NC Math 3 Released Test Oct. 2018

Okay, okay. Today we are going to look at the released math three tests. This is the latest version from October 2018. The latest one North Carolina has released. I'm going to go through the problems and we will work them out. I do need asthma so let me real quick. All right, number one, while Desmond chrome is open. What is the remainder when HQ minus one is divided by X plus two. You're going to use synthetic division on this. Remember you count down coefficients from three. So you got one is for X cubed. A squared don't have one X don't have one negative one and sort of single one. And then X plus two equals zero. So you would get X equals negative two is what you divide by. Okay? First number comes down. Which is one. These two multiply. And add. This equals here. So that goes to negative two. And you get negative two. This gives me negative four, I'm sorry. Pause the four. This gives me a four. The excuse me negative 8. This gives me negative 9. This question is asking for the remainder. And the remainder would be negative 9. Number two, let's give you a function. Give me a very large function. It's a lot going on here. It's asking for the number of title real zeros. That's how many times it crosses the X axis. This problem is best done, graphing. So if you go to desmos. Type now, I used anti test version because that's the version that will be linked into your family exam. It does have a few limitations. That traditional desmos does not. Big thing I found has been data. It does not have a theta button you have to write theta out. But I like for my students to practice with the actual version that they will be working with on the test. All right, and here's our graph. We call the X axis three places. You want to make sure that's it, zoom out. You'll notice there's no more. So you got three places. So that means there is three. Real. Zeros. That's all you had to do on that one. Number three is going to be another synthetic division. This is also going to be a quadratic formula. You want coefficients again, one, three, negative two, negative four. We're going to develop a negative one because that's what they gave me. One comes down, negative one. Two, negative two. Four. Negative four, pause the four, zero, which is what it should be. So this is telling me negative one is is zero. I'm left with a squared plus two X minus four. We're going to use our quadratic formula. A is one. B is two. And C is negative four. I was going to plug this DM. We're going to say negative two. Plus or minus square root, T squared is four. Minus four. Times one. Right here. Okay. Tom's negative four. All of that is under the radical. All over. Two times one is two. Inside that radical, I'm looking at square root of 20. So this is going to equal negative two plus minus square root 20 two. Square root of 20 is the same as square to four Times Square root of 5. So that's negative two plus or minus. Negative two plus or minus two to square root of 5. Over two. And all your twos with canned so to give you the answer choice C. Number four would be long division. You're going to tighten the inside. And you're going to ride it by the outside. Hi. X squared. I squared a little nice grade one time. So everything comes down. You have to change your songs when you divide. You cancel this becomes X plus three. Here I answer is a. Number 5 is a little different. Number 5, you've got to come up with that common denominator. The way you get that common denominator is you multiply the two of them together. Basically, I don't like showing it this way. It's cross multiplication. This kind of what you got to do, you got to multiply the top of the first one out of the denominator. The second one and vice versa. So you're going to say in three X -5 times 7 X minus two. Plus, negative two X plus one times four X plus three. Okay. So we're going to distribute and we're going to multiply. That's going to be 21 8 squared. -6 X -35 X plus ten plus negative 8 X squared. Now you're going to. Three. Okay. So I'm just going to combine like terms. My a is going to go with my egg square. This is going to be right squares. This is going to be your exes and C is going to be our constant. So let's see, I've got 21. And negative 8. That's going to give me a is 13. Which is a choice right there. That's our answer. What you do on these is you drag that number up. Now, so it would be as we have negative 6 dollars. Negative 6 negative 35. Negative 6 and positive four. So that's negative 41. Negative 47 plus four is negative 43. So this is negative 43. So the value for B is negative 43. And then C is everything else. I have a ten and a three. So I have a 13. So that would be your 3 a.m. search for that one. Okay. Next, on this one you have to first, everything has to be a positive exponent. And then we gonna do keep flip chains. It's negative on the top. It goes to the bottom. It's negative on the bottom and goes to the top. X minus G squared comes out. And X squared -5 X plus 6 goes down. On the other side, I have X minus two, goes up and remember when you move it, your eggs probably becomes positive. And I have X minus three. That's the negative. Now we got to keep change flu. So we're going to keep the first one. I mean, if you flip change, we're going to factor the denominator. You should be able to tell me that your spiders is X minus two and X minus three. We're going to flip the sacrifice. And we're going to have X minus three over X minus two. And we change that to multiplication. Here we come here. Sure. Lean a lot. Okay. Now we're going to just cross out a quarterly and cross out diagonally. And horizontal are in vertically, but you can't cross out horizontally. Everything crosses out, but one X over two X minus two in the denominator. That gives me an answer, D is my answer. Next one. This one here is just talking about a box. If you have a ball, it's a box is going to be X the box is supposed to hold 32 ounces. There's a deviation of .25. So I'll say X -32. Absolutely value because the deviation can be positive or negative. Can not be any more than .25. So that one there is just making sure you read that question carefully. Number 8, number 8 is absolute value one. Before we do it, I just want to show you the difference in what the actual absolute value graph looks like. Obviously, values start at zero. And everything is. Got. So if I connect the lines, why is the parent for absolute value? So if I'm looking at these two graphs, what happened in the red ones in the black one? We went down. And it got skinny. Okay. So I forget scanning. That means it's all whole number in front of the egg. And filling down, that means there's a modest after the function. So which one of these has a whole number in front of the eggs and a minus after a function? Well, these two are left moments in right members who read the right movements. So between a and B and a and B B has that whole number where I just has a one. All right, number 9. Mark, we can paint a room on one hours, one room and two hours. Jamie component one of them is 6 hours. Together how much can they pay? The common denominator here is a 6. One half is the same as three 6. So three 6 plus one 6 is four 6. So this will give me four X equals 6 X equals three over two or 1.5 hours. So you're doing that one. Number two is just going to be graphic. What is the values of raw when they equal? So we're going to grab these two functions and find out when they cross the or when they intersect with each other. Let's get a dance bus. So we're going to put both of these functions in. Two X cubed. Two X minus three. Now I get a .5. Absolute value. All right, so mine is four. And that's my function. Now if you look at these are very distinctly different graphs. But right here, they intersect. That wild value is negative. 1.75. Negative 1.75. You can put that number in or you could say negative 7 force. It would take both answers. Either one's fun. Number 11, you got a bad strategy out of GCF, our GCF here. You should know 48 and two 43. If you don't know that, you go to your calculator and whether you have the newer version or an older version this works, you can go to math. And get a number 9. Put your two numbers in. 48, comma. Two 43. And it'll tell you the physical numbers of three that you need to pull out. I can pull out of three. And now I have an X cubed in the X X is the smallest of X 48 divided by three if you don't know it is 16. That's a 12 to 16. This can be 16 X squared minus two 43 divided by three is to be 81. Okay. Mine is 81 Y squared. Now this 16 X squared -81 Y squared is a different to perfect squares. Recall, a squared minus B squared. But what you fat through that is use that under a plus B times a minus B, which is what we've got here. Three X is baggage. He just comes down. Just by that, you can get rid of a and B 16 is a square to a would just be four plus four. Comes four, four squared is 16. It's actually four X 81 is B squared, 81 Y squared is actually B squared, so that would be 9 Y and then of course we also have the same numbers. But with a plus then our answer is D dog decibels. Okay? Number 12, this one here is just trying to match the equation. So we're going to put these together now, whatever the zero is when you write the equation, you write an opposite sign. So X minus one so that would be X plus one. Multiplicity of J means I have a power to X minus two, multiple C one, you don't have to write it. And X minus four or multiple C one, you don't have to write them. So the first thing, how many X's do I have? I have two here here and here. But then this also gives me two. So I have X to the fourth. That means these two are gone. So before distributing anything, that's sure no. Couple as you can do it, we can expand this out, which I'll show you. You also can graph this and see which answer choice lays on top of it, either way, works. We reset this real quick, I'll show you how to do that. I have X plus one squared. X minus two. X minus four. I forgot my eggs. X minus four. That's my function. Now my two remaining answer choices. I have X to the fourth. Minus four X cubed. Minus three X squared, whereas I am recording. Plus ten X. Plus 8, mutual background. Just completely took over the other one. There because they are the same graph tells me that would be the answer. And that was the first answer choice so the answer should be seen. When you expand this out, you would do like your box method or distributed a method which I'm where you like. X plus one squared, I'm going to do square double squared, just got faster. That's the same as X plus two X plus one. X minus two is from X minus four is 8 squared. Minus four X and two X is 6 X plus 8. So that's good. So now I'm going to have X to the fourth. Mine is 6 X cubed. Plus 8 X squared. That doesn't help me completely yet. Now I'm going to do the two X so this is going to be two X cubed. -12 X squared. Plus 16 X now this does help me a little bit. I know 6 negative 6 X cubed and two X cubed is negative four X cubed, which is what C has. So that is your answer. All right, number 13. If K. Of X minus two to the fourth, which is positive, what is the effect the graph is K increases? SK gets bigger. The graph is going to get skinnier, which means it will stretch vertically. All right. This one here, a couple ways we can do this. We can put it in our calculator. Or we can compute it by hand to me hands on this easier. I'm going to do it with my hand. I each of two is where it equals two, so we that function. So I'm going to say four times two or the X is plus one. That's what it's asked me to do. Plus four times, now I'm G of one is less than three. So four times one squared plus two. So this is 8 9 so this is three times 9, which is 27. This is three 12. So this is four times three. Which is 12. I have an answer of 30. 9, which is a. Prime number 15. Function is Chamberlain. What's the value same thing what we just did? I give negative four. Negative four equals here. Negative two is bigger than negative four. So the next going to be out in the other one. So I'm going to say negative one half, negative four, because that's my ex -15. Plus three times. Now this one's here because it's negative change greater than negative four. 20 minus three times negative two squared. That's right. Here is going to give me a negative two. That's going to give me a positive two. 15 positive two -15 is negative 13. Okay. Here, this is going to give me a four. So now you have 12, that's 8. So that would be a 24. Negative 13 plus 24 is indeed 11. This would be a greater response. 70 minus two is 68. Probably the next thing we're going to look at this graph about increasing decreasing is giving you this. This is a drop in drag. Okay. I honestly, this is a drop in drag, so you have to click these boxes and put them in the right place. These are just the four things you're going to be looking at. So on the first interval, it gives us is negative four to one. Negative four to one. I'm sorry, it's negative four negative one. Negative four to negative one is this. Do you see how that graph is completely irony X axis? That would make that a positive graph. So positive is going to be that negative four negative one. All right, the next one to give us is negative two zero. Negative two zero. Which is right there. That drop is going down, so that would be a decreasing gram. So that's going to be negative two zero. And negative two is part of the function. All right, and the next one I give me is zero. Looks like zero positive zero right on it. Yeah. Zero positive two. And I just want to zero positive change. So this is going to go from the Y axis up. That is increasing. That is also negative. It is going up. The united two are stopped and I'm still under the X axis. So this won't be zero two. Two is not an endpoint. So we stopped. That's why we don't put it at the increasing. And the increasing is actually zero. Zero four. It goes all the way up. Which is increasing. This is zero fourth. That's all you do on that one. You need to drag those in to choices of. All right, number 17. Function of shamble, what is the distance? To the nearest hundreds between the two zeros. But that are the closest. So let's graph this. You have four X cubes. Mine is 5 X squared. -23 8. Plus 6. Are zeros are negative two. Negative .25 and three. So negative two, negative .25 and three. So which one's cards for .1 thousand in the middle? Is it question negative two or to three? So let's see, we're going to say .25. Minus negative two. That's going to become positive. So this is 2.25. All right, let's go to the next one. Three minus 0.25. That's going to be 2.75. So the distance between those are greater than a distributor between the previous two. So this would be my answer 2.25. Okay. Next, 18. Which function does not have a set of real numbers in the domain. Rational functions never will have a set of real numbers on the last. Everything cancels and it's actually a linear function. But as a domain restriction, it don't have a set of real numbers. If you look right here, because of this X minus Rx plus R in the denominator, that tells me X can not equal negative three. So domain restriction. So B can not have a domain of all real numbers. We do not have nothing at negative three. All right, the question saw our blood, we want you to solve it. This is a logarithm. So at 9 two three X plus two equals 48, so this is a log base 9, a 48. E goes negative three X plus two. I'm not sure which calculator you use if you have an older one. You don't have the alpha menu. To do this, if you do, if you got a newer one, you do, but if you have an older one you have to use a change in base formula with the change of base one, I'm just going to write it over here. It's a big, I mean the little number is log 9. I really big number, which is 48. You'll get the same answer, but I'm going to use the alpha menu because I have it on my calculator. So I'm going to go out the window. Wrong is number 5. And I can just type it in. I have a base of 9. And a number 48. And I get this decimal. I do not want to write that just one down. I don't want to do nothing with it. I might store it, store it and just makes it where I can recall it. So if I clear my screen, I still got the number there. So I got escorted as a are stored as a so we're going to solve this equation with it as a and I'm going to put it in the calculator and award. So I'm going to subtract my two. I'm just going to solve this like normal. And I'm going to buy them a negative three. So X is going to equal a minus two over three. So I'm going to go back to my calculator. I'm going to bring in a flagship which is another alpha menu Apple Y equals. Alpha map brings up a we said it was a modest two, iron negative three. And you give the answer .07938. X equals 0.079 three 8, which gives you answer choice. That's all you have to do on that one. Next, we're going to look at this segment. This area, you have paid very careful attention to two. This is telling me that point of VMs X coordinate is negative one half. If it's negative one half power unit circle, the other one is going to be negative square root of three over two. You need to recognize this. This is telling me to do it in radians, I believe. Yeah, so that means in your calculator and you need to make sure you change it to writing. So all I'm going to say is that my reference angle here is going to be this angle. Well, this angle is in relation to true red angle kind of right here. On the other side, which is pi over three. So this reference angle also is pi over three. Now from the start to this angle is path. So you would say pop plus pi over three. Jacket. Carrots, pie. I was three. And I got 4.8879. Four point. Three. Yes. That's your answer. Matt wrapping it up. We got number 21. Number 21 is another one that is dropping drag ones. This time dropping dragon is kind of interesting. Very different ways. One thing to remember is with them drop and drags. They're kind of giving you answer choices without giving you answer choices. Congrats. So everything under number one goes for a two is B and H is three. These are possible answers are not necessarily true answers only one of them is the truth. It's not a one time first, the easiest is the period. And based on this formula, the period comes off B we know the period formula says over B so we know it says in the problem, though, that the period is 6. So that equals the number 6. So that would be 6 B oh man, that big B so we have different. Ecosystem. I can divide by 6, 90 B equals pi or three. That is that one right there. Right? We also know. That think about candy cane. Please don't leave it all over everywhere. That the minimum value should. I'm going to so we need to know the difference between the vertical shift and the amplitude should equal two. So I would give my possibilities a one. And see which one of these is going to give me two. I'm sorry, it's H minus. So you look when you look at H minus a, which one of these combinations is going to give me two. I see four minus two will equal two. Then I see 6 minus four equals two. None of the rest I'm equal to. So I'm going to be looking between these combinations. On amp, two on a vertical shift or 6 on amp. And I'm sorry. This is H one vertical shift two on the amp or 6 on the vertical shift to inform you. So we're going to go ahead and loan button. As much. We're going to type in just a basic equation. Basically an equation we know is Y equals. Son. I run three X that's where everything we know from my period. Now if you notice your graph does not grab, you got to go to this gear. Change it right in and you'll see your squiggly lines. Now we need this minimum point in this at negative one to go to two. So our first combination was an amplitude of two and a height before. Let's see, if I do amplitude that goes in front, and I'm going to hide the forward that goes in hand. Does that move my minimum value to two? It does. Now the thing is problem solvers was that F of 2.5 equals 5. So I want to graph Y equals 5. I got it at .5. And I have a 2.5, which is what the problem says. So that means this combination works. So a is two. B is pi over three. And see our H is four. That's all you had doing that one that one does. Involve a little bit of thought process. Next one 30 or 22, I'm sorry, I'm ready to get started. This thing got a graph. And second one throw in. Two. Well, if I can get it again, my content. Oh yeah, they wipe my memory. That's right. They wipe mom computer. I messed up. Same bounce and graph paper on her real. All right, there were. Okay. The bottom of me some paper. So Robert undo is we're going to make this straight to just kind of quickly. And I guess it's right now. We're going to grab these points into what happens at zero zero. Change our colors to the cloud. I think. I'm 9 three. And you have a triangle. All right, now this is samus rotating about Y equals X Y equals X means X and Y just switches location. Thanks for coming to wildlife becomes X but 6 6 and zero 0% trash. 6 6 and zero zero don't change. The only one that changes is 9 three. But do that one in purple. It would become three. Three 9, so it comes like this. That part is part of the rotation. Now, when you rotate a triangle, you actually get this shape of a and so this is cone. You get a cone. The volume of a cone is found by a pi over three R squared H, you need to know that. They're not giving you formalists. I am we need to know our distance formal, which we talked about before. X two minus X one squared plus Y two, minus one one. Squared. All right. So let's look at this one. So I want to see, I need to figure out R and why. Well, the right is if you notice is the base of these triangles. So we need to figure out the distance between non three and 6 6. The final radius. So RE goes to square root. And I'm going to go from 9 three to 6 6. That's X one, Y one. X two Y two. So I'm going to say 6 -9 squared. Plus 6 minus three. Squared. 6 -9 is three, three squared is 9. 6 minus three is also three, three squared is again 9. Square root of 9 plus 9 is 18. The squared 18 will break down to. A non induced, this would be three to square root of two as a radius. So R is three discovered at two is what we just found. Now we need to figure out our height, which is that long red line. So that's between zero zero and 6 6. So we're going to our formula again. We'll do it in larger disgraceful. Glaciers are doing great. This is going to be my height. I'm going to say I'm square root. And this one I've got zero zero. And 6. This is going to be pretty easy. It's basically going to be 6 squared plus 6 squared. Because zero minus R 6 minus zero is zero -6 squared. It's still just going to be that 6. So that is the square root of 72. Which is greater than two is the same as 36 times that 6, the square root of two. So the height is 6 the square root of two. So now we're just going to plug them into my formula. So I'm going to say V equal pi or three. Time. This is R squared. So I'm actually going to leave in the square root of 18. Because that would just make my square root go away. I kind of like it better that way. So you subscribe to two. So this is going to be V equals pi over three times 18 times 6 square root of two. Those two will cancel to be 6. 6 times 6 is 36. So this is 36. Square root of two. Which is answer choice C that one is a little bit more thought provoking. We got just a few more and we are almost done with these guys at one 30. All right, number 23. And parallelogram. I'll draw bad, sorry, apologize. I think every math teacher does. Not all of them, but I'm sure there's some of them out there that I'm just not want to measure angle in a zigzag plus TM. Measure angle in his father's plus ten .5. How many degrees is measure angle T? Well, I would get it this way. Measure angle of T and measuring or supplementary means they add it to give me one 80. The measuring M and measure angle and also do that. So that tells me T is congruent to Ian. Okay? So both we got to do is find T are fine a, then plug it into in the equation. And I should be able to get my answer. So the question is saying. We're going to say 6 X plus ten plus 5 X plus 10.5. Obviously equals one 80 coming out of room. I want to combine my terms. I have 11 eggs. Plus 20.5. Equals one 80. I'm a subtract 20.5. One 80. I'm seeing like one 79.5. One 59.5. So I have one 59. .5 equals 11 X. We're going to buy about 11. X equals. Not about 11. 14.75. I'm sorry, 14.5. 75 I apologize. Now what you got to do is once you find your 14 point 5, you need to plug it into tease equation. So we're going to say 5 times 14.5 plus 10.5. So we're going to plug this in, we're going to say 5 times 14.5. Plus 10.5. Then you get an answer of 83. Which is a great answer. All right, the next one is about diagonals. Now that goes up a trap, our rectangle you need to remember are congruent. That's a big help. If IE and EG are given to you in equations. And we know IG is congruent to FH, because diagnosed with rectangles are congruent. Also, because of diagonals being cut in half, IE is also congruent to EG. So by doing this, I can set these equal to each other. Three X plus four plus 5 X -6. I'm sorry it should be an equal sign. My movement three X and my 6 at one time. Bam, ten, two X, bam. X equals 5. 5 is X noticed by the answer choice for 5 is not the correct answer choice. Now you have to plug it back into the sum of these two. So we got to say. Three times 5 plus four plus 5 times 5 -6. That's 15 plus four, which is 19. This is 25. So try 6. Which is also 19. 19 times night or plus 19 is 38 units, which is what I answer is. Okay, good job. Next. This way you gotta recognize some vocabulary. It's telling me that the angles are all being congruently in bisected. They're being cut equally in half. This tells me that I have an end center at J when the end center, that tells me all the distances to the sides are the same. So in MGH, our measure of GH is X plus three. Measure PG is four X plus one. And DJ is two X minus one. Question is asking for segment PG. So I know all of these sides are equal. So I just need to say two X minus one equals X plus three. I'm going to add one. I'm going to subtract eggs. Bam bam. I get X equals four. Now once you get X equals four, it asks for PG. So PG is four times four. Plus one. Four times four is 16 plus one is 17. The answer choice is D all right. Next question. 25. 6. What is the length of the radius of the circle? So we got to complete the square. So we first need to get our X's and Y's together. So I'm going to say X. I'm going to say X squared minus four X plus Y squared. Plus point plus Y squared minus four Y plus blank. Equals negative four. This is negative two squared. Which is four. This also is negative two squared. Which is also four. So the equation is X minus two squared plus minus two squared. E goes. These two force cancel out. What's left is four. Now the question is asking for the radius. Remember that four is radius squared. So if you take the square root of the four, you will get a, then the answer is two. Okay. We can have temperature of 61°F. Bag of plans to cover the floor in this oscillation. So let's draw a trapezoid. A sausage trapezoid is basically a rectangle when two triangles on the side. Bases are 16 and 26 by the rectangle sides are equal. I got ten left over on the bottom, so I'm going to run it back to you. So that's how I would look at my trapezoid. These are right triangles that are created. And I also know that these angles are congruent. So this is start chain. On both sides. So what I need to do first is I'm going to solve for H and software height to triangle. Some say 13 squared -25 squared. I'm sorry managed 5 squared, which is 25. Sorry. So one 69 -25. You get one 44. So that makes 80 equal 12. So these sides are 12. Okay. Now the question is asking the area, how many pieces does he mean? If he won't see area. Based off of how much each piece will cover, the square foot area is far pieces so much square foot. Well, the area of 400 trapezoid is one half the height times base one plus base two. My two bases are 16 and 26. So I have 16 plus 26. Hike this trail. I'm 12 times one half. Equals a so you get a E goes 6. Times 42. Which is like two 52. Is the area. Please notice that his answer choice, but that is not the correct answer choice. That's the overall area, but the questions ask how many pieces does he need? Each piece has an area of 2.5. So you take your area you found that you 52. And you divide by 2.5. And when you do that, you get, I think it's one O one. Approximately a 101 pieces of wood or whatever. Is needed. Which method is most likely to produce a random sample of fast food from a school club. Selecting 5 club membership brown hair, so let me remember if she raised the most fun. Slightly 5 5 members from a hat containing all the members or sweating in 5 members who arrived last, what meeting. There's only one of them that's actually random. And that would be from the hat. We don't know which one we're going to pick. All right? Last two, yay. Hi, the margin in here is what this one's about. They've given you the formula as you're just going to deviation in as the number of objects. Possible when we select this any 5 of the 200 seniors to take the quiz on college entry exam sample, and the mean grade point average was 2.85 with standard deviation .4. What is basically the questions they want you to do this is a quick one. They want you to tell how many statements are true. They're all dealing with the margin of error. So as you can imagine, there is a margin of error is going to equal two times. The standard deviation, which is 0.4. I really square root of 75. So this is in the calculator two term. .4 over square root, 75. I get this number. Okay. So I .0923. So if you look back here, that number is one of my answers. The margin of error for the mean grade point average is about that's one of my one of my sentences, not the top one, just the second one. Now again, the margin error would decrease if the sample size changed to one 25 or the margin error would increase. The bigger the sample, the less area you're going to make. So by that logic, it would be that second and third. Lastly, the police chief is long to determine the average speed to random sample. You got all this information. He's got the margin of error formal, which choice would decrease the margin of error, decrease in the sample size, increase in the sample size, change in the time that that is quite an or change in the room. Which one would decrease the margin of error? Your margin of error only decreases when your sample size increases. And that is it. Hope you enjoy this. And if you got questions, she may message the video