CSEC Maths - May 2024 Paper 1 (Terry David)

Added: 2026-05-27

[00:00:11]Hey guys. Uh, good night everybody. Uh, just let me know if you guys can hear me before we start, please.

[00:00:35]Right.

[00:00:42]So, I'm just going to dive in here.

[00:00:45]Those who come in late, they could just fall in.

[00:00:48]All right. So, this this paper that I'm doing here is May 2024, paper 1. Uh, this first question here, we have minus 3^ 2 + - 2^ 2.

[00:00:59]So - 3^ 2 -3 * -3 will give me positive 9, right? Plus -2^2 will give me pos4.

[00:01:09]So that's going to give me 13. So it's not the same paper I did last night. But as you can see what's happening here in terms of questions. All right. So that's the answer for number one.

[00:01:25]Question two here we want to know what's the value of this digit six in this number here. So first of all we have 486 21 and we want to know what's this value for this digit here. Now this position here is in the 10th position. So this number is actually 6 / 10. It's 6 / 10.

[00:01:47]So the answer is going to be B. Okay.

[00:01:55]All right. Um, this next one here now, question three. Yeah, if you all know the answer, you all can just, um, put what you think in the chat, right? It's fine.

[00:02:09]So this one here uh this next one here we have what number when added to 1 and 1/3 gives two. So this feels like a a primary school question here. So we have 1 and 1/3 plus some number which we don't know what it is. But when I add it up here I should get two holes here. So you already have one here. So if you want to get two, it simply means that I just need to put 2/3 here. That's it.

[00:02:40]Right? Because 2/3 plus 1/3 will give me one. One plus this one and we're going to get two here. So the answer is going to be 2/3. The answer is B, right?

[00:02:59]All right. So for those of you who are here right now, I know you all have English e I believe tomorrow. Um but you can share the link with your friends. Um so we have we have um a sequence here.

[00:03:14]We have one, we have six, we have 13, we have 22, we have 33. And we want to know what comes next here in this sequence here.

[00:03:25]Now, whenever you have a sequence and you're trying to figure out what am I going to put here, all the first thing I would normally do, I would check to see if there is what's the increase here or what's the decrease. When I jump from this to this here, you realize you are adding five.

[00:03:42]Right? When you jump from here to here, you are adding seven.

[00:03:46]When you jump from here to here, you are adding nine. And when you jump from here to here, you are adding 11. Right?

[00:03:53]That's our increase there. So what you notice here is that the numbers 5, 7, 9, and 11, those are odd numbers in sequence. So if I want to figure out what's the next term in the sequence here, after after 11, we're going to add 13. So if I add 33 + 13, we're going to get 26 as our next term in the sequence here, right? Sorry, not 26. um 33. I add that wrong. Right.

[00:04:26]Right. So this is going to be six here.

[00:04:28]It's going to be four. Right. I don't know why I subtracted it. So it's 46.

[00:04:32]Okay. So the answer is going to be C.

[00:04:39]Right.

[00:04:41]So that's number four.

[00:04:48]Let's see number five here now.

[00:04:55]All right. What's the least number of apples that can be shared equally among 6, 10, and 15 children? When we see a question like this, and we're trying to figure out the least number that can be shared equally between 6, 10, and 15.

[00:05:09]What you're really doing here, you're finding the LCM. That's what you're doing. So, you're trying to find the LCM of these three numbers here. Now, LCM simply means lowest common multiple. So in the case of six here let's count in sixes to find the multiples. So we have six, we have 12, right? We have 18, we have 24, right? We have 30, we have 36.

[00:05:31]And so we keep going, right? Um, in terms of tens, the multiples of tens would be 10, 20, 30, 40, and we keep going, right? Multiples go till infinity. U multiples of 15, you're counting in 15. So that's 15, that's 30, that's 45, right? Um, in this case here, uh, we're looking for the lowest common multiple.

[00:05:56]So, it's the lowest number that's common to all of them. If we check here, you realize you have 30. You have 30 here, and you have 30 here. That 30 is common to all three numbers, and it's the smallest number that is common to all of them. So, the LCM is going to be B 30.

[00:06:13]Okay, for this next one here, what do we have here?

[00:06:22]A certain amount of money is shared among G, Troy, and Jordan. So we have G, we have Troy, we have Jordan, right? And it's being shared in a ratio of two to three to 9. Now, if Troy received $40. Now, these these kinds of questions are sometimes a bit tricky.

[00:06:50]All right, these kinds of questions are a bit tricky. Even in the 2026 paper two, um the paper two question, the first question, there was a question along these lines here. So, in this case here, they're telling us that Troy, right, received $40 more than G. So, first of all, let's figure out how many parts we have here. So, we need to add this up first. So that's 9 and 31 12 and 2 is 14. So there's a total of 14 equal parts here in this ratio. Now Troy received $40 more than G. So we're going to focus our attention on G and we going to focus our attention on Troy. So this question is very similar to what came in the paper 2. So first of all, the difference between these two here is actually one part because Troy received three parts and J received two. So therefore, the difference between the two is actually one part and they told me that um Troy actually received $40 more. So that means that one part of this money that is being shared is actually $40. That's what they actually telling us here. So to figure out then the amount of money shared. So if you want to get all the money that is shared, we need to find for all 14 parts. So to do that, all we need to do is to take 14 and we need to multiply that by 40. So leave the zero there for now. 4 4 are 16 1 4 is 4115. So that's going to be $560.

[00:08:14]So that's the total amount of money that is shared in this case here. Okay.

[00:08:23]What else do we have here?

[00:08:27]So just be prepared when it comes to sets. So sets there at least five questions in the exam on sets. So we have three sets here. We have P, we have Q, we have S. And we want to work out P union Q union S. So we have P is 2 3 5 and 7. So that's P. We have Q is equal to 2 3 6. And we have R sorry S which is 2 415.

[00:09:06]All right. Now, when it comes to union, so you want P union Q, union S. So that's basically everything. Once you see the word union, it means every single thing that is common to all of them, right? Or everything that makes up P, Q, and S. If you look at the numbers there, if I were to write out P union, Q union S, it'll be two, it'll be three, it'll be four, it'll be five, it'll be six, and it'll be seven. So, it be all of these numbers here that makes up P union, Q union, S. Okay.

[00:09:48]Right. Um if you want to see this visually could look something like this. Uh let's say this is P right? Uh P union Q, right? So if I were to visually look at this here, this is PQ and S. What is common to all of them is two. So two is in the middle here. We have three common to P and Q. So we have a three here.

[00:10:17]Then we have um what else we have there?

[00:10:22]Four, five. We have five common to P and S. We have a five here.

[00:10:28]Q and S, right? Uh 2, three, five.

[00:10:35]This is seven here.

[00:10:37]But Q is 2, three, and six. Six is here.

[00:10:41]And then 2 4 and five. Four is going to be here. Right? So this is what P what the set will look like when it asks you for um P union Q union S that's all of this right it is all of this here right this is what P union Q union S actually means so it's basically checking all of these here okay so that's number seven Um, question eight here looks a little different from the one that we saw last night, right? The one last night, the answer was P complements, but in this case here, we have a a differentiated region here. What do you all think is the answer for number eight?

[00:12:01]Right? So be careful if you are trying to learn off answers. Make sure you understand how to get the answers. So first of all, what you've shaded here, if I have a set here, let's say this is P and let's say this is Q, right? This region in the middle here is what we actually call P intersect Q. Okay, that's what that middle region represents here. Now, if you look at the diagram they gave us here, they've shaded everything except the middle. So, if they shaded everything except the middle, you're going to say P intersect Q complement, right? P intersect Q complement is what we're looking for here. So, the answer is going to be B.

[00:12:41]Okay.

[00:12:52]All right. Question nine.

[00:12:57]We have the elements of this set here and x is an integer. So first of all x is such that we are going from six less than x less than or equal to 10.

[00:13:11]So first of all um we have to look at the inequality signs here. Now this inequality sign here it's a greater than sign. Now when you have an inequality like this I want you to sit in the middle here. Right? When you look this way you're going to read that statement as x is greater than six. So therefore we're not including six in our answer.

[00:13:33]So we're going to have five sorry um yeah five not five sorry seven.

[00:13:39]Right. Right? So the first integer after six would be seven 8. Right? If we look this way here, you're reading a statement as x is less than or equal to 10. Now this means you're going to include 10 in your answer. So you're going to go 7 8 9 and we must include 10 in our answer. So the set that we're looking for here will be 7 8 9 and 10.

[00:14:02]Okay? So the answer is going to be C.

[00:14:06]Right?

[00:14:11]What else we have here? So, we seen some different set questions here uh tonight compared to yesterday.

[00:14:21]All right, we have two sets here. We have M and we have N. And we want to see which of the following statements is true. Now, if I were to draw a vin diagram to represent this, this is M.

[00:14:34]And based on where N is, n is actually inside of this, right? So this is N here. This would be P and this would be Q and R would be on the outside here. So if I had to draw this information here on a vin diagram, that is what it's going to look like. So they said which of the following is true. M is a subset of N, right? M is a subset of N. This statement is not true, right? What is actually happening here is N is a subset of M. That statement is true. Okay, so that's out. They said M union N is equal to M. Now M union N. So first of all, let's write this out here. M union N is basically everything in M and N which would be P, Q and R.

[00:15:23]And they said that is equal to M, right?

[00:15:26]M is equal to P Q and R. Okay. So that that looking like it could work, right?

[00:15:35]M union N is PQR which is equal to M. So this looking like it correct, right?

[00:15:40]Yeah, because this one don't make sense.

[00:15:42]This won't be correct. And then M intersect N is a null set. No, this this doesn't make sense either. So the answer is going to be B, right? The answer is B. Right? So these are some newer questions. So look at the answers.

[00:15:58]Right? So that's number 10.

[00:16:11]Number 11. All students in a class place crabble or checkers or both. Okay. So based on the information here, I can go ahead and draw a simple vin diagram here, right?

[00:16:32]So we have um scrabble or we have checkers.

[00:16:39]So all the students in a class play scrabble or checkers are both 36% of the students play scrabble only. Now when they say 36% right and they said scrabble only that's this piece here right? So this let me just put this here. This is 36%. this piece here, right? Not the whole circle, but just that piece alone because this part here actually represents Scrabble only, right? That's what that is. Um, and 48% play checkers only. So, this here is your 48% and this here corresponds to checkers only.

[00:17:24]All right. um what do they want? Uh 48% play checkers only. What percentage um of the students play both games? So what we trying to figure out here? You're trying to figure out um for both games.

[00:17:36]So that's the middle here, right? That's the middle. That's what we're trying to figure out. So first of all, how we going to do that? Right? How we going to do that? Now we're going to make an assumption here, right? Because they said, well, actually, no, that's not Hold on.

[00:17:51]They said you're either playing Scrabble or you're playing checkers or you're playing boots. So that means that there's nothing on the outside here, right? That's what that means. So when I because we're dealing with percentages here, when I add up the percentages, I should get 100%. When it comes to a ven diagram and we're speaking about percentages, it's going to add up to 100. So all I need to do is to add up the 36 plus the 48. So 8 and 6 is 14.

[00:18:16]437 and 18. So that's 84% accounted for.

[00:18:21]So if you want to get that piece in the middle, all we need to do is to take 100%. And you're going to subtract this 84, right? So let's borrow from this 10 here. This becomes 9. This is 10. 10 take away 4 is 6. 9 take away 8 is 1. So that's going to be 16% in that middle.

[00:18:38]So the answer is going to be B.

[00:18:45]Right?

[00:18:50]What else we have here?

[00:18:54]Right. Somehow it feels like a lot more than just six questions though, right?

[00:18:58]On set on um on sets.

[00:19:04]All right. This one here, there are different versions of this question as well. So, we have a vend diagram. It shows two sets T and C where T is tennis and C is chess. How many students play tennis but not chess? Right. How many students play tennis but not chess? What you all think is the answer for number 12?

[00:20:05]right I've seen people saying see so first of all let's look at the diagram carefully you see the circle on the inside here this circle here represents everybody who plays both chess and tennis right that circle on the inside that's what that represents it. Now, you're looking for the people who play chess, right?

[00:20:25]Um, oh, sorry, right, who play sorry, play tennis but not chess. So, if you're playing tennis, you have to be in the bigger circle. So, that includes Alli, Alex, Tom, and Kayla. They all play tennis, but not chess. So, that's four of them. The answer is C. Okay, answer is C.

[00:20:46]Right.

[00:20:53]So that's number 12. So that's it for sets.

[00:20:59]All right. Let's go number 13. Here we have a dress. It costs $180 and it's sold at a discount of 10%. So they want the discount. So the discount is simply going to be 10% multiplied by 180.

[00:21:13]So 1 10% is 110th multiply by 180 one the zero will cancel with this so we get $18. We just want the discount so it's going to be $18. So the answer is C.

[00:21:36]All right. Um what else we have here?

[00:21:50]Right. So, we saw a different version to this question yesterday where we had a tax when we were converting from US dollars to EC dollars. So, now they're telling us that EC250 is a dollar. Then 25 EC is how much? So, first of all, EC $2.50 50 is equivalent to US $1 and we want to work out for EC $25 right um how many US dollars that is so first of all when you're doing this conversion you're taking this number multiply by this number divided by this here you just cross multiply so that's going to be 25 by 1 all over 250.

[00:22:39]Now, when you're dividing by uh a decimal, what you need to do is to turn the decimal into a whole number. So, on the denominator, we're going to move the decimal point one place to the right.

[00:22:52]So, this will become 25. And we have to do the same thing on top. So, if we have 25 and you move the decimal point one place to the right, you're going to get 250, right? And when you work this out here, you're going to get $10, right? So you're going to get uh $10 here, right?

[00:23:10]So this is going to be US $10, right?

[00:23:20]So the answer is going to be B. So just be careful. There are different versions of the same question.

[00:23:26]Um what is this next one here?

[00:23:33]This one is a commission question.

[00:23:40]For every sale amounting to $1, a salesman is paid 10% as commission. If his sales for a particular month is $1,020, how much commission was he paid? Right?

[00:23:57]So they said for every dollar, right, he gets 10 cents commission. So if he has this amount here what is the commission?

[00:24:07]So basically we have to take 1020 right?

[00:24:13]Yeah we have to take 1020 and we need to multiply that by 10 cents right because for every dollar he makes 10 cents. So this is 0.1. Now that's the same as saying 120 over 1 multiplied by now 0.1 is actually 110th. So this zero will cancel with this. So you'll end up with $102.

[00:24:35]Okay. So this here is going to be C.

[00:24:38]That's a commission that is going to be paid. Okay.

[00:24:47]All right guys. So uh please remember to hit like and subscribe and please share the link with other people who um who this might benefit. All right. So we know there are a lot of weak math students out there. All right. So just share the link with your friends, right?

[00:25:03]Let them um get some help here.

[00:25:07]All right, number 16. What we have here now? A man's basic wage for a 40hour week is $160.

[00:25:14]He is paid overtime at a rate of 1 and a4 times his hourly rate. If he works six and a half hours overtime, his wage for that week is what? All right. Now, this is a a very worthy question here.

[00:25:28]So, first of all, for a 40hour week, he is paid a total of $160, right? He's paid a total of $160. Now, the thing is, we don't know what the basic wages, but we can work that out.

[00:25:46]So, the basic hourly wage or hourly rate, right? All I need to do is to take the money that you paid, which is 160, and you're going to divide by the total number of hours. So, this will cancel with this uh 60 divid by four is going to give me four. So, this is his basic hourly rate here. He's paid $4 per hour, right? Now, let's look at the overtime now. So, the overtime, right, hourly rate, right? They said it's one and a quarter.

[00:26:23]Now the funny part is when we speak about um being paid, you are normally paid at double time, right? You're normally paid at double time, which means multiply by two. You also be paid at time and a half, right? These are the these are actually how you are paid in some instances. So you multiply by one and a half, right?

[00:26:51]1.5 and you can also be paid triple time, right? This is in actuality what really happens in real life, right? This is how you normally pay. So this one and a quarter, I don't know where to get that from, but all we need to do is to take one and a quarter and you have to multiply by the basic wage rate which is $4. So one and a quarter is actually 14 is 415. So this is 5 over 4 multiply by four. fours will cancel and you'll get $5 per hour. All right, so the overtime is actually $5 per hour. Now, in this case here, he works six and a half hours overtime. So, the overtime, right? Now, 6 1/2 here is going to be 6 and 1/2 multiplied by five. So, this here is going to be 6 are 12. So, that's 13 over 2 * 5, right? So that's the same as saying okay so we need to work this out here. So that will be 6.5 right 13 over 2 is 6.5 multiply by 5 are 25 65 30 so that's 32 right so this is going to be $32.50 50, right? So that's his overtime. The question was um what is his wage for that week? So first of all, he's being paid 160 cuz he already worked for the full week. So that's 160 plus we're going to add the overtime part of this here, which is 3250, right? So this is going to be 50. This is two. This is nine. This is what so $19250 that's his total wage for this particular week which is D.

[00:28:41]Right? I realize this question long right. What else we have here?

[00:29:00]So that's 16. What about number 17 here?

[00:29:06]Right. This one here is probably one of the only um higher purchase question that they keep repeating over and over.

[00:29:12]We have a television set here. It cost 350 cash. When it's bought on higher purchase, you make a deposit of $35. So first of all, the higher purchase, right? Right. So, the high purchase price here will be you're making a down payment of $35, but you're making 12 monthly installments of $30. So, that's 12 months by 30. So, that's 12 trees at 36. So, you're actually paying $360. So, $35. That's your down payment. Plus, you're going to add your installments here, which will be $360.

[00:29:53]So when I add this, you get 0 0. This is five. This is nine. This is three, right? So $395. That's your higher purchase price. But you could have purchased this item at cash at 350. So if you want to work out your savings, it'll be 395, right? Minus 350.

[00:30:16]So this will be five. This is four. So that's your savings here. If you bought this item cash price, you'd pay say $45.

[00:30:23]Answer is D, right? That's number 17. I think number 18 is the same one we saw yesterday.

[00:30:41]So, we're talking about um depreciation, right? So we have Jan 2021 and we have December 2021.

[00:30:52]Um so first of all when we speaking about um depreciation they said the car at the end of the year is worth 5% less.

[00:31:01]So let's start at the beginning of the year and let's assign a percentage of 100%. Now at the end of the year and the value of the car is being reduced. They say it's worth 5% less. So that means the value of the car is now 95%.

[00:31:16]Now they told you that the car is worth so at the end of the year it is actually worth 9,500 and what we're trying to figure out what's the value at the beginning of the year. So this is what we know. We know that 95% right is equivalent to 9,500 and you want to figure out for 100%.

[00:31:38]That's what you're trying to figure out for. So all we do, we cross multiply this number multiplied by this divided by this. So that's going to be 100 multiplied by 9,500 all over 95. So this 95 can go into this one time. This can go into this one time. So that's 100. And when I multiply this here, you're going to get one, one, two, three. So the value of the car at the beginning of the year is a thous I'm sorry. um 10,000, right? It's 10,000 at the beginning, right? So that's number 18.

[00:32:32]Number 19, we have a loan.

[00:32:36]The loan is 15,000 and it's repaid in 24 equal monthly installments of 750. The total interest paid as a percentage of the principal was what? So first of all, we have $750 and it's being paid over a period of 24 months. So let's figure out the total amount that is paid back. So 0x4 is 0. 5 by4 is 20. 7 4s are 28 29 30 right? Then we shift 0 by 2 is 0. 5 2's are 10. 7 2's are 14 and 150. So let's add this up here. So this is zero. This is zero. This is zero. This is eight.

[00:33:15]And this is eight. So you're paying back a total of $18,000, right? But the actual amount that you borrowed was only 15. So the interest, we need to work that out. So the interest is simply going to be um 18,000. That's the amount you actually paid back minus 15,000, right? So, you're going to get 3,000 here. So, that's the interest you pay back on this loop. So, they want the percentage. So, the percentage that they're looking for here is simply going to be the interest, which is 3,000 over the principal, which is 15,000 multiplied by 100. So these three zeros here will cancel and then three can go into this one time and this will be five. So 100 divid 5 will give me 20. So this works out to 20%. So the answer is D. Right? That's the answer.

[00:34:23]All right. How you all doing? Are you okay?

[00:35:08]right? Um, what's the next one we have here? This one is 19.

[00:35:23]All right. At a sale, a discount of $3 off the original price was offered for each book. So, you have a sale and you're getting a discount of $3 on each book. Daniel paid $46 for two books that had the same sale price. Okay, so it had the same sale price. What's the original cost of one of the books? So, first of all, he bought two books for $46, right? So therefore, one book, right, because they said uh two books had the same sale price. So one book will be 46 over two, right? And that's going to be $23. So that's the price of one of those books here. Now, he they want us to work out the original cost of one of the books. Now, the thing is, if you're getting a discount of $3 of the original price, it means that this $23 he paid here was the discounted price. So the original price, right, is simply going to be $23, right? We need to add back what the discount was, which in this case was $3.

[00:36:34]Okay? So that means that this will be 26.

[00:36:39]All right? So you would have paid $26 or $26 would have been the original price of this book here. The answer is eight.

[00:36:49]Yes. Um, somebody's asking, yeah, all of this here falls under consumer arithmetic. All right. Sometimes students get trouble with consumer arithmetic in the exam.

[00:37:00]So that's number 20.

[00:37:06]All right. Uh, 21 here we have to do a multiplication. So we have 3x^2 * 2 x cub. Now you want to multiply this here but we have to make use of an index rule here which says a ^ m * a the power n is equal to a ^ m + n. So you're adding indices if we have the same base.

[00:37:34]So the first thing we do in a question like this here you multiply the two whole numbers here. So 3x2 is six and then this will be x to the power because you have the same base here, right?

[00:37:44]You're going to add your indices. So this here is going to be 6 x ^ 5. That's what the answer is going to be. So it'll be 8, right? It'll be eight.

[00:38:14]right? So that's 21 question 22.

[00:38:25]So we have an equation here to solve. We have 5 y - 2 is equal to 3 open brackets y + 4. And we want to solve this. So first of all, if you want to solve this, you need to remove your brackets. So we're going to use the distributive law.

[00:38:42]5 by y then 5 by - 2. You have to multiply 3x y and you have to multiply 3 by + 4. So if I remove the brackets, this becomes 5 y - 10 is = 3 y + 12.

[00:39:01]Um, carry all the y's on one side. So this is 5 y - 3 y is = 12 + 10. 5 y - 3 y will give us 2 y. 12 + 10 will give us 22. And therefore y is 22 / 2.

[00:39:20]So y is equal to 11. So the answer is going to be d right. Um right. So we saw the same question last night. So it's seven times times mean to multiply. Uh the product of two numbers product also means multiply and it's a and b. So it's a by b. So when I multiply this here we're going to get 7 ab. So the answer is b right. Um I'm not sure which class I know I did this a question like this recently. Um so they gave you uh two binary operations here. We have three star 6 is equal to three and we have 2* 4 is equal to zero. Now we're trying to figure out what is the binary operation.

[00:40:34]Now when you get a question like this here it is going to be trial and error.

[00:40:38]That's what it's going to be. So first of all um let's start with the first one we have a square. So let's check this one here a^ 2 minus b. So let's try working out um so hold on.

[00:40:54]So let's say that a star b is defined as a^ 2 minus b. So the first thing you're going to do you're going to work out three star 6 and see what you get. 3 star 6 will be 3^ 2 - 6. So this here will work out three t 3's are 9 - 6. So that's going to give us 3, right? Let's work out 2 star 4. So in this case here this will be 2^ 2 - 4. So 2 ^ 2 will give us 4 - 4 and we get zero. Right? So right now this particular binary operation here right when I work it out it works for both of them. Now if you all get a question like this make sure it works for both not just one. So the answer is going to be eight cuz there's another question where the answer works out to be D. And this one is eight.

[00:41:49]So that's 24.

[00:41:53]Question 25.

[00:41:59]So we have um x is = -2 we have y is = 3 and we have t is = to three as well. But what we want to work out we want to work out x / y raised to the power t. So x / y will be um - 2 all over 3 and you want to raise that to the power three here.

[00:42:27]So you're basically cubing this. So that's the same as saying - 2/3 * -2 * - 2/3.

[00:42:37]So first of all, you're multiplying three negative numbers. So I expect the answer to be negative. 2x 2 by 2 that's 2 2's are 4 2's are 8 all over 3's are 9, 3's are 27. So this works out to min - 8 over 27. The answer is B. Now there are different versions to this particular question here. So look out for that.

[00:43:07]Right. So that's 25. Where is 26?

[00:43:25]All right. So what do we have here? we have 1 / 3 ^ 2x is equal to 9 and we want to solve this. So first of all um I'm going to use an index rule that says this a ^ - n is 1 / a ^ n. So on the left hand side I can actually write that as 3 ^ - 2x 9 can also be written as 3^ 2. Now if you notice something here, we have the same base. So if we have the same base, we can say minus 2x has to be equal to 2. So the indices have to be equal. So therefore x is going to be equal to 2 / -2. And therefore x is equal to -1. So the answer is going to be 8.

[00:44:16]Right? So that's 26.

[00:44:26]Right. 27 they give us a matrix E and that is given by one.

[00:44:38]Right? So if you want to work out 3 A that's a scala product. So you're basically taking three and multiplying by all of this here.

[00:44:46]1 3 3 0 minus 35. So that that tree on the outside here, this tree on your outside here, it's a scala. So you have to basically multiply by every single one of these things here. That's what you do, right?

[00:45:02]To get your answer, right? It's called a scalar multiplication. So this will be three. This will be nine. This will be min - 9. This will be nine. This will be zero. This will be 50. Right? So this is going to be which one?

[00:45:20]So 3 9 - 9 9 50. Answer is going to be eight. Okay.

[00:45:31]Right. So that's 27.

[00:45:35]Uh question 28. We saw this one last night.

[00:45:43]All right. So we have our identity matrix which is given by 1 0 0 1. You want to work out your determinant. Your determinant is simply going to be 1 * 1 minus 0 by 0.

[00:45:58]So we get 1 - 0 which is 1. So the answer is B. Now, if you notice what they did, they switch around the answers. Last night, the answer was E, right? Last night we had a version of this question as well. Um, so we have P is given by 37.

[00:46:28]We have Q is given by min - 2 and 5 and we want to work out P minus Q. So P in this case here is 37 and you're going to minus Q which is - 2 5. So you're subtracting. So this is going to be 3 - - 2 and the bottom here is going to be 7 - 5.

[00:46:52]So 3 - - 2 is the same as saying 3 + 2.

[00:46:55]So this works out to five and 7 - 5 gives us two. So the answer has to be five which is C.

[00:47:20]Right. So that's 29.

[00:47:32]Right. Question 30 here. They give us a parallelogram. Now, if they ever give you a parallelogram, look at the vectors. So, if this vector here is U, that means that here will also be U. If this vector here is V, it means that if I go this way, right, that vector is also V. Now let me write that V on the outside. So that's V as well, right? But they want me to work out RW, right? So they want this vector here, R W. So draw a line from here to here, right? That's the vector they want, RW. Now, how do we get from R to W? So R W is equal to R Z can go RZ plus Z W. Right? That's the possible route I can take to get there. Okay, you could go from R to Z and then from Z to W. Now, what is R to Z?

[00:48:31]So, R is actually the midpoint, right?

[00:48:35]So, that means that if um YZ is V, it means that RZ is going to be a half of V, right? Because of the fact that R is the midpoint plus the vector ZW. Now, look at something carefully though.

[00:48:49]Right? Now wz is pointing this way and it's the vector u but we want this vector here. They're going in the opposite direction. So therefore we have to change the sign. So this is going to be minus u. So this is simply going to be a half v minus u which is going to be a. Right?

[00:49:08]to present it to the answer is E, right? Uh, question 31. We saw the same thing last night.

[00:49:33]They gave you the conversion.

[00:49:35]So if you want to convert 2500 mm that's millimeters to meters all we need to do is to divide this by,000 right that's basically what we need to do if you divide this by a th00and you're going to get 2.5 uh m okay so they gave you the conversion you have to divide by th00and so in this case here the answer is going to be All right. Question 32. Um, what's the length of the edge of a cube that has a volume of 27? So, first of all, what is a cube? So, this is what a cube here looks like. That's a cube. Um, they give us the volume. The volume of the cube here is 27 cm cub. Now to find the volume of a cube, it is essentially one side cube, right? So that's equal to 27.

[00:50:34]So if you want to get one side, we need to find the cube root of 27. What number when I multiply by itself three times will I get 27? That number is going to be 3, right? 3x3 by 3 will give me 27.

[00:50:49]So the answer is E.

[00:50:58]Right. I also think we saw this one last night as well. Uh the perimeter of a square is 48. So you have a square, right? And the perimeter is 48 cm.

[00:51:14]So remember in a square all the sides are the same.

[00:51:18]So that means that 4s is actually equal to 48. So s is equal to 48 / 4. So therefore s is equal to 12 cm. So that's the length of one side.

[00:51:33]Question wants me to work out the area of the square. So area of a square is side squared. So this is going to be 12 squared. So that's 12 * 12. So that's going to give us 144 cm 2. Okay. So the answer is right that's 33.

[00:52:03]We have 34 here.

[00:52:06]All right. So in this question here they gave us the area of the trapezium. So the area of the trapezium is 65 cm squ.

[00:52:16]Now the area of a trapezium is given by a half the sum of the parallel sides multiply by the height. So we're just going to say a half multiplied by a I'll take eight as a I'll take 18 right as b and the height we don't know.

[00:52:36]So we're trying to find and this here is 65. So now um this will be a half multiplied by 8 and 8 is 16. So that's 26 * h is equal to 65. So therefore 13 h is equal to 65 and therefore h is equal to 65 over 30.

[00:53:00]Okay. So now let's see if I take 13 and I multiply by five. Let's see what we get. 3 fives are 15. 1 5 is 56. So therefore 13 into 65 will give us five. So this here is 5 cm which is C Right.

[00:53:48]So that's 34.

[00:53:53]See what else we have here. This one is 35.

[00:54:03]All right. So we have a diagram. It shows a sector. The angle is 60°. The radius is r. And we want to get the length of the ark. So length of ark is actually theta over 360 * 2 pi r. That's the formula that we use to work out length of r. In this case, the angle is 60 / 360 * 2 pi r. Now 60 / 60. This will cancel.

[00:54:34]This will cancel. So this is actually 16 * 2 pi r.

[00:54:40]So in this case here we have 2 over 6.

[00:54:43]So this is actually 13 pi r right 1/3 pi r which is going to be e right.

[00:54:58]So that's 35.

[00:55:03]Right. Question 36.

[00:55:10]Right. Question 36 here. The area of a compound shape in terms of pi. All right. So, first of all, we want to find the area of this compound shape here.

[00:55:20]So, this here, all right, is a semicircle. This here is also a semicircle. So, what you can do, you can work out that as an area of one full circle. But we need to know what the radius is though. So first of all, we have to look at some dimensions here. We can actually work out what is this length here from here to here, right?

[00:55:40]You can work out that length, which will be the same as this length here. How do we do that? Well, all we do, we're going to take 27 cm. Let's subtract the 15. So that's 7 take away 5, that's 2. So that's 12. So if that is 12 cm there right that means that the radius right this here has to be 6 cm and this here has to be 6 here. So the radius is 6 here. So the area right of one circle which is p<unk> r² is going to be pi ultiplied by your radius. So when we work out the radius now we got 6 cm. So this is going to be 6^ squ. So that's going to give us 66 are 36. So that's 36 pi. Now that's the area of the two semicircles combined. We need to work out the area of the rectangle in the middle. So first of all, if the radius of the circle is six, it means that this length here has to be 12. So this length here has to be 12 here. Okay. So to work that out, so the area of the rectangle is simply going to be uh 12 * 15, right? Um I'm looking to see the answers here what they did.

[00:57:01]All right, let's work out the actually wait let's add the So the total area I want to see if I can make use of this here.

[00:57:09]So the total area is simply going to be your 36 pi plus the 12 by 50, right?

[00:57:31]All right. Now I'm just going to show you how we could probably break this up.

[00:57:34]Right. So this is 36 pi plus. Now 12 x 15 could be written as 12 by 3 by 5, right? Because 15 could be broken up as 3x 5. So what you're going to end up with here is 36<unk>i plus 36 by 5.

[00:57:54]And if I factoriize this here, I'll get 36 open brackets pi + 5. Right? Do we have anything looking like that? 36 5 plus Yeah, we have this here. That's me.

[00:58:09]All right. Pay attention to this question. Right.

[00:58:23]Right. I think this is probably the first time I worked this problem like this. I didn't break it up like that.

[00:58:27]Right. But you could have multiplied this first here and then try to write it in the format that they gave us there. Okay.

[00:58:37]So that's 36.

[00:58:50]Let's see 37 now. So the area of a rectangle is 40 cm. So we have a rectangle, right? And the area is 40 cm squ.

[00:59:08]Okay. Um, now we don't know the length and we don't know the width, right? So let's call this L, let's call this W.

[00:59:15]Now they said if the length is multiplied by four and the width is half, so you're multiplying the length by four. So now this thing is doing this, right? So this is 4 L and you're halfing the width. So you're making the width smaller.

[00:59:34]So therefore, this here is a half W, right? And they want me to work out the area. So you want to work out the area of this new rectangle here. All right?

[00:59:45]So from the first rectangle here, we know that L multip is equal to 40. That's what you know from the first rectangle. Now, if you want to work out the area of this rectangle here, right, the area of the new rectangle here is simply going to be 4 L * a half W. So, this 4x2 will give us 2. So, it's 2 L W. But from the first equation here, we know that LW is 40. So, this is going to be 2 by 40. So that's going to give us 80 cm squ, right? So that's a new area here. It's going to be C.

[01:00:42]All right. Um, yeah. So, some people asking if I'm doing another paper tomorrow. Yes, I might do another paper tomorrow, but I may do it in the daytime. I'm not sure as yet, right?

[01:00:53]Tomorrow is what? Uh, Tuesday.

[01:00:57]I might be able to do it in the night. I might.

[01:01:05]Yeah, I was hoping to do Yeah, I was hoping to do as much as I can. I was going to do the 2020 I think the 2022 today, but I didn't like the copy of the paper. It was a little blurry, so I didn't want to use it. That's why I ended up choosing this paper, right? Um yeah, some people asking about the day before the exam. Yeah, hopefully hopefully I'll I'll be available. I think that's Wednesday, right?

[01:01:30]I have two classes during the day though, so we'll see. We'll see how it goes, right? I will try to come on um the day before the exam as well.

[01:01:41]All right. This is 37.

[01:01:44]See 38 here.

[01:02:00]All right. Um, we have a compound shape here. We have a a triangle on top. It's sitting on a square and we want to calculate what is H. So I think this is the same question we saw last night. So this here is going to be 5 cm, right? Um the total area is 35. Then the height of the triangle is okay. So this here this area of the square is going to be 5 by 5. So that's 25 cm squ. So I can work out the area of the triangle.

[01:02:37]That area of that triangle would be 35 minus 25, right? Uh 5 - 5 is 0 3. So it's 10. So the area of the triangle is 10 cm squ.

[01:02:51]I'm not sure if it's the exact same question. Well, I don't if the numbers are the same. So the area of the triangle is going to be a half by the base which is five multiply by the height and that is equal to 10. Right?

[01:03:06]If I multiply everything by two I'll get 5 h is equal to 10. So therefore h is equal to 10 over 5 and therefore h is 2 cm. Right? I'm not sure if the numbers are exactly the same as last night.

[01:03:20]Could be could be wrong.

[01:03:36]Right. I see a set of people said the answer is B. Right. So, double check that to make sure.

[01:03:44]Or did I make a mistake? Let's see. I feel I make a mistake there.

[01:03:51]What did I do wrong? half base by height.

[01:04:00]Oh, my bad. I made a mistake.

[01:04:09]If I multiply this by two, this becomes 20, right? So, this is uh 20 over 5, right? H is four, right?

[01:04:18]Sorry about that. So yeah, the answer is right answered.

[01:04:26]All right, that's when you're trying to move fast, right?

[01:04:29]Um, okay. So that's number 38.

[01:04:32]What else we have here?

[01:04:37]Right. 39 and 40 based on this table here.

[01:04:44]Yeah. Know two, two is wrong, right? Two is two is wrong, right? The answers will be four, right? The answer is four. My bad.

[01:05:00]All right. Uh let's see.

[01:05:03]All right. This next one here is based on this table here. So we have a frequency frequency distribution of it shows the average mass of a group of children in school.

[01:05:13]The number of children who have a mass of at least 41 kg. So when they say at least it means 41 kg or more, right? That's what it means. So when it comes to a table like this here, we're looking at um 41 kg or more. All right? So first of all, where is 41 kg?

[01:05:33]41 kg falls like right here. So if you want to figure out the number of children who have a a mass of at least 41 kg, right? What you're going to do, you're going to add up the 12. You're adding up this, this, and this. So that's 12 and 38, right? Plus 20.

[01:05:53]So 8 and 2 is 10. 3 into 5 and 2 7. So we're going to get 70 students. The answer is C.

[01:06:15]Right. I see people asking what about the two.

[01:06:21]Oh, right. The answer is 70 here. What CXE should have really said here is not 41 kg though. They should have said 40.5. That's what they should have said, right? If we're using proper statistics um analysis here, it should have been 40.5, not 41.

[01:06:40]Uh the lower limit of the modal class, right? So, we want to figure out what's the modal class. So the modal class is the one that has the highest frequency.

[01:06:48]So highest frequency here corresponds to 38. So your model class is this here, right? 51 to 60.

[01:06:57]Now the question says what is the lower limit? Now be careful with questions like these. The lower limit here is actually 51, right? The lower limit is 51. The answer is going to be D. If they had asked me for the lower class boundary, right? Then the answer would not have been 51, but it would have been 50.5.

[01:07:28]All right? So, you notice they have 50.5 as one of the answer, but they just ask you for the lower limit. If they had asked you for the lower class boundary, then this would have been the answer.

[01:07:38]So, look out for little changes like that in the exam questions. Okay.

[01:07:43]Um, we have an X part here as well.

[01:07:46]That's 14, right? Uh, 41. We saw this one last night. We know what the answer is. Once you're arranging test scores in order of size, we're talking about the median, right? That's 41.

[01:08:12]have a pie chart here drawn to scale.

[01:08:15]It shows how many how a student use 12 hours in studying English, maths and French and geography. The amount of time spent on maths is approximately what?

[01:08:28]Now, if you look at maths there, right, this to me looks like about a 90° angle.

[01:08:33]So if you want to work out for hours, we take 90 over 360 multiply by the total number of hours, which is 12, right? So 90 over 360, right? Is a quarter ultip by 12. A quarter of 12 will be 3 hours. Okay? So the answer is going to be C.

[01:09:08]Right. So question 43 here. If the mean of four numbers is 10, right? Then x is what? So we have four numbers here. We have four x 8 sorry plus x + 12.

[01:09:24]So if you find the mean of this here, we have to divide by 4.

[01:09:28]But they're telling us that the mean is 10. So we need to solve for x here. So if you multiply both sides of the equation by 4, we get 4 + 8 + x + 12 is equal to 10 x 4, which is 40. So on the left side here, we have x + 8 and 4 is 12 and 12 is 24 is equal to 40. So therefore x is equal to 40 - 24.

[01:09:53]So therefore x is equal to 60. Right. So that's the missing number here. X is equal to 60.

[01:10:02]What else we have here?

[01:10:09]So I know some of you guys are in my my my normal maths class. You know, this is one of my uh I have a little pet peeve with this question here. Uh I dislike this question completely. All right. I don't even know why CXE has this question in any exam whatsoever. All right. So, we're talking about uh people's attitudes towards mats, right?

[01:10:30]People's attitudes towards mats and their ethnicity, right? What does this have to do with anything? Right? It's a dumb question as far as I'm concerned, right? Um so, what are they asking us here? A respondent is selected at random. Whenever you see they don't specify from which um from which grouping are we taking the se the selection we're going to assume we're going to take from the whole here. So when they say a respondent is selected at random we're looking for the total total here. All right. Now what is the probability that the selected respondent is of ethnicity P and has a positive attitude towards mats. Right. So in this case here right um P and a positive attitude. So P and a positive attitude that'll be 25. So therefore this is going to be 25 over the total. So 25 over 100 is 0.25. So the answer is going to be eight. Right? The answer is going to be eight.

[01:11:41]Yeah. Right. So, like I said, I don't like this question at all. Right. I honestly don't like this question. I don't even know why it's here. Right.

[01:11:50]So it's number 45.

[01:12:06]All right. Which of the following best illustrates a function? Now when you all have a mapping diagram and you want to determine which one is a function what you do you look on the left hand side and you ensure that only one arrow is leaving every and each element on the left hand side. So first of all this cannot be a function because we have two arrows leaving that there. So this is out right. This definitely can't be one as well because we have three arrows leaving that one element and then we have the same problem happening here again. So this is out. So the only correct answer is going to be B and that's a one to one mapping there. Okay.

[01:12:49]Right. Question 46 and 47 based on this diagram here.

[01:12:54]Right. So this is 46. Let's get 47 one time.

[01:13:01]All right. So we have these two um questions here based on this here. So we have a straight line AB and the straight line AB crosses the horizontal axis. So we're speaking about the horizontal axis. Horizontal axis is the x-axis. So that means it cuts at b and this coordinate here will be 3 0. So the answer is going to be a. All right.

[01:13:25]For 47 they want the equation of the straight line. So first of all we know the y intercept already but we need to work out the gradient. So that is 3 0 and this point here is 0 - 2. So if I want to work out the gradient, right?

[01:13:41]What you could do? So you have two ways you can work this out here. You can actually just complete a right angle triangle here if you want.

[01:13:51]Right? Now the height of the right angle triangle here is going to be 2 units in height. Right? And the base is actually three units in length. Right? So therefore the gradient m is actually going to be 2/3.

[01:14:08]Okay. So you can look at the height of the triangle here which is two units.

[01:14:13]Right? You can use this axis here to work that out. The base of the triangle right that's this. You can use this axis here to work it out. Right? So when you're working out gradient m is simply your change in y over the change in x.

[01:14:30]So your change in y is 2 and the change in x is three. So the gradient is 2 over 3. So if you want to write down the equation of that line ab all equations of straight lines are y= mx + c. So this is going to be a half sorry not 2/3 x plus the y intercept which in this case is minus 2. So it's 2/3 x - 2 which is c.

[01:15:01]Right. So that is 47, right? So we have 48 and 49 based on the same quadratic here. So they want the coordinates of the maximum point. So we saw in a the paper yesterday they asked about the turning point. So the turning point is also the maximum point right.

[01:15:31]So this point here is actually two and four. So the answer is a they want the equation of the axis of symmetry. So the axis of symmetry will be this vertical line here. And that line actually passes through two. So this here has to be x is equal to 2 which is e right. So that's 49.

[01:16:04]Uh question 50.

[01:16:07]We have g of x is equal to 7 x - 3 all over 5. So we want to find g inverse of minus 2. So the first thing I'll do I'll try to find the inverse function. So we let y = 7 x - 3 over 5. Second step in the process is to interchange x and y.

[01:16:30]So this becomes 7 y - 3 all over 5. And the third step is to make y the subject of the formula. So to do that we're just going to put this as x over one and then we're going to cross multiply. So when you cross multiply you're going to get 7 y - 3 is = 5x. So 7 y is = 5x + 3. So therefore y is = 5x + 3 all over 7. So therefore the inverse of this thing here is actually going to be 5 x + 3 all over 7. So therefore uh g inverse x sorry you want to find minus2 is simply going to be 5 by - 2 + 3 all over 7. So that's going to be - 10 + 3 all over 7. So - 10 + 3 will give us -7 um all over 7. So we get minus1. So the answer is B, right? That's 15.

[01:17:54]Question 51. We have a parking lot here.

[01:17:56]It charges $1 plus 25 cents for every hour. And they want the parking function. So this is your parking function here. So, first of all, you are being charged $1 plus right uh 25 cents for every hour. So, that's going to be 0.25 multiply by each plus the fixed charge of 1.00.

[01:18:19]All right. So, this is what our uh cost function is going to look like. Um, which one is that? C, right? That's going to be C.

[01:18:36]All right. So, um, what else we have here? 52, 53, right? So, that's 51, 52. We saw the same question last night. Um, the answer would have been D, right? The answer would have been D. Basically we have to work out x cube for all of these here starting from min -2 -1 0 1 and 2. So this will be - 8 um -1 this will be zero this is one this is eight right. So these numbers here correspond to this.

[01:19:19]Right. Uh question 53. We saw the same one last night.

[01:19:24]All right. So the sum of the interior.

[01:19:26]So the answer was a quadrilateral.

[01:19:41]Question 54. They said which ratio right is equal to 4 over 8? Okay. So if I look at x here right this could be my opposite and this could be my hypotenuse. So if I work out the ratio 4 8 that is going to be opposite over hypotenuse.

[01:20:02]So that is going to correspond to opposite of hypotenuse is sign. So sin x is equal to 48. Right? So the answer is going to be 8.

[01:20:24]Right. Question 55. We have an isoclesles triangle. We want to find the value of x. So all we need to do is to say 180° minus right 30 + 30.

[01:20:37]So that's going to be 180 minus 60. So that's going to give us 12, right? So the answer is C.

[01:20:57]All right, we have two similar triangles here. What you need to understand when it comes to similar triangles, the interior angles would be identical. So both angles you have 31, this is 59, and we have a 90 as well. Now the ratio of their lengths are going to be the C. Now we want to work out the length M O which is this length here. Right? So when it comes to similar triangles we can see that the length of 7 right that's the larger triangle hypotenuse divided by M O is equal to 6 that's the base of the larger triangle divided by the base of the smaller triangle. Right? So basically if I want to get M o we can cross multiply. So 6 by m o is equal to 7 by 3.

[01:21:46]So therefore m o is 7 by 3 all over 6.

[01:21:51]So therefore m o is equal to so 3 can go into three one time. This will be 2. 7 / 2 will give us 3.5 or 3 and 1/2. So therefore m o will be three and a halfs here.

[01:22:16]right? We saw this one last night as well.

[01:22:21]All right. So, we have um a translation taking place here.

[01:22:26]So, all we need to do is to look at A and let's say A prime. And if you want to get the translation vector, we just have to take a prime and subtract b in terms of column vectors. So this is 4 6 - 25.

[01:22:43]So 4 - 2 will give us 2. 6 - 5 is 1. So the vector we're looking for is 21, which is 8.

[01:22:57]All right, this next one here, we also saw this one as well. Uh, so we have an enlargement and we want to work out what's the scale factor. So all you need to do to work out the scale factor is simply you can take this length here if you want, right? and that is four units divided by this corresponding length here which is 2 units. So your scale factor here is simply going to be two.

[01:23:32]So the answer is D.

[01:23:44]All right. For this one here um we want to work out FG. So FG here is the base that we want to work out. Now first of all, if that angle is 30°, it means this angle here is 30°. It also means that this angle here is 60°. Okay? All right.

[01:24:04]So how do we work out FG? So we have options, right? We have options.

[01:24:10]So if I work with the let's say I work with the 60°, right?

[01:24:15]Let's say um this could be called your opposite over adjacent. So we could say tan um theta is opposite over adjacent.

[01:24:29]So tan 60° is equal to fg all over the adjacent which is 25. So therefore if I cross multiply I'll get FG is equal to 25 * tan 60°. Okay. So we don't have any answers like that. Right? So that's not it. If we decide to go with use the 30° angle instead we can say that this here is now my opposite and we have adjacent. So we can use tan again. tan theta is opposite over adjacent.

[01:25:09]So we can say that tan of 30° this time is opposite which is 25 all over the adjacent which is fg.

[01:25:18]So again if I cross multiply I'll get fg by tan 30 is equal to 25.

[01:25:28]So fg is equal to 25 over tan 30.

[01:25:34]Okay. So that'll be a is the correct answer here in this case here. Right? So there are two ways or two things to check and the only one that makes sense is the second calculation.

[01:25:53]Right? And the last question here question 60.

[01:26:02]Right. Um, we have a surveyor here and he stands 12 m in front of the foot of a building. He records the angle of elevation. We want to estimate the height of this thing here. So, first of all, we know that you want to estimate the height of the building. So, this here is 1.6. So, you know that length.

[01:26:21]We just need to work out this length here. So, let's look at that right angle triangle.

[01:26:26]So we have this we have this angle here is 40° the base is 12 that's 12 m and I need to work out this height here. So this here right so we can use um tan theta is opposite over adjacent.

[01:26:51]So tan 40 is equal to h over your adjacent which is 12. So if I cross multiply I'll get h is 12 * tan 40.

[01:27:04]Right? So the total height of the building which is this here. So we call that big h.

[01:27:11]So big h is simply going to be equal to the this height here right which is 1.6 six plus the height this piece here that we just calculated which is 12 tan 40 right we have any answer looking like that yeah it's going to be eight right answer is going to be eight right um yeah so I see you all talking about English right Um all right guys so these are the solutions to the May 20 24 paper right so I hope that the session was useful for you guys I will try to come live tomorrow so just remember to hit like and subscribe um I may come live during the day I'm not sure as yet but I know you all have exam in the morning so it doesn't make sense coming live when nobody here right doesn't make sense doing that. So, thank you all for showing up, right? Uh good luck with your studying, guys. With respect to English, I can't be any help there, right? Try to practice as much multiple choice as possible. Uh the English does repeat as well, right?

[01:28:30]So, good luck with your studying, right?

[01:28:33]Um I'll see you guys tomorrow, right?

[01:28:36]So, have a good night, guys. Be safe.

[01:28:38]Right. Yes, this is recorded. You all you all could um access this after. It is being recorded. So, you can access it after, right? Um, yeah. So, good night everybody. Right.

[01:28:50]Have a safe night and I'll see you guys tomorrow. All right. Later people.