🔴 EGZAMIN ÓSMOKLASISTY 2026 — ROZWIĄZANIE ARKUSZA NA ŻYWO! | Matematyka 12 MAJ

Added: 2026-05-17

[00:01:29]เฮ oho હ હ Good morning. Good morning, dears.

[00:10:02]Hello everyone.

[00:10:04]Okay, let's start a little earlier, because I figured since you 're already here, there are already over 200 of you, so I'd love to read your comments. I haven't seen Jarkusz yet and I don't know, I don't know a single task. Uh, I guess it's fine. 18 difficult, right? Super simple. I guess that's good.

[00:10:27]Aims 100% very well Sapli.

[00:10:30]Beautifully.

[00:10:32]Hello, hello. How did it go?

[00:10:34]Overall, was it easy or difficult? What do you think?

[00:10:39]I did a survey like this on YouTube and it seems very good to me there, I mean I'm happy with your results, because over 50% I'll see more, I'll refresh now, 54% of you wrote that it was great, I'm proud of myself, it went great. 17% said it was very good, 7% of students only said it could have been better on average and 22% said what was it? For now, we'll see what the results are at the end of today.

[00:11:09]Okay, thanks ma'am. There will be 30% more. I'm really glad. Easy, stupid mistakes, easy.

[00:11:18]Okay, I'm aiming for a hundred. 85.

[00:11:22]Someone writes here, it was a massacre. It will be 60 70%.

[00:11:26]All right. It was even easy. It was easy.

[00:11:30]Poor in open.

[00:11:32]Okay.

[00:11:33]Well, that's great. Great. Worst 18.

[00:11:37]Okay. What was this 18th about if it was so bad?

[00:11:40]M. Good. Yesterday I was on your live show.

[00:11:43]Well, I'm very happy. Yes, it's definitely worth being there.

[00:11:48]97% one error. Well, that's great too. 100% fantastically terribly difficult. Okay, it will be about 50% maybe. Oh people, I see that there are different opinions, different views. Well, write again what it was about. Will you count with us or just show us the answers? Well, I'll count because I don't know the answer. Well, as always, I will count with you, because the spreadsheet will only be available at 1:00 p.m. So Julius it was easy. Well, that's fantastic.

[00:12:18]Great. A cube and a sphere in it and something of volume was needed. Good at this 18. Yes. Mhm. Well, I'll probably take advantage of the fact that it will be 1/3 of the volume of the cube, but okay, we'll see, we'll see. Pretty cool. Okay.

[00:12:35]M Well, dears, if there were 30 points for the entire exam, then one point is about 3, something like that, right? 3.1/3.

[00:12:46]The pyramid was three times smaller and it worked out for me, but there was no data provided.

[00:12:50]Okay. Well, we'll see, we'll see, because I say, no, I haven't seen the content, so I can't comment either.

[00:13:00]Okay, great. Well, generally speaking I see that no, the standard sheets had 30 points. The standard was 30 points.

[00:13:10]Mhm. The cube was next to A. Well, that's it.

[00:13:12]If the cube had side a and you had, then the volume of the cube would be a to three, and the volume of the pyramid, if it has the same base as the cube and the vertex would be as if m touched the upper base of the cube, then it would be 1/3 a to three. Yes.

[00:13:31]Well, I don't know if there were any numbers or not. Mhm.

[00:13:37]Okay, but I don't know, I have to see the sentence, because you know, I'm just saying what you write to me.

[00:13:43]But it may be different. Ostros. I see. On the base of a triangle. Okay, okay. Well, we have to see. We have to see. Well, then it's different.

[00:13:53]Yes. We start in 7 minutes. I just wanted to connect with you earlier, because I see you're already here in the chat. Well, you know, I'll accompany you.

[00:14:02]Yes, there may be mixed answers, so remember that if, for example, our live broadcast shows the answer A or B, it doesn't mean that you have to have the answer A or B, but you have to have the same answer or number, right? But not the same letter, so the letters can be as different as possible.

[00:14:19]Mhm. There was some kind of museum, a shelter.

[00:14:22]Okay. Thank you for your help yesterday.

[00:14:25]You're welcome, Inka. I recommend myself for the future.

[00:14:28]M. with sides contained in the edges of the cube and the diagonal of the base. Okay, so Beata, I have to see the task because I don't want to confuse you or scare you into thinking you've got something wrong. Okay.

[00:14:40]NWD and NW. Okay. Thanks to you, this is the result I will have. I'm very happy, Julka, thanks to your efforts, because you had to come to the live and count something, right?

[00:14:53]The height of the pyramid is the sum of the height of the cube and its half. Okay, I need to see the assignment.

[00:15:00]There were trivial tasks, Nikodym writes, trivial. I'm really glad. Well, that's fantastic. Well, listen, the truth is that if someone has been studying with us here for a longer time, er, studied from the course, then you know that every single paper from the course was probably, or even I would say with absolute certainty, more difficult than your exam today. You don't know, these trial tests that I prepare are also designed to teach you as much as possible, to prepare you for everything. And thanks to the fact that the exam was easy in your opinion, from what I can see, you will be fantastically prepared for high school, because you are already sensitive to such tricks and things that can happen to you, so great.

[00:15:43]100. Beautiful. Very good. Mhm.

[00:15:47]Problem with trapezoid and plot. This was the case with the trapeze and the plot. Okay. Mhm. What else?

[00:15:56]Pyramid. Some apples. Okay.

[00:15:59]Okay, 4 more minutes. How many packets of seeds? And it used to be similar, that you had to sow something and exactly how many packages for how many seeds you had to buy.

[00:16:09]Okay. Well, very similar. All right. All right. Okay, dears. Great. I'm really glad. You 're great at listening. Thank you.

[00:16:22]This pyramid is the worst. Okay, so that's 18 what you're saying. Yes, the worst. Tymek, what a nice simple sheet there was today.

[00:16:30]Great. You know, it was simple for those who were very well prepared.

[00:16:34]Okay, that's how it is with everything.

[00:16:35]Listen, I always say that the best way to make any exam easy is to simply prepare well for it, because if you prepare well, listen, every exam will be easy. So you explain very well whether you are a soldier teacher. I mean, I don't teach at any school, like a stationary one. I teach at a cloud school, but I am a teacher here, so to speak, on my own platform. So thanks to this, each of you can study with me, even up to the first year of high school, if you need it. I recommend myself. Yes, we will do all the tasks one by one.

[00:17:12]All tasks in order as soon as the sheet is available, which is in about three minutes according to what they announced. So I refresh the page here regularly and look.

[00:17:27]Easy. Great. I'm really glad. TKE does n't seem to like us. Hania. Well, quite the opposite. The majority of votes here are that the worksheet is easy.

[00:17:37]18 was super easy. Oh, Ania is writing.

[00:17:40]Okay, because everyone here seems to be complaining about this 18, because with this cube, so is the pyramid in the cube. I don't know what this is about, but we'll find out soon. A very nice sheet. I'm really glad.

[00:17:53]Ah, the arithmetic mean.

[00:17:55]All of them, Oh, you see, Kamil writes all the simple tasks, and Martyna right next to him. This sheet was terrible. Well, it varies. Yes, the live show will be recorded, of course, so if someone can't make it now, they'll be able to watch it later. Absolutely. Mhm.

[00:18:15]Yes, all of them, all in order.

[00:18:17]Always, my dears, always after every exam, whether after the high school final exam or after the eighth-grade exam, we do everything from the beginning, because I haven't seen that sheet either. I will do all these tasks with you. Okay, this is the first time I've ever seen them, but it's very cool.

[00:18:34]So we'll make them all soon. There were a lot of tasks from it on the mock exams, on your mock exams. Oh. So great. Great, Sarah. Well, that's great. But I had nothing to do with it, like anything.

[00:18:49]Mhm. I'm very happy about that. I'm really glad. But you know, we also did some of those trial runs in the course a dozen or so meters, so of course things had to be repeated. After yesterday's Polish exam I thought it would be much more difficult. He has penalties. Well, I'm glad that mathematics surprised me on the positive side.

[00:19:08]Easy compared to the trial. I wrote down the answers on my hand and will check them now. Great. Very good.

[00:19:14]Well, we'll see, we'll see.

[00:19:17]Listen, I'm refreshing the page, but it's not there yet, it's not there yet, so just a moment, just a moment.

[00:19:28]I'll just remove the background here for a moment to send myself the spreadsheet.

[00:19:38]But wait a minute, it's not there yet.

[00:19:41]Mega easy worksheet today. Great.

[00:19:43]Weronika's Polish exam was completely different than the mock exams, but the math was similar. Well, I'm glad. I'm glad. Also easier than the trial one you write. Okay.

[00:19:53]Good morning, Mrs. Paulina.

[00:19:55]Thank you very much for this year. I think I only made one mistake in the closed one. I'm very happy, Bartek. Congratulations. Mega easy, but that's bad because they will raise the thresholds.

[00:20:03]I see. Well, we'll see, we'll see if it's super easy, because you know, it is easy for some people. Oh, there is mathematics.

[00:20:13]Attention, attention, we are sending and already starting to solve. Listen, I'm pasting it for you now, if something is going to happen, it's already there.

[00:20:29]Just a second.

[00:20:36]One minute, one minute. Let 's download and see what you've done so well today.

[00:20:49]Okay, May 12, 2026. I'm showing you the screen now.

[00:20:57]So is this the sheet? The sheet is on the CKE website. Okay. on the CKE website thanks to your challenge I definitely have 90%.

[00:21:05]Fantastically. Listen, if someone took part in this challenge 50 days until the eighth-grade exam, it was also really, really useful to him.

[00:21:13]I think so, because there were also such typical tasks there. Okay, dears, so let's buckle up, focus and get on with the tasks. If there are any questions, I will of course try to answer them, but perhaps we can leave a deeper explanation after we have resolved everything. All right?

[00:21:30]Of course, write what answers you had here. All right? In the first one, remember, I don't care what letter A, B, C, D, only what number.

[00:21:38]Okay, so if someone had a different group, look what the answer was on this sheet that we have in front of me. Let there be some consistency here. All right. This is what it says on the CKE website. I just downloaded it. Well, first task. The math test consists of 40 tasks. The diagram shows the percentage distribution of the number of tasks in the test into tasks from five sections: algebra, planimetry, stereometry, arithmetic and statistics. The number of arithmetic problems in this test is equal. Well, my dears, it's a trivial task. Yes, we know that in a pie chart all percentages don't have to be 100, right? Well, that's the whole thing.

[00:22:13]So we have 20% + 25, it will be 45 + 15, we have 60 and here it will be 65, so the arithmetic will be 35%. This will be our arithmetic. And, uh, since it consists of 40 tasks, we have to count 35% of 40. Well, look, 40 will be our 100%, because these will be all 35% tasks.

[00:22:41]So, for example, it will be x and we make a simple, very easy proportion. So we have x = 40 x 35% and we divide it by 100%, so we can quickly reduce the percentages. We cancel Z0O with zero and we can multiply 4 x 35, which will be 140. We have 140/10, so it will be 14. Of course, the answer is A, which means the first task is very, very easy.

[00:23:09]Okay. e, no matter how you count, whether by this proportion or another. And it turns out to be very easy. My dears, thank you very much too, I will just say for the thumbs up and the hearts. And if you want to receive more materials like this, subscribe, because cool things will also appear during the holidays. And later, when you're in your first year of high school, I also think my channel will be quite useful to you. So I would be grateful for your subscription. Especially since, let me tell you, I have a challenge.

[00:23:36]I'm aiming for 100,000 subscribers on YouTube, so if you'd like to support me, I'd be very grateful. Ola opens her locker using the four-digit code Yxxy, where X is the greatest common multiple of 18 and 27, and y is the least common multiple of 2 and 4. What is the code to open Ola's locker? Note, X is the greatest common divisor, or the greatest common factor, or GCD, of 18 and 27. What will this be exactly? It will be nine. The greatest common divisor, i.e. what is the greatest common number by which both 18 and 27 are divided. Well, of course it will be 9, so in the middle we have y nines, and y is the least common multiple, the least common multiple LCM for two and four. Remember that it doesn't have to be a multiple, i.e. it doesn't have to be more than these numbers. The least common multiple will be ctery.

[00:24:44]Four is also a multiple of four. Okay? So, as someone wrote here, there was an option that eight, there was an option that eight, right? But we know that four is the least common multiple of two and four. So we have the answer 4 9, so we have answer B here. Okay, so this is how we calculate the least common multiple. Please just no spam, okay? No spam.

[00:25:12]Give one answer once and that's it. Okay, I had it good and I changed it bad. And my dears, we talked about it, um, I don't remember if it was at the great replay of the champions or at one of them, and whether yesterday there was even such a sentence that someone there asked me when it was. I think we had it at the checkpoint, right? Does anyone remember that there was also a question about whether four is a multiple of four. There was a different number involved, but there was also a question like that, so you see how we got there.

[00:25:43]Okay, task three. There are four numbers given. W, x, y, z. Which of these numbers is equal to 0? Well, let's count. Oh, wonderful. And these are examples that I have simply been going over with you so many times.

[00:25:56]I hope no one made mistakes here. Yes, yes, you explained.

[00:26:00]Exactly. Yes. And each of you already knows that we must first perform the operation under the square root. So I'm very glad that there were such tasks. Listen, I'm satisfied.

[00:26:10]100 - 64 will be 36, so we have the square root of 36 - 2. The square root of 36 will be 6 - 2, which will be 4. Let's also calculate x, which will be 12 - and here again we have to perform the operation under the square root first, so it will be 100. The square root of this will be 10, so we have 12 - 10, which will be 2. As for y, you wrote that this would be the correct answer. 25 - 16 will be 9 - 3√9 3 - 3 will be 0. But let's calculate it for this, it will be 7 - pi 25, so 7 - 5 will be 2. So of course the answer is C, i.e. y is equal to 0. And if someone learned these roots, they couldn't have made a mistake here. Okay, because this is already a task that has been dragging on for so many weeks. Beautiful, beautiful. Very good. Very good. The fourth task.

[00:27:09]Just smaller here so as not to cover it.

[00:27:11]The value of the expression 2 to the power of 5 x 3 x 3 to the power of c x 2 to the power of trj is equal to the value of the expression. And see that in the answers you have either twos and threes, or fours and nines. So you write that the answer is A, so we reduce it to twos and threes. Well, let's try it. All right? So yes. When it comes to twos, we kind of connect these twos with each other. 2 to the power of pi x 2 to the power of 3j, then maybe I'll write 2 to the power of 8j here, because we add the exponents of the powers of 5 + 3, it will be 8 x 3 to the power, remember that there is an invisible one here. 3 to the first power x 3 to the power cj will be 3 to the fifth power, so we write the fifth power here. So you're right.

[00:28:01]Answer A. Yes, it was trivial. It really was cliché, I admit. Well, I didn't expect it to be so easy when it comes to the fourth one. M. Well, the first one was easy too, the third one wasn't difficult either. Okay, so far it 's very easy. In a certain cattery, a purebred male cat costs x and a purebred female cat costs y PLN. Janek bought a purebred male cat from this breeding farm with a 40% discount and a purebred female cat with a 20% discount. Which expression correctly describes how much zloty Janek paid for these cats? Note how much he paid, not how much the discount was. And we also repeated these tasks so many times that it was beautiful, beautiful, very, very good. You have very good answers.

[00:28:47]If the discount is 40%, we pay 60% of that price. And 60% is of course 6x.

[00:28:58]Mhm. Um, if the discount was 20%, i.e. this discount, then we pay 80% of this price, i.e. 0.8y. Very, very good.

[00:29:07]Well, listen, if someone simply listened in class, listened in the practice exams, then there is no way they would make a mistake. Beautiful, great.

[00:29:18]Dear friends, the answers themselves will also be available later on all my social media, so when we make the spreadsheet, I will also post the answers themselves, and if anyone wants to continue solving, then let's continue. The sixth task.

[00:29:31]There were 11 balls in a box numbered consecutively from 1 to 11.

[00:29:36]Five balls were drawn from this box. The sum of the numbers on any two balls left in the box is even.

[00:29:44]Once again. Five balls were drawn from 1 to 11.

[00:29:49]The sum of any two balls remaining in the box is even.

[00:29:54]After the drawing, only balls numbered with even or odd numbers remained in the box. And now attention, here you have to think for a moment.

[00:30:05]The situation is such that if we add two even numbers, the result will be even. If we add two odd numbers, the result will also be even. But if we add an even number plus an odd number, the result will be odd. So, see, either they had to be all even numbers, or they had to be all odd numbers. from 1 to 11, so we have 11 balls, where there will be six odd, six odd and five even.

[00:30:36]Five even numbers. Since five balls were drawn, well, must have, must have, there is no such word. I guess it was necessary.

[00:30:46]The conclusion is that five balls were definitely drawn that were even and six were left that were odd. Therefore, the answer will be A. Mhm. Exactly.

[00:30:57]Answer would be A. Those were odd. Well, that was an unusual, but cool task. I like it. The sum of the numbers on the five balls drawn is equal. So what? We need to add up these five even numbers.

[00:31:09]Yes? So even numbers will be 2. Maybe we'll give it plus 2 + 4 + 6 + 8 + 10. And we can add 4 + 6 = 10, 2 + 8 = 10, and + 10 will be 30.

[00:31:27]Of course, answer C. Great. Uh, so yeah, cool task, unconventional, I admit. It might have surprised you a bit, but if someone put a little thought into it, I think it worked out for you. Besides, you write here, you write answers, so it's fantastic.

[00:31:45]Seventh. Apples were placed in 10 empty baskets. Oh, so you said there was something about apples. Apples and oranges. A total of 400 pieces of these fruits. In each basket the total number of fruits is the same and in each basket the number of apples is six more than the number of oranges. How many apples are there in total in these 10 baskets? Select the correct answer from those given.

[00:32:10]So yes. Since there are six more apples in each basket and there are 10 baskets, there are 60 more apples in total than oranges. So if we write that there are x oranges, then apples will be x + 60. We're talking about the total number, and there are 400 of them in total.

[00:32:31]So we can create an equation that equals 400, I'm looking at your answers. Oh, things turned out differently for you here. D B C still appears there. Okay, let's check. So 400 equals oranges, which is X plus apples, which is X + 60. We move 60 to the left side, i.e. we subtract it. We have 340 = 2x pr 2. X = 170. But the question is about apples, so there are x + 60 apples, which is 170. Maybe I'll write it down for you. 170 + 60 will be 230.

[00:33:14]We have answer B. I arranged 400 = 10 x x + x + 6 in parentheses.

[00:33:28]Mhm. Yes, yes, that's right. Julius very good. Beautifully. Mhm. Yes, yes, yes. Dear friends, this task, this equation that I am creating, is not the only possible answer. So, so, so if someone came up with a different equation, that 's okay too. All right. Phew, I was already scared.

[00:33:46]So I made a total number of apples here, but if someone divided them into baskets, that's fine too.

[00:33:53]The important thing is that the answer is 230 and the equation can be arranged differently.

[00:33:57]Also absolutely great. Mhm.

[00:34:01]Good, so far 7 on p. Great Marcin. Beautifully.

[00:34:07]Good job, Tymek. Great. Great. It can be too. Listen, someone could have made it so that there were 40 pieces of fruit in one basket and made it into one basket, so of course it is possible. Great, beautiful. Cool task. It was a cool assignment.

[00:34:22]Eighth. The sum s = 1 + 2 + 3 + n. The consecutive natural numbers from 1 to n can be calculated using the formula. S = 1/2 n x n + 1.

[00:34:33]Complete the sentences. The sum of 100 consecutive natural numbers from 1 to 100 is equal. Uh, okay. Well, let's try it.

[00:34:43]Let's see if we can apply this pattern. Let's write s = 1/2 x 100, i.e. we substitute n for one hundred. times and in brackets 100 + 1 1/2 of 100 it will be 50 x 101 and listen, I used to record a roll like this, I used to record a roll exactly, exactly even these numbers, how to calculate the sum of numbers under 1 to 100, how to do it cleverly, but there was no formula given there and you had to calculate it yourself 5 x 101 it will be 505 and we add this zero that is here, so it will be 5050.

[00:35:27]Answer B. Fantastic.

[00:35:30]The formula for the sum S after the correct transformation has the form, what is it? All you need to do is multiply what is in front of the bracket by each element of the bracket. So we have S = 1/2 n x n. Then remember that there will be n². 1/2 n x 1 will be simply 1/2 n. So we have answer D. Of course, B and D are the correct answers. Fantastically.

[00:35:57]Uhm.

[00:35:59]Great. Great. Great. Very, very good. Beautifully. Well then, let's go to the ninth. Maybe I wo n't turn the page here just yet, just so you can see everything perfectly. The arithmetic mean of two numbers x and y is equal to 4, and the arithmetic mean of three numbers x, y, z is equal to 5. Guys, this problem also appeared several times in the practice tests, so if someone did the practice tests, it was incredibly simple, right? So yes, we know that x + y by 2, because the arithmetic mean is 4, so we multiply by 2. This way we find out that x + y = 8.

[00:36:36]We do the same with x + y + z. We know that the arithmetic mean is 5. So we write x + y + z by 3 and we know that this is equal to 5.

[00:36:50]So we multiply both sides by 3, so x + y + z = 15. We have to calculate for, but we already see that instead of x + y we can substitute 8em. So, it's incredibly simple. So we have 8 plus, there was something similar in the video you sent us. Exactly. 8 + z = 15 so z = 7. Of course the answer here will be D. Beautiful. Mhm.

[00:37:20]Great.

[00:37:22]All right. Task 10. A triangle is given.

[00:37:26]Oh, someone is late, because the assignment about purebred cats was already here. Task five, but someone was late for the live broadcast. Oh well, Simbuś. So there was already a task about you.

[00:37:38]10th task. There is an equilateral triangle with side length 2. The height of this triangle is equal to the square root of 3 and is the area of ​​this triangle also equal to the square root of 3? Of course, here are square centimeters, here are regular centimeters. Well, listen up, role models.

[00:37:56]Yes, you had to know the patterns. Well, let's write down these patterns. The formula for the height of an equilateral triangle is a pier3/2. I admit that the task is trivial, because we only need to substitute the two into the formula.

[00:38:12]You write 2√3/2 very well. We remember that we can reduce it and we have the square root of 3, so it will obviously be true.

[00:38:20]Regarding the area of ​​this triangle, the formula for the area of ​​an equilateral triangle, we have a² pier/4, so 2² pier 2² will be 4. We cancel with four, so it will be square root 3. Of course, units, right? Here are centimeters, here are square centimeters, but here and here we have the square root of 3. I did Pythagoras. Well, Pythagoras, I mean, you can, but why bother? Yes, you have ready-made patterns. If someone didn't have Pythagoras, then by all means. Mhm. Okay, well for now I'll tell you it's easy. For now, for now it's very easy, but let's move on. The interior angles of a quadrilateral are labeled alpha, beta, gamma, delta.

[00:39:05]The measure of angle beta is 70 degrees greater than the measure of angle alpha, and the measure of angle alpha is twice the measure. The measure of angle gamma is twice the measure of angle alpha. The delta angle is a right angle and we have to calculate this beta. Okay, let's write down what we have, because without writing down the data here we can make mistakes.

[00:39:26]So yeah, yea, alpha is alpha. We know that beta is 70 degrees more than alpha, i.e. beta is alpha + 70 degrees. Then gamma is twice the alpha, so it will be 2 alpha.

[00:39:41]And we know that delta is a right angle, so we have 90 degrees. And everyone knows that in every quadrilateral the sum of the measures of all the interior angles is 360 degrees. So let's set up an equation that alpha + beta, so we substitute alpha + 70 degrees plus gamma, which is + 2 alpha + delta, which is + 90 degrees, equals 360 degrees. On the left side we are left with 4 alphas, so we have 4 alphas = 70 degrees and 90 degrees, if we add them up, we get 160 degrees. If we subtract 360 degrees, it will be 200 degrees. We divide by 4, so alpha equals 50 degrees. And if someone has already marked answer A, I hope no one else has done that.

[00:40:33]The question is about the measure of the angle, the measure of the angle beta. Yes, remember to always read the answers to the questions to the end.

[00:40:40]Since alpha is equal to 50, then beta is equal to 50 + 70, so this will be the answer C. 120 degrees. Fantastically.

[00:40:48]Exactly yeshm. I will just write down here that beta = 50 degrees + 70 degrees, i.e. 120 degrees. That's why there will be such an answer. Beautifully. Great. Very, very good. Okay, task 12.

[00:41:05]Y, wasn't that what we did in our review yesterday? Exactly like that, only the triangle was the other way around. Something seems to be going on here. No, you don't have such a dejavi.

[00:41:16]12th task. Jurek made a drawing on a squared piece of paper. In this figure, the MWS points mark the locations of the museum, the observation tower and the mountain hut, respectively. it was so similar. Well, whoever was there knows and probably benefited from it. The observation tower is located 3 km north and 4 km west of the shelter. So, yes, 4 km west of the shelter, that's where the 4 km are and to the north, that's a bit of geography, right? 3 km. The museum is located 5 km east of the shelter, so it will be 5 km here, because there are five squares. And now the straight-line distance from the shelter to the museum. The distance from the shelter to the museum is equal to the straight-line distance from the shelter to the observation tower.

[00:42:08]Well then, Pythagoras is just asking for it. Yes, and we talked about it yesterday too. How to calculate such distance? Of course, from Pythagoras, so we count. Let there be some x here. And we have 4² + 3² = x². 16 + 9 = x² 25 = x² If we take the square root of this, x = 5, so the distance is the same. Of course it will be true. Mhm. The distance in a straight line from the museum to the observation tower is less than 10 km. This is a very cool task, because something with a strange uncomputable root will probably come up and we will have to estimate it. So now we have to calculate this distance. And here you see, we have a right triangle again, only this time it's 3 by 9, right? So we have some other letter here, for example y, and again we use, we apply the Pythagorean theorem, so it will be like this, in a straight line, see, this is the straight line.

[00:43:13]This is a straight line, because it wouldn't be a straight line. Okay, that's a straight line, which is exactly what we mean.

[00:43:20]These are the straight lines, so we have this. 3 k.

[00:43:26]Maybe I'll start a little higher. Here you can see more. So yes. 3² + 9² = y².

[00:43:34]9 + 81 = y², so we have 90 = y². If we apply the square root, then y = square 90. So will this distance be less than 10 km? See, the square root of 90 is less than the square root of 100, and the square root of 100 is 10. So the square root of 90 is actually less than 10, so that will also be true. If someone said true, true, they had a very, very good answer. The square root of 90. Exactly. Or 3 roots of 10? Yes, but Harris here the square root of 90 looks nicer because nicer we can use it better. Okay.

[00:44:20]Beautifully. Yes, because it's between nine and ten. Exactly. Exactly, Milena. Beautifully. Mhm. Great. Well, let's move on to the next task. But this 12th was cool. I really like this 12th task. They came up with a great idea. 13.

[00:44:35]Diagonal AD.

[00:44:37]AD divides the pentagon ABCDE into the triangle ADE and the square. The area of ​​triangle ADE is equal to 28, and the height drawn from vertex E to side AD is equal to 7.

[00:44:49]So yes, we know that this height will be equal to 7.hm, so you write answer D.

[00:44:54]We'll see in a moment. The area of ​​square ABCD is equal. Oh, that's also a nice task.

[00:45:00]Very cool. Well, yes, we need to calculate the base of this triangle. Let's call it the letter A. Since we know that the area of ​​a triangle is equal to 28, let's write the equation that 28 = and the formula for the area of ​​a triangle, which is the usual formula 1/2 x a x h, or x 7. Remember, this is the same formula as a x h/2. It's exactly the same. Well, let's multiply by 2 for example. Or okay, maybe let 's divide by 7 first, it'll be easier for you. We divide by 7 on both sides. 28 over 7 would be 4. 4 = 1/2. And we either multiply by 2 or divide by 1/2. a is equal to 8. It's great that there is no such answer, because someone could already get in here and give this eight.

[00:45:48]The question is about the area of ​​square ABCD. So we calculate the area of ​​a square using the formula A to the square, so we have 8 to the square, so it will be 64.

[00:45:59]Answer D. Fantastic. A pleasant task. Very, very cool task.

[00:46:04]Okay, let's move on to the next one, 14.

[00:46:07]Three identical cubes with edges of length 5 are placed on top of each other to obtain a cuboid. the total surface area of ​​the resulting cuboid is equal to Also a pretty cool task, because yes, since we know that a cube has an edge length of five, then we can either calculate the total surface area of ​​the cuboid, listen, with two formulas, or we can use the formula for the total area, which is a x b + bc + ac. Okay? either by this formula, or simply by saying that the total area is two base areas plus the lateral area.

[00:46:43]No matter how you count, it still comes out the same. All right? All right. So since we know that the edge of our cube is 5 long, we have a base of 5 x 5, and the height will be 3 x 5, so the height will be 15.

[00:47:01]So let's calculate the total area using the formula. Okay. I think it will be clear to most people, that is, 2 times the area of ​​the base is the area of the square, i.e. 5² plus the lateral area. And the lateral area can also be calculated in many different ways. Let's calculate the area of ​​one rectangle, i.e. 5 x 15. And we have four of these rectangles, i.e. these side walls, so let's write + 4 x 5 x 15. And it will be 2 x 25 + 4 x 5, that's 20 x 15. 2 x 25 will be 50. 20 x 15 will be 300. So we have 350.

[00:47:47]Answer A. Great.

[00:47:51]Why did you get 375? Yes. And why so?

[00:47:58]M a will count. Okay, okay, okay. You got B because you did the volume, and here the total surface area.

[00:48:14]Okay. Yes. If someone calculated the volume, it would be 25 x 15.

[00:48:20]Yes. And then it comes out 375.hm.

[00:48:25]So, attention, attention. Well, well, stupid mistake, right? Confusing integral surface area is volume, so here, y, so here, okay, I see, well you have like this, 13, 14 points. Great, very good. So what, we have 15 here, right? We have 15 on another sheet. Just a sec, I need to download a new sheet. Just give me a moment.

[00:48:52]I'll download the second one now. This is how they've been separating it recently.

[00:49:10]Okay, it's the same here. Wait a minute, wait a minute.

[00:49:14]Where are they open? Okay, here they are open.

[00:49:21]And I think we have it.

[00:49:24]Okay, here they are. It is already showing itself to you.

[00:49:30]Okay, now the hard stuff begins.

[00:49:32]Okay, okay. Well, we'll see.

[00:49:35]To make origami, Ela prepared a total of 160 cards. Each of these cards was in one of four colors. White, blue, green or red. There were 37 white sheets of paper. Okay, I'll write down the data. So yes, 37 white cards, blue cards, there were one and a half times more blue cards than red cards, and there were 10 m more green cards than red cards. Listen, if someone was paying attention on the live yesterday, they already know perfectly well what to give here for XA. It's best to give red cards for XA here, because the whole thing is related to them. And if someone did that, I don't think they had a problem with it. So yes, there were 1.5 x blue cards, and there were 10 fewer green cards, so we still have green ones, than red ones, so we have x - 10. And red, if I write red nicely, it will simply be x. So what?

[00:50:42]We add it up and it will be 160. A super easy task for two points. Very easy. So we have: 37 + 1.5x + 10- x plus another x, sorry, x - 10, x - 10 + x and that equals 160. Okay, that's good. So on the left side we have 1.5x + x + another 1x, so we will have a total of 3.5x.

[00:51:12]3.5x = 37 - 10 will be 27. And if we move this 27 to the right side, it will be 160 - 27.

[00:51:28]I will answer your questions in a moment. Okay, just let me finish because I'm about to make a mistake somewhere and it would be stupid.

[00:51:36]160-27 would be 133.

[00:51:40]Now I would multiply it by 2 m, which would be 7x = 266.

[00:51:54]And let's divide it by 7. And 266 by 7, maybe in writing, I won't use a calculator.

[00:52:02]So 26 contains seven three times, so -21 will be 5 56, so we have 8 here, so our x is equal to 38.

[00:52:17]Here, of course, -56, to finish it off nicely. The question is, how many blue cards did Ela prepare? Here, the blue ones are 1.5 x, so we have 1.5 x 38. That will be 38 plus half of 38, which is 19. 38 + 19 will be 57. And the answer, of course, 57 blue cards.

[00:52:48]Mhm.

[00:52:50]Okay, now I'm waiting for the question. What are the points for in this task? Why times 2? Times 2 so we don't have any fractions here. Okay, I made it easier for myself m yyy what points for. I think the first point would be for solving the equation, but I'd have to see the grading scheme. So the first point here is rather for setting up the equation. If someone made a mistake somewhere, then of course what if I give x for green and x + 10 for red? It can also be like that, only here the blue ones get a bit complicated. Okay.

[00:53:28]Mhm.

[00:53:36]Okay.

[00:53:41]Well, if someone got a different result, they won't have a full set of points, they will have one point. All right. Carrot, ma'am, I only have 100%. Thanks, ma'am. I love you. I will recommend the course to all my friends. I am very happy and congratulations on 100%. Beautiful, beautiful. There will probably be no points for just writing down the data.

[00:54:04]Although if you do it correctly, I would have to see what they are like, what the ratings are, how it is assessed. Okay, so I won't say that it's 100%. Okay, we're doing another task, because we have to get to the 18th one that you said was so scary, that is, from the clearing, from the clearing to Dębina there is one road through Jodłowo and it is 123 km long. The road from Polanka to Jodłów is 48 km long and the car covered it in 40 minutes.

[00:54:36]This car travelled the distance from Jodłów to Dębina at the same speed as the distance from the clearing to Jodłów. Justify that o, so it is not easy. Justify that the journey of this car from Jodłów to Dębina took more than an hour. So once again from the clearing. Let's write down what we know here.

[00:54:57]From the glade to the oak tree the only road leading through jodłowo, i.e. glade, jodłowo, oak tree. And from the clearing to the oak tree our road is 123 km long.

[00:55:11]The road from the glade to Jodłów, i.e. this road is 48 km long, so we can already calculate how long the road from Jodłów to Dębina is. So we can 123 km - 48 km will be 115-40 more it will be 75 km, so here it will be 75 km.

[00:55:44]Okay, here the car ran over it in 40 minutes.

[00:55:50]Here we have the same speed from Jodłów to Dębina as from the glade to Jodłów. Okay, so what? We have to calculate how much time it took him. And here, has anyone made a proportion like ours? Did you count it on distance, speed, time? Because if someone calculated this proportion, I think it is much easier, because look, he traveled 48 km in 40 minutes, so he traveled 75 km in x minutes and we can calculate this very easily using the proportion. So x = 75 km x 40 minutes for 48 km.

[00:56:35]Well, let's count. So, for example, we shorten kilometers, we also shorten 75 and 48/3, so here we will have 25, here we have 16, and let's shorten 40 and 16. Well, let's say it's divided by a by 8, so here we will have 2, here we will have 5. So 25 x 5 we have 125 over 2, and here we will have minutes, so we have 62.5 minutes. And that's the end of the task. We had to justify that the journey took longer than an hour.

[00:57:17]And for example, the journey from Jodłów to Dębina took 62.5 minutes.

[00:57:35]minutes, i.e. longer than an hour.

[00:57:39]That is, longer than an hour than an hour. O.

[00:57:46]I have exactly the same. I was brilliant for one and one one hour and 124 m hours.

[00:58:03]Okay, I'm looking now.

[00:58:08]If I changed 40 minutes to 2/3 hours, it 's also okay. If I didn't reduce the fraction, I'll get credit. Yes, yes. 75 72 my dear ones will also recognize it. It's just over an hour. Well, it's over an hour, so it's okay. And I got 1.04 hours.

[00:58:28]Listen, do you need an answer? Well, it would be appropriate to give some answer. All right. Wow, so many questions, guys. Let's do it like this. Let's make it so we do everything and then the questions later, okay? Because I see here that there are so many questions that we won't be able to cover everything. Okay, so let's do another one and then we'll come back to the questions and I'll be there for everything. I hope I have enough time to answer. Okay, so what do we do? 17.

[00:58:58]During sports day at a certain school, three sports tournaments were held. Every child who participated in this sports day took part in exactly one sports tournament. The table provides information on the number of children taking part in individual tournaments. The total number of girls was eight more than the total number of boys participating in this sports day.

[00:59:22]Calculate what percentage of all sports day participants is the number of children who took part in the table tennis tournament. Okay, so first we need to calculate how many girls were here, how many took part in the table tennis tournament. And we calculate this from the information that the total number of girls was eight greater than the total number of boys. So yes, let's write boys.

[00:59:49]How many were there? 46 + 16 + 34. What nice numbers. Here we have 50 + 46, so it will be 96.

[01:00:00]Girls, we have 15 of them + 65 plus some x. Okay.

[01:00:09]So it will be 80 + x. And we know that there are 8 more girls. 8 more, so there must be 96 girls + 8 will be 104, so 104 will be girls, so we have 80 + x, so we know that x will be equal to 24.

[01:00:32]So 24 girls took part in the table tennis tournament. Now, what percentage of the total number of participants is the number of children who took part in the table tennis tournament? Well, we know that 24 + 34, let's write it 24 + 34, that will be 58. That's how many people took part in the tournament. I will only write this five so that you have no doubt that it is a five. So 58 will be our unknown. We've already used X, so let's write Y. And let's see how many children there were in total who took part in the sports tournament. 96 boys plus 104 will be 96 + 104 girls will be 200 people. So 200 people will be m it will be 100%.

[01:01:29]So what? And we have to calculate it now.

[01:01:32]Okay, so we have this. Well, we can actually do some calculations in our heads, but okay, let's write it as a proportion. How we started. Y = 58 x 100% over 200.

[01:01:47]So we reduce 2 zeros. 58 plus two will be 1.9, so we have 29%.

[01:01:58]Beautiful, you write great. So what percentage of the total number of participants is the number of children who took part in the tennis tournament? Well, let's just write the answer 29% so as not to write too much. Okay.

[01:02:11]What will the points be for?

[01:02:13]Well, I think the first point would be for counting either xa or simply the number of girls, that there were 104 girls. Okay, that would be the first point. Second point for the calculation and here it can be different. Or how many people were playing table tennis in general, or that there were 200 people in total. I say, I'd have to see the score. And the third point, of course, for the correct proportion and the right answer, so something like that. Okay. The whole class didn't do it, only Weronika did it on the 17th. Well, it wasn't particularly difficult. There were quite a lot of details, but when someone wrote a percent sign in the result, well, theoretically it's an error. So, we'll see how the evaluator approaches this. Okay, this is the task that scared you. Yes. Okay, so let's get down to this 18 thing you've been talking about here from the very beginning. A cube with edge length A is given. Point S is the midpoint of edge dh of this cube. Points AC, DS are the vertices of a triangular pyramid.

[01:03:33]Calculate how many times the volume of the pyramid is smaller than the volume of the cube. Mhm. 12th time. Y, I think it will work out that way, but I have to count. Okay, not to say anything bad to you. When it comes to the volume of a cube, we have the formula a to the third power. And if the edge of the cube is of length a, and this is what we have in the command, then the answer will actually be like this. And now see, when it comes to the volume of a pyramid, the formula for the volume of a pyramid is 1/3. First, I'll write down the formula for the area of ​​the base times the height, so we have 1/3 x. You'll see that the base will be a right triangle, which is half of the square, so its area is calculated using the formula a x a/ 2, i.e. the base times the height, these are the sides of the square, and we divide it by 2.

[01:04:28]However, when it comes to the height, it will also be half the height, because we know that S is the center of the edge dh.

[01:04:40]So in a moment I will tell you, I will answer your questions. So yes, we multiply these denominators. 3 x 2 x 2 will be 12, so it will be 1/12. Sorry, not 1/2 h here, but 1/2, because we determined that the edge of the cube will be equal to a, right? So 1/2, or 1/12a to the third power. Now the question is, how many times is the volume of a pyramid smaller than the volume of a cube? Well, of course it will be 12 times smaller. And how to calculate it? Well, for example, we can divide a to the power of three by 1/12 and to the power of three it will be 1 under 1/12, so it will be 12, because we multiply times the reciprocal.

[01:05:26]Uh, so that's the answer. He will now respond to questions.

[01:05:32]Volume of a pyramid. A nice task, pleasant, yet so difficult, but it has to be so. The volume of the pyramid is or is, because here it is not even, but how many times smaller it is. It is 12 times smaller.

[01:05:53]12 times smaller than the volume of a cube than the volume of a cube. Well, it was such a massacre, but it wasn't that tragic.

[01:06:09]The answer is as if it had to be written. Well, there will be no point for the volume formula itself.

[01:06:15]Okay. How did he calculate the volume of a cube but incorrectly the volume of a pyramid?

[01:06:21]Well, I don't know if there will be a point for something like that. volume of a cube and probably something else I think. Okay. So it seems to me that if, for example, someone were to calculate, it's for two points, listen, so if someone were to calculate, for example, the area of ​​the base and the volume of a cube, it might already be a point, but I repeat, I haven't seen the answer key, so you just have to wait for the key. M if someone calculated that the area of ​​the base will be a² pr 2 and that the height is 1/2, and this can probably have one point. It's all calm now. All right.

[01:07:01]Can I substitute a six for a? Well, you're not allowed to substitute, although maybe there will be some points. Okay. If someone sets it up, you'll get it back too, it's 12 times smaller.

[01:07:16]If someone calculated it backwards and got 1/12, but answered that it was 12 times smaller, it would also be fine. It 's okay too.

[01:07:25]Mhm.

[01:07:27]As I wrote, 12 times less. It 's good. Okay. 12 times less. Mhm. Yes, yes. Very good. Mhm.

[01:07:37]Just as someone wrote that the volume of a cube is 12 times larger, it is the same as the volume of a pyramid is 12 times smaller. There shouldn't be a problem here and it will be okay.

[01:07:47]Okay guys, let's try again. Another task. Mrs. Anna's garden is trapezoidal in shape. You talked about that too, right? The bases of which are 12 and 18 meters long, and 9 meters high. Mrs. Ania wants to turn her garden into a flower meadow. One package of seeds selected by Mrs. Anna is enough to sow 25 m of flower beds.

[01:08:08]It costs 23.80.

[01:08:10]Calculate how many zlotys Mrs. Ania must pay for the smallest number of seed packages needed to sow the entire garden area. It was similar with the lawnmower, right? That this lawnmower also cuts grass and it also had a very similar task. So what? In the first step, we need to calculate the area of ​​our trapezoid, i.e. the area of ​​this garden. We know that the formula for the area of ​​a trapezoid is base plus base times height over 2. So okay, you probably got 14280, since most of you have the same answer.

[01:08:41]18 m + 12 m x height 9 m/ 2. So we have 18 + 12, which will be 30 m x 9 m/ 2.

[01:08:52]We shorten 30 and 12, for example, to 15. 15 x 9 will be 135 m² and one package is enough to sow 25 m². So we have to count how many packages of these seeds are needed. So we divide 135 m² by 25.

[01:09:16]If there can also be square meters, as we already write the units. Eh, we can shorten that by five. If we reduce this by 5, we get 5, and 135 divided by 5 is 27. 27/5. And here's a note, we have 5a and 2/5.

[01:09:35]We remember that we cannot buy half or 25/5 of a package of grass, we must buy six packages of seeds. Yes, so let 's write, we have to buy, we have to buy six packages of seeds.

[01:09:59]E, if someone drew an isosceles trapezoid, it doesn't matter what kind of trapezoid, it doesn't matter whether it's isosceles or not, the trapezoids don't affect the area. Okay, the important thing is that we have these bases and height. So when someone draws a straight line of arms, nothing happens either.

[01:10:14]Well, now we have to calculate how much these packages will cost. 6 x 2380 will be 6 x 80 gr will be m 4.80, so it will be 84 then 6 x 23 we have 120 138 142. Yes. And so I think you wrote 14280.

[01:10:43]Yes, you did. Okay, so everything is correct. And this will be our answer.

[01:10:49]She will pay, so there Mrs. Anna will pay 142 zlotys and 80 groszy. Mhm. Will I get points for setting an example and trying? Dear friends, I do n't know how you tried, because if you tried and something came out, maybe you'll get a point, but if your attempts didn't actually result in anything, then there won't be a point for the pattern itself. Okay? If someone did not write an answer, but clearly wrote that this is the final result, then they will probably get a point. There will probably be maximum points. All right.

[01:11:24]All right. Beautifully. So what? The last one, not the last one yet, it is still there. Oh yes, there were only 20 tasks. Okay, so there were only 20 on this exam, so what? There were 30 points. Yes, I'll just check if there were points for the whole thing. M, is it written somewhere?

[01:11:48]Either I don't see it or it's not written down how many points the exam is worth.

[01:11:52]How many points can you get? Okay, so if anyone can, count how many points there were at most? 30. I think so, right? that they didn't change anything.

[01:12:01]20th task. A rectangle ABCD with dimensions of 3 by 9 was cut out of cardboard, so we have 3 by 9. Then this rectangle was cut into two shapes. Right-angled trapezoid and right- angled isosceles triangle.

[01:12:16]These pinks were used to make the parallelogram KLMN, which is not a rectangle. Calculate the perimeter of the parallelogram KLMN, i.e. like this.

[01:12:26]right-angled trapezoid and right-angled isosceles triangle.

[01:12:35]Okay, so let's say we cut off this isosceles right triangle here.

[01:12:45]Since it's isosceles, we have 3 and 3 here. And now let's draw this triangle, or wait, I'll draw it on the other side, it will be easier for you to see.

[01:12:56]Okay, so let's do it like this. And now this is it, this is this length.

[01:13:03]Okay, so here we have three and here we have three.

[01:13:07]And we flip this triangle to the other side. I think it will be visible now. Okay, so this is where the triangle that we're adding will be. So what? We need to calculate the perimeter of this parallelogram.

[01:13:23]Okay, that's it. As for the perimeter of the parallelogram, our number nine here has not changed at all. So there will be two here and there will also be nine here. Here we have nine, so there must be nine here too. Um, and the only thing we have to calculate is, listen, just the hypotenuse in this triangle and that's for three points. There is no catch here.

[01:13:49]Right-angled trapezoid and right-angled isosceles triangle. Okay, okay.

[01:13:56]I thought something here was more difficult because it was a bit easy. So to calculate the length of this side, we either do the Pythagorean theorem, or it is also half a square, so we can also use these formulas. So we will have let it be from Pythagoras, so here it will be x.

[01:14:12]3² + 3² = x² 9 + 9 = x² 18 = x² after taking the square root of x it will be square root 18, i.e. 3√2, so since this is equal to 3√2, here we also have 3√er2 and here we also have 3√er2, so the perimeter of this parallelogram will be equal to 2 x 9 + 2 x 3 square root 2, so we have 18 + 6√2 and even here there are no units, so we don't give any units. And ma'am, I only have 97%.

[01:14:56]Well, I guess more than one person would like to have only 97%.

[01:15:02]So, dears, how did it go? Because I think it's quite a nice sheet. It was very pleasant to solve.

[01:15:09]Um, I wrote 18 + 6 + 6.m, so no, there will be no point, there will be no maximum points. Okay. 70% 80% Mhm. How many hundreds? Way to go. Beautiful, beautiful.

[01:15:23]Great, Olaf, beautiful. 97% also a great result 97 86 Good, great. Macarius. Oh, one point and it would be a hundred. Natalia, congratulations 100% beautiful Kaj, it's beautiful 100. Zosia 98 I'm so happy, fantastic Zosia, congratulations.

[01:15:47]Marcin 93, fantastic, very cool. I only lost it in the sixth sentence. Mhm.

[01:15:55]Okay. Well, my dears, it's really clear that the vast majority of you have great results and are very satisfied.

[01:16:05]previously opened. Okay, if you want some earlier ones, tell me, although you know, there will be a recording, so I think there's no point in going back there. All right.

[01:16:18]And now listen, regarding this, because I received a dozen or so email requests, whether I would solve the two-part worksheet, i.e. for people with autism, whether there were different tasks there, because from what I've seen in recent years they were the same, so I don't know if there were any differences between these tasks, because it seems to me that they should all be the same. So if so, we just won't be the same. Well, that makes no sense. there's no point in making this sheet. Also, people who wrote two hundred, you can also watch this one live and it will be useful to you too.

[01:16:54]As I wrote 3 root, because it is half the square. All right. Yes, Patka, if you wrote that you used these properties, then absolutely.hm Yes, there were groups, Joanna, there were groups.

[01:17:07]So if someone has different answers in different places, different letters, then there were definitely groups. There were 30 points to be earned 11/24 h I'm already looking because there is so much information here.

[01:17:27]62.5 so Mateusz are you satisfied or not?

[01:17:33]Beautiful Joanna stówka. Way to go.

[01:17:37]I miscalculated the field and continued with it. Well, no, if someone calculated the area of ​​a trapezoid, well, not really, because Harris is still in fashion here. Is it good that in 16 I have 11/24 hours? Is this good? 1124 hours. But in what?

[01:18:02]Y, well, it doesn't fit with anything. That's 1124 hours. Okay. Mm. If you wrote in 20 that it is equilateral, that will also be an error. Okay, that would also be a mistake.

[01:18:15]If I gave the units, it's wrong. Ania, if, for example, you simply gave units, it would be okay, but if you gave square units for the circumferences, well, on average it would be an error. Yes. Mhm.

[01:18:29]E, I'm still looking at your questions.

[01:18:32]18 roots of 18.

[01:18:38]Oh, someone here didn't calculate this root.

[01:18:43]Well, there can be points, right? So it will be 18 plus 2 roots of 18, then it would be better to give the pre-root, right?

[01:18:57]Dominika, stupid mistakes. Well, sometimes it happens like that. And how many percent? Yes, actually I still look at how I left 18 + 3√2 + 3√2 in the answer. Well, it would be better to add it together.

[01:19:18]Well, that's not entirely correct, is it? 21 + 6√2.

[01:19:25]Aha, so you've added another nine to that. and you thought that here is nine so far, you added three here or something like that. Well, that's a pity. Well, there definitely won't be maximum points, listen. There will definitely be a little less points.

[01:19:41]M well Mateusz, as I said, there may be full points, but we'll see. Yes.

[01:19:50]Mhm. Julius, that's very cool.

[01:19:54]I will post all the answers on social media soon. So there will be a post with answers on Facebook and YouTube soon.

[01:20:01]Okay, I'll just screenshot everyone here and you'll have your answers. 97% stupid mistake. Well, that's it.

[01:20:10]We can check 16. Of course, I'm already showing 16. It's 104.

[01:20:20]Hmm, it's 104, because um, you got it as a decimal fraction, so 1 whole and 1/2 um, hour. Okay, so you got the result in hours, and I wrote the result here in minutes. That's why it's a little different.

[01:20:36]Mhm.

[01:20:38]Can 16 be 1.4 hours?

[01:20:42]Well, definitely not. 1.4 hours.

[01:20:46]Certainly not here. Something, something there was a mistake.

[01:20:51]Natalia, as I said, 21 + 6√2. Well, there will probably be some point, because you counted correctly up to a certain point, but there won't be a full set of points, because, like the previous ones, you added three to one of the bases, and there were supposed to be two bases equal to 9. hm, I'm still looking, I'm still looking. Oh my, so many questions.

[01:21:19]How many questions do you have? Julka 90. Very nice result. Beautiful, congratulations. How did you count? Ania, beautiful. Ania 97% fantastic. How did you calculate the speed itself in 16? Will there be points? Certainly yes, for sure. Well, because here it is a task for three points. Well, the easiest way to do it is to use the proportion method, which I taught you, I taught you it very, very often, because it saves time, but of course you could calculate the speed first. m of this road of this section, and then use the same speed for this section and calculate how long it took. Yes, just a little longer, but if someone wants it, of course they can.

[01:22:01]Mhm.

[01:22:09]And that's good. Haris fashion. Yes, it will be so. Okay, okay, okay. Okay.

[01:22:13]One whole and 14.

[01:22:19]24 or wait, because here we have 2 and 1/2 minutes already, to answer you 2 and 1/2 minutes, if we want to convert it to an hour, we have 5/2 minutes xaz 1/60 and it will already be in hours. Y, let's shorten it here. Here we have m 12.1, so it will be 1/4 hour. So if someone wrote 14 hours instead of m so many minutes, they have a good result, because it is exactly the same result as these minutes.

[01:22:56]But I also saw the answer in the chat here 1.04 and 104 it will not be the same. So 1.04 is the wrong answer. And if someone wrote one whole and 1/4, that 's an okay answer. All right.

[01:23:13]1.4 even less so.

[01:23:18]E.

[01:23:22]Mhm. I'm still looking at about 80. Stanisław is also a nice result. That's cool too.

[01:23:30]I'm already showing the first five tasks. Okay. in this second file I already have um here I'm showing you the tasks.

[01:23:43]Here are the first three. Great overview.

[01:23:46]Thank you very much.

[01:23:49]As I wrote in 16 that 75 is greater than 72, can it also be?

[01:23:56]What does 75 and 72 mean? Because I don't quite get it here.

[01:24:09]it's about speed. Aha, because that's how fast you got it.

[01:24:16]No, it is not proven, because it was said that it would take over an hour and it does not prove what needed to be proven. There will be some points, but there will not be a full set of points. Okay.

[01:24:29]Mhm.

[01:24:31]Aleksandra, I think it can be accepted, but it's kind of borderline, right?

[01:24:45]Okay, okay, okay. I'll move on to the comments, because I'm way behind on these comments. Oh my. Uh, okay. And if you want the second page, please do.

[01:24:57]And there were several groups. There were definitely several groups. Mhm.

[01:25:02]If I substituted A2 for momentum, will there be any points? There may be some point. There may be some point.

[01:25:14]If instead of 62.5 minutes I wrote 63 minutes, is it good or not? This is not good. This is rounding, and you cannot round unless instructed to do so. So there will not be a full number of points. Unfortunately, Phlox, unfortunately.

[01:25:34]Mhm.

[01:25:36]Okay, dears. I think I have addressed most of the questions. I think so. If I only wrote things down in the drawing and calculated the circumference correctly without Pythagoras.

[01:25:52]Well, there was no need to do Pythagoras, because you could use this, this half-square, you just would have to write that you were using half- square. All right.

[01:26:02]Mhm. Okay, here's another page of your answers. Remember that in a moment Yes, there sits a kitten here. Here sits the kitten from this task, from today's exam, but it was bought without a promotion.

[01:26:18]So listen, in a moment we'll finish the live and I'll post all the answers, so you'll have the entire sheet solved. I'll also post it on our group platform, so people who are course participants, you'll have everything already on the platform, and the rest of the people will send it to you on social media anyway, so you'll have it there in the post, literally give me 15 minutes or half an hour to do it and it will be okay. Listen, my dears, I am very, very proud of you. If you liked the solution and my explanation, I would be grateful for a thumbs up and a heart if you watch on Facebook, and if you want, as I've already told you, I would be very grateful for subscribing to my YouTube channel, because we're going for 100,000. We're really close. We're already a few thousand subscribers short. And I guarantee you that you will find this channel useful for your math exam, so there will be some very interesting things coming up. So, dear friends, thank you very, very much for today.

[01:27:23]I think you gave it your all.

[01:27:25]I am very pleased with your results, because most of you had really turbo high scores here. If you want to write me a private message, of course write by email on Messenger, I read everything. So thank you very, very much. You've done a great job this school year and you can be really proud of yourselves.

[01:27:44]Especially people who have achieved their dream results. Thank you very much.

[01:27:48]Take care, get some rest.

[01:27:50]All the best. Bye bye.