A1 Ch 10 Exam Delta Math

Hello there algebras and welcome to the chapter ten exam sample. So I'm going to take a few pieces of your chapter ten exam in delta math. So you should be able to see my screen on Delta math. So this is my student screen. So I made a separate student account for myself, so I could do things like this. You should also be able to see this is actually my document camera. So I've got a whiteboard. And a blue marker so that I can show any work that I'm thinking through as I do each of the problems. And then, of course, you should also see my graphing calculator right here. So especially since the next unit we're going to have to do is going to be really graphing calculator heavy. I'm going to eventually link where I got this graphing calculator from. So you could see how to use this as well and have it on your Chromebook. Okay. All right, so here we go. You can see that I had taken the chapter ten quiz for you earlier, right? So I did a few samples from that. I just got to move my calculator over for a minute. I just want to show you a little bit about the exam. So quadratic formula, there's going to be rational solutions and irrational solutions. You're going to have one of each of those. With completing the square, you're going to have an even B term as we know those are the only ones we deal with anyway. So that's good. You're going to have three of those. And then we've got a complete the square irrational only one of those in a complete the square. Rational only one of those. All right? So let's dive right in and let's do the quadratic formula rational solution. Okay? So here we go. Solve the equation for all real solutions. Okay, so first of all, since I'm using quadratic formula, I need to make sure that my equation is in standard form. So let's move my graphing calculator out of the way so you can see my whiteboard here. So I have 15 C squared -16 C plus three equals negative C squared. So the first thing I need to do is standard form. That means add this C squared over and combine it with the 15 C squareds I already have over here to get 16 C squareds -16 C plus three equals zero and now I have standard form so I can pull my a as the number that's in front of my X squared term. My B and its sign is the number that's in front of the C term. And my C and its and its sign will be this number that's at the end. And then of course we're going to plug those into the quadratic formula. Here's hoping you have that memorized after all my husband's awesome songs. Okay, so let's plug that guy in. There's our quadratic formula, so the negative of negative 16. Plus and minus the square root of 6 squared negative 16 squared. Excuse me, minus four times 16 times three, and all divided by two times 16. Okay. So to simplify this, I'm going to want my graphing calculator. So I just turned it back on. And let's see. So let's do 6, squared. Minus four. Times. My a is 16 times three, and let's see what we get. This is the number under our radical. Okay, we get 64, got it. So X equals the negative of negative 16 is positive 16. Plus or minus the square root of 64. All divided by two times 16 and just in case you don't know that, I'm just going to show you how I'm using this graphing calculator on my screen, right? To do my basic operations and simplifications. Now I got lucky here because 64 is a perfect square. And the square root of 64 just in case you don't know. Second X squared gets you my square root sign. Plug 64 in and parentheses enter. Okay? So X equals 16 plus and -8 divided by 32. Okay, so this is two different options. It's X equals 16 plus 8 divided by 32. And X equals 16 -8 divided by 32. All right? So let's see. 16 plus 8. So hold on. Getting used to. I'm pretty sure. Oh yeah, yeah. So I'm actually the wrong thing. See, that's why I was a little nervous about it. Okay, so 16 plus 8 is and 24 divided by 32. Gives me a decimal. Now, we probably know what that decimal is equivalent to in fraction form, but I'm just going to show you if you press math. And one, you'll actually have that changed into the fraction three fourths for you. So you're graphing calculator can give you the fractional answer, which I usually do. Okay? Then, of course, we'll have 6 teen -8, 8 divided by 32, which again is going to give you a decimal answer, right? One we probably know the fractional equivalent to, but if you press math and number one, it will change that into a fraction for you. So both of these answers are rational numbers. They're both fractions. And now I need to plug that in on my answer right here. So now I go back and I put this here. Now I would bet if you put .75 comma point two 5, that will be a perfectly acceptable answer. But I would also bet that if you put one divided by four as one fourth and three divided by four, as three fourths, you would also get correct answers. Now, I love that it asked me, am I sure that that's what I want. So I just kind of looked back over here. That's what I have right here. So that's what I want typed in here. And it tells me I'm right. Okay. That's how we want to do this. Just like that. So I can go to the next problem. Oh, I've met all the requirements for this section. So I can go back and I click on the next section. Now actually I want to show you this one because there's three of them in here. Now this will just be quadratic formula where there'll be a radical leftover. So it won't be a perfect square right here. All right, so that's going to be really the only difference in that particular place. Let me just clear my whiteboard before I get started on my next section. Okay. So let's go to oops. Well, it got me in there anyway, right? Let's say I just wasn't ready for that and I wasn't really sure what was going to go on here. It'll show me an example. Come up to the top right show an example. Shows you the quadratic formula shows you plugging it in and then shows you simplification. This radical doesn't simplify. We are done. That's what you would then have to type in in the answer, okay? So let's actually go to the original problem. You know what? I will do this one. I want to show you how to type in and submit your answer here. Okay, so let's get N squared -5 and minus two equals zero. Let's get that on my whiteboard. We are lucky this time. We are automatically in standard form. So we can just pull our a, our B, and our C right out. Remember the signs come with. So then we have X equals negative B plus and minus the square root of B squared minus four a, C, all divided by two a it's really hard not to say it without being sing songy after you know the song, right? So then X equals the negative of negative 5. Plus or minus the square root of negative 5 squared minus four times one times negative two, all divided by two times one. Let's see what we got here. Positive 5. Plus or minus the square root of let's see. So I'll just use my graphing calculator real quick. Oops. I don't know how I got signed out. Hold on. I'll pause it and come right back. Okay, I'm back. Sorry. Just trying to get my graphing calculator up the screen and I lost my account. Thankfully, came right back to the problem I was working on. So that's good to know. If you accidentally get signed out, it'll go right back to the problem you were working on. All right, so I was continuing here. That's right. I came to my graphing calculator because I wanted to be able to type in negative 5 in parentheses squared minus four times. So I'm just reading what I've got right here, right? Negative four times. One times. Negative two, and that'll give my number under the radical. So I get 33. All divided by two times one is two. Okay, so now is one I think. All right, let's see. Is 33 a perfect square. Nope. It's not a perfect square. Is 33 divisible by any perfect squares. No, it's not divisible by any perfect squares. So actually this is going to be my final answer. I'm just going to leave it like this. Now do remember that this is two completely separate answers. It's X equals 5 plus radical 33 over two and 5 minus radical 33 over two. So it's two completely separate answers, but still I get to write it as one. And if you notice over here, the plus and minus symbol and the radical symbols are right there for me as I'm typing this in, okay? So here's what I'm going to do. Are you ready? So my answer. I'm going to do in parentheses. 5. Plus or minus radical, 33. And then see that's in parentheses. So over here, I'm going to be out of the parentheses and then do my division sign to put my two on the bottom. Okay, so I made sure that all that was on the top and then that too was on the bottom. Do I want this to be my answer? Just double check. That's what I had. Okay. And there you go. All right? And that is record one of one. So I did the one problem I needed for this section. So now I can go back and I can move on to the next section. Okay. So this is multiple choice. So that's why it says MC right here is the type of question. That's why there's three of these. So we're just looking for an equivalent equation to the one that we were given. And actually, the one that we were given kind of got us started as far as having a number on the other side of the equal sign, right? So let me just clear my whiteboard up. And get this going. So X squared -8 X plus 16 equals negative four. Actually, I want to move the rest of the numbers over to the side of the equal sign and leave the X squared and the negative 8 X on this side all by themselves anyway. So let's subtract 16 over here. And let's leave a plus blank where the 16 used to be. So X squared -8 X plus blank equals negative 20 plus blank, okay? So now let's fill in the blank. 8 divided by two is four and four squared is 16. So 16 goes on the blank. And then over here, I can now, since I have a perfect square trinomial, I can write it as one binomial squared. So how to do that, I just divide negative 8 by two. So negative 8 divided by two is negative four. So X minus four in parentheses squared. Add these numbers up, you get negative four. And now that's all I needed to do because I just needed to find an equivalent equation that had an even B term. So I look at my options and low and behold. I found an option. There we go. Okay? Now I'm almost complete because I have to do two more of them. All right, I'm not going to do that right now. So let's say I just, I don't want to do that one right now. I'm going to come back. Go back. And come down to complete the square irrational only, right? So here we go. I've still got plenty of room on this whiteboard, so I'm just going to push this guy up. And get started on my new one, which would be X squared plus 20 X plus 86 equals zero. Now this guy is in standard form, but that's actually not what we want. So we're going to want our number to be on the other side of the equal sign. So I'm going to subtract 86 over to the other side of the equal sign and leave a plus blank in its wake. And now I'm going to fill in the blank 20 divided by two is ten, ten squared is 100. So 100 goes on the blank. Now this is a perfect square trinomial, so I factor it into one binomial times itself, or a binomial squared. And how I get that is take the middle number and divide it by two. So 20 divided by two is ten. X plus ten is what goes in my parenthesis squared. Over here, meanwhile, I add those two numbers up and I get 14. Just in case you were unsure how to add those, right? So negative 86 plus one hundred. Okay. Just so you know, you can use this graphing calculator right here. All right, continuing on, take the square root of both sides. The whole point of getting this binomial squared is so that I can actually get the X out of that binomial squared by taking the square root. Meanwhile, over here, I have to put a plus and minus in front of the radical. I think to myself, will 14 is not a perfect square. And 14 is not divisible by a perfect square. So actually, radical 14 is as simplified as that particular radical is going to be. And last but certainly not least, subtract that ten over to the other side. Remember when you move that number over to the other side of the equal sign, it always goes in front of the plus and minus. Also remember this is actually two completely separate answers. Of ten plus negative ten, excuse me. Plus radical 14 and negative ten minus radical 14. So it is those two completely separate answers. But I have the ability to write it as one. So that's what I'm going to do when I go to submit my here. So negative ten and then here's my plus and minus button. Here's my radical button. And then I just double check to make sure that that's what matches up to what I had right here. Okay. And there you go. Okay. That an even shows you exactly what you were doing each step along the way. Okay. Guys, I really think you're ready to do this. You know, if you're not, whatever, try your best, okay? You're trying to do this completely on your own, which I get is not an easy thing. And this is not an easy topic, even if I were in front of you in person every single day. Okay? So again, please do your best on this delta math test and keep in mind that I can see a lot more information than the grade that they show provides. So don't worry about the braid that they show, just worry about doing your best on each step. Have scrap paper with you so you can do your work to get that answer over here. So have that scrap paper ready to go. That will really help notice that really helped me. And I'll link to where I got this graphing calculator from really cool little place. And hopefully we'll do a lot more work with the graphing calculator at another date. Okay. All right, good luck, guys. We'll see you soon.