SAT Prep: Test 4 Section 8 Part 3 Video

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SAT Prep: Test 4 Section 8 Part 3

Welcome back, it think I was rushing that problem so let me just make it clear again. So I will just say that you don’t get confused because I try to get to that 10 limit. But they want to know what the perimeter of this Red is, that is the kind of the outside of this thing that looks like a flower or something. And what I am saying is that the perimeter of the red part is equivalent to the sum of the perimeters of the triangles. The sum of the perimeters of the triangles but if I was just to take the sum of the perimeter of the triangle. I would also be - just beginning the red part and also be getting in these parts. Because those are parts of the perimeters of the triangles, so if I want just the red bar, I subtract out. This would I drew in blue and the blue is the perimeter of that inside square and the perimeter inside square is 9+9+9+9+9 of 36. So I just take the perimeter of all four triangles, each of them has a perimeter of 30 so together they have a perimeter of 120. And I subtract out the perimeter of the square inside which has the perimeter of 36. So 120-36=84 and that is choice D. Next problem, problem number 13 - the graph of G of is shown above, essentially look at the graph and figure how to value. So it starts at roughly -- and I will try my best to draw like they have. So the line starts like roughly a little bit above six, and now even now we are up to seven. And then where does it go? It starts a little bit about six now even up to seven, looks like it at about at one. It starts here and then it goes to the point 4,2 it looks like and then it goes from 4,2 to 6,3 roughly. Or maybe even exactly 6,3 and then it looks like it goes to 8,8 is like there roughly. And then it goes down to like - I don’t know almost it’s 11,2, it goes down some place like that. And they are asking, so they say this is the graph of G of X and they are saying if G of 2=K which of the following could be the value of G of K? G of K is what? So what could K equals? Let’s figure out G of 2, so when X=2 what is Y equal to? Well it looks pretty darn close to five if not exactly five. So K=5, G of 2=5 and they want to know what G of K is. Well we figure out the K=5 so now we all know it G of 5 is, so we got a five -- it looks pretty close to three. G of 5 asks you the way they drew it, well actually the way that they do it, it doesn’t look close to three. The way they drew it, if you look it where five is - it looks actually less than three, it looks like two and a half actually the way they drew it. That is when my drawing is a little off, so if you look down. Look at the X value when X=5 you go up to the graph, it looks like the graph value there is right around 2 1/2. So I should say this is 2 1/2 and that is one of the choices B. Next problem, problem 14 if zero is less than or equal to X which is less than or equal to 8 -1 is less than or equal to Y which is less than or equal to three. Which of the following gives the set of all possible values of X(Y)? So really we want to figure out how low can, X(Y) be and how high X(Y) be? Well what is the lowest possible value for X(Y)? The lowest possible value of X(Y), well if we make Y negative and we make X really big or as bigger it can be. If X is 8 and Y is -1 and that is the lowest value for X(Y) I can think of. So XY is going to be greater than or equal to -8 because we take a negative number, you want the other number to be as big as possible so you get a large negative number. And it’s going to be less than or equal to, well what is the largest number that I can think of? Well if I take 8 and I multiply it times the large value of Y and this is a positive value and then I get 24. So XY is going to be greater than or equal to -8 and less than or equal to 24. And that is choice E. And once again, how do I get -8? This is probably the part that is not intuitive for you. Is because, I mean mine is invincible, the minimum X is zero. So I will take zero so this is going to be zero but you can actually get a smaller value for XY by using -1 and 8. So that is where we got the -8 from. Next question, 15 -- and then they write this is N° right there. And the figure above, what is the sum in terms of N of the degree measures of the four angles marked with arrows - fascinating. So they want to know that, plus that, well let’s just do the angle game. If this angle is N, what is this angle here? It supplementary to N, so this is 180-N and so is this; this is also 180-N. And so what are these? What is the sum of these two angles? Let me call this AB, what is the sum of A+B? Well we know A+B+ this angle, plus 180-N is equal to 180 because they are all the same triangle. So A+B= 180-180+N, I just took this and subtract with 180 and added N to both sides. This cancels out, so you get A+B=N and similarly if you had C and if this were C and D - you can do the same thing. C+D+ this angle, 180-N=180 because they are all the same triangle. Subtract 180 from both sides and then add N to both sides, you get C+D=N. So if you want to know what A+B+C+D is, A+B=N, C+D=N, so the whole thing is going to be N+N or 2N and that is choice B. Let’s see if I have to do problem 16 considering I have a little lower under a minute left. Problem 16, after the first term, each term in a sequence. Actually this going to be - I think this will take some explanations, so I will do 16 in a video by itself - I will see you in the next video.

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Welcome back, it think I was rushing that problem so let me just make it clear again. So I will just say that you don’t get confused because I try to get to that 10 limit. But they want to know what the perimeter of this Red is, that is the kind of the outside of this thing that looks like a flower or something. And what I am saying is that the perimeter of the red part is equivalent to the sum of the perimeters of the triangles. The sum of the perimeters of the triangles but if I was just to take the sum of the perimeter of the triangle.

I would also be - just beginning the red part and also be getting in these parts. Because those are parts of the perimeters of the triangles, so if I want just the red bar, I subtract out. This would I drew in blue and the blue is the perimeter of that inside square and the perimeter inside square is 9+9+9+9+9 of 36. So I just take the perimeter of all four triangles, each of them has a perimeter of 30 so together they have a perimeter of 120.

And I subtract out the perimeter of the square inside which has the perimeter of 36. So 120-36=84 and that is choice D. Next problem, problem number 13 - the graph of G of is shown above, essentially look at the graph and figure how to value. So it starts at roughly -- and I will try my best to draw like they have. So the line starts like roughly a little bit above six, and now even now we are up to seven. And then where does it go? It starts a little bit about six now even up to seven, looks like it at about at one.

It starts here and then it goes to the point 4,2 it looks like and then it goes from 4,2 to 6,3 roughly. Or maybe even exactly 6,3 and then it looks like it goes to 8,8 is like there roughly. And then it goes down to like - I don’t know almost it’s 11,2, it goes down some place like that. And they are asking, so they say this is the graph of G of X and they are saying if G of 2=K which of the following could be the value of G of K? G of K is what? So what could K equals?

Let’s figure out G of 2, so when X=2 what is Y equal to? Well it looks pretty darn close to five if not exactly five. So K=5, G of 2=5 and they want to know what G of K is. Well we figure out the K=5 so now we all know it G of 5 is, so we got a five -- it looks pretty close to three. G of 5 asks you the way they drew it, well actually the way that they do it, it doesn’t look close to three. The way they drew it, if you look it where five is - it looks actually less than three, it looks like two and a half actually the way they drew it.

That is when my drawing is a little off, so if you look down. Look at the X value when X=5 you go up to the graph, it looks like the graph value there is right around 2 1/2. So I should say this is 2 1/2 and that is one of the choices B.

Next problem, problem 14 if zero is less than or equal to X which is less than or equal to 8 -1 is less than or equal to Y which is less than or equal to three. Which of the following gives the set of all possible values of X(Y)?

So really we want to figure out how low can, X(Y) be and how high X(Y) be? Well what is the lowest possible value for X(Y)? The lowest possible value of X(Y), well if we make Y negative and we make X really big or as bigger it can be. If X is 8 and Y is -1 and that is the lowest value for X(Y) I can think of. So XY is going to be greater than or equal to -8 because we take a negative number, you want the other number to be as big as possible so you get a large negative number. And it’s going to be less than or equal to, well what is the largest number that I can think of? Well if I take 8 and I multiply it times the large value of Y and this is a positive value and then I get 24. So XY is going to be greater than or equal to -8 and less than or equal to 24. And that is choice E.

And once again, how do I get -8? This is probably the part that is not intuitive for you. Is because, I mean mine is invincible, the minimum X is zero. So I will take zero so this is going to be zero but you can actually get a smaller value for XY by using -1 and 8. So that is where we got the -8 from.

Next question, 15 -- and then they write this is N° right there. And the figure above, what is the sum in terms of N of the degree measures of the four angles marked with arrows - fascinating. So they want to know that, plus that, well let’s just do the angle game. If this angle is N, what is this angle here? It supplementary to N, so this is 180-N and so is this; this is also 180-N. And so what are these? What is the sum of these two angles?

Let me call this AB, what is the sum of A+B? Well we know A+B+ this angle, plus 180-N is equal to 180 because they are all the same triangle. So A+B= 180-180+N, I just took this and subtract with 180 and added N to both sides. This cancels out, so you get A+B=N and similarly if you had C and if this were C and D - you can do the same thing. C+D+ this angle, 180-N=180 because they are all the same triangle.

Subtract 180 from both sides and then add N to both sides, you get C+D=N. So if you want to know what A+B+C+D is, A+B=N, C+D=N, so the whole thing is going to be N+N or 2N and that is choice B.

Let’s see if I have to do problem 16 considering I have a little lower under a minute left. Problem 16, after the first term, each term in a sequence. Actually this going to be - I think this will take some explanations, so I will do 16 in a video by itself - I will see you in the next video.

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