Algebra EOC Review Strategies

What's good everybody? My name is Mr. Peters. In today's video, we're going to be looking at an algebra EOC review. So in the first problem, we're looking at properties of exponents, and we're going to go through this like it's a real test. So what I'm going to do is, I love to use process of elimination, and when I look at the first problem, I know that we could automatically eliminate two answer choices, which are B and D. Reason why, guys, we know that after we multiply 8 and 3, that's going to give us 24. And now we're talking about properties of exponents. So in this situation here, we're multiplying with the same base of x and y. All we have to do is add our exponents. So we would get 24x to the 7th power, y to the 4th, right? multiplied our coefficients, and then we added our exponents. So the correct answer should be c. You know, the only time that we multiply exponents is typically when we have parentheses. So just out to the side, let's say we had 3x to the fourth, y to the ninth, and then on the outside I had a exponent. This is a type of problem where I would multiply the exponents. So just try not to forget that helpful tip. Right. So problem number two, they're asking us to basically combine two expressions, right? Combine like terms, combine expressions, same thing. But there is a very important trick and we're going to highlight that trick. So basically that negative sign, that subtraction sign, it's going to change the sign of every number after, right? So I'm going to rewrite this as 2x squared minus 7x plus 9. And now when I focus on the second set of parentheses, the numbers inside, we're going to flip the signs now because of the negative on the outside. So now I have minus 5x to the second power minus 4x and plus 1. So at this step now, guys, we're just combining like terms. So 2 minus 5 is going to give me negative 3, right? So we have negative 3x squared after we combine our first two terms. Now let's just cross these out in red. Then I'm going to go to my next term, which is negative 7 and negative 4. So when we're adding numbers with the same sign, meaning they're both positive or both negative, we're just going to add those numbers and keep the sign. So this would be... negative 11x, and then positive nine plus one will give us 10. So I boxed my answer off, I looked over it, and I should know that the correct answer choice is going to be letter B. Right, so when you have a problem like this, guys, where we're subtracting polynomials, functions, or expressions, just remember that. Anything after the subtraction sign, the signs of those terms will change. All right. So now we go on to the next one and we're talking about inequalities. Right. So greater than, less than. And they want us to solve. And after we solve, they want us to match the correct graph for the inequality. So we're going to solve this. So what we need to do is focus on using distributive property. Right. So rewrite the first part. We have 6x minus 14 is less than or equal to 6x plus 6 minus 4x. Don't forget, guys, when that negative 4x is outside the parentheses, so I do not need to multiply or distribute, I should say, 6 to negative 4x. So we're going to add our like terms now. And once we do that, our equation is going to simplify to 6x minus 14 is less than or equal to 2x plus 6. And just like a regular equation, we want to have variable on one side of the inequality, numbers with no variable on the opposite side of the inequality. So what I'm going to do is I'm going to subtract 2x from itself and its like term. And that will give me. this expression here. 4x minus 14 is less than or equal to 6. All right, so we're almost done now, right? So next step, we continue to combine our like terms. And I have 4x is less than or equal to 20. And once we divide by 4, everyone, our final answer should be x is less than or equal to 5. So very, very quick tip, right? When we have, and let's see, let's go over to red. When we have greater than or less than, that means we have an open circle on the graph, all right? Doesn't matter which direction left or right. When we have a or equal to, that means that the circle on the graph is going to be closed. OK, so typically right here, I could go ahead and eliminate answer choice number B and answer choice number D. So now we're looking for closed circle and is going in a direction where the numbers are smaller than five. less than 5 so we should know that our final answer is going to be a right it's going our graph is going to the left where the numbers are less than or equal to 5 all right so our next problem we're focusing on how to rearrange equations and they're basically asking us to solve for L right So we're trying to solve the equation for L. So what I'm going to do, I'm going to come out to the side, I'm going to rewrite this equation, and we're going to figure out how can we manipulate this equation so that we could get L by itself. So the first thing I'm going to want to do is I'm going to subtract pi r squared, right? So when I subtract pi r squared from itself, I'm going to have, and I'm going to do it on the other side as well too, guys. So everyone's with me. So after the first step of subtracting, we're going to have s minus pi r squared is equal to pi r l. And remember, we want to get l by itself. So in our last part of this problem, Understand that pi, r, and l are all being multiplied together. So for us to get l by itself, we're going to do the opposite of that, right? So I'm going to divide by pi and r because that will leave l by itself. And once I do that, I will get a final answer of what I have boxed off. So l should be equal to s minus pi r squared divided by pi r. which will give us an answer choice of A. So just remember, first step, right? Highlighting it real quick. We're adding this to pi RL. So the opposite of adding guys, that's how we subtracted for the first step. To get it to the other side, to cancel it out, we had to subtract it. Then that next step, we divided because our three terms are being multiplied together, okay? So just a little bit more explanation. If you did not understand that, we're following the same steps for solving an equation. Now we're just mostly working with variables. All right. And this is what I mean. So imagine that L was X. Right. We'd have to basically group all the terms together if we can, if there's like terms. So I'm going to show you guys what I mean. So in our last problem. Right. I'm going to distribute. So once we distribute, we had five X plus. 20 right and this is equal to negative 8x minus 28 plus 5x so right here guys we're gonna continue to simplify by combining like terms 8 and 5x so once i do that now on the other side we're gonna have negative 3x minus 28 now just please understand in this step guys we could you manipulate, I'm sorry, the equation anyway, we could bring x from one side to the other, or we could bring 28 over to the other side or 20 over to the other side. As long as we had the right steps and the variables on one side and a number with no variables on the opposite side of the equal sign, then we could solve correctly. So what I'm going to do, I'm going to add 3x on both sides, right? And what that does is it's going to give me 8x. plus 20 is equal to negative 28. Oops, and I put 20 by mistake. All right. Next step, we're going to continue combining like terms. So we're going to subtract 20 from itself and from its like term, which is 28. So now they're telling me that, hey, Mr. Peters, 8x is equal to 20 plus 28, which is 48. We know both of those numbers are negative. So this is going to be a negative 48, right? And now final step for us to figure out what our x is, right? times a certain number x will give us 48 we're going to work backwards and divide by 8 so that we can figure out what our answer is and once we do we'll get x is equal to negative 48 divided by 8 which is negative 6 so thank you guys for joining us today this is Algebra Room with Mr. Peters if you find our EOC review helpful We're going to ask that you smash the like button for us, subscribe to our channel, and check out any videos that you guys need help with. And comment below for any videos you'd like to see in the future. Thank you.

What's good everybody? My name is Mr. Peters. In today's video, we're going to be looking at an algebra EOC review.

So in the first problem, we're looking at properties of exponents, and we're going to go through this like it's a real test. So what I'm going to do is, I love to use process of elimination, and when I look at the first problem, I know that we could automatically eliminate two answer choices, which are B and D. Reason why, guys, we know that after we multiply 8 and 3, that's going to give us 24. And now we're talking about properties of exponents.

So in this situation here, we're multiplying with the same base of x and y. All we have to do is add our exponents. So we would get 24x to the 7th power, y to the 4th, right? multiplied our coefficients, and then we added our exponents.

So the correct answer should be c. You know, the only time that we multiply exponents is typically when we have parentheses. So just out to the side, let's say we had 3x to the fourth, y to the ninth, and then on the outside I had a exponent.

This is a type of problem where I would multiply the exponents. So just try not to forget that helpful tip. Right. So problem number two, they're asking us to basically combine two expressions, right? Combine like terms, combine expressions, same thing.

But there is a very important trick and we're going to highlight that trick. So basically that negative sign, that subtraction sign, it's going to change the sign of every number after, right? So I'm going to rewrite this as 2x squared minus 7x plus 9. And now when I focus on the second set of parentheses, the numbers inside, we're going to flip the signs now because of the negative on the outside. So now I have minus 5x to the second power minus 4x and plus 1. So at this step now, guys, we're just combining like terms. So 2 minus 5 is going to give me negative 3, right?

So we have negative 3x squared after we combine our first two terms. Now let's just cross these out in red. Then I'm going to go to my next term, which is negative 7 and negative 4. So when we're adding numbers with the same sign, meaning they're both positive or both negative, we're just going to add those numbers and keep the sign.

So this would be... negative 11x, and then positive nine plus one will give us 10. So I boxed my answer off, I looked over it, and I should know that the correct answer choice is going to be letter B. Right, so when you have a problem like this, guys, where we're subtracting polynomials, functions, or expressions, just remember that. Anything after the subtraction sign, the signs of those terms will change.

All right. So now we go on to the next one and we're talking about inequalities. Right. So greater than, less than.

And they want us to solve. And after we solve, they want us to match the correct graph for the inequality. So we're going to solve this.

So what we need to do is focus on using distributive property. Right. So rewrite the first part. We have 6x minus 14 is less than or equal to 6x plus 6 minus 4x.

Don't forget, guys, when that negative 4x is outside the parentheses, so I do not need to multiply or distribute, I should say, 6 to negative 4x. So we're going to add our like terms now. And once we do that, our equation is going to simplify to 6x minus 14 is less than or equal to 2x plus 6. And just like a regular equation, we want to have variable on one side of the inequality, numbers with no variable on the opposite side of the inequality.

So what I'm going to do is I'm going to subtract 2x from itself and its like term. And that will give me. this expression here. 4x minus 14 is less than or equal to 6. All right, so we're almost done now, right? So next step, we continue to combine our like terms.

And I have 4x is less than or equal to 20. And once we divide by 4, everyone, our final answer should be x is less than or equal to 5. So very, very quick tip, right? When we have, and let's see, let's go over to red. When we have greater than or less than, that means we have an open circle on the graph, all right?

Doesn't matter which direction left or right. When we have a or equal to, that means that the circle on the graph is going to be closed. OK, so typically right here, I could go ahead and eliminate answer choice number B and answer choice number D.

So now we're looking for closed circle and is going in a direction where the numbers are smaller than five. less than 5 so we should know that our final answer is going to be a right it's going our graph is going to the left where the numbers are less than or equal to 5 all right so our next problem we're focusing on how to rearrange equations and they're basically asking us to solve for L right So we're trying to solve the equation for L. So what I'm going to do, I'm going to come out to the side, I'm going to rewrite this equation, and we're going to figure out how can we manipulate this equation so that we could get L by itself.

So the first thing I'm going to want to do is I'm going to subtract pi r squared, right? So when I subtract pi r squared from itself, I'm going to have, and I'm going to do it on the other side as well too, guys. So everyone's with me.

So after the first step of subtracting, we're going to have s minus pi r squared is equal to pi r l. And remember, we want to get l by itself. So in our last part of this problem, Understand that pi, r, and l are all being multiplied together. So for us to get l by itself, we're going to do the opposite of that, right? So I'm going to divide by pi and r because that will leave l by itself.

And once I do that, I will get a final answer of what I have boxed off. So l should be equal to s minus pi r squared divided by pi r. which will give us an answer choice of A.

So just remember, first step, right? Highlighting it real quick. We're adding this to pi RL. So the opposite of adding guys, that's how we subtracted for the first step. To get it to the other side, to cancel it out, we had to subtract it.

Then that next step, we divided because our three terms are being multiplied together, okay? So just a little bit more explanation. If you did not understand that, we're following the same steps for solving an equation. Now we're just mostly working with variables. All right.

And this is what I mean. So imagine that L was X. Right. We'd have to basically group all the terms together if we can, if there's like terms. So I'm going to show you guys what I mean.

So in our last problem. Right. I'm going to distribute.

So once we distribute, we had five X plus. 20 right and this is equal to negative 8x minus 28 plus 5x so right here guys we're gonna continue to simplify by combining like terms 8 and 5x so once i do that now on the other side we're gonna have negative 3x minus 28 now just please understand in this step guys we could you manipulate, I'm sorry, the equation anyway, we could bring x from one side to the other, or we could bring 28 over to the other side or 20 over to the other side. As long as we had the right steps and the variables on one side and a number with no variables on the opposite side of the equal sign, then we could solve correctly.

So what I'm going to do, I'm going to add 3x on both sides, right? And what that does is it's going to give me 8x. plus 20 is equal to negative 28. Oops, and I put 20 by mistake. All right. Next step, we're going to continue combining like terms.

So we're going to subtract 20 from itself and from its like term, which is 28. So now they're telling me that, hey, Mr. Peters, 8x is equal to 20 plus 28, which is 48. We know both of those numbers are negative. So this is going to be a negative 48, right? And now final step for us to figure out what our x is, right? times a certain number x will give us 48 we're going to work backwards and divide by 8 so that we can figure out what our answer is and once we do we'll get x is equal to negative 48 divided by 8 which is negative 6 so thank you guys for joining us today this is Algebra Room with Mr. Peters if you find our EOC review helpful We're going to ask that you smash the like button for us, subscribe to our channel, and check out any videos that you guys need help with.

And comment below for any videos you'd like to see in the future. Thank you.

Transcript for:Algebra EOC Review Strategies

Transcript for:
Algebra EOC Review Strategies