gre math prep workshop part 1 - continuing education · so, these workshop goals, as i said before,...

Elizabeth Jachens: So, we're going to start by going over the workshop goals, which I sort of started. I'm sure, some general introductions and some basics about the GRE and then we're going to talk about the three categories of questions you might expect on the math portion. And, then we're going to do a little bit of subject review. The subjects are arithmetic, algebra, geometry and data analysis. And, then I sort of want to leave you guys with some additional resources. How you can continue to study for the test, as well as, I'm going to send you home with an official practice test. We don't really have time to go over that in here but I want send it back with you guys with the answer sheets. So, that way you can, not only practice. You know, time yourself and see what's going to be like. As well as like, kind of getting more familiar with the different subject areas.

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GRE Math Prep Workshop Part 1Student Learning Center

So, these workshop goals, as I said before, this is the first time that the Student Learning Center has had a math GRE review and, so definitely want your feedback. And, this is, we meet once, it's sort of, of the main goal is to be familiar with the exam. Kind of what and is called the quantitative reasoning but it's really math. And, then I sort of want to tell you guys what subjects you are going to expect and hopefully by going over a couple of these, they're going to spark your attention. And, so you will sort of clue into which subjects you need to study more and maybe which ones you know that you have in the bag. And then, yeah then we're going to do a couple of examples, so mainly this is try to get you relief some of the stress. If it's your first time test taker for the GRE, kind of relieve some of the stress, so you don't go in blind. So, I just want you to hold up the two books that I used when I went to, not the first time. The first time I took the test cold turkey. The second time though, I studied, so I bought two books. The first one was a math practice workbook and I would really recommend if you think you need additional help in math. Kind of get these, the practice problems are going to be very similar to questions that you're going to see because this is like an officially endorsed company. And, this is through Kaplan and then the other one is from ETS, which actually holds.

And, so the second booklet that I got was actually from ETS, these are the people who make the test and this was a comprehensive study guide. So, it had all three sections, so I read up a little bit about that also but this is something that I recommend. These books are okay on priced I guess. So, that's the workshop goals.

Student Learning Center GRE Math Prep Workshop Part 1

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I sort of want to know, who in here has already has a date for the test? Awesome planning ahead. And, have you guys done much preparation, ahead of this? Or, is this sort of the beginning of your prep? Okay, that's awesome. Good place to kind of start out your review. How many of you have already taken the test before? Okay, a couple, not very many. So, you guys, you'll deftly hear some of the same information again but for the rest of you, I will start out some about the GRE basics kind of get familiar with that. And, then anyone who has already taken the test, do you want to share anything that you were, maybe particularly surprised about the test? Something that you thought you had a lot of room for improvement? Or, mhmm.

Audience Member: I think just getting to know the structure of the test. Like how the questions are worded, and how could I work with the chunks of questions. That really helped out a lot, so like you said it wasn't [inaudible].

Elizabeth Jachens: Okay.

Audience Member: I've done some previous, studied just on my own but like you did, you know, you can just study by yourself.

Elizabeth Jachens: Yeah, and I feel like that's pretty typical. People would take it once with maybe minimal studying and then you sort of get a good baseline about how much you need to really attack it for the second one.


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So, a little bit about the GRE basics, this is particularly for the math section. You're going to have two math sections. You have 35 minutes to complete this and so there's and there's always going to be 20 questions. So, if you sort of break that down you're going to have less than two minutes per question. So, that just a good sort of time frame, to know when you're looking at these problems they should be taking you under two minutes. Something I didn't know the first time I took is, that you can actually skip questions as you're going through the test, so if one seems particularly hard, maybe to subjects that is not quite one of your favorite, you can skip a question and come back to it. So, that's a good thing to know and in the next slide I'll actually show you what the screen is going to look like. So, you, won't be the first time you seen it either. You can also mark questions when you get to them, you know if you think you're really close but you're not positive, right? If you had to guess A or C, you can mark it, so you could put an answer and put like, go back to flag and so if you don't have time to go back to it, it saves your answer. But, if you have time, you can always go back to that and unflag that. And, then before you submit each, each section, you're going to have pain that says, would like to review your questions and you can kind of see which questions you did answer, which ones you have not answered and which ones have marks next to it still. There is an optional timer on the top right of your display. If you decide to turn it off, it will give you a five minute warning but that just means for the first 30 minutes you can kind of go at your own pace.


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And, so you can sort of decide for yourself if you would like to have that timer up there. Some people like that time constraint. It makes me more nervous, so I hid mine and it does at five minute gives you a warning and that's usually a good time to sort of go back and review any questions. This is an online test, so you do have an on-screen calculator. This is the exact calculator, so it's very simple, nothing fancy but that is something you can expect to utilize because you will be using it. And, the other thing I didn't add in here but I feel like it is important. When you go in to take the GRE because it's an electronic test, you have to go to a testing center and I explain it like going through airport security. When you get there, they're going to ask you to empty all of your pockets, take off your shoes and even things like headbands, glasses. They make you take off, so they can expect, inspect them. Like if you have a jacket, you have to take it all the way off. They like, roll up your pant legs, like check there's nothing attached to your ankles. You're not allowed to bring any food, water into the testing center and if you have like glasses you have to keep them on the entire time. So, that's just something I didn't add but I thought was, I guess an afterthought. It's sort of like airport security, so don't let it stress you out. Once you do it your second time, you know the drill.


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So, this is, what I was telling you about. This is the pane that the math section is going to look like. Up on the top you can see buttons that say quit test and all of these have, you can write it, you don't just quit it and then it disappears in case you accidentally. It says are you sure? It has an exit section review and that's what I was telling you guys about. If you guys want to grab chairs, you can probably, yeah. Review where you can see all the questions, which ones you have and haven't answered. If you want to mark something, so you can come back to it. All those are on the very top and of course I will have it saying, your calculator and your hide time. So, those are kind of good to be familiar with, where they going to show up. And, this is also, you know a typical question, how it's going to look like. You do get scratch paper on the exam, so I would encourage you to use it. I can't do that stuff in my head, so and if you guys have any questions as were going through, I'm talking too fast, I'm not talking loud enough, please wave me down and I'll try to switch.


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So, this is the review pane. I found this probably one of the most useful pieces about this math section. They also have it for the verbal section but for the math section is really great. You can see, if it was answered or not answered and then if it's marked or not. So, the mark, for me it was like, this is a question I think I can do if I had more time. And, so I think that's a very powerful tool and I'll tell you to leave at least the last three minutes to go through your, if not five, to go through your, like review panel and to check any of the questions that you think that are marked.


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So, I start telling, yeah?


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Audience Member: On that last one, it says [inaudible]

Elizabeth Jachens: Yeah, there is a difference between unanswered and incomplete. And, that's actually something I'll get to later


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but I'll sort of show you. Some of, some answers allow you to pick two answers or more and something that's not answered means everything is blank. Something that's incomplete means you have only one answer chosen when you should have multiple chosen. So, that's a good distinction that you can see and then there are also, so there couple types but both of those will be marked incorrect. So, incomplete versus not answered, both would be incorrect.


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So, there are three types of questions which is a perfectly lead on to the next one. So, there's three types of questions and I'm talking about answer format that you can have for the GRE math section. The first one is called the quantitative comparison and usually have 7 to 8 questions on this. And, these are comparing two quantities and I'm going to go into each of these in a little more detail. Then you have problem solving, which they usually nine or 10 questions and these are more of your typical math questions. The first one I think has all a little bit more logic in it and I don't prefer those but math or problem-solving is very typical math problems. And, then you have data interpretation and this usually has three questions and they're going to be based on reading tables or graphs.


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So, your directions for your quantitative comparison, once you see these it's going to be really clear kind of what, what they're asking. Usually have some sort of an initial statement. In this it says, that W is greater than one and then you have two quantities. You have quantity A and quantity B and your goal is to compare them. So, for quantity A have, it's going to have some sort of an expression that you need to evaluate. Given that initial condition and you're always going to have the same for answer choices. You have that quantity A is greater. You quantity B is greater. You have that, the two quantities are equal and then you have that you can't determine some sort of relationship with the information given. Answer D does happen, it's a little intimidating because when you first look at it, it’s kind of saying, I don't know but when you see this if you truly think that's the answer it does come up. It's not a trick answer of any sort. And, so that's the quantitative comparison.


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And, then when you have problem-solving questions, this is what I would consider more like your typical math problem. You first, you start by reading the question, you sort of identify what tasks you're dealing with and then you approach it and you need to confirm your answer. And, there are three types of answer choices for this type of problem. You either have these ovals and the ovals, which it doesn't explicitly tell you the directions. Your oval means you can only check one answer and so that's really important. So, you can only check one answer, for it to be marked correct. And, an incomplete answer in this one is if you had two of them checked. If you had two different ovals checked, that would be an incomplete answer because you’re only allowed to check one. So, the computer will allow you to mark two of them, even though you're not allowed too. And, then there's check all that apply and these look like indented square boxes. And, of course it will let you pick any number of them that you want. Typically there's only going to be 5 answer choices. There's sometimes labeled A through E. And, for this one, as I mentioned, there are not trick questions in the sense that, check all that apply, one of them has to apply, okay. And, one of, but more than one of them can apply but one of them can also, if you only check one on here, it will tell you that it is an incomplete answer. But, there are example problems in here, in my books that only have one answer. So, you can check anywhere from 1 to 5 answers, for check all that apply but you can only check one for the oval answers.

If you just want grab a chair.


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Audience Member: Where?

Elizabeth Jachens: From another room.

Audience Member: [inaudible]

Elizabeth Jachens: And, then you have numeric entry problems and we're going to go through all of these sorts of problems again, so you'll see them again really easy to determine. And, these are just going to look like, they are not going to have answer choices A through D. It's more like, a fill in the blank. And, they are going to be very explicit about how many decimal places or if they want to fraction or not, so that something you don't have to worry about. It will say to the hundredth place or to two decimal places.


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And, then the last one is the data analysis section and this is maybe a little more, a little more abstract for some people. You're going to get tables or graphs that you need to analyze and from there you pick off your, the information that you want. This is a funny example I just found, talking about the breakdown of the hipster priorities and then for this one, which is sort of typical. The second pie graph is just a subset of the first pie graph, so you need to consider on your answers. And, just like the previous word problems, the problem-solving ones, you have the same three types of answers. You have ovals, which is only one answer, you have boxes that are check all that apply and then you do have some numeric entry where you just click in the box and type normally. So, that sort of just like your brief overview of your GRE basic, sort of what to expect. It might be new information for some of you but I felt like that was the information I wish I would've known. The first time I took the test, I did not know there was a difference between the oval than the box answers, so for obvious reasons I did not do as well as I had hoped. Hopefully you guys can start off on the right leg. So, within those subset of different types of problems you can have, you have different math disciplines and we're going to go over each of these four. The first one is arithmetic and then you have algebra, geometry, data analysis and this covers everything, as far at Chico State from math. Math 11 up to math 119, so it's a sigh of relief for a lot of people, that there is no calculus in any of these problems to solve. Even if I try to use calculus on these problems it would not get me anywhere, so it always sort of nice to know that, by this level you will have seen almost all, if not all of these types of problems.


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So, for arithmetic, so this is sort of where it's a good idea if you're looking at some of my, like examples of arithmetic. If you can say, oh man, I'm not strong on this or I don't remember how to attack these types of problems. Just to put a little tick mark next to it, so you can come back to it when you study. So, you can hit all those. It’s generally agreed-upon that integers, fractions, ratios, decimals, real numbers, exponents and roots and percentages are the main portions of the arithmetic section. And, they can be asked in a variety of ways and you can also have combinations of the two. Right, so this is just my notes write integers, it could ask you about successive whole numbers and you need to make sure you can kind of distinguish between those. Fractions you need to know the, like the basic functions of them. You need to know how to add them, subtract them, multiply and divide. And, also fraction reduction shows up pretty frequently. You need to make sure you know how to reduce it, simplify them. And, then with decimals there's quite a bit of convergence between your decimals and your fractions. And, you know these are mainly like subsets of larger problems but they really do turn into key roles in getting your answer. And, then you have some questions that they'll ask about real numbers, which are just numbers expressed from the number line. And, then you exponents and roots and, so these are your exponential properties that you probably learned about, you know in like algebra two. Which we're going to go over a couple of them because I found these really important and there's so many rules. And, then you have percentages, we're using parts of a whole, discount, tax rate, interest rates, things like this.


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And, so these are the seven rules of exponents. Which are, so they’re a little small but you can but you can find online also. So, I just wanted to go over a couple of the key ones with you. The first one is if you mult. Or excuse me, the second one up there if you multiply two exponent to two numbers together, to have the same base, it's like adding exponents together. Can you all see that or do you want me to write it any bigger? Can you see it?

Audience Members: Yeah.

Elizabeth Jachens: Okay. So, that's a key one that shows up and then any number to the power of zero is always going to equal one. And, then if you have number seven, it says if you have an exponent, right, raised to another exponent, it's like multiplying them together. So, I found, like throughout tutoring at the tutoring center, there's sometimes people get a little shaky but they're definitely used quite often. Yeah?

Audience Member: Isn't there also something like exponents [inaudible] like a math class I heard that you would just add them together, for the exponents.

Elizabeth Jachens: Yeah.

Audience Member: After the [inaudible]


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Elizabeth Jachens: Yeah, so that's the one, so that's number two, right? If you have, awe man. So, yeah that's like number two, right? If you have X to the power of A. That's multiplied by X to the power of B. Right? You all, if they have the same bases, right. You can just add the exponents together, so it's like saying X to the power of A+ B.

Audience Member: Oh, okay. But, if there's just outside the parentheses then [inaudible]

Elizabeth Jachens: Mhmm. Yeah. So, yeah these are, these were the ones I wanted to highlight, probably the most common. Some of the other ones, you know, you may or may not use but these are ones that show up maybe a little more repeatedly. That, are often forgot. So, if you were to type in the arithmetic rule of exponents, this is the first image that does come up in Google. That's why I wrote the, the title on the left hand side. So, if you wanted to look at them, again and there are examples for all of them sort of how to apply them. You can find those. So, we're going to get into a couple, like practice problems kind of, I want to show you guys what a problem is going to look like. Kind of how to attack it. Always good to see a couple examples before you dive in.


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So, the first question is all about radicals. So, for the first couple problems and I have, I think sixteen example problems, so not quite a full test but some are close to it. For the first couple I'm going to kind of go through with you guys kind. Kind of get a grasp and as we get further on, I'm going to let you guys try it yourselves. You can talk among the group. If you kind of want to discuss, like where to attack it first or maybe if you don't, if your answer doesn't show up maybe where it is. And, then we’ll kind of come back up to front and we'll talk about the correct approach to solving the problem. So, do you guys want to start, so we can either start by me going through an example or do you guys want to start in, in small, like by yourselves in small groups?

Audience Member: You can do it.

Elizabeth Jachens: Yeah. Okay, so this is, alright radicals are pretty big piece of the arithmetic. And, for some people these are going to be the harder problems, in some people these are definitely going to be the easier problems but if you know the rules you're definitely going to see that there are basic questions, their intermediate questions and they're really hard questions. So, for the arithmetic section, this is considered an intermediate question, so if this doesn't immediately come back to you, definitely know there are easier questions than this on the GRE. Okay. Can you all see on this side or should I go to that side?



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Elizabeth Jachens: Okay. Okay, so we start with, right. Your initial problem and it's always first good to sort of identify, I told it is arithmetic here and radicals but what sort of rules you're going to need to try to consider. And, it's always good if you see a radical, to try to think of some of your rules that you have associate with radicals. About how you can, you know, multiply them and how you can add them. So, does anyone have any rules of radical they want to share? So, it's really silly but honestly the arithmetic was the hardest portion for me. It's the part I don't, use as much. You're going to get a little farther on and it's going to be like solving equations. We've all used those a little more frequently. I like to start out with this one because once you see a couple them you'll get started. So, there are two huge rules of radicals, as far I'm concerned and the first one is anything that is on the outside has to say on the outside. Anything in the inside has to stay on the inside. And, we're actually going to use both of these rules. So, when you multiply, right? The numbers on the outside has to stay on the outside, right.


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So, this is like the two right here, right it's on the outside of our radical


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and the numbers on the inside of your radical have to stay on the inside. So, that's the first rule.


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And, then the second rule is you can only add radicals together if they have the same number underneath their square root. So, those are the two that you can use. So, for this first one, using PEMDAS, I forget what's it called. But, your order, order of operations, right we have to do multiplication first and feel free, in your scratch paper there are things that you want to write down like, PEMDAS, like some basic like, trigonometry things. If you write in your scratch paper, first the scratch paper doesn't get taken away from you, so if you have some basic things that are always good to look back on, you can always write that in there. So, multiplication is first and using that first rule, when we multiply we can only multiplied outside, the coefficients together. We can only multiply these numbers inside of our radicals.


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So, we have two and then, this like having a coefficient of 1,


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so we still get a two, right here.


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And, then inside of our radical, we have our 2 x our 6, which is our 12.


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And, then we haven't used the next one yet. Okay, so yeah.


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Audience Member: So, if you're multiplying, then you just multiply the numbers on the outside and the numbers on the inside.

Elizabeth Jachens: Yeah so, this 1 and this 2 got multiplied together and this 2 and this 6 get multiplied together. So, the numbers on the outside are coefficients, are going to get multiplied together and separately those numbers inside of your radical get multiplied together. Okay, and then this is the part where, I sort of mentioned earlier, that you do your algebra first and then you have to confirm your answer because there isn't an answer that look like this on my multiple-choice, I know I have something missing, right? I have more steps that I need to do. Any guesses?

Yeah.

Audience member: You break the 12 down, so it's like 2x2x3.

Elizabeth Jachens: Yeah, so something like 12, if you do know has a perfect square in it. It's a good thing to simplify all of your answers that are going to be given. Theoretical, well, all of your potential answers are going to be in their most simplified form. So, anything you can do to your original problem to simplify, it's always going to be the right thing.


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So, 12 can be broken down into its prime factors, which are 2×2×3 and don't be afraid if it's a large number to break out into, like a number tree. Always better to fully explain it


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and then because you have two 2's in here, right? It's like saying that's two square and if you have 2 squared and you take the square root of it, those cancel out, right?


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Okay, I'm seeing a lots of head shakes, so this is good. So, that's just a little piece, so you bring out the 2, so you have, the 2 gets pulled out. And, then you have your 2x2 which is your 4, square root of 3 because 3 doesn't have, it can't be pulled out. It's not a perfect square of anything


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and then you still have plus 2 square root of 3.


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And, this is where we get to use our second rule. We can only add radicals together if the inside of the radicals are equal to each other. And, so the way I explains this to someone this morning who couldn't make it, I said if you just said that the squared of three, right? Is just like an orange, what is 4 oranges plus 2 oranges, right?


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You would always have 6 oranges. So, your root 3, even though they are being added together, whatever is in your radical doesn't also get added. It's more like it's a unit, it's a count of something. So, it's just your coefficients that are going to get added.

Audience Member: I kind of got lost with the 2x2x3 is how... So, the 3 doesn't disappear because [inaudible] it’s the 2 to the 2nd power there [inaudible]

Elizabeth Jachens: Yeah, so in your factor tree, right? You have 4 and 3 that's like your...

Audience Member: Right.

Elizabeth Jachens: Factorization and then this is all underneath the square root, so what is your 4, right. The square root of 4 is also 2.

Audience member: Right.


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Elizabeth Jachens: So, all I did was I took 2, these 2 become another 2 on the outside time my square root of 3. So, because you have 4 inside of your radical, you can simplify it by pulling it out by its perfect square, which is our 2. And, then these 2 get multiplied together to make the 4.

Audience Member: Oh, okay.

Elizabeth Jachens: Did that clear it up a little bit?

Audience Member: Yeah, yeah. Thank You.

Elizabeth Jachens: Yeah. I have a terrible habit of skipping steps. And, so yeah, okay. Just double checking.


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And, so I don't have the slide included in your guises printed packets. Just because I figured we would go over quite a few of them but if any of you do want the complete PowerPoint in a PDF version, you can always go back to the Student Learning Center and requested it. And, those will have the complete answers and maybe a little more of a breakdown on how to do the steps. So, you can always ask for that in the Student Learning Center. Alright, one problem down. Can you do in under two minutes?

Audience Member: Maybe.

Elizabeth Jachens: Maybe. Alright, so we're going to jump into our second practice problem.


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And, this one is all about percentages. So, a retailer charges, oh this is another, all example problems I'm giving you today are intermediate problems. All the example comes from here are intermediate problems, so I'm just kind of be aware there are going to be easier problems and there definitely will be harder problems. But, the intermediate problems will take up about 50% of your exam. Right, 25 will be easier and 25% will be harder. That's like the general rule, it will change and very slightly but this will be kind of like the bulk flow of your question. So, as you're reading these just know you're going to have some harder and some easier.

Okay, so it says a retailer charges 25% more for his purchase price for any appliance he sells. When the retailer has a clearance sale all appliances are marked down by 10% off. If the retailer sells the vacuum cleaner during the clearance sale, his profit which is his selling price minus his purchase price. Is what percentage of his purchase price for the vacuum cleaner? So, if anyone read this, exactly how I said it, you would have, it's a lot of words, right? It's a lot of words, so you sort of need like a place to stay. A lot of these questions will not give you as much information as you need. There's a couple things that you need to assume and this is why I picked this particular problem and the thing that generally, not generally but for percentage ones, something you probably need to assume is, whatever his purchase price is.


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And, for percentages, are really good place to start with. It's saying that his purchase price is hundred dollars. So, this will give you a good starting point and because we're working with percentages out of 100, it sort of works out easily that way. That's a good place for you to start. So, if this is the purchase price of $100 and you know the first piece of information says, that he charges 25% more. So, his selling price is 25% more of his purchase price, right? So, his selling price is 25% and again, just a conversion from percentages and diffraction or decimals.


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Right, 25% more than his purchase price. Okay, so I've broken it down and this way because this is the additional price that he charges and then this is added onto his initial purchase price.


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Some people would also write it as, they'll add the 1, right? It's just another way of writing it, so some of you may be more familiar with that than others.


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So, his selling price is 125 dollars, so when the retailer has a clearance sale, all appliances are marked down 10%. So, if he sell the vacuum cleaner during the clearance sale, what is his profit? So, that's his clearance sale price minus his purchase price and what percentage of it is of his original purchase price? And, because we started with 100% the end of this problem is going to be a little bit clearer.


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So, if you have a clearance, right? So, your clearance price it says that it is 10% off, so you can write this again and in kind of two ways. You can either say that, you can say it's his, right. It's his selling price minus 10% of his cell price or you can also write it as 90% of his sale price. Right? I'm, I'm getting the .9 by his whole priced, right? If it's marked down 10% marking something down from hundred percent, if you mark it down 10%. It's just your 100% minus your 10%, which is where I get that .9. Yeah?

Audience Member: Yeah, if you [inaudible]

Elizabeth Jachens: Yeah.

Audience Member: Okay.

Elizabeth Jachens: I sort of showed you, like, on the top right, every time you click to the next problem, your calculator disappears. So, you have to reclick it if you need it. I'm not using anything fancy here but you don't have parentheses on your calculator, so that's just something to kind of keep in mind. You're going to have to do some of your intermediate calculations on your page. And, actually for the most part I would do all my calculations by hand before I do that. Okay, I don't have a calculator with me today. So does anybody has one on them or else we can just use our phones because at least my phone calculator is very similar to the GRE calculator. It has 12 buttons, okay.


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So, 90% of 125. Okay. So, I don't know this maybe a nerdy engineer thing but when I go into a store, you guys can practice when you're going in clothes shopping and it says its, oh 25% off retail. And, my head just sort of goes through it. Good GRE study practice. Okay, and so the final question says, what profit does he make? So, what two numbers do we have to subtract to find his final profit?


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Audience Member: The clearance price.

Elizabeth Jachens: Okay, so yeah. Our clearance prices one of them.

Audience Member: Minus the purchase price.

Elizabeth Jachens: Yeah, so what do we get? We get 100, no sorry, we get 12 1/2 dollars. Right, and if we change that into a percentage-based, right? Out of 100, we do get 12 1/2%. You could've done this with any number for your purchase price and gotten the same answer. Just for me 100 because it's all based off of hundreds you kind of lose some of that extra algebra work. Yeah?



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Elizabeth Jachens: So, his profit is calculated by taking whatever he sells, his clearance item for minus your purchase price. Which is your 112, oh man I'm in the way, right minus your 100, which gives you 12 1/2 and this is in dollars but if you just wanted as a percent you take the dollars divided by your purchase price. Which gives you that percentage you want. You guys ready for the next one? Yeah, go ahead.

Audience Member: Sorry, what formula was S?

Elizabeth Jachens: So, this is, S oh I took that as like your sale price and so he says that he charges 25% more when he sells it. So, this is just 25% more than his purchasing price.

Audience Member: Okay, so C is the clearance price.

Audience Member 2: Right, so how did you do that? Like is that, what formula is that though? 0.25 x 100+100

Elizabeth Jachens: Yeah, so this is, I wrote this way. This is like called his markup, right? So, this is how much additional he's charging on top of his purchase price.

Audience Member: Out of [inaudible] because he picked 100 originally.

Elizabeth Jachens: Yeah, yup this is just your original amount. And, again, you could've picked any number. So, we're going to get through...


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Alright, again, this is the same sort of thing we did. You guys can definitely ask for these answers. They aren't on your packet, so because I wanted, we are going to do some of these independently and I didn't want you guys to have the answers and then try to work them out.


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Alright, so just a heads we're going to go through the algebra section and I have three examples and then from there we do have a break. Algebra is where I think quite a few people have their strong points. So, this algebra, the only difference is you have the introduction of variables, so an expressions, equations, qualities, things like that. You do have linear equations and quadratic equations, those are the only two you're going to find. You won't find anything with the power higher than two, just to cut down some of the competition work. And, because you are limited by your calculator. For functions, you need to know the domain and the range. Then you have some like applications and word problems and then you do have some coordinate geometry, so just dealing with our X, Y plane.


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So, here are my important, this is my important algebra equations. You of course have the slope, excuse me, you have the equation of a line, how to calculate slope, quadratic formula. On the right you have the different, like inequalities with them each mean. And, then the one on the bottom it's like a minor one and I added this on here just, so that you could be familiar with it. This is the interest rate. This is not a formula you have to memorize, if you do need to calculate interest rate on any problem, it will give you this formula. So, that's not something you need to memorize, you just need to be familiar with this is how you calculate interest. And, kind of know each of your variables go.


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Okay, so this is one I'm going to have you guys try by yourself? Definitely work with someone next to you, if you want. So, this is a pretty typical intermediate problem with two variables and, so you have two expressions and it ask you, not for like the value of a particular point but it says what's the value of x+2y? So, I'm going to give you guys about two minutes to sort of work through it. Get some ideas, bounce around your neighbors and then we will go over it, as a group.


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Alright, so does anyone have an answer out of curiosity?

Audience Member: I did.

Elizabeth Jachens: You got an answer?

Audience Member: Might be completely wrong.

Elizabeth Jachens: How confident are you? Give us, give us a range?

Audience Member: I don't even know. Any from 0 to 100.

Elizabeth Jachens: Alright, so you want to share with us. What did you get?

Audience member: I got 3.

Elizabeth Jachens: Mm. anyone else get 3? For their answer D? You guys are correct. Congratulations. Okay, so there are two ways, well I should rephrase that, there are lots of ways to attack this problem. Two ways I know how, the first one that you can do, is that you can isolate X and isolate Y. Right? And, make equations out of those. Is that what you guys did or did you use the linear combination?


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Audience Member: I just [inaudible] yeah I just don't really know. I got is so I have y= something and I put that in there.

Elizabeth Jachens: Yeah, so that's the first way that you can do it. You can solve one of the equations for Y equals, right? So if you have an equation that says X equals, right? You can add it to 2 times an equation that, that is expressed only in Y. And, then the other way that you can do it, which is the way I'm going to show you guys. This is my thought process behind it.


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Okay, so the way I did is, I saw and you can do this with quite a few problems, right? If you want to eliminate variables, you can always add to equations together algebraically. And, so I did is I took the first equation which is like this and then the second equation,


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all I did was slightly rearrange, right? Where the X's and the Y's are positioned. But, I made sure that i kept all of my signed conventions correct.


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Right, so then I have, this my first equation and here's my second equation and you can algebraically add them together. And, so this is, it's called the method of linear combinations but it's really just a fancy way of adding equations together.


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And, so if you have these two together you get 3x- 2x, which is just X. You guys see where this is going?


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And, then you have Y+Y is 2Y


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and then for the right-hand side you have -1+4, which is 3. So, this one very nicely gives you your answer. So, this is like the sneaky way to do it but you can always solve it for X independently and solve Y independently. Do you guys want me to go the other way as well or?


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Elizabeth Jachens: Okay. Can I erase this one? I'm going to go through the next one.


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Okay, so the other way that you can do it, is you can solve one equation, right? For X, so we can go ahead we can do that, which equation did you pick to solve for X? The first or the second one.

Audience Member: The first one.

Haley: I'm Haley.

Elizabeth Jachens: Brave.

Haley: So I got to this and then I just plug that into Y.


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So, I did 3x+4+2x=‐1.


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So, then I got 5x+4=‐1.


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And, then 5x=‐5 and then x=‐1. You guys get how I got through that. Yup. And, then, so once I got x=‐1


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You plug that back and get 3(‐1)+y=‐1.


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So, then ‐3+y=‐1. Then y=2.

Elizabeth Jachens: So, you did x+2y

Haley: Yeah, yeah.


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So, the x I did ‐1+2(2) and that got to ‐1+4=3

Elizabeth Jachens: Give her a hand. Okay, so you can see there is definitely 2 ways to do it. Like this way, it's always going to work, this you, isolate variables and you solve for it. But, if you can't find any shortcuts, it's definitely a great way to do that. I have a very hard time turning around. I don't have glasses on, so I cannot see the board. Which is part of my problem, if I have not worked out a problem. They broke this morning. Alright.


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Okay,


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so we have two more problems before we have a break. We may only do one of them, so we kind of stay on track. So, for this simple problem this is about changing areas and, so it says the length of a rectangle is increased by X % and the width is increased also by X %. You can kind of see what, like a comparison of the two problems, so you have A is greater, B is greater or they're equal or it's indeterminate. And so, I'm going to have you guys kind of try this one out. Or, start is out by yourselves and then I will go through it. I would recommend always starting, not always but if you need to, like start this out with a picture.


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Right, so here's your rectangular campus. I'm going to call this my length and I'm going to call this my width and,


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so it's is increased by X%. And, so this is just how I'm going to start...

Audience Member: [inaudible] decreased.

Elizabeth Jachens: Oh, It's deceased.


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Yeah, so with this decreased by X%. So, this is just how I set it up.


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My length because it is increased, it's like having 1+, whatever percentage.


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And, if it's decreasing kind of like we showed in the first percentage problem. You have 1-. So, this should give you a good starting point and then try to decide which quantity is bigger. So, I'm going to put my timer on again for two minutes and we'll see where we get. Alright, so that is two-minutes. And, so also another, do you remember these are intermediate problems, so the easy problems you're going to have time to spare that you can spend on some of the problems that, you know you're real close with. So, these problems, the disadvantage for them, at least for me, you kind of have to solve two equations per problem. Right? You have to solve quantity A and then you also have to solve quantity B.


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So the area of a rectangle is your length times your width. So, for quantity A, if your X value is 20, you get area, so you have your width which is going to be 1- your 20% which is your .8. And, that's multiplied by your length which is your 1+ your 20% of 1.2. So, always beneficial to write these, in terms of decimals instead of percentages.


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[Silence]


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Audience Member: Where did x go?


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Elizabeth Jachens: In this, so x=0.20 in this equation. Just for quantity A.

Audience Member: Oh, we're good.


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Elizabeth Jachens: I did not express that, this is my quantity A category, this is my quantity B category.


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So, we get an area of 0.96 times my width, times my length. And, it's definitely okay if you wanted to start out with numbers like 1 or 10. This is just your, your .96 is just your 2 factor filling. So, that's your .8×1.2.



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Elizabeth Jachens: Yeah, so no definitely. If I’m skipping steps, I'm happy to go through all of them. So, your area, what you have is you have your width which gets decreased by some percentage, so I just have W, as a variable but you could add any number that you wanted.


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And, then this will be your 1- whatever X value you have which is your .20. So, that just my percentage that have expressed in form of a decimal.


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And, then that's multiplied by whatever initial length you have and then 1+ that same 20%. So, this guy gives you your .8 and this factor gives you your 1.2. As I was saying, you could put in numbers for these but because we're comparing quantity you don't actually need exact values. You just need a comparison.


81

So, you can do the same thing for quantity B which is your area equal to your width times 1-000.4 times your length times your 1 +0.4.


82

So, the good news is for these problems you're usually doing the same thing twice, so the second one will always go a little bit faster.


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[Silence]


84

So, with your two quantities and it is explained in the answers in more depth


85

but right here you have 96% of your original area if you do this


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and you only have 84% if you decrease or increase by a factor of, or by of 40%. So, for this example quantity A is going to be greater because it has that greater coefficient and so having quantity A greater is always going to be answer A. So, no worries about that. Yeah?


87

Audience Member: Can you just do it where you make the length and width 100 and then the [inaudible]

Elizabeth Jachens: Yeah, so we assume we start with a square, which is a good place to start because a square is always a rectangle. If I have my L equals hundred to start with and I have my W equals hundred start with.


88

So, my final length and my final width are all just going to be, using, right, your hundred as you’re initial.


89

Like, so for your quantity A you will still have your area, which is equal to your 100 okay, that's your initial length. Right, and then it's increased by factor of 20%, so that's your 1.2.


90

And then you have times your width which is your initial width. Right? Times, that scaling factor, which is your 0.8.


91

If you go through this, you have your area equals, you still have, that still equals .96 and this is your 10,000.

Audience member: Yea, that's what I got.

Elizabeth Jachens: Okay.

Audience Member: But, would you, wouldn't just be like, your length would end up being 120 X 80 and I ended up getting like 9,600.


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Elizabeth Jachens: Yea, that would be the same way to express it. Just in a different order.


93

And you would do the same thing with this one, you would get an area of 140 times an area of 60, right? Yeah. So, something like this you can either have initial values or you can keep them as variables.


94

Alright, so we're pretty much on time. We're going to have a 10 minute break and we're going to come back and we have two more sections of geometry and data analysis.


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gre math prep workshop part 1 - continuing education · so, these workshop goals, as i said before,...

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