm right. If you catch me making a transcription or copying it down wrong or doing stupid math, if you're the first one to point it out, you get a candy and going shopping this weekend. Remind me on Tuesday you get a sour gummy bear, okay? Sometimes if I sense you guys are drooling and not paying attention, I'll start making mistakes on purpose just to see who's actually following along. I talk a little bit about being an active learner and that's part of it. Really, you do suffer, oh yeah. One of my funnest ones, I had an honors class, honors 10, about 10 years ago, and I gave them a multiple-choice quiz, 20 questions, and I made every single answer beep, everyone. And I watched after about six questions as these kids were looking up at me and kinda, oh, I can't look at someone else, he'll think I'm cheating on how honors kids are. And then they would go, I could see them, they were going back and checking their work, because you can't have a multiple-choice test where every answer says, yes you can, if true randomness is random, at least once there should be a multiple-choice test where every answer was the same. Actually, I was really mean. I made number 19A. Now, I had a couple of kids who were really smart who knew me. They said, after about seven questions, they just filled in Bs all the way because they knew that I would do this just to torment them. And they all got number 19 wrong. I had one kid who was really smart who knew me really well. She said after the quiz, actually, Mr. Derrick, I know that you like to mess with our minds. So as soon as I got eight Bs in a row, I did number 20 and number 19. And whenever 19 was there, I figured that's where you put the one to trick us. I filled the rest in for B, though. I'll mess with you guys, come on. Okay, 1.58, negative 2.46. There's the quadratic, turn the page. Topic two is formula manipulation. This is a great skill. It will save you lots of time in your homework. I really, really, really encourage you to get good at doing math with letters in your head. For example, question two A says, solve that thing for A. And what that means is get the A by itself. I know I emphasized this in my physics 11 class last year. How would I get the A by itself? Matt, what would you do to get the A by itself here? No, I would not. I always divide last. I do something else first. Yes, yeah. Minus C and then. And if you can go without showing any work, I prefer that. You said minus C from both sides, right? I did that. And then divide by B squared. If you can go straight to that, great. You don't have to. Oh, but you'll be a happy camper if you can. One of the things that we're going to be doing very, very frequently is cross multiplying. When we get to orbits, the equation to figure out how high something is in orbit is this. It looks ugly, but it's really just one fraction equals one fraction. It's cross multiplying. So, oh, I should have said don't write that down. Don't write that down. Cross multiplying, get the A by itself. Well, first, let's get the A squared by itself. How would I get the A squared by itself? Have you guys picked up the great shortcut for cross multiplying when you have one fraction equals one fraction? You know what the real trick is? You move stuff diagonally. I don't even cross multiply anymore because that's too much work. I know if I have one fraction equals one fraction, that E can move there just fine. Or that A squared can move down there just fine. Or that B or that C can move up here. Stuff moves diagonally. And all I do is move stuff around until whatever I want is by itself on the top. So, you know what I would do? That BC, I move it across and to the top. And I have A squared equals BCD over E. I wanna get rid of a squared. Sean, great big square root of BCD all over E. Is that okay, Jeanette? Zip, zip, zip. We're up, hey. Grade 12, I'm in the shortcuts. Grade eight, yes, I make you show all your work because I have to assume you're all at the lowest common denominator and I have to teach you the basics. But grade 12, let's free you up. C, solve D equals VIT plus a half AT squared. Hey, that should look familiar. 4T, if VI equals zero. Now, VI equals zero, what does that mean? That. I'll write this in our notes but I would be okay if you didn't bother dropping all this down. The other thing that I do though is I don't think of this as one half. What I really think about this is AT squared over two. Is that not the same as multiplying by one half? Now, why did I do that, Adam? Because now, technically I have one fraction equals one fraction and stuff can move diagonally except you will never get me to put that stupid one there. I mean, that's got better things to do. If I wanna get the T by itself, the two moves up diagonally to the top, the A moves down diagonally to the bottom, and Sean, how'd I get rid of a squared? By the way, technically in math, we would say this, don't write this down. Technically in math, we would say it's actually plus or minus the square. Remember last year, math 11, you learned the square both like plus or minus. But because we're talking about time, time is positive, we're kinda sloppy that way. I should have because this was generic, technically put a plus or minus right there but in physics, we're a little sloppier because we know we're talking about positive terms. So the handy shortcut by one fraction equals one fraction, I can move terms diagonally. This class ends at 11.15, so we have 40, 39 minutes. Okay, I should be done pretty quick, I hope. Next page, trig. Connor, you need to make sure that your graphing calculator is in degrees. You know how to do that? Probably press the mode button. Who's math 12? So especially, I know I hand out the graphing calculators, I think Mr. Gerard does too. The graphing calculators by default go to radians. In physics 12, whenever you're doing trig, whenever you're getting triggy with it, you need to make sure you're in degrees. And so all of you on your calculators right now, make sure you're in degrees. How do I know? It's your calculator. Here's how I can check. Find the sine of 30, if it's not 0.5, you're not in degrees. Sine of 30 is 0.5, that I know. So if you're not in degrees and you don't know how to go into degrees, this is your chance to raise your hand and ask and I'll show you on your calculator. But I won't show you next week because I expect you to have learned it today. We're all good? Okay, trig. Sokotoa, the sine law, and the cosine law. Most of you will get so good at trig this year that writing stuff down will almost be tedious. I always do write one line down on a quiz or on a test. In my homework, I'll sometimes try doing the whole thing on my calculator because I always attach the answers. I'll try and see if I'm right. And then if I'm wrong, I'll write one thing down. So we have two main types of trig. Right angle trig and non-right angle trig. Example A, is that solved for X? Is there a right angle or no? There is. Then I can use good old, remember, sokotoa. I'm gonna label the sides. Here's my angle. This side here, Trevor, opposite adjacent or hypotenuse. Good comeback, yes. What about this side here? Which one? I agree with you. Put your pencils down for a second. I have to be honest, I have a beef with some teachers when they introduce trig to you. Some of them just tell you to label all three sides. Some of them would tell you to put an A there. I think that's dumb. Here's why. Is that extra writing? Yes, and to me it makes it more confusing. Trevor, if I leave it like that, isn't it clear that it's O and H and sine? I don't have to think about it. Where if that A is also on the diagram, I now have to go, which one am I gonna use? Oh, don't use the A. I need to find the one with the O. It's more thinking and more writing. To me, silly. So I always leave it blank. If I don't need it, I won't label it. Which trig function is this? You say sin? No, sin is when you swear in my class. That's a sin. Sine is the trig function, yes. How do I know it's sine? The handy-dandy acronym O and H, opposite hypotenuse stands for sine. What always goes next to the trig function, the angle. What's the angle here? 58 equals opposite over hypotenuse. Adam, call me silly, but isn't that once again, one fraction equals one fraction? Can I not just move stuff diagonally? Does not the X move to the top over on this side and the sine move to the bottom over on this side? And now I've got the X all by itself. I'm gonna write this in my notes, but if you go straight to the answer in your homework, I think that's great. In our notes, just so that we know what the heck we did, it is gonna be 13.1 divided by the sine of 58. And I better check my calculator. I'm going to bet mine is in radians. It is. 13.1 divided by the sine of 58. Close bracket on my calculator. 15.44, oh no, wait a minute. Two or three sig figs. I'd accept 15, but I think 15.4 would be better. Units, units, meters. You yawned yesterday too, right about this time. I think I picked it on you then. Note to self, come up with ways to keep Emily away. Done. B, is there a right angle, Mottz? Do I know the angle? I start out the same though. I'm gonna label the two sides. Opposite adjacent or hypotenuse. Which trig function? What I was doing at Disneyland last week. Ha ha ha. Zzz, okay, fine. 10. What always goes next to the trig function? The angle. What's the angle this time? It's a variable. What do we call that thing? Theta, it's a zero wearing a belt. Why do we traditionally use the letter theta for an angle? You're gonna find the more math you take, we like to reserve certain variables for certain mathematical functions because that way, when you see that variable, right away, oh, it's an angle. What do we use X and Y for? Points. What do we use A, B, and C for? Two things, Pythagoras and quadratic form. It gives you context. So generally, we tend to use Greek letters, often theta, for an angle. Tangent equals, tangent equals what over what? From Sokotoa, what is it? And what is opposite here? 12.6 over 3.7. Adam, I agree, this is one fraction equals one fraction. However, this is not cross multiple, yes? Sorry? I've been calling you Adam like three times in a row. Just told me, Andrew. Dear internet, I am an idiot. I've been calling my student the wrong name. His name is Andrew, for posterity. So, scene one, act one, and take two, action. Andrew, this is not cross multiplying, even though it looks like it is one fraction, it was one fraction because the variable is inside a function. All right, Rainy X, how do I find an angle on my calculator? It's actually easier. Yeah, second function or shift or invert, whatever your calculator calls it. So, on mine, I go second function tangent, and then I just type in the fraction, opposite over adjacent. Now, you do have to use brackets because there's more than one number. Mine does an open bracket right away, which I kind of like, to be honest. And I get an angle of 73.6 degrees. How do I show that step? Now, in your homework, I'm not too fussy, but on a test or on the provincial, which doesn't exist anymore, you would go like this. Theta equals the inverse tan, that's the symbol for second function tan, of 12.6 over 3.7, and that's how we got the 73.6 degrees. Brett, thank you for telling me, by the way, because otherwise I would have really learned his name wrong. There's right angle trig. Non-right angle trig is a bit trickier. Turn the page, or next page over. You've already done, Brett. Take a look at C. Brett, my friend, is there a right angle in C? Then Sokotoa, Noah, can't use it. Instead, we're either gonna use the sine law or the cosine law. On this one, I can instantly tell that it's the sine law. Does anybody know how you can just glance at a diagram and say, oh, sine law will work? That's actually really easy. What you do in your mind is you pair up an angle with the side across from it, an angle with the side across from it, an angle with the side across from it, and if you have a complete pair, it's sine law. That tells me it's sine law. By the way, no, no, no, that's how I know that one's cosine law right away. It's that easy. It's like connecting the dots, but I don't like drawing the lines. It messes up my diagram. Now, what is the sine law, oh, pray, tell? It is on your formula sheet. The sine law says this. The sine of big A over little A equals the sine of big B over little B equals the sine of big C over little C. Or they might have flipped the whole thing. I can't remember how they wrote it on your formula sheet. Mitchell, the sine law has three parts, but we only use two at a time. What do they want me to find in this question, Brett? Solve four. So I'm gonna use this part. What pair do I have? I'm gonna use sine of big A over little A equals the sine of big C over little C. And now it's plug and chug. Sine of big A, 48 degrees, the angle, over what's little A? What's little A? Yep, the pair. Big A goes with little A, big C goes with little C, big B goes with little B. So 6.2 pulls the sine of 72 degrees all over little C. Andrew, my friend. Call me silly, but once again, do I not see one fraction equals one fraction? Stuff moves diagonally. The C's gonna move to the top over there. The sine 48 moves to the bottom. And am I doing that backwards? No, for you guys it's backwards, sorry. The sine 48 moves to the bottom. The C moves to the top over there. And the 6.2 also moves up. For what it's worth, C is going to be 6.2 sine 72 divided by sine 32. 48. And I'll write that in my notes. I would be okay in your homework if you tried going straight to the answer from there. Breanna, I would never do that on a test or a quiz. I'm hoping you guys are smart enough to clue in. You take shortcuts on homework, tests and quizzes. You always write everything else so you don't make mistakes, right? But try and get better than you need to on the homework. What's the answer? Is it 7.93? Yep, 7.93. Units, centimeters. We use the sine law when we have a pair. You understand what I meant by the little pair trick? Works great. We are gonna use the sine law this year in unit four. It'll save you, there's another way to do those questions using components but using the sine law turns an eight line question into one equation, cross multiply, and you're done. And as a math nerd, since a math mathematician has invented a good shortcut, I'm gonna use it. D, touchy mid-yawn, so of course, you know I'm going after you, Kara. Is there a right angle? So no soca pillow. Is there a pair? There's no sine law. Then it has to be cosine law. There is no, as far as I know, there is no tangent law, by the way. Might be but I don't recall ever learning that. What's the cosine law? Now the cosine law starts out looking like Pythagoras. The cosine law starts out like this. C squared equals A squared plus B squared but Pythagoras only works for a right angle triangle. This is not a right angle triangle. I tell people the cosine law is Pythagoras and then a fudge factor because this is a slanty triangle. It's minus two A, B, cosine, big C. And that's on your formula sheet as well. Is it not? Right, you got your formula sheet in front of you. You can double check the cosine law on there. Is the cosine law on there with the C squared by itself or with an A squared by itself? Okay. You can also, by the way, rewrite this as A squared equals B squared plus C squared minus two B, C, cosine, big A. Emily, you see the pattern? This letter and this letter are the same. The other two go here minus two of the other letter. In fact, you know what? B squared would be what? Oh, A squared plus C squared minus two A, C, cosine, big B. But you have this version on your formula sheet. End of this straight plug and chug. C squared equals, look at this lovely diagram. What's little A, 6.2 squared plus, what's little B, 8.4 squared minus two little A was 6.2. Little B was 8.4, cosine of 65. And this is really one of the main reasons I told you to get a good calculator. You're gonna be using the cosine law when we do two-dimensional momentum, when things collide at angles, cosine law. You can type this whole line in in one line. 6.2 squared plus 8.4 squared minus two times 6.2 times 8.4 cosine 65. And as it turns out, C is 65 meet, what? Oh, I haven't found C. What have I really found? C squared, Jeanette, what do I have to remember to do? And since I have it on my calculator, I'm not gonna make you rewrite it. I'm just gonna say, don't forget to square root it. And you'll know because your answer will be way too huge otherwise. Square root of my previous answer, 8.06. We use the cosine law when we have, you guys do some geometry in math 11 last year, a little bit in currency. We use it when we have this, side angle, side. Now, here's what I have not covered, turn the page. Look at E, Mitchell, right angle, pair. This is sin law, finding an angle. I am not reviewing that with you because I've talked too much. It's in your homework. If you can't figure it out, first thing you'll do on Tuesday, ask me. And I'll go over that in your homework. F, Emily, is the right angle. Pair, 38x, no, 78, I don't know the angle. 119, I don't know the angle. This is using the cosine law, not to find an angle, to find an x, practicing the cosine law. See the side angle side? That one I'm not gonna do. I already did one like that. You can also use the cosine law to find an angle, but it never shows up in Physics 12, so I'm not gonna worry about it. Oh, G, there's the one I would, I knew I'd put one on there. Can you see, not right angle, no pair, all three sides to find an angle. Let's use the cosine law to find an angle. I'll let you see if you can figure that out. How do you find an angle? Get the cosine by itself and then go shift sine or shift cosine when all is said and done. But I wanna give you the rest of class to work on the homework. When does this class end? That 25 minutes passed. So I'm giving you 20, 30 minutes, 25 passed, yes? Good, I'll give you a full 30 minutes to work on the homework. What is the homework? It is this thing here, let me pause the recording. Take a look at the hand that I just gave you. I called it basic math review. It's actually not basic math, but I wanted to give you a feeling of confidence like it's supposed to be easy. So it's got some trig on the front page. It's got some quadratic formula and some formula manipulation, and I believe I attached the answers, yes? Good, all right. You can knock yourselves out, except.