2026 05 11 - Maths F5 - May 2019 P2 solutions - Set 3

Added: 2026-05-12

[00:00:00]I honestly don't post some people like three different people around.

[00:00:28]It's okay. All right, folks. Good afternoon. Sorry for the little delay.

[00:00:31]All right, so we back now um from not about we could go to about quart to 4 if you all want, right? But then it's a short break between 4:00. All right, so we aim to knock off question eight and then nine and 10. Let me did I did I give you nine and 10 already?

[00:00:45]>> I give Anna.

[00:00:52]>> Let me I have to get the question for Non.

[00:01:02]24 to 27. I give no I I don't know about that.

[00:01:48]No, I think >> schools.

[00:01:59]>> Which ones?

[00:02:00]>> My friend said >> I have no idea. I'll keep track of that.

[00:02:08]>> Want to make it right?

[00:02:11]>> I wanted to make same. I was like confident about >> I was I was so I was so like I'm making marriage this was like >> I was so ready for anything except those two topics >> which which I'll be for yourself >> why would just I find >> okay we have a functions and there's actually there's a piece of this question didn't print out because there like one small piece on a whole page all right so we we just finished question seven yes >> um it should say this at the All right. So, relations, functions, and graphs.

[00:03:29]Oh, what's going on? I don't know.

[00:03:33]Okay, so the functions f and g are defined by that. State the value of x that cannot be in the domain of f of x.

[00:03:42]So this is f of x here is what you call a rational function which is in the form of of a fraction, a numerator and a denominator.

[00:03:48]All right. So what are they talking about here? How could there be a value of x that cannot be in the the domain?

[00:03:55]An x value. What what what is an x value that cannot exist in the function?

[00:04:00]That's correct. Why?

[00:04:04]>> Correct. So anytime you have a rational function, there is a vulnerability. What what I call a vulnerability in the in the denominator. Any value that makes your denominator equal to zero is a problem because if you divide by zero, it's undefined.

[00:04:19]All right. So if 2x + 1 is equal to 0 then f ofx is undefined.

[00:04:43]All right. So anytime you divide anything by zero we can't get an answer.

[00:04:47]All right. And it has to do with how we define division. Division is repeated subtraction of the same number until you get zero or until you cannot subtract that same number and get a positive value. For example, if I did 10 divided by by two, I'm asking how many times I could subtract two until I get zero or one second.

[00:05:07]All right.

[00:05:09]Hey. Hey Christina, how you doing? Okay.

[00:05:11]So, so Ana, Anastasia, Christine, Kristoff, Mr. Elliot, Hannah, Haley, uh, I'm not seeing J. Okay, maybe right. So, James went already, right? Jonathan didn't come. Kim has exams, right? Kana here.

[00:05:27]Luna also has art. Non is here. Payton is here. Risa, no. Salom, not yet. She has R2. Sanjie, Shazar, Shar went out.

[00:05:38]Okay.

[00:05:40]All right. So, that's basically, right?

[00:05:42]So, yeah. 10 - 2 is 8 - 2 is 6 - 2 is 4 - 2 is 2 and - 2 is 0. So that's 1 2 3 4 5 subtraction. So that's why 10 divided by two is five. But if you subtract zero from 9 what you get 9, right? If you do 9 - 0 you get 9 - 0 you get 9 - 0 you get 9. And so we continue.

[00:06:05]Right? So some people say when you divide by zero you get infinity. I I don't know that that's a correct mathematical statement, but I understand why they would say. Anyhow, so long story short, whatever value of x renders the denominator equal to zero is cannot be in the domain of f ofx.

[00:06:23]All right.

[00:06:26]So if we like so therefore if um if the so so if 2x + 1 is equal to 0 we'll subtract one firstly from both sides of the equation and then we'll divide by 2 and that there's your answer x= minus a half is the value of x that cannot be in the domain of f ofx there cannot be an x value in this function. Okay.

[00:06:56]Right.

[00:06:58]And then find in a simple. Okay. So, there actually two questions. I didn't print out this page for you guys cuz all this page asked for was f inverse x. All right. So, I'm going to put it below there as well. One second.

[00:07:37]right? So fg of x. So when they want fg of x, they want you to substitute the entire function of g into x. So the sorry so this entire expression here will sub for x.

[00:08:12]Did I finish my water?

[00:08:41]All right.

[00:08:54]Right? So when you apply distributive law in your denominator, what happens?

[00:08:58]2x becomes 2x and 2 by minus becomes minus 6. And when and you have - 6 + 1 that simplifies to - 5.

[00:09:09]So 9 / 2x - 5 is the expression for fg of x. Again they call it a composite or a composition function right um for this one.

[00:09:24]Right? So for f inverse so what's the process we have to let y equal to f ofx right? So we'll let y = 9 over 2 x + 1.

[00:09:48]We'll then swap x and y.

[00:09:51]So we get x = to 9. So so swap 9 right right 9 over 2 y + 1 and now with the transpose and make y the subject.

[00:10:06]So the first thing I would do here usually with fractions is I would multiply by the denominator to kind of as I say clear it out.

[00:10:14]Hold on if I think bases will come. Uh that's a good question boy. I think it came recently. It came recently.

[00:10:25]>> No, I was like I skipped question.

[00:10:38]I'm like, what is this? Why is it not?

[00:10:43]>> I think we could just stick a touch on it. Yeah, that's not right. So, if we expand in distributive law, we got 2 xy + x = 9. Now you want to make y the subject. So the first thing to do is let's remove the x to the back there. So we'll subtract x from both sides and then we'll divide by 2x to make y the subject. So 9 - x all over 2x.

[00:11:11]All right.

[00:11:12]Therefore f inverse x is equal to 9 - x all over 2x >> I did >> yesterday >> no Friday I said that was I is the mat.

[00:11:49]She's a transformation.

[00:11:58]>> Study talk boy to the rescue.

[00:12:10]>> All right. In class people, are we okay with the functions question so far? Any issues, problems, questions? Anybody?

[00:12:17]Anything?

[00:12:24]Yeah, All right. Um, Christina and H give a quick genie chat or some kind of feedback if you're on the screen. Please unt Yeah. All right. Cool.

[00:13:50]Okay, let's go again to the next page.

[00:13:54]Oh, no, that was the F inverse. All right, cool.

[00:13:57]All right. H, look what they have here.

[00:14:00]They have a measurements and quadratics question all of a ton. All right, cool.

[00:14:04]Diagram below shows two rectangles. ABCD and GFE. So ABCD is the bigger rectangle and GF is the smaller kind of cross-hatched one, right? ABCD has an area of 44 square cm. GF has sides four and two and a G and E C okay hold on hold on this have are equal with a length of 3x. So by writing an expression for the area of triangle ABC D show that X2 + 2X - 4 is 0. Right? Okay.

[00:14:40]Sorry. So A B C D is the bigger of the two rectangles, right? G FED is the smaller of the two rectangles.

[00:14:51]The bigger rectangle has an area of 44 square cm and the smaller one has dimensions. Sorry, hold on.

[00:15:00]Four on the vertical, two on the horizontal, and a G, which is this section here, and EC, which is the section down here, are both the same measure of 3x cm.

[00:15:11]All right, so by writing an expression for the area of the rectangle, all right, how do we find area of rectangle?

[00:15:20]Length by breath. Okay. So whether you call this the length and this the breath or width or whatever you call it, right?

[00:15:27]So we need to multiply this by that.

[00:15:33]All right.

[00:15:35]So we have 3x here and four. So the whole length in one expression is 3x + 4. Down here you have 2 + 3x. So the whole thing is 2 3x + 2 or 2 + 3x.

[00:15:49]Doesn't matter cuz it's addition.

[00:15:52]So what we have to do now is simply multiply the length by the width and the tool set that is equal to 44. So we have to put that equal to 44.

[00:16:21]Okay. All right. So, please go ahead there.

[00:17:16]Sorry.

[00:17:33]What the hell?

[00:18:14]All right. Ready? So if we expand, right? So we do 3x 3x that'll give us 9 x^2. 3x 2 will give us 6 x. 4x 3x will give us 12 x and 4x2 will give us 8.

[00:18:52]Okay. So what we're going to do here is we are going to simplify the x terms in the middle. 6 and 12 will give us 18.

[00:19:00]And then we're going to um subtract the 44 to bring it across from right side to left giving us a zero on the right hand side of the equation. So now we have 9 x^2 / 18x - 8 - 44 is 36.

[00:19:16]Now 9 8 and 36 are all divisible by 9.

[00:19:22]All right. So 9 x 2 / 9 is just x^ 2.

[00:19:24]18x / 9 is just 2x and - 36 / 9 is just 4. And of course, whatever happens on one side of an equation, what's happening the next side? But 0 / anything is just zero.

[00:19:37]And that is exactly what they wanted us to show.

[00:19:46]All right.

[00:19:48]In class people, we okay with that one?

[00:19:49]Any questions, problems, issues? You want to reex or rework it? You good? All right. All right. Christine and Haley, just let me know if you go with that, please.

[00:20:04]Okay.

[00:20:08]All right. Factoriize. Yeah, it factoriize it.

[00:20:12]Okay. Next piece.

[00:20:15]Calculate to three decimal places the value of x. Right. So, we have it was x^2. What? + 2x - 4. Yeah.

[00:20:24]Now this cannot be factorized. So guess what you have to do to solve for x. You use the formula which is x is equal to - b + - root of uh minus 4 a c. Very good. Yeah.

[00:20:45]Where a is the coefficient of the x² term. Hold on.

[00:21:02]Yeah.

[00:21:04]>> Uh, that has been borrowed.

[00:21:09]>> No.

[00:21:10]>> Uh, Christine's older sister, Caitlyn.

[00:21:12]So, her um her cape accounting unit to pay for tomorrow. Sorry.

[00:21:17]>> Tomorrow. Same day as early on. So I had to that's why we could have class Saturday cuz I had them. It was their last day Saturday and I put them on the days that you all had exams last week but then I wanted to put them Thursday as well and but they had an exam Thursday. So yeah, I wish I could have done both classes right up until the exam but unfortunately that isn't what it's >> cheap accounting unit too paper two. No, I don't. But I have an included.

[00:21:52]>> All right. I get myself in trouble before our next post go up on a different teacher comments.

[00:22:03]>> Miss first name.

[00:22:08]>> Miss what? It was like it was >> that first.

[00:22:15]>> Well, then that narrows it down. Okay.

[00:22:17]>> Yeah.

[00:22:25]>> All right.

[00:22:26]So, I'll give you a minute or so again to plug it up. See what you get. Now, it says to three decimal places. Now, you're probably also going to get a two values here, a positive and a negative.

[00:22:34]But we can't consider the negative value because x is a length and we don't have negative length. So only the positive value.

[00:22:49]I hear the joke. You could actually do part three to this without doing either part one or part two.

[00:22:58]Yeah. Cuz the area and will be what? the area the or the big big rectangle minus the small rectangle. Right? They told us the big rectangle is what? 144 >> and the small one is is 8. 4x2 is 8.

[00:23:14]What?

[00:23:15]>> Which one? The last one.

[00:23:18]>> Oh, the parameter. Wow. Look at that. I said area. Wow. Okay. Sorry. So, I'll take back my statement.

[00:24:07]I'm trying to focus.

[00:24:29]Cool. Let's go.

[00:24:34]So minus b is - 2 plus or minus square root of b^ 2 minus or a is 1 and c is - 4 all over 2x 1.

[00:24:57]So 2 ^2 is 4. Now - 4 - 4 is a positive 4. Right?

[00:25:03]So that is plus or minus 4 + 16 all over 2.

[00:25:12]All right. So that's - 2 plus orus of 20.236.

[00:25:31]So 1.236 1.237 >> decimal places in the question.

[00:25:54]>> Right? Make all the mistakes today before tomorrow when you go in the exam.

[00:25:58]Read the question carefully and make sure you give it what it asks for.

[00:26:07]>> Six. That's correct. Sorry. One.

[00:26:10]>> Yeah. Cuz it's 1 plus is minus 1 plus root five, right?

[00:26:13]>> Root 5 is 2.2367977.

[00:26:15]So I forgot the zero. Sorry. Yeah. So minus one plus that is You see, I'll see if we can this question.

[00:26:35]>> I might take a nap between class for pressure.

[00:26:43]>> Yeah, I up since 5. Went to bed after 12.

[00:26:47]Anyway, yeah, watching the roast of Kevin Hart. I was like, "Okay, >> you fine."

[00:27:02]>> There's this movie with the >> whole >> It had times in the early >> No, >> was that serious or he had to kill somebody on it, right?

[00:27:16]>> No, no, no. So like >> No, he was the one like >> his best friend >> Mhm.

[00:27:23]>> like settle had like children and then he wanted to go on like a boy trip.

[00:27:27]>> Mhm.

[00:27:28]>> And he went with him on the boy and crazy.

[00:27:34]>> White chicks.

[00:27:35]>> Yeah.

[00:27:41]>> Right. So the parameter of the unshaded region, right? So we come back here unshaded. So that's the 3x plus this piece here plus this piece here plus this piece here plus that piece plus that unshaded. Good. So you have that's like six sides.

[00:28:00]All right. So let's come across here and do it as we have a visual. Right. So perimeter of unshaded right.

[00:28:12]So, GA plus AB plus BC plus CE plus E F plus FG. Okay, so the GA is 3X, right? So that's 3X plus the AB is the same as the horizontal below. That's 3x + 2.

[00:28:45]The BC is 3x + 4.

[00:28:49]The C is 3x again. The EF is 4.

[00:28:55]And then the FG is 2.

[00:28:58]1 2 3 4 5 6. Right. Okay. Cool.

[00:29:11]Okay. So, one, two, three. You have four sets of 3x.

[00:29:23]You have two twos and two fours, right?

[00:29:31]So, that's 12 x + 4 + 8. So, that's 12 x + 12.

[00:29:40]All right. So, plug it in your calculator.

[00:29:53]>> 26.832.

[00:30:10]shape and I get the same answers.

[00:30:12]>> Yeah.

[00:30:14]>> And I get the same answers.

[00:30:19]>> Right. That's right. Because look, this piece here matches to this piece here.

[00:30:23]Right.

[00:30:23]>> Yeah.

[00:30:24]>> And then this piece here and this piece are the same, right?

[00:30:27]>> Yeah.

[00:30:36]Uhhuh.

[00:30:43]Because that's area they want perimeter >> because then you'll miss out the little kind of L piece in the middle to the bottom left hand side.

[00:31:22]Oh, 26.

[00:31:24]How do I have that intricate?

[00:31:27]I don't know.

[00:31:29]Oh, yeah.

[00:31:34]Let me see.

[00:31:36]Yeah, I did 12 by the 1.236 and added the next 12. Yeah, that's all I get, >> right? Cuz it came back to 12 x + 12, right?

[00:32:04]Sorry.

[00:32:07]>> Okay.

[00:32:09]>> All right. In class people, are you okay with that perimeter?

[00:32:12]>> Yes.

[00:32:13]>> Yeah. No, maybe. All right. Uh Christina, he talk you good there.

[00:32:21]Okay. All right.

[00:32:27]All right.

[00:32:44]more.

[00:32:52]It's not in here.

[00:33:07]>> I did it like this.

[00:33:16]>> Yeah.

[00:33:32]unlocked it.

[00:33:34]Wait, I think I need money button.

[00:34:09]I don't know anymore.

[00:34:38]Don't get one.

[00:34:58]I don't know.

[00:35:21]You have to minus 46 from 90.

[00:35:27]>> Because it's a triangle and a semicircle.

[00:35:32]>> I forgot about this.

[00:35:48]I know. I'm not.

[00:36:00]Oh my gosh, you guys. Don't you This place 180.

[00:36:24]I thought I >> I don't know what they call Quadric.

[00:37:05]Yeah, but like >> I'm all right. So, let's take a look.

[00:37:37]diagram below shows a circle where AC is a diameter. So quick question, a diameter cut a circle in half half a circle is called a >> and the angle on a semicircle is 90°.

[00:37:49]You have a 90° angle here and 90° angle here.

[00:37:53]You have two 90s, right? B and D are two other points on the circle and DC is a straight line. C A B is 28, DBC is 46.

[00:38:02]Calculate the value of each of the following angles. Show detailed working when necessary and give a reason to support the answer. So DBA.

[00:38:13]So the first angle I want is angle DBA. So DBA as this angle here.

[00:38:29]Okay. So with DBA now right so we just said that the whole angle here is 90° right because the angle in a semicircle is 90° so if we have this piece as 46 to find this other piece all we have to do is take 90 and - 46 All right. The angle in a semicircle is 90°.

[00:39:15]>> All right. So, that's the first part there.

[00:39:24]Next piece is what?

[00:39:27]DMC and DCE. Okay, cool. So, let's go.

[00:39:31]DMC.

[00:39:36]Um, sorry. What did I say? Right. DMC.

[00:39:43]D A C. Wow.

[00:39:46]D A C and BC. Okay, cool.

[00:39:52]D A >> C right that's simple as well that's 46° because if you take off that >> oh yeah >> angles in the same sector standing on the same arc angles in the same segment yeah so again if you look at Yeah. So angles in the same segment standing on the same arc are equal.

[00:40:32]So that's equal to DBC.

[00:41:01]Uh in the same segment standing on the same arc Uh, deco.

[00:41:48]>> All right. And the last one they wanted was um, BCE.

[00:42:00]Okay.

[00:42:02]B C E.

[00:42:10]Okay.

[00:42:12]>> That's here, right? So that's equal to 46 and 28 cuz the the exterior angle of a cyclic chord is equal to the opposite interior angle.

[00:42:43]Oh my gosh.

[00:43:07]Yeah.

[00:43:12]The exterior angle of a cyclic quadilateral is equal to the opposite interior.

[00:43:37]Hey guys, I have to take a run upstairs just to get some uh ice to pour myself because I'm knocking out here.

[00:43:47]>> Yeah, I can't make I want to make this today. So, I want to I just going to rub. So, I get some I have a ice pack waiting. Just going to just rub it on myself a bit and then come back.

[00:44:17]All right. Check it. Anna, if you blank off this line here and blank off this line here.

[00:44:25]>> Yeah. You kind of see the kind of double triangle thing where all the vertices touch the circumference. New rule applies.

[00:44:40]>> All right. Okay. That's it.

[00:44:42]>> Yeah. I'll come back.

[00:44:44]>> Yeah. Hold on. Hold on.

[00:44:51]All right. Later.

[00:44:56]Okay. In class people, are we okay with the initial three questions here? DBA and then these two here.

[00:45:07]If not, let me know if you need me to go over it again. That's not a problem. But you got to tell me.

[00:45:22]>> Yes.

[00:45:26]with a bunch of questions.

[00:45:29]>> I'll send you a link to the drop box and you could download your papers and go through. I mean I do have the pass for >> All right. Um oh there it is here.

[00:46:34]Okay. All right. I'm going start with question nine. I'll go upstairs and take a little wash and come back. Okay.

[00:46:41]Sorry. Um Christine and Healey, how are you okay with the circle geometry question? Just give a little feedback, please. Yeah.

[00:46:49]Right. I seen one.

[00:46:52]Okay.

[00:46:55]Yes.

[00:46:57]Thank you.

[00:47:15]Wait.

[00:47:36]All right.

[00:47:38]So, quadrilateral. So, basically what they look how they're looking at it is they're kind of blocking out this line here. So, you just have the four lines, right? Right? You have the four sizes.

[00:47:53]So it's a trapezium more or less, right?

[00:47:56]PQ and SR are parallel. That's interesting. So they're telling us that PQ and SR are parallel.

[00:48:10]>> And you have a Z angle there. Yeah.

[00:48:13]>> Okay. Interesting. I'll put I'll put the arrows on them. Yeah.

[00:48:27]Bang bang from creepy nuts open for Marshall, >> right?

[00:48:34]>> Yeah.

[00:48:37]>> You have a 82°ree angle, a 30° angle.

[00:48:39]Okay, cool. Um, we have a 90° angle up in the top left hand corner there.

[00:48:45]Where else we seeing?

[00:48:49]SP 60 >> SP right yeah cuz if those two lines are parallel this is also 90° angle here this angle here has to be 60° good observation and this this has to be 30 as well >> yes >> Z >> yeah this one is kind of more F angles all right so they want PS as a basic a basic trick one length of PQ >> length of PQ you could but if you find the length of PS then the length of PQ could be found either by reversing Pythagoras or yeah >> PS well Hm.

[00:49:53]>> Basic um tricks. All right, guys. Are knocking out here? I'm going to take a wash and come back.

[00:50:15]All right, we're back in like 5 minutes.

[00:50:33]>> Yes.

[00:50:35]>> Wait, what did you do?

[00:50:37]>> I did call R. Oh, why?

[00:50:42]>> Cuz you have the adjacent side.

[00:50:45]>> You have to find the adjacent.

[00:50:48]So >> it's approp Wait, you said you're a Tik Tok.

[00:51:17]>> Just air drop it.

[00:51:26]>> No, no, no. There should be I found it >> cuz it's public.

[00:52:05]by you know I love Okay. Okay.

[00:52:56]proper >> Oh my gosh.

[00:53:25]Why does that look so real?

[00:53:26]>> Cuz it >> No, that is actually real.

[00:53:30]>> That was kind of like last month.

[00:53:33]That >> is not real.

[00:53:36]>> You know, she put that on her bottle.

[00:53:38]>> She put that on her bottle.

[00:53:42]>> She said I wasn't there.

[00:53:43]>> She said she didn't want to tell me.

[00:53:50]>> You're right next to Christian.

[00:53:52]I got the most devious thing of Christian yesterday. You have this one.

[00:54:05]>> She didn't show it to me.

[00:54:09]I actually have like two or three of >> you like for like 2 years.

[00:54:34]>> Who are you with?

[00:54:42]It's okay. I respect your privacy.

[00:54:58]>> My voice.

[00:55:08]No, it's off. It's off.

[00:55:10]>> No, it's true. It's always behind the wheel.

[00:55:19]>> Yeah, it's >> Wait, what?

[00:55:25]>> I cried.

[00:55:27]No, I was saying I like >> that's me when I was born and nobody else actually nobody I was like actually everybody like one of my friends I just want to I'm going to go find a lot of Oh my gosh.

[00:56:48]That means like >> they're from here from everybody from Jamaica.

[00:57:01]See, you just said that.

[00:57:17]What did you get for the um >> do it PS >> for PS?

[00:57:24]>> Don't PS me. Don't mess.

[00:57:28]>> I got 14.

[00:57:30]>> 42 42.

[00:57:31]>> No, I got four also.

[00:57:34]Okay.

[00:57:49]>> That's right.

[00:57:52]>> Which one?

[00:57:59]>> It's like Yep.

[00:58:04]>> All right. Yeah. Yeah. Sorry, >> I'm back. Okay. So, the length of PS.

[00:58:10]So, we have the presence of a right angle there. So, we could use basic trig functions. Right. Now, here the thing, right? So, the length for which we are looking is actually opposite this length, this angle, sorry. Right.

[00:58:30]Um, there's no Okay, let's try that again.

[00:58:48]Could you hurt?

[00:58:51]Right. So it's opposite that side and the one length we have is opposite the opposite the right angle which makes it the what? Hypotenuse.

[00:59:02]So which ratio uses opposite and hypotenuse?

[00:59:06]Sine sin 30 is equal to PS / 8. So therefore 8 by sin 30 give us PS. So for the add maths above add math people about the sign is a half and 8 by a half will give us what?

[00:59:23]>> Yep.

[00:59:25]>> I use cos of 60 that's fine cuz sin 30 and cos 60 is equal.

[00:59:33]>> So if it wasn't 60 >> it depend on how you work it. I've been given you a process so I can know what you was doing. So I I think it should be okay.

[00:59:48]Okay. Next. The only length of PQ. So PQ is the third length in a right angle triangle. So guess what? We could just reverse Pythagoras, right? So Pythagoras tells us that PQ 2 + PS 2 is equal to QS 2.

[01:00:08]So pq^ 2 + 4^2 is equal to 82. So to solve a pq ^2 we'd subtract 4 squ from both sides of the equation. Right? So 8 square is what? 64.

[01:00:22]42 is 16 and we get 48. So pq is equal to the root of 48 which is pretty close to 7. Practically equal to 7.9.

[01:00:34]What's that?

[01:00:37]6.9. Did it give us a degree of accuracy?

[01:00:41]No.

[01:00:43]Right. So about 6.9 cm. Correct. One decimal place and the area of PQRS.

[01:00:59]PQRS.

[01:01:01]So that's the whole triangle, the whole trapezium.

[01:01:04]Okay. So what do we need? Area of trapezium is half of the sum of the parallel sides. So take that out. So half the sum of the yellow sides plus sorry multiply by the perpendicular distance between which is the four. But to that end we would need SR. Okay.

[01:01:25]Oh my go.

[01:01:33]>> Okay. Okay. So to find SR we would need to use sign rule.

[01:01:40]Yeah. Cuz this angle across here 30 and 82 is 12. 112 from 3 from 1868.

[01:01:55]>> All right. So sign sorry not sign. So SR so using SR which is the that is over sin 82 is equal to 8 / sin 68.

[01:02:12]So we multiply by sin 82 so about 8.5 cm.

[01:02:48]>> Okay. So this is 8.5 down here. What was the value we solved just now? 6.9.

[01:02:55]Yeah.

[01:02:57]>> So the formula for the area of a trapezium is 12 of the sum of the parallel sides. So 6.9 + 8.5 by a half multiply by the perpendicular distance between >> no problem.

[01:03:22]6.9 as or 15.4 half of which is 7.7 7.7 by 4 is 28 + 2 which is 30.8 Hit.

[01:03:41]>> Whoa.

[01:03:43]>> Go over here. Go over here. Go over here.

[01:03:49]>> Where is that?

[01:03:53]>> Yeah.

[01:03:55]>> Yeah.

[01:03:58]Here again.

[01:04:34]Okay.

[01:04:37]All right. In class people, talk to me.

[01:04:38]Are we okay with >> Yeah.

[01:04:40]>> this aspect of question nine?

[01:04:43]>> Do any of you have any questions, problems, issues? Anything I want to go over, reexlain in more detail, different way?

[01:04:50]Anything? Anything you missed? Anything you're not sure about? All right, Christine Haley for you. If you guys are good with that, let me know, please. And thanks. Yeah. All right.

[01:05:00]Lovely.

[01:05:11]Okay. Um, so we have one more question to go, but not too much time.

[01:05:19]Question 10.

[01:05:22]Well, we could get these matrices done for sure. Find the matrix product 1 - 1 3 4 H K5.

[01:05:31]So, I'm assuming they wanted in terms of H and K. All right. So, well, we did some matrix multiplication last week when we were talking about the matrices of transformation, right?

[01:05:41]So, we had to go row by column. So - 1 by k + 3x 5 and then row by column. So 4 by k and h by five.

[01:06:10]You go again. So if you had if you had a second column, you just go the row by that column and that'll give you a a thing there and then row by sorry column again.

[01:06:26]>> Yeah, if you're not sure, I have a playlist on YouTube and I have separate videos for each part of it. So I have addition, subtra subtraction, and multiplication one. No, I haven't separate >> on since 2019. Yeah.

[01:06:42]Right? So when you simplify minus 1 by K is simply minus K. 3x 5 is 15. 4 by K is 4 K and 5 by H is just 5 H. So you can leave it like that or you can put K minus 15. Um and and then 4 K + 5 H or whatever the case. Okay. Now it says hence find the values of H and K that satisfy that matrix equation down there where the answer is equal to zero. So we could state that we say hey hold on hold on wait a minute.

[01:07:15]So if - k + 15 over 4 k + 5 h is equal to 0 0. It means each of those statements is equal to zero.

[01:07:32]Right?

[01:07:36]Then min - k + 15 or 15 - k is equal to 0 in which case 15 would be equal to k or k is equal to 15 and 4 k + 5h is equal to z. Now if k is 15, you have 4 by 15. Sorry, one sec.

[01:08:01]+ 5 h 4 by 15 is 60.

[01:08:08]Sorry, I getting too small there. So therefore 5 h would be equal to - 60.

[01:08:15]And then h will be equal to -60 over 5, which is -12.

[01:08:22]K is 15.

[01:08:24]>> Yeah. K is 15, H is -2.

[01:08:29]>> Right? So you let the matrix. So of course this here is the same as this.

[01:08:34]And if we told that this is equal to 0 0, it therefore means that this is equal to 0 0.

[01:08:42]And then you take each corresponding element between the matrices, right?

[01:08:46]Minus K + 15 is 0. K is 15.

[01:08:50]If 4k + 5 h is zero, 4 by 15 is 60. 60 + 5 h is 0. Well, 5 into 60 goes 12 times.

[01:08:57]So, minus 12.

[01:08:59]All right. In class people, we okay with the first page here? Questions? Anybody?

[01:09:03]Anything? No. All right. Christine and Haley's a quick check in with this page.

[01:09:09]Thanks.

[01:09:15]Seen some jotting down still going on.

[01:09:17]So, I'll give you a minute or two.

[01:09:29]No. Um, but it also does depend on how the exam comes just like with accounts, right?

[01:09:44]>> What is no CXC never say what the partial anything was? Somebody said like 48% >> where they get that from nothing.

[01:09:52]>> How many people pass?

[01:09:56]>> Oh, okay. The percentage of people.

[01:09:59]>> Right. Okay.

[01:10:00]>> Right. Right. Right. Okay.

[01:10:07]>> Okay. That's the daily test. Okay.

[01:10:15]>> So using a matrix method solve the simultaneous equations that all right.

[01:10:21]So what's the first step here? The first step is to extract the coefficients and make a 2x2 matrix with them. So 2 - 2 3 - 5 and 1. Then put the algebra in a separate matrix there. and put that equal to the five and 13.

[01:10:44]Okay. Then we'll call this matrix A.

[01:10:46]It's being multiplied by an X matrix and that's equal to matrix B. All right. So in order to solve for the X, you have to kind of move the A over. Now we have no division operation with matrices. But we can multiply the matrix the inverse matrix on both sides of the equation. and a inverse by a will give us something called i, the identity matrix. And of course, the identity matrix is the matrix equivalent of multiplying by one, which gives us back to the same old x.

[01:11:19]So we got to find a inverse. Okay, cool.

[01:11:21]Let's find a inverse, shall we?

[01:11:25]So a inverse is equal to 1 / the determinant of a multiplied by a a joint.

[01:11:38]The determinant of a is the product of the elements along the lead diagonal by >> a d by bc minus the product of the elements along the second area. So that's 3 by - 5.

[01:11:52]And the adjint is a rearrangement of the elements of the matrix. So the elements on the lead diagonal switch positions.

[01:11:59]The elements on the other diagonal take the opposite sign of what they originally had. Whatever was negative becomes positive. Whatever was positive.

[01:12:06]Now 2x 1 is 2 - 3 by - 7 is + 17.

[01:12:15]You have 1 / 17 by 1 - 3 52. My advice, leave the one over 17 outside for now.

[01:12:22]CPO, you're welcome. No problem.

[01:12:27]Right now, the final thing is to basically execute the last line using the matrices you have. So, the X matrix is the XY matrix. Hold on one sec.

[01:12:36]>> Uh-huh.

[01:12:37]>> Then 2 + 15 then you have 17.

[01:12:39]>> Oh, yeah.

[01:12:43]Thank you. Right. 17 below.

[01:12:48]Okay. So xy = to 1 over 17 by 1 - 3 5 2 by 513.

[01:13:06]Okay. So again row by column. So 1 - 3x 53.

[01:13:12]So that's 1 by 5 + - 3 by 13 and then 5 2x 5 13 1x 5 is 5 - 3 is - 39 and that's 25 + 26 5 - 30 - 34 25 and 26 is 51.

[01:13:50]Now we have - 34 over 17 and 51 over 17 which gives us -2 and 3.

[01:14:01]Therefore x is -2 and y is 3.

[01:14:08]All right, we have one more part to go, but it's basically half three. We'll take a quick look at it. Maybe we could rush it down in a 2 minutes, but um yeah, but if you had to go, you had to go. All right, good luck tomorrow in both exams. Let me know how it goes.

[01:14:29]If I get a copy, I'll keep it to myself.

[01:14:35]>> You're across the road.

[01:14:37]summary that you posted the answer thing. I left my physics lessons just so I can go like a paper.

[01:14:45]>> I think I just cry.

[01:14:49]>> I left my home lessons and I lost it.

[01:14:52]>> Oh, I didn't find it back. All right.

[01:14:54]>> In class people, are you okay with what's on the screen here? The pink, the green, and the blue. If there's any particular aspect you're not sure about, let me know. I could dive more into or reexlain at the very least. All right.

[01:15:05]Uh Christine and he know quickly with that please. But of course if you have any questions. Yeah. Okay. Good.

[01:15:32]>> Okay. All right. Good luck tomorrow. Let me know how it goes. I'll be in touch with you if I want. Right. All right.

[01:15:37]Later.

[01:15:59]Here's my list is on 12. I'm going to write about like my day so far and 12.

[01:16:13]>> What I was about 12 scratch up instead.

[01:16:38]I can take my drink.

[01:16:55]>> All right. Okay, guys. So, it is 3:30.

[01:16:58]But if you had to go, cool. If not, then you could um Wait. It's missing a page.

[01:17:07]Hold on. Let's not That's three marks.

[01:17:16]Two and a seven 47.

[01:17:28]Okay. So, hold on. That's not 2019, boy.

[01:17:31]The last page gone then.

[01:17:37]Oh, okay. You can hear it. Yeah. OD and >> Yeah. So, DBE, >> not the hottest. Sure.

[01:17:54]>> No, I feel like I'm going to get like a >> So, I brought it because yes, it was one of the slightly slightly more challenging papers in a while, but it wasn't I I wouldn't call it the hardest, per se.

[01:18:15]Okay. All right. So, if if you could if you could hold on. Cool. If you can't hold on then go is no problem. All right.

[01:18:27]>> What was that?

[01:18:31]>> Yeah. Yeah. Yeah. Just in number 10 either part A or part B. Right. So relative to the origin. So in other words, you have position vectors. So O8 to go from O to A. Sorry, that's not A.

[01:18:44]It's just nine. So 9 on the horizontal, zero on the vertical. To go from O to B, three horizontally. Then six vertically, right? D and E are Uhhuh. So it's a 1/3 one or 1/3 2/3. So this piece here is clearly the 1/3 of AB.

[01:19:07]>> So one of three and six >> one third of this piece here.

[01:19:11]All right. If you look at it, to go from I guess from either from a um A to B, you had to go backwards six places and up six to go from 9 to three. backwards six and from 0 to six this is up six right positive six but it means that this piece here so if that bottom piece is um 1/3 this piece here will be >> 2/3 >> 2/3 and the same with the E right O E is 1/3 right so this piece here is 1/3 of O A which means that the whole piece the rest the rest of it is traction okay so So the first thing they want is the vector area. So to go from A to B, like I was saying, you could look, you could go from A to O and then O to B.

[01:20:06]A O is the inverse of O A.

[01:20:15]Oh, that's K.

[01:20:17]>> What?

[01:20:26]>> Right. Again, to go from nine back to three, you have to move six spaces to the left. So, that's minus 6. To go from 0 to six, that's six paces up. That's positive six.

[01:20:35]All right. What's part A?

[01:20:48]All right. O D. All right. Oh dear.

[01:20:52]Okay. So to go from O to D, we want to go from this point here to this point here. The easiest way to go is from O to A and then A to D.

[01:21:05]Let's write that. O A plus A D. Hold on.

[01:21:26]And as we know a d is 1/3 of ab.

[01:21:36]So that's equal to 9 0 + 1/3 of - 66 is 9 0 + - 22 it becomes 72 out where?

[01:22:05]>> Uhhuh.

[01:22:07]So that that's that's the owner of them.

[01:22:10]>> Yeah. And then be E is the last one.

[01:22:15]All right. So I'll copy and paste this across to the next side.

[01:22:30]be. So, let's go back here and we could work with BE.

[01:22:36]>> Yeah. Okay.

[01:22:38]So, BE means you're going to go from here to here. So, that's B O plus O E.

[01:22:51]B is the inverse of OB and O E is 1/3 of O A.

[01:22:58]So OB is - 3 - 6 and you have 1/3 of 9 0 - 3 + 3 is 0. - 6 + 0 is - 6.

[01:23:31]Okay.

[01:23:33]All right. So, we went a little over time there. Sorry about that. Um, but yeah, one if I if I start back on time and two, not taking a short break, then we could have finished on time. Anyhow, it wasn't so bad. All right, guys. So, that was the 2019. That was the final paper before >> co that that no that that was a toughish one relative to stuff you've done but >> okay so what we're going to do right um is ask if there any questions now um if you have any questions now is a good to ask right if however If we're not then again we will take like a 20 minutes I could take like a real short nap cuz yeah I'll need that for the next 4 and a half hours >> 30 then we'll start it again but the question is what do we do after do we find a next paper to kind of just browse through or do we work specific aspects like for example we haven't really worked questions with major issues of transformation >> so do we >> so we did transformations but we >> transformation I think we >> do some community square.

[01:24:54]>> So, I'll take it.

[01:25:11]>> All right. So Christine Haley um I'll check it back around for >> all right YouTube. Sorry >> I was sent by spring. Oh okay cool that's 247. Wow afternoon sorry guys 644 right.

[01:25:34]>> Yeah still want to sleep. That was correct.

[01:25:40]text box, please.

[01:25:42]>> Oh, yeah. Yeah. Sorry, on the lines.

[01:25:48]>> Yeah, sorry. I went um >> Yeah, >> it's okay. But like >> your children are too noisy. They should help us solve the questions.

[01:26:02]>> Wait, who?

[01:26:03]>> That was 309. That half hour. That's when I went to watch.

[01:26:06]>> Who said that?

[01:26:07]>> I didn't know what they said.

[01:26:08]>> Is there anything? Yeah, I don't teach like anything sciences or language or geography.

[01:26:18]Next for two I think I don't know the person what year 2019 sorry all right May 2019 amber May 20 no I don't have May 26 no I don't learn maths today and pass tomorrow if the exam come a real nice year right we were kind of lost yeah sorry I was kind of rushing on that last part there Um, >> I can't deliver right now. No, don't leave nothing.

[01:26:51]>> All right. Any guys, I had to take 20 minutes. I'll check on their back.

[01:26:55]>> No, I really That's not you.

[01:27:00]>> You said leak it and I watch you. I have no comments on Tik Tok.

[01:27:04]>> I'm not just there's a there's a delay like a sixsec delay or 7second delay between now and when on YouTube.

[01:27:21]But yeah, I take I take a short break like a 20 minutes like a 10 minute nap.

[01:27:29]>> Yeah. Buddy was like good.

[01:27:34]>> All right. Uh Tik Tok. Uh check it back in 20 minutes.

[01:27:40]>> Yeah.

[01:27:42]What?

[01:27:45]>> Yeah.

[01:27:48]>> I am >> study buddy. Are you hearing me?

[01:27:54]>> YouTube will hear, man. Sorry.

[01:27:58]Yeah. 20 minutes. I think I have 20 minutes. You on which which chat you on?

[01:28:02]Is YouTube or Tik Tok?

[01:28:06]>> Yeah. Yeah.

[01:28:08]>> Okay. Cool.

[01:28:10]Yeah.

[01:28:13]Oh my gosh.

[01:28:16]>> It's very sensitive.

[01:28:19]>> Here I know. All right. Cool.

[01:28:25]>> Yes.

[01:28:29]>> Yeah, I am.

[01:28:32]Yeah. Finish up like 15 20 minutes and we come back and we start again. We're doing some um I'll pick out some questions. It should be mod.

[01:28:42]>> It should be mods.

[01:28:43]>> Yeah, >> mods. Yeah, that's on a real looking for people to over family