Live session Math paper 1 with Bally + Part of Math paper 1 past paper Marathon with Ms. Ottley

Ajouté : 2026-05-28

[00:00:25]Hey, let's come on for a little bit.

[00:00:28]I reach home there. Hi, Jenna.

[00:00:31]just run through paper one with you all and then I will um I'll just run through some with you all and then I will switch to the Zoom that's going on right now cuz I have a paper one marathon going on right now on Zoom I will switch across to the after we stay on four I going to do this paper with you all and then I'm going to switch to the I have a Zoom going on right now with um a paper one marathon I will switch to that with um Miss Utley, one of my math teachers, and you can go through with her.

[00:01:06]Let's take a look at these. Number one, what is the value of the digit two in the number 48.620?

[00:01:15]So, it's real simple, right? The number the amount of numbers after the point is the amount of zeros you're putting in the 100. This is um 20 23 John.

[00:01:29]So one number that is one zero. So this will be 6 over 10. Second number so that'll be two zeros. So that'll be two over 100. The third number that is three zeros. So that'll be one over a,000.

[00:01:41]We'll be looking at the two. So that'll be one two over 100. Right?

[00:01:47]The what percentage of 50 is 10?

[00:01:50]You take 10, you put it over 50, and you multiply it by 100. To change a number to a percentage, you multiply it by 100.

[00:02:05]Cross out that zero. Cross out that zero. 5 into 5 1 5 into 100 20.

[00:02:15]So the answer is 20%.

[00:02:18]Boom.

[00:02:22]Right?

[00:02:25]0.02 086 is written as so they have 2.0806 by 10 ^ 2 that would move the point to the right which is the wrong direction.

[00:02:43]Same thing with 20.806.

[00:02:46]That'll move the point to the right again, which is the wrong direction. We need to get it to the left. But point by 10 ^ -2, we'll move the point to the left twice, which will get it exactly where we need it to be, 0.02.

[00:03:01]So, the answer would be C. Right? So, positive numbers will move the point to the right. Negative numbers to the power of negative will move the number the point to the left. We needed to move it to the left to make it 0.02. 02. We need to move it to the left twice which is what happens here. 10 ^ -2 the point will move to the left twice which will make it 0.02 086.

[00:03:30]Number four ratios question.

[00:03:34]In a school the ratio of a number of pupils to the number of teachers is 20 to 1. If the number of pupils is 840, how much teachers are there? So the pupils will be 20.

[00:03:53]Teachers would be one.

[00:03:57]We're going to change this into a fraction. We're going to put the one as the numerator and the denominator would be the two numbers combined. Uh see what everybody saying the answer already.

[00:04:10]And then you'll multiply this by 8 40 everybody done calling out the answer 8 21 into 211 21 into 8 40 42 two.

[00:04:41]The answer will be B.

[00:04:43]We're going on. Good night. Good night.

[00:04:45]Good night. Just doing a little maths and then I'm going to switch to the zoom with the marathon. This is 2023.

[00:04:54]Let's see if they start back one.

[00:05:02]So 100 All right. Number five. A bag of apples can be shared equally among either six, 10, or 15 children. The minimum number of apples that is likely to be in the bag is so they asking for the lowest common multiple, right?

[00:05:29]So 6 could go into 30, 10 could go into 30, 15 could go into 30.

[00:05:38]And since 30 is smaller than 31, 60, and 90, I don't even have to check the others. I know 30 is the smallest out of all the options. And it works. So the answer is a number six. Now if hey I just did this question if 4.3 * 0.37 is 1.591 then 43 by 0.37 is so let's see to go from 43 4.3 to 43 I'll have to move this point to the left to the right once right so I move the point to the right once and then the 0.37 stays is the same. So all I'm going to do is move this point to the right once as well.

[00:06:33]So that will be 15.91.

[00:06:39]Yeah, this is um 2023 Jan.

[00:06:46]So the answer will be B.

[00:06:53]Number six. Which of the following sets is defined by -2 is less than or equal to x which is less than or equal to 4. A 1 2 3 4 but there's no -2 there.

[00:07:10]B 0 1 2 3 4. There's no -2. C no -2. But D has everything -2 all the way to four.

[00:07:20]Food number eight refers to the following vin diagram which shows two intersecting sets P and Q. In the di in the vin diagram the number of elements in P is five and the number of elements in Q is nine and the number of elements in Q P union Q don't ask what Q is John 2023 is 10. So the number of elements in the shaded. So they want to know how much in P and Q intersecting right. So it have nine have five in N and it have nine in Q.

[00:08:13]So in total that's 14 right.

[00:08:19]But they're saying P into P union Q is 10.

[00:08:26]So if I minus 10 from this, what remaining will be the amount that's in both P and Q, which is what we're looking for.

[00:08:38]What we looking for and the answer is four. It's like a lyrical phenomenon.

[00:08:43]So the answer will be B.

[00:08:46]All right. So add the number of elements in N plus the number of elements in Q which is 14. But some of the numbers would be double counted because some of the numbers are both in P and Q. So if P union Q is 10 to get to get the amount that's in P and Q. I subtract the 10 from the 14 that I calculated earlier.

[00:09:09]If you didn't cook tomorrow, you can't cook, dog. You can't cook. Have no fear.

[00:09:16]Number nine is real repeat. And here's the thing, a lot of these questions is repeater. Every Cxe subject questions is repeat. They want to know which of the following pairs of sets are example of disjointed sex. Sets. Disjointed sets are sets where none of their elements will be in the other element at all.

[00:09:38]Will be in the other set at all. And that's a there's no even number that's also a odd number. And there's no odd number that's also a even number. This exact question word for word does rare repeat in maths.

[00:09:56]E number 10.

[00:09:59]All students in a class play scrabble or checkers or both. So we're looking at a set question here.

[00:10:07]If 36% or let me read it first. If 36% of students play Scrabble only and 16% of students play both Scrabble and checkers, what percentage of students play checkers but not Scrabble? And this is pretty straightforward, right?

[00:10:32]36% play Scrabble only and 16% play um scrabble and checkers.

[00:10:45]That adds up to 52.

[00:10:49]The remaining amount will be the ones who play checkers only. And since the total is 100% 100 minus 52 will give you B48 where Tik Tok didn't get a notification. Tik Tok lapsing man.

[00:11:07]So the answer would be B48. That wasn't even a set question. That was barely a set question. It was more maths. So it's common sense.

[00:11:18]Thanks to the follow.

[00:11:21]All right. So I'm willing to learn. That is the most important thing. I um I know how I feel about your name though.

[00:11:30]I know how I feel about your name. How I get 48 you say? So I'm going draw the s right.

[00:11:39]Boom.

[00:11:41]Boom. If it's one thing, I'm not a art teacher.

[00:11:45]So blimer, right?

[00:11:48]They say all the students in a class play scrabble and checkers or both. If 36% of the students play scrabble only, so let this be scrabble, let this be checkers.

[00:12:00]They say 36% play scrabble only. So that is this amount here.

[00:12:10]They playing scrabble only. Then they say 16% of students play both scrabble and checkers. That will be the intersecting area right don't worry about the name focus on your match right now but your name worrying bro name is quite worrying so the 16% to be here so all we need to do is calculate how much will be here which will be the remainder the whole is 100%.

[00:12:38]This is 36% this is 16%. When I add this together, I get 52. The remainder is what will make it 100%.

[00:12:47]100% minus 40 minus 52 is what gave me the 48. That's how I got the remainder to be 48%.

[00:13:00]Mom, don't worry. Like I just supposed to ignore his name.

[00:13:06]You do have a ignorable name, bro.

[00:13:13]How much papers I now come on live number 11.

[00:13:23]Very concerning indeed. Um refers to the following vin diagram. Somebody say 11 is C like you do this one already.

[00:13:33]Vin diagram. It shows two intersecting sets. The number of students in each set is indicated. So it have five that's in H only, two that's in both H and V and four that's in V only. Right?

[00:13:53]You see in the vin diagram you students who play games. H is you know so everybody people play games right? So three of them they know and that um H is students who play hockey.

[00:14:07]So that is five here. VA students who play volleyball. How many students play neither?

[00:14:14]How many students play either hockey or volleyball but not both? So these five here play hockey only.

[00:14:25]These four here play volleyball only.

[00:14:29]These two play both. So they not they not a part of it. And these three them them them them them them them them them them them them them them them them them them them them them no no no no no game thing them don't play no games so it just be the five and the four which adds up to nine food number 12 the set of twodigit positive integers that are divisible by seven are adv are example of and that would be Herbert I don't want to hear you talking about food I don't I don't want want to know what is food for you, right? I don't know what I don't want to know is food for you. It's not a it's not B. It's not a infinite set. There's a limited amount of numbers that are um divisible by seven.

[00:15:18]All right?

[00:15:21]There's a limited amount of twodigit positive integers that are divisible by seven. So that will be a finite set.

[00:15:28]It's not infinite. I saw some people saying B.

[00:15:32]All right. I trying a trying number 13. Now you all you understand? All you understand the 12, right? Well, how I get how I get D, right? They say twodigit positive integers. There's only so much twodigit positive integers and then there's only so much that are divisible by seven. So it's not an unlimited amount, right?

[00:15:57]Number 30. Now, for every $100 sales or part thereof, a salesman is paid $10 as commission.

[00:16:08]$10. But hey, better than nothing, bro.

[00:16:10]Don't worry. If his sales for a particular month were $1,020, how much commission would he get? So, from that 1,00 and 20, he's getting $10 commission.

[00:16:25]Let's see.

[00:16:29]Now, here's the thing. I seen y'all saying 102, right?

[00:16:38]For every $100 sale or part thereof, he's getting $10 commission.

[00:16:47]So, let's make it easy. I'm going to let make it easy to help you to understand, right? We're going to separate that th00and from and the 20. So you'll have a,000 and we'll separate the 20 from it.

[00:17:01]Right?

[00:17:02]This first part easy for you all to understand. Every $100 sale he gets, he gain $10. How much hundreds it have in a,000?

[00:17:13]10, right?

[00:17:18]it have 10 hundreds in a th00and.

[00:17:23]So he will get 10 by 10 which is $100, right?

[00:17:34]Now that $20 is part of a 100. Remember they said every $100 sales or part thereof he getting a he get $10. So this $20 which is parts of 100 is also going to earn him a next $10.

[00:17:55]So in total he's going to get $110.

[00:17:59]So the answer for this is going to be D.

[00:18:02]It's not as simple as just dividing 1,020 by 10.

[00:18:08]That's how some people got see, but that's not what it is. They said every $100 sales or part thereof, he's getting $10. So every time he sell $100 in sales or part of 100, he gets $10. So he sold a,020. The first,000 he sold $100 in sales 10 times because 100 by 10 is a,000, right? So that means 10 times he earned $10.

[00:18:41]10 by 10 is $100.

[00:18:44]And then that $20 that he sold that is part of a 100. They said every part of $100 in sales is earning him $10.

[00:18:56]So that $20 extra that he earned that he got in sales is earning him a next $10.

[00:19:03]So in total he would earn 100 plus that $10 $110.

[00:19:11]This is Jan 2023. I don't want to move on until everybody understand. Or you want me to go it over again.

[00:19:18]Let me know. Let me know. Go it over again. Will this be uploaded on YouTube?

[00:19:23]No. But I have a marathon going on on Zoom right now with my next math teacher that started since 4 that will be uploaded on on YouTube.

[00:19:38]I'm doing it again.

[00:19:43]All right. They said for every $100 sales or part thereof, the salesman is making $10. So if he had have a sale for $105, this would earn him $20. The first 100 in this $105 would earn him $10. And the next $5, which is part of a 100, could you said part thereof would earn him a next $10. So that would be $20 in total he earn.

[00:20:18]All right? Even if you don't sell the full 100 in sales, but you sell part of it, it's earning you $10. That's what they're saying.

[00:20:28]So when they sold a,020 when they sold 1,020 the first 1,000 they getting $10 every time he sells a 100, right? A,000 divided by 100 is 10, which means he sold he got a $100 sales 10 times. And each time that would have earned him $10.

[00:20:55]So 10 by 10 is $100 he earned there.

[00:20:58]Right?

[00:21:00]Now he didn't sell a,000. He sold a,020.

[00:21:04]That $20 which is part of a 100.

[00:21:11]Part thereof is also earning him $10 even though it's not a full 100 because it's part of 100 and they said part thereof that is earning him $10 as well.

[00:21:23]So that $20 extra above the,000 is earning him a next $10.

[00:21:30]Here it is, John. 2023.

[00:21:33]So in total, the $1,000 would have earned him $100 and that $20 extra will earn him a next $10. So in total, it would be $110.

[00:21:47]Right? It's really important to read the question carefully, right?

[00:21:55]But they didn't say um to divide it by 100 or anything like that. They said every $100 sale or part thereof. If they didn't say the or part thereof, he would have just earned the the $100. But because they said or part thereof, that $20 extra, which is part of a 100, would have also earned him $10 in commission.

[00:22:19]something about Herbert saying something easy just to feel right. Let me stop reading too much into the messages.

[00:22:27]Number 14, the simple interest on $600 for T years at 5% perom is 120.

[00:22:40]The value of T is somebody hit me the formula.

[00:22:45]Somebody hit me the formula in the um in the chat there.

[00:22:51]Somebody hit me with the simple interest formula.

[00:23:00]Yeah. The other answer was 110.

[00:23:06]All right. I'll give you a hint.

[00:23:09]The answer is B.

[00:23:12]Somebody hit me the formula. Let me see now. Nobody hit. Nobody can hit me the formula.

[00:23:24]H see principal by rate by time over 100. Thank you dude. I will take I will I believe your name.

[00:23:34]What's the principal?

[00:23:42]Which one is the principal? The 600.

[00:23:47]The rate is and the time is t over 100.

[00:24:10]and that giving you 120.

[00:24:16]So all you're doing is making t the subject of the formula.

[00:24:21]So you're going to move everything that's on this side to the next side except t. You're leaving t there. When you move something from one side to the other side, it has to do the opposite of what it was doing before. So when I move this 100 to this side, right now it's dividing. If I move it across here, it has to multiply. This six and this five is multiplying. So when I move it to the next side, it has to divide.

[00:24:47]So I'll have t cuz I'm moving everything to leave t by itself. Is equal to 120.

[00:24:58]I move the zero I move the 100 to the next side. So it's no longer dividing, it's multiplying. Multiply by 100.

[00:25:05]And that 60 and five was multiplying. So when I move over to the next side, it's dividing divided by 600 by 5.

[00:25:20]Simple. Simple as that. Don't overthink it. Why tra always get the best teachers. Wow. I appreciate that. Right.

[00:25:28]But don't don't overthink it. As simple as that, right? They want to know the value of t. So you're just making the T the subject of the formula. You take everything that's on the side with t and move it to the next side. And when you move it to the next side, it does the opposite of what it was doing before.

[00:25:45]So this 100 was dividing. You move it across, it multiplying. This 60 and five was multiplying. You move it across the dividing. And that's how we get B, right? 100 by 120. 120 by 100. Same thing. Over 60 by 5. Over 60 by 5.

[00:26:05]make sure they know their formulas.

[00:26:08]I mean to have all this up here to be fair, but have you don't have your simp your simple interest formula, right? So make sure you know that please.

[00:26:26]Number 15.

[00:26:30]Yes, we cooking that we talk about um this same question or similarly worded questions like this this comet often right at a bank $2.60 EC is equivalent to one US right for every one US exchanged 10 EC is deducted as an exchange tax. How many EC dollars will Leon receive if he if he changes 1,000 US? Right. So firstly, ah I see some saying C 2500 right or they cooking all your cooking. You all are correct.

[00:27:20]Anybody chat could tell me how you guys see or or you're just remembering from past um questions you have done.

[00:27:41]All right. So there's two ways you could do it, right?

[00:27:48]You could multiply 2.6 by a dollar which will give you 2.6 26 by,000 sorry which will give you 2,600 and then for every $1 exchange is 10 you have to pay 10 EC right so since it's a,000 you can multiply 1,000 by 10 cents which is 100 EC and then you can minus it and that will give you 2500 that's one way you could do it or you could just minus the 10 cents from this 2.6 six, which will give you 2.5 and multiplied by the,000. So, I see both ways in the chart already. So, there's two ways you could have done it and you have gotten the same answer.

[00:28:32]All right? If you if you don't understand the second way and you need to do it the long way, do it the long way. If one US equals $2.60 EC, then a,000 US would equal 1,000 * 2.6.

[00:28:47]If you need to do it the long way, do it the long way. Nothing wrong with that, right? Which is 2,600.

[00:28:55]And then you calculate how much you have to deduct. For every $1 US, you have to pay 10 cents EC. So since it's a,000 US, it will be a,000 by 0 by 10 cents, which is 100 and you deduct it and you get 25. If you need to do it like that, do it like that. If you understand that, you could just minus the 10 cents from the $2.60 and multiply it by the,000 and get the same answer, do it like that. It's whoever works for you. You're getting the same mark either way.

[00:29:34]Number 16.

[00:29:37]A calculator which is marked at um at $120 is sold for cash at a discount of 30%.

[00:29:48]Right.

[00:29:50]How much change would Susan receive if she pays for the calculator with a $100 bill? So the first thing you have to do is calculate how much it's going to be sold for and then deduct that from the 100. So it's 120 sold for 30% discount. Let's calculate the discount.

[00:30:12]120 over 1 * 30 over 100.

[00:30:24]Let's cross out some zeros.

[00:30:27]Boom. Boom.

[00:30:30]Boom.

[00:30:32]Boom. 12 by 3 is 36.

[00:30:36]So there's the discount. So you're going to be paying 120 minus 36, which will give you for $84.

[00:30:59]If you pay with a $100 bill, you'll get a 100 take away 84, which will give you 16. I don't think I already working for that, right? 100 minus 84 and you'll get a which is 16.

[00:31:17]Number 17.

[00:31:19]A man pays 60 cents for every 200 meters cube of gas used plus a fixed charge. If he pays 1,78.75 when he uses 55,000 m cube of gas, how much is the fixed charge? So the first thing we're going to do, somebody say C number 17.

[00:31:48]No, it's not C or D. Ah, somebody say the answer there. The answer would be A.

[00:31:53]Let's see. What we going to do is calculate how much you would pay for the meters, right? Every 200 m paying 60 cents. So, what I'm going to do is calculate how many times he he um drove 200 m. If you use 55,000 to calculate how much times you drove 200 m, I'm going to divide that by 200 m.

[00:32:25]Let's cross out some zeros.

[00:32:30]Bam.

[00:32:32]Bam.

[00:32:34]Bam.

[00:32:36]Bam.

[00:32:38]So that leave us with 550 / 2 2 into 21 2 into 550 275.

[00:32:54]So he drove 200 m 275 times. Let's see how much that charge would be. That would be 275 multiply by 60 cents 0.6.

[00:33:15]And what I would do, I would move this point to the left once and then multiply 275 by 6, which will give me 1,650.

[00:33:26]And then I'd move move back the point which will leave me with 165.

[00:33:35]So 275 by 0.6 is 165. Right? What I paid $178.75.

[00:33:46]So, the difference between the two would be the fixed charge cuz I would have paid this plus the fixed charge to get $178.75.

[00:33:58]So, I'll take $178. I'm not posting this, but my math teacher, Miss Utley, who's really good, she is doing a a Zoom class right now that started since 4. So, they would have done a good bit of multiple choice questions. It's finishing at 10. I will be posting that recording.

[00:34:21]So 178.75 minus 165 and that would give me a 13.75.

[00:34:33]Yes, it is $100 TT for the um the zoom.

[00:34:40]I'm going to be switching to that just now though, so you will get a follow.

[00:34:45]I am not sure. I um kind of had something to do in a bit. So I stayed on with you all as long as I could and then I would just um pull up the zoom and let it run on the live so you all could follow her class.

[00:34:59]Right.

[00:35:01]So either way a will get through number 18. Now a plot of land presently valued at 12,000 appreciates.

[00:35:11]appreciates means it goes up in value at a rate of 2.5% perom.

[00:35:21]What will be the value of the plot of land one year later? So all they they know that you could calculate 2.5%.

[00:35:31]They just want to make sure that you know that you have to add add in value and and I could tell you and know that is what they want you to know because D is literally the only answer where it increases in value.

[00:35:48]So they're just really testing that if you know what appreciate means.

[00:35:54]Right? Do you have work pass papers on YouTube? Yes, I do. same Miss Utley who's doing the Zoom right now. There is a mat a paper one matt marathon with her on my YouTube right now um by the suit of professionals. But the one that she's doing on Zoom right now, I will also be posting when she's finished. Thanks for the follow. If you're not following yet, I'll appreciate the follows a lot if you all don't mind.

[00:36:22]All right. So they really just testing that you know appreci what appreciate means cuz once you know what appreciate means you don't have to calculate none of this cuz the D is the only one. Wow there's a lot of follows. Thanks guys.

[00:36:33]Big up for you. I really appreciate that. D is the only one that is increasing in value. So you got to calculate nothing. I'm not going to waste my time with any calculations there.

[00:36:44]Number 19.

[00:36:47]A loan for 8,000 was paid back in two years in monthly payments of 400.

[00:36:56]The interest on the loan as a percentage was so let's see it's 2 years or proper lapse like I should skip this one. Everybody see the answer is D and you all are correct.

[00:37:20]Very good. Anybody want to see how they get D?

[00:37:27]How they get D?

[00:37:29]Is it all they just remember the answer or they um was able to calculate it?

[00:37:45]All right, I'll do it. I'll do it. So, somebody guess. All right, so it's 2 years, right? Monthly payments of 400 paid it off. There's 12 months in a year. So, 2 years would be 24 months.

[00:38:00]So, they would have paid 400 24 times, right?

[00:38:08]400 by 24 will give me 44s are 16.

[00:38:20]Cross out the six.

[00:38:23]Put it in.

[00:38:25]Four twos are eight. Add the one outside. Nine.

[00:38:29]Put in my zeros.

[00:38:32]So, this would have given me $9,600.

[00:38:36]The loan was $8,000 and they paid $9,600 to pay it off. The difference between the 8,000 and the 9,600 is the interest they would have paid.

[00:38:50]So, then minus 8,000 from it. The difference is the interest that they paid on the 8,000.

[00:38:57]9,600US 8,000 is 1,600. So, they paid $1,600 in interest. If I want to know what percentage that is now, I will take the 1,600 divided by the original amount or the principal, which was 8,000, and multiplied by 100 to change it into a percentage.

[00:39:23]Let's cross out some zeros.

[00:39:27]Boom.

[00:39:29]Boom.

[00:39:31]Boom boom boom boom. 8 into 81 8 into 16 2. So that's a two with this zero that's 20. So 8 into 81 8 into 160 20 20 by 1 20.

[00:39:55]That is how they got D. a lot of work in but so we just go with the math paper one sometimes. So again the the $8,000 loan was paid back in full in two years of monthly installments of $400. 2 years of monthly installments will be 24 payments in all. 24 by 400 is 9,600. So they paid 9,600 in total to pay off the 8,000. The additional money they paid would have been the interest. So that $1,600 extra they paid would be the interest. So can you put the working on the paper itself? Of course.

[00:40:37]All right.

[00:40:38]Um All right. And what I did to calculate the percentage, I took the interest, which is 1,600, put it over the original amount, and multiplied it by 100.

[00:40:57]And that's how I get the 20%. Everybody follow, right?

[00:41:06]At least all your good memories or they memorizing the answers.

[00:41:14]Yeah. Is it yes or you get your paper to write on? Correct. Or your memory. Good.

[00:41:19]Number 20 is indeed B. But let's see if we could calculate it. Right.

[00:41:25]An article bought for $125 was sold for $175.

[00:41:32]The profit as a percentage of the cost price is so the profit would be the difference between 125 and 175. Right? This is Jan 2023.

[00:41:47]The difference between 125 and 175 is 50.

[00:41:52]They want it as the cost price. The cost price is how much it paid for it, which is the 125.

[00:42:01]All right. So minus. So I take 175 and minus the 125 to get the profit, the selling price minus the cost price.

[00:42:15]And then they wanted to know the profit as a percentage of cost. The cost is 125. So I take the 50 divided by the 125 and multiply that by 100.

[00:42:31]50 into 50. Um 25 into 52 25 into 125 5 into 51 5 into 120 2 by 20 40%.

[00:42:57]That's how you get B.

[00:43:00]So, I calculated the for the um profit.

[00:43:05]I hate how we don't get to bring our calculator. It will kind of defeat the purpose. Maths, they the testing your ability to do maths. The calculator would be doing the maths for you. So they you wouldn't really be testing your ability fairly.

[00:43:24]Paper two, they testing your ability to understand the problem and solve it.

[00:43:29]That is why you get to use the calculator. They use the calculator because they not they not only testing your ability to do All right, I get disconnected for a second there. Am I back?

[00:43:45]Are you Am I back?

[00:43:55]All right.

[00:43:57]The product of a number 2 p over 3 and it reciprocal may be written as how much questions going to repeat I think. Um if you do enough past papers more than half n you switch to your neighborhood.

[00:44:29]I hope your neighbor live to see that.

[00:44:31]What do y'all think? A, B, C, or D?

[00:44:35]Number 21.

[00:44:45]I see B. I see C and C.

[00:44:52]So, they want to know if you know what the reciprocal is.

[00:44:57]The reciprocal is when you flip the fraction and product means multiply.

[00:45:07]So the product of this and the reciprocal will be this multiply by the reciprocal. The reciprocal will be this fraction flipped. So instead of 2 over 2 P over 3, it will be 3 over 2 P. So the product will be 2 p / 3 * 3 / 2 p. And there's only one answer that says that it's not d because d is -3 over 2 p.

[00:45:35]It's 2 p / 3 * 3 over 2 p. So when they say the reciprocal of a fraction, it's that or the reciprocal of a number is just that number flipped. So the reciprocal of four will actually be 1 over 4 because 4 as a fraction is 4 over 1. So the reciprocal of 4 will be 1 / 4.

[00:46:03]You're just taking the number and flipping it.

[00:46:07]The reciprocal of a half would be 2 over 1. The reciprocal of 3/4 will be 4 over 3. You just take the fraction and flip it.

[00:46:24]You'll understand if I'm going to post this. I don't have a posting this because again I have a matt marathon going on and she is recording and that started since 4. So that'll be a lot of hours maths. I may just post that one.

[00:46:45]might be more helpful than this.

[00:46:48]We'll see. Number 22 now refers to the following diagram of a rectangle.

[00:46:56]2 cm here x - 4 cm here.

[00:47:05]The area of the rectangle in cm 2 is x^2.

[00:47:10]The equation that may be used to find the value of so the area of a rectangle is length by width.

[00:47:21]So it's going to be this multiply by this.

[00:47:27]If you look at a, it has two right outside the brackets of xus 4.

[00:47:35]So is it true that July 31st you can pay to see a result? I don't know about that. I never hear anything about that.

[00:47:41]Jenna when there's no symbol or anything between the two and the bracket between a number and a bracket it's understood that there's multiply there. So two open brackets x - 4 closed brackets is the same as 2 * x - 4. And that's the formula for the area of a rectangle.

[00:48:02]Length by width. So the answer has to be a. I'm not even going to bother looking at B, C, and D.

[00:48:09]cuz I know they're wrong.

[00:48:12]Boom.

[00:48:14]In the exam, you also look at B, C, and D just in case. I just playing gangster thing. Boy, you make sure and look at all the all the options first. Number 23. Alia normally saves X each month. I don't save no I don't save no X.

[00:48:32]I receive no X. Anyway, but in June, she saved $4 more than twice her usual amount.

[00:48:42]In June, she saved. So that means she saved $4 more than twice, right? So that'll be x by 2 + 4.

[00:48:56]$4 more than her usual amount.

[00:49:01]All right. So let's see.

[00:49:04]A. No. That's four times the usual amount. B. No. That's six times the usual amount. C. No. Because that is 2 * x. That's 2 * the amount. And plus four.

[00:49:19]But that plus four is being multiplied by two as well. So that actually be four twos are eight. So that will be 8 more than twice our usual amount. That can't be it. D is correct. 2x + 4. This will be 2 * our original amount plus 4. So, it's $4 more than two times the original amount. D number 24. Now, Matt need to understand his ex not come. Exactly dog.

[00:49:56]Exactly dog. Who save ex's boy? My girl ever let me save any one of my exes.

[00:50:03]Madness. Tell them call somebody else to be saved. Anyway, if three plus x / 2 is equal to 1, find the value of x.

[00:50:16]Again, we making x the subject of the formula. Not my x though. Anyway, let me stop that. We're making it the subject of the formula. So you're going to take everything that's on this side besides X and move it on the next side to leave X by itself. When you move stuff from one side to the next, it does she don't want to be saved in. She does it does the opposite of what it was doing before. So when I move that three to the next side, it becomes -3. When I move the two to the next side, it becomes multiply by two instead of divide by two.

[00:51:00]All right.

[00:51:04]So, let's do it.

[00:51:07]X will equal one.

[00:51:13]When I move that tree across, it becomes -3.

[00:51:28]And then when I move that two across it becomes because it was dividing it becomes multiply.

[00:51:40]1 - 3 is -2.

[00:51:43]-2 by 2 negative and a positive will give you a negative will give you -4.

[00:51:50]So x will be equal to -4.

[00:51:56]Mhm.

[00:51:58]All my x is -3.

[00:52:02]Number 25.

[00:52:05]5 to the power of n + 1 * 5 to the power of n + 2 is equal to n and n that's 2 n's 2 + 1 3. So that'll be 5 to the power of 2 n's + 3 that is b n by n is 2 n's 2 + 1 is 3.

[00:52:48]If a star b is equal to a 2 + b 2 then 3 star 4* star 2 is equal to so the first thing we'll have to do is the 3 2 + 4 2 right 3 3's are 9 4's are 16 9 + 16 is 25 so now we have 25 stars at 2 which will be 25^ 2 + 2^ 2 and that is where we have to stop calculating because that's the answer they have there 8 right so I did the 3 2 + 4 2 3's are 9 what happened there oh 3's are 9 4's are 16 and I add them together I get 25. Then I had to do the 25 star 2 which will be 25^ 2 + 2^ 2 based on this formula here. And that is how we got a.

[00:54:00]So far we cooking number 27.

[00:54:07]If a is equal to zero then a is what type of matrix?

[00:54:14]I wish all this come back tomorrow.

[00:54:17]You never know what type of matrix would this be?

[00:54:23]It is called a singular matrix.

[00:54:31]Anybody could tell me what a singular matrix is.

[00:54:42]Thank god at the right it's a square matrix that determinant is equal to zero and since it's equal to zero since the determinant of a is zero then it is a singular matrix somebody asked me to go over 26 please sure so they said a* b is equal to a 2 + b 2 so they asked what three star 4 in brackets Star two means. So I have to do the brackets first. Three star 4 means 3 squared 3^ 2 Now let's write to the pencil 3^ 2 + 4 2 I have to do what's in the brackets first right three t 3's is are 9. So 3 squar is 9.

[00:55:48]4s are 16. So 4 squar is 16. 9 + 16 is 25.

[00:55:57]So now I work out what's in the brackets I have to do. So 3 star 4 is 25. Now I have to do 25 star 4. According to this a* b is a 2 + b 2. So 25 star two sorry would be 25^ squar + 2^ 2 + 2 2 and I didn't have to calculate this because that is where the answer stopped 25 + 2 2 right number 28 Eight.

[00:56:43]We have a matrix question. They want to know the order of the matrix.

[00:56:52]We have a row.

[00:56:58]We have three rows, sorry.

[00:57:01]And we have four columns.

[00:57:08]All right. So it's always row then column.

[00:57:12]Row then column is row then column.

[00:57:18]Row then column. I hope you remember that for the exam. Right? Row then column.

[00:57:26]Row then column. It are three row four column. Three row four column. So the answer would be C.

[00:57:38]Right?

[00:57:40]If this question come, I hope that song play in your head so you can remember which is which. Right? It's row then column, row then column, row then column, row then column. Right number 29.

[00:58:04]All right.

[00:58:05]I um are going to be switching to the zoom just now. Well, I'm going do number 29.

[00:58:18]All right.

[00:58:20]So just ving if the vectors P and Q are 3 2 and -1 4 then P - 2 Q will be what?

[00:58:41]Seeing people saying B.

[00:58:44]Seeing people saying B and wondering how could this be? because I know it is D.

[00:58:51]Big up me.

[00:58:54]Cuz the answer is D.

[00:58:57]Big up me. I can't give you the Zoom link. The Zoom link is a The Zoom is a paid class.

[00:59:06]So I can't um I can't give you the Zoom link.

[00:59:11]Well, big up me.

[00:59:15]But how did you get D?

[00:59:29]Can you explain how you get D for extra points?

[00:59:59]Mimi, you can explain how you get D or is it that you just um remember the answer.

[01:00:13]All right, working it out as long. Okay. So, P would be -3 over -2, right? -3, -2.

[01:00:37]All right.

[01:00:39]And 2 q would be 2 by -1 is -2.

[01:00:47]4 by 2 is 8.

[01:00:57]So Q is - Q sorry is -3 over -2 and 2 - P sorry is -3 over -2 and 2 Q is -2 over 8. So -p - 2 q will be equal to let's see -3 - -2 which is the same as a negative a negative is a positive. So that'll be -3 + 2 and then -2 - 8.

[01:01:52]-3 + 2 is -1 and -2 - 8 is -10.

[01:02:08]So big up Mimi.

[01:02:10]The answer is D.

[01:02:13]I say big up Mim me cuz the answer is D.

[01:02:18]Vo make it as a teacher or you know what um career going into.

[01:02:26]So we're going up to I going do number 30 now and then I going switch to the zoom with Missly. Right.

[01:02:35]Miss Utley supposed to be finishing 10.

[01:02:38]Last time I see her go up until 12 and last year. I don't know if she doing that this year, but I will um leave the zoom running with her teaching right number 30. Now they have um number 30 refers to the following diagram of a triangle OM in which R is the midpoint of O C exhibits A here R.

[01:03:15]He said further O R O O to R is 3 A minus 2B.

[01:03:31]So only math said I teach or other subjects too. I actually teach POB, POA, economics, office administration. Those are my four main subjects. I have other teachers for maths, English, social studies, chemistry, HSB, biology, right? Um, I used to teach maths before.

[01:03:52]Maths was actually the first subject I ever taught, but full-time I teach business subjects.

[01:04:00]So, what I normally do, I like to in for my company, I like teachers who teach subjects full-time in secondary schools to work for me, to work with me. Sorry.

[01:04:11]So, the math teacher I have, she works in a secondary school where she teaches maths full-time. So, she does the maths class, not me. Right? It's just because I used to teach maths before. It was the first subject ever taught. You know, could always brush off the cobwebs and hit a little something something, right?

[01:04:32]But Miss Utley is the math teacher for Bali Professionals. The one who swap to Right.

[01:04:41]So they want LM expressed in terms AB.

[01:04:49]We know O to R is 3 A - 2 B is the zoom on live. Well, I am I am going to switch to the zoom and just the live. So you will see you will see it right. and O to the M is 2 A plus 3 B.

[01:05:18]So what does they want again?

[01:05:21]LM. So they want here LM expressed in terms AB that would be all right. Right. So, I'm going to give you the answer and I want to see if you all could tell me how I got the answer.

[01:05:41]This is the last question.

[01:05:44]So, let me see. The answer is just calculate. The answer would be B.

[01:05:56]Let me see if anybody could tell me how I got B.

[01:06:12]Anybody could tell how I got be two minutes. Try it. Intuition.

[01:06:23]Intuition. Yes.

[01:06:25]I want more intuition. I want more than intuition.

[01:06:33]Sequin. Yes.

[01:06:35]Again. Yeah. We're 1 minute and 30 seconds.

[01:06:40]Somebody say 2 B - 3 A + 2 A + 2 B.

[01:06:58]All right.

[01:07:13]So, O R.

[01:07:23]So, O right.

[01:07:27]So if R is the midpoint right O R and O R is 3 A minus 2 B right then O L is two O RS or in other words two two open brackets 3 A minus 2 B.

[01:07:54]Oh gosh. 3 A minus 2 B. So O L is 2 O R cuz remember O R is the midpoint. So this is this to this is 3 A minus 2 B which means here to here since that's the midpoint is also 3 A minus 2 B. So the entire thing will be 3 a minus 2 b * 2.

[01:08:25]All right. So this will give us 2 3's are 6. So that is 6 a minus 4 b right now given that m is 2 a + 3 b.

[01:09:00]The vector lm will be OM take away O.

[01:09:10]So the OM which is 2 A + 3 B take away O which is 6 A - 4 Okay.

[01:09:51]So, lm trying to get a space to write it.

[01:10:04]= to 2 a + 3 b minus open brackets 6 Okay.

[01:10:38]Minus how much are those?

[01:10:44]4 B which will be equal to 2 A - 6 A is - 4 A Oh gosh. So plus 3 B + 4 B is 7 B.

[01:11:36]So that is - 4 a + 7 b or 7 b - 4 a same thing right.

[01:11:50]So what anz said is actually correct. So the answer would be b pops 10k likes. Yes. I appreciate you.

[01:12:04]All right, guys.

[01:12:06]So, I hope that was helpful.

[01:12:10]I am going to swap across to the zoom now.

[01:12:26]And I'm going to let you all follow with me. Right.

[01:13:06]and you never type the right thing first. So I try to type it fast the wrong thing.

[01:13:26]Anyway, the code in the password invisible anyway.

[01:13:56]by which >> recording in progress >> which A is mapped on to A prime. B prime is represented by so we're looking >> B as in boy two one meaning we went two spaces to the right one space up. All right guys, good luck.

[01:14:17]>> Number 53 54.

[01:14:21]>> Item 54 refers to the following diagram.

[01:14:25]In the diagram, PQ and RS are parallel.

[01:14:29]Which of the following best describes the relations between P and Q?

[01:14:36]A >> A they are equal.

[01:14:49]All right. A ship sailed 8 km due east from A to B.

[01:14:58]It then sailed 6 km north to C.

[01:15:03]Which of the following best describe best represents the path of the ship?

[01:15:10]So look at A. So I'll scroll down for you all to see all at the same one by one. Okay. A B C and D >> C. The ship went The ship went east eight kilometers from A to B.

[01:15:37]Then it went north 6 km from B to C.

[01:15:47]All right.

[01:15:48]56.

[01:16:04]All right. In each of the following diagrams, O A prime is the image of O A. Which of the diagrams shows a reflection in the y ais?

[01:16:23]So look at a. Remember we're looking for reflection in the y axis. Right, B C and D boy.

[01:16:43]>> B as in boy.

[01:16:51]Right? Reflection in the yaxis would mean that my yaxis is my mirror line.

[01:17:04]In triangle ABC, angle A is X and angle B is 2X. What is the size of angle C?

[01:17:22]D >> D item 54 refers to the diagram which shows an enlargement.

[01:17:40]In the diagram, triangle A B C is mapped onto A triangle A prime B prime C prime where the origin is the center of enlargement. What is the scale factor of enlargement?

[01:17:56]to D V >> right it is twice the size.

[01:18:10]Item 59 refers to the pair of similar triangles.

[01:18:17]So we are trying to find the length of M o in cm.

[01:18:26]Look at our two triangles.

[01:18:28]>> 3.5 >> 3.5. Thank you.

[01:18:37]Item 60 refers to the right angle triangle which trigonometric ratio represents four well sorry is equal to 48 >> sin >> x you sure >> yes >> yes that's the All right. So, another paper completed.

[01:19:11]How are we feeling?

[01:19:14]>> Ready?

[01:19:15]>> Should be good.

[01:19:17]>> I feel >> you're feeling >> normal.

[01:19:21]>> Okay. This paper had less repeated questions, but we still saw a few. All right. And even with the new questions, you all did well.

[01:19:35]So, get some water. You'll have five minutes and we look at one more paper.

[01:19:43]Okay.

[01:19:46]>> Recording stopped.

[01:25:00]All right guys, so let us begin.

[01:25:10]>> Recording in progress >> and we are looking at May 2028.

[01:25:18]>> What the hell?

[01:25:20]>> What happened?

[01:25:27]Are you all ready?

[01:25:37]First question. The number 3.14063 written correct to three decimal places is >> B as in boy. B >> as in boy.

[01:25:53]What percentage of 40 is eight?

[01:25:58]>> 20%.

[01:25:59]>> 20%.

[01:26:03]And this is a repeat question. We've seen it a lot already.

[01:26:06]Using the distributive property, 49 * 17 + 49 * 3 is equal to a move.

[01:26:20]The next term in the sequence >> C >> C okay >> 0.45 four five written as a fraction in its simplest form is >> a >> a lovely let's see right a certain amount of money is shared in the ratio 2 three 2 to 3 to 9 if the difference between the first and second shares is $40 what is the total amount of money shared How much was shared?

[01:27:02]How do we find how much was shared?

[01:27:06]>> Fine for one.

[01:27:08]>> Finding for one. But they already we could we don't necessarily >> one is 40.

[01:27:12]>> One is 40. It is there because the difference between the first and second share is one, right? 40 by all the shares.

[01:27:21]>> So 40 by the total amount of shares which is 360 >> 14 shares >> 14 shares >> D.

[01:27:38]>> So 14 multiply by 40 is >> D.

[01:27:46]Which of the following sets is equivalent to the set A, B, C, D?

[01:27:58]right? Same number of elements.

[01:28:04]>> Item eight refers to the ven diagram.

[01:28:09]The shaded region represents >> D.

[01:28:24]>> Why is it A instead of the others?

[01:28:27]>> Because a not flag thing like forget their name.

[01:28:38]Q >> is compliment. So that means everything except P everything that is not in P.

[01:28:45]That is why the entire set P is not shaded. Right? P complement everything else but that set. Okay.

[01:28:59]This question came already. Remember what the complement is.

[01:29:09]Right. Item nine.

[01:29:13]Item nine refers to the ven diagram. In the ven diagram, U is the students who play games.

[01:29:23]H students who play hockey. V students who play volleyball. Volleyball.

[01:29:30]The number of students in each set is shown. We could see that how many students do not play volleyball.

[01:29:40]>> C.

[01:29:46]>> Look at the set.

[01:29:51]>> D >> A >> D. Answer is eight. Let us look at the set together.

[01:30:01]In the set V which is volleyball we have two and four. They want us to know how many students do not play volleyball which meaning that they are not in that set V. So we have five and we have three which would give us eight.

[01:30:24]Okay look at this look at the ven diagram properly.

[01:30:30]Number 10. If set Q has the elements A, B, C, how many subsets can be obtained from set Q?

[01:30:40]>> C.

[01:30:44]Remember it is 2 to the power of the number of elements and there are three elements in the set.

[01:30:54]Item 11 refers to the information on the description of three sets. P is the set of prime numbers. Q is the set of odd numbers and R is the set of even numbers.

[01:31:08]>> Which of the following sets >> is an empty set? Someone is saying D?

[01:31:18]We agree with D. Yes, we agree with D because >> Yeah.

[01:31:24]Q intersect R which is odd numbers intersect even numbers is going to be empty.

[01:31:33]If P and Q are two sets where the number of elements in P union Q is 13 and the number of elements in P intersect Q is 16 and the number of elements in P is nine.

[01:31:56]How many do we have in Q?

[01:32:05]B.

[01:32:08]>> Wait me. Sorry. Did I walk in again?

[01:32:10]>> How we do this working? Okay, let's find the pen. Right.

[01:32:16]So, let's read over what they give us.

[01:32:19]They're telling us that the union of the two sets has 13 elements, right?

[01:32:28]And the intersect of the two sets. So let me underline while I speak.

[01:32:35]Right.

[01:32:36]So the union of the two sets has 13 and the intersect of the two sets have six. P has nine. How much does Q have?

[01:32:51]So we're trying to find for Q only.

[01:32:56]Right?

[01:32:58]So we are going to say number of Q would be P well sorry the number of elements in P subtract the number of elements in P intercept Q right so that is going to be 9 subtract six to give us three.

[01:33:34]You all with me?

[01:33:38]And then if we know that out of that out of that intersection in between P and Q, six elements they share, three of them are just for P alone. Well, Q alone. No P sorry this is P 13 in total 13 subtract three 10 this working would be different from the others that we did. This question is different.

[01:34:24]All right. A man's taxable income is 20,000.

[01:34:29]He pays a tax he pays tax at a rate of 28%.

[01:34:35]The amount of income tax he pays is what are we finding? We are finding 28% of the 20,000 Anybody has an answer for me?

[01:35:18]28% or C.

[01:35:23]>> Yes, the answer is C.

[01:35:25]>> Miss B.

[01:35:26]>> C.

[01:35:28]28% of 20,000.

[01:35:32]Do any working on screen? Cross out of my zeros. So, I am now multiplying 28 by 200.

[01:35:42]Bring down my two zeros. 28 by 2 is 56.

[01:35:47]My answer is C.

[01:36:00]Number 14. A man's basic wage for a 40hour work week is $160. He is paid $5 per hour for overtime.

[01:36:15]If he works six and a half hours overtime in a certain week, what is his wages?

[01:36:37]>> D.

[01:36:38]>> Which answer?

[01:36:41]>> D.

[01:36:42]>> D.

[01:36:44]All right. Do I need to do the work for this or are we okay on how we found D?

[01:36:51]>> Yeah, miss.

[01:36:53]>> All right.

[01:36:57]If TT $6 is equivalent to$1 US, then TT $15 in US dollars is C.

[01:37:16]See $2.50 without even calculating. If $11 US is $6 TT, then 2 US would be $12 TT, right? And then between 12 and 15, I have $3. So that'll be 50 cents.

[01:37:45]The annual interest rate on a 15-year mortgage on a house assessed at a value of 450,000 is 5 cents on every dollar.

[01:38:01]What is interest paid on the mortgage in the first for the first year?

[01:38:09]Pick up at the question.

[01:38:12]for the first year alone, not the 15 years we are calculating. We're calculating for the first year, right? But we are also paying 5 cents on each dollar.

[01:38:27]That's the that's the tax we pay. How do we calculate that?

[01:38:46]Anybody?

[01:38:55]>> I don't know. Miss >> we're going to divide um >> we have to take our amount that we're paying cuz we're paying on every dollar.

[01:39:08]So, we are paying for each dollar of this $450,000 house, we are paying 5 cents.

[01:39:27]This is what we're multiplying, right? We are multiplying that 450,000 by that 5 cents.

[01:39:46]Do we know how when we multiply it? So, someone multiply it and tell me the answer.

[01:40:04]B >> B right in the previous question they would have given us how much we were paying on each 100 things like that. So read your questions carefully. In this question we are paying on five cents on every dollar. So for every dollar we have to multiply it by the five cents.

[01:40:23]Okay, remember I told you all that this section we need to read questions carefully.

[01:40:30]Number 17. Mary invested $200 for five years at 5% perom.

[01:40:39]John invested $500 at the same rate. If they both received the same amount of money in simple interest, how many years how many years did John invest his money? So this would be a two-part working question. We need to find out firstly what is the interest and then use that interest amount to calculate the time for John.

[01:41:11]So let's calculate the interest using Mary's information.

[01:41:15]So we know that our interest is principal by rate by time over 100. So that's 200 * 5 * 5 over 100.

[01:41:34]Our interest is $50, right? So now let's calculate his time. So we know that the time is interest by 100 over principal by rate. So my interest is 50 multiplied by 100 over he invested 500 at the same rate.

[01:42:09]So, we're just canceling out. And he invested for 2 years to get the same amount of money.

[01:42:22]Are we okay?

[01:42:24]>> Yeah.

[01:42:32]>> All right. Number 18. A salesman sells a car at 11 for 11,000.

[01:42:39]He is paid >> a commission of 4.5% for the first 10,000 and 7.5% for the remainder.

[01:42:50]The commission he receives is so working. This is also a two-part working question.

[01:42:56]We need to work out his commission on the first 10,000 and then add the commission on the remaining what? 1,000 at 7.5% to give us So, we have 10,000.

[01:43:38]The first 10,000 at 4.5% that would give us $450, right?

[01:43:52]And then we have the remaining 1,000 at 7.5%.

[01:44:04]Which will give us $75.

[01:44:11]And then when we add it, we get $525.

[01:44:18]So his answer is B.

[01:44:25]Can you all see that?

[01:44:29]>> Mhm.

[01:44:31]Makes sense.

[01:44:36]>> Y'all were calculating percentages so quickly just now. Y'all tired.

[01:44:43]>> So it goes it starts at four. A television set cost $350 cash. When bought on higher purchase, a deposit of $35 is required, followed by 12 monthly payments of $30. How much is saved by paying cash?

[01:45:01]leaving you all >> 45.

[01:45:15]>> All right.

[01:45:18]>> Mr. Jones bought a car for 64,000. The car depreciates by 20% in the first year and 10% each following year.

[01:45:31]What is the value of the car at the end of the second year? This is also a two-part question.

[01:45:50]Anybody have an answer for me? Let me give you all time to work it out. Sorry.

[01:45:55]Work it out and then let me know if you'll have an answer for me.

[01:46:13]C >> C.

[01:46:16]>> Thank you. That is correct. So what we had to do, we had to find the value of the car after it depreciated for the first year.

[01:46:28]Right? It appreciated by 20%. So, we could have found 80% of that 64,000 and then use that answer to find the 10% that it would have gone down by and subtract.

[01:46:47]Okay. So, subtract to find the first part. We could have also found 20% of the 64,000 then subtract it. Then find the 10% against you. We had to find percentage twice.

[01:47:02]Number 21.

[01:47:08]What is my answer?

[01:47:12]>> D.

[01:47:13]>> D.

[01:47:15]Right. A repeat question. And remember when our denominators are different we find the LCM even when it is in terms of x number 22 x is equal to >> 4 d.

[01:47:40]>> Thank you.

[01:47:43]Number 23. 3x^2 * 2 x cubed is equal to >> a a yes. We multiply 3 by 2 and then we add our powers to get five.

[01:48:08]Sorry.

[01:48:11]Number 24.

[01:48:14]Which of the following can define A and B?

[01:48:22]So, we're going to work it. You're going to work it out.

[01:48:27]Remember how we work it out?

[01:48:36]>> D as in dog.

[01:48:38]>> D as in dog.

[01:48:40]Right. So we did the substitution and we need to find which one works for both.

[01:48:51]Number 25. When eight is subtracted from a certain number and the result is multiplied by three, the number the answer is 21.

[01:49:06]What is the original number?

[01:49:11]One >> one mm >> I don't know. Tell me.

[01:49:18]>> No.

[01:49:20]If eight is subtracted from the number >> the as in >> Yes. And then that result is multiplied by three.

[01:49:40]All right. If x is -2 and y is 3 and t is equal to 2, we need to work it out. So let's do the substitution. We have -2 over 3 to the power of 2. What is my answer?

[01:50:03]B.

[01:50:08]Right. So, do the substitution in order to figure out your answer.

[01:50:19]Item 27 and 28 refers to the two matrices P and Q. Number 27. What is the order of matrix Q?

[01:50:34]A >> A thank you. It's a 3x4 matrix.

[01:50:41]Three rows going across, four columns coming down.

[01:50:51]The determinant of P is 27 28 link.

[01:51:03]>> Yeah. So, you're using Matrix?

[01:51:07]>> Yeah. Miss the um kind of highlight color thing blocking me from seeing >> Sorry.

[01:51:19]>> I don't know how to move that.

[01:51:26]Right. -2 that is B.

[01:51:36]All right. If a vector If the vectors P and Q are 32 and14 respectfully, then P subtract 2 Q is P is 3 2 and we have to subtract 2 Q. So that's 2 * -1 which will give me -2 and 2 * 4 which would give me 8.

[01:52:20]When we work it out, my answer is going to be >> 56 a.

[01:52:29]>> So that is a lovely 30.

[01:52:46]Item 30 refers to the parallelogram WXY Z.

[01:52:52]In the parallelogram, R is the midpoint of XY.

[01:52:59]Based on the information above, Z R would be equal to take this off.

[01:53:11]If I want to go from Z to R, which of those would work?

[01:53:20]>> Miss A.

[01:53:23]>> A.

[01:53:31]>> A is correct. Can everybody see how we get a?

[01:53:36]>> No.

[01:53:37]>> All right. Let me get my pointer because it's the parallelogram.

[01:53:44]Right? If you look at our answers, they didn't give us they told us that R is the midpoint of XY. But in our answers, we don't have any midpoint of XY. You see that?

[01:54:02]>> What we midpoint is half. So we are seeing halves half of WZ because they are parallel they will be equal.

[01:54:15]So XY would be equal to W Z.

[01:54:21]Remember if we're going the opposite direction it will be negative.

[01:54:26]So let us go where we would usually pass. If we were doing it, we would have gone Z W and then Y R. Right? In this case that we can't go that way because they didn't give us those options. So we are now using the parallel sides which would be ZW is the same as WX right. So wx and then because we are going y to r that is negative so it's subtract half of wz.

[01:55:07]So remember in a parallelogram the parallel sides are always equal and that is what they played on in this question.

[01:55:17]If you were to write it out, you would have gone here and then half of here.

[01:55:25]Because they are using the parallel sides, we have to use these letters.

[01:55:37]Okay.

[01:55:38]>> Okay, miss. Thank you.

[01:55:40]>> No problem.

[01:55:51]Item 31 refers to the diagram of a square and a rectangle.

[01:55:59]Square A has sides of 12 and 12 and rectangle B has sides of 9 and 16. Which of the following statements is true about the perimeter of the square and the rectangle? Parime not area is less than paramet.

[01:56:34]Repeat your answer for me please. Love >> parimeter A is less than parameter B.

[01:56:40]parameter A is less than parameter B.

[01:56:44]It should mean that D is my answer.

[01:56:53]We all agree with that, right?

[01:57:04]3,800 ml expressed in meters is >> B >> B 3.8. We looked at this question with different values before.

[01:57:22]The circular distance the cir the distance around the edge of a circular pond is 88 m.

[01:57:34]The radius in meters would be c d.

[01:57:51]All right. So let's think the circumference of a circle, right? That is the distance around. So the circumference of a circle is 2 pi r, right? They're telling us that the circumference is 88. So 88 would be equal to same 2 pi r. If they want us to find the radius, I am now going to divide both sides by 2 pi.

[01:58:21]So my radius is equal to 88 over 2 I >> 34 refers to the following figure which shows a triangle resting on a square.

[01:58:47]The length of one side of the square is 5 cm and the height of the triangle is 4 cm. What is the total area?

[01:59:00]So, we're going to have to find the area of the triangle and then find the area of the square and add them.

[01:59:20]A >> A thank you. The area of the square would be 25 and the area of the triangle would be 10.

[01:59:38]I need to move this in order for you all to see the question.

[01:59:42]The volume in centime cube of a cube with an edge of 3 cm.

[01:59:58]How do you find the volume of a cube?

[02:00:00]>> C. Thank you.

[02:00:10]The area of a rectangle is 53.6 cm squared. If the length is multiplied by four and the width is half then the area would be causing on YouTube.

[02:00:40]>> All right.

[02:00:43]So we have a rectangle.

[02:00:48]So we have a rectangle.

[02:00:51]Hold on. Right. So we know that first was the area of a rectangle.

[02:00:58]>> I see remember started >> length by breath. Right. So whatever was my length by my breath >> that is equal to 50 >> cm cubed.

[02:01:10]Then they said that my length is multiplied by four and my width. So you have a a be and my width is half, right?

[02:01:32]Okay.

[02:01:34]So therefore, if I were to work this out, so I'm going to do some calculation, right?

[02:01:46]2 into 2 1 2 into 4 2. I have 2 * the length time the width which would give me 2 * the original area >> by width is >> which works out to the 107 by area. So >> 2 * >> um miss where where you get the um 41 from >> it's not 4 L. Oh, length >> cuz they told us that the length is multiplied by four. So L by 4 would be 4 L >> and then the width is half. So that's why I have the W / two.

[02:02:39]See it?

[02:02:41]Please see it.

[02:02:51]On leaving Trinidad, the time on a pilot's watch is 2,300 hours. When he arrives at his destination in the same time zone on the next day, his watch shows 300 hours. How many hours did the flight take?

[02:03:19]4 hours.

[02:03:20]>> 4 hours. My answer is A.

[02:03:27]Item 38 refers to the diagram of a trapezium.

[02:03:33]Titulate its area.

[02:03:40]This is a repeat question.

[02:03:43]Remember how we find the area of a trapezium?

[02:03:56]We have 65.

[02:03:59]Yes. A + b * h. Right.

[02:04:06]where this is our A and this is our B and this is our H. Someone said the answer was 65 and that is correct.

[02:04:25]Items 39 and 40 refer to the histogram which shows the number of children aged four, five, six, seven, and eight who took part in a survey.

[02:04:38]What is the modal age?

[02:04:43]>> C seven.

[02:04:50]>> How many students took part in the survey?

[02:04:53]>> B.

[02:04:58]She can't see her.

[02:04:59]>> I add up the values.

[02:05:00]>> I am streaming. 3 + 4 + 2 + 5 + 1.

[02:05:08]Number 41. What is the median of those numbers?

[02:05:13]>> Bm.

[02:05:22]When three coins are tossed simultaneously, the possible outcomes are well H's heads, T's tails, right? So we are seeing the outcomes. They want us to find what is the probability of randomly obtaining at least two heads.

[02:05:45]So look at our outcomes and see how many we have where we have at least two heads. Was it over the total >> and give me nine?

[02:05:56]>> Yes, love.

[02:05:57]>> Four, which is a half.

[02:06:00]>> I don't get that.

[02:06:01]>> You don't get it? Okay.

[02:06:04]>> All right. So, they want us to find the probability that we get at least two heads. So, we can get two heads or more.

[02:06:16]So, let us select the options where we got two heads or more. Right. So that's this one.

[02:06:23]Two, three, >> four, >> four.

[02:06:29]Those are the four that has at least two heads, right? So those are the four outcomes that we could have possibly gotten out of the total 1 2 3 4 5 6 7 eight outcomes.

[02:06:44]So when you're finding probability always remember is the number of expected outcomes which in this case is four because we we are looking at the results and we have four of them that has at least two heads right? One has three the other one has two well the other three has two heads three heads. Two heads each. Sorry. So four times out of the eight tosses we had two heads appearing.

[02:07:16]So when we break this down we get >> one half.

[02:07:22]>> Yes.

[02:07:23]>> Okay. Answer is C. So if a question possibly comes like this tomorrow please read what they're asking you for properly. They said at least two heads.

[02:07:34]So it can be two or more. And that's why I would have underlined the ones that had two or more hes in the results.

[02:07:46]600 students write an examination. The probability of a randomly selected student failing the exam is 1/5.

[02:07:57]How many students are expected to pass?

[02:08:02]>> B.

[02:08:03]>> B. 480 students, right? Another repeat question that was all right.

[02:08:16]Item 44 refers to the following diagram which shows accumulative frequency polygon of the length in meters of 20 fish that are caught by two fishermen.

[02:08:35]They want us to find the interquartile range of the length of the fish. Sorry.

[02:08:48]All right. Firstly, before we begin solving anything, what is the interquartile range? How do I find interquartile range?

[02:09:00]Anybody?

[02:09:03]Mhm.

[02:09:04]>> How do I find it?

[02:09:05]>> Pressure.

[02:09:11]>> Anybody on the live now?

[02:09:14]>> Nobody.

[02:09:16]>> Isn't it half of the total number?

[02:09:22]>> 3/4us like a quarter, >> right? So quartile 3 subtract quartile one right so that's three quarters >> and this would be one quarter however what does that mean for my graph how do I calculate that if it's 20 m and I need to find 3/4 of 20 where where am I looking at >> 15 >> 15 so okay so my first step would be to find come find 15 in the cumulative frequency come across touch my graph and then come oh gosh my line crooked sorry and then come down right and this value would be the length that I am about to subtract right so let's figure out what's that value is if I have >> so we know it's between three and four but it's going to be 3 point how much >> seven >> seven yeah 3.7 >> saying 3.7 >> let's go with what you're saying 3.7 and then we need to do the same thing for Q1 >> five >> five lovely so find five drawing our line touch our graph and then come down we have one point how much 1.2 >> 1.2 two.

[02:11:30]>> So it will be 2.5 C, >> right? So 2.5 and our answer is C everybody. Okay?

[02:11:51]>> Yes, miss.

[02:11:52]>> Yeah, miss.

[02:11:55]>> All right. Number 45. Which of the following best illustrates a function?

[02:12:01]>> What are you going to do?

[02:12:03]>> I just want to go away.

[02:12:06]>> See?

[02:12:08]>> All right. I got it back.

[02:12:11]>> If we looking at that, >> in order for it to be considered a function, it can only be mapped onto one It can only go one place. So if you look at A, the second one is going two places. Definitely not a function. B, third one also two places. Not a function. C, second one going three places. No. But D, each element of the first circle is mapped on to only one in the second circle, making that the best illustration of a function. All right.

[02:13:03]The equation of the line that passes through the point 05 and has a gradient of four C.

[02:13:21]Right? Because the equation of a line is y is equal to mx + c where m is the gradient.

[02:13:34]Item 47 refers to the diagram of a number line.

[02:13:41]The graph of the inequality in the diagram is defined by we have an open circle and the arrow pointing to the left. What is that?

[02:13:55]>> Less than >> x is less than how much?

[02:14:00]>> One.

[02:14:00]>> One, >> right? X is less than one. So my answer is a right.

[02:14:16]Item 48 refers to the straight line graph. They want us to find the gradient of a b.

[02:14:34]Remember gradient is rise over run.

[02:14:43]Gradient rise over run.

[02:14:51]So what is my rise? How much am I going up from A to B?

[02:15:01]>> Two.

[02:15:02]>> Three.

[02:15:02]>> And my run, how much am I going across?

[02:15:05]I'm going across four. Break that down.

[02:15:08]My gradient is a half. Can you all see that? This is my rise.

[02:15:18]And this is my run.

[02:15:23]Okay, it went up two spaces, went across four.

[02:15:35]My answer is D.

[02:15:48]49.

[02:15:52]If f ofx is equal to 2x^2 -1, then f of -3 would be equal to so we're substituting here.

[02:16:08]Wherever I see x in the function, I am replacing it with -3. So I have 2 open brackets -3^ 2 - 1. So that's 2 by 9 - 1.

[02:16:23]>> 18.

[02:16:23]>> 18 subtract one is 17.

[02:16:30]My answer is C.

[02:16:43]All right. Item 50 refers to the graph of a quadratic function.

[02:16:54]They want us to state the maximum point on the graph.

[02:17:03]Maximum D. Thank you. 2.

[02:17:09]>> Thank you.

[02:17:12]What is the gradient of the straight line? 2y = -3x subtract 8.

[02:17:31]Don't I need to divide by two?

[02:17:35]>> B.

[02:17:37]>> Thank you.

[02:17:49]Item 52 refers to the following arrow diagram which shows a function f.

[02:17:57]Which of the following best describes the function?

[02:18:01]>> What is the relationship between x and y?

[02:18:06]>> Thank you.

[02:18:14]Each exterior angle of a regular polygon is 60° then the polygon is a >> external C >> C that is correct. Remember the sum of the external angles are 360°.

[02:18:45]So if we were to work it out, let's think about it, and we had to multiply the amount of sides by 60 for each of them, whichever one gave us 360° would be our answer, which is 6 by 60 is 360.

[02:19:03]You okay?

[02:19:10]This item 54 refers to the following diagram.

[02:19:18]In the diagram, A, B, and C, D are parallel.

[02:19:23]Which of the following best describes the relationship between X and Y?

[02:19:30]>> Miss A.

[02:19:31]>> A. They are equal.

[02:19:40]Item 55 refers to the diagram of an isosles triangle.

[02:19:46]In the triangle, the value of x is >> 120.

[02:19:52]>> 120 >> 120. Thank you.

[02:19:57]Add the two angles that we know we get 60 subtracted from 180.

[02:20:03]120°.

[02:20:09]The image of a point P under the translation 3 4 is so if I'm at two three and I am moving this point three spaces right and four spaces up where would I end up? A >> uh we not multiplying. We moving the point if Okay. So >> Miss B.

[02:20:48]>> Nope.

[02:20:50]>> Cu D.

[02:20:56]So look at this. I'm doing a makeshift thing here. This is 01 -2 1 2 3 All right. Four. Then I have 1 2 3 4 5 6 7 8. Okay. And my first point it at -2 3. So that's here, right? That's P.

[02:21:25]And I am moving P three places to the right. So that's one, two, three. So now I somewhere here. So I know that definitely it is going to be one on the X. And then I need to move four places up. So from here I go 1 2 3 4.

[02:21:46]I am now here at 17.

[02:21:53]Can you all see that?

[02:21:57]Yes, sis.

[02:22:01]>> Right. Someone would have multiplied just now to give me the answer. Don't multiply. Add.

[02:22:10]Right. If we were to add If we were to add 2, -2 and 3, we would have gotten one. If we were to add three and four, we would have gotten seven.

[02:22:26]Item 57 refers to the following diagram of two straight lines.

[02:22:35]In the diagram above the line CD is the image of A B.

[02:22:42]All right.

[02:22:44]After what happened? What happened to the line? Is it a rotation to 90° at the center? Is it a reflection on the Y ais? Is it a translation or a reflection on the x- axis? What do we think it is?

[02:23:01]>> A reflection in the y ais.

[02:23:03]>> A reflection in the y- axis. The answer is B.

[02:23:12]Item 58 refers to the pair of similar triangles.

[02:23:18]The area of triangle A B C is 20 cm.

[02:23:24]What would be the area of triangle MN O in cm squared?

[02:23:32]>> 10.

[02:23:35]>> You sure >> 2.5 3.3 >> All you just guessing now the answer is five.

[02:23:52]Why is the answer five?

[02:23:55]Because when we are thinking similar triangles.

[02:24:01]So we can see that the scale factor is two. Right? The regular scale factor of the two triangles is two. Right? Yes.

[02:24:11]So the scale factor for area is going to be 2^ 2 which is 4.

[02:24:21]So 20 / 4 is if it was a shape where you were given where you were given volume. The scale factor for volume would have been the cube of the scale factor. Okay.

[02:24:43]Hence they emphasized cm squared here.

[02:24:49]You're squaring the scale factor.

[02:24:56]All right. You all just noticed that the scale factor was two and you divided by two the area by two. That's not how it works.

[02:25:12]Item 59 refers to the diagram which shows an enlargement.

[02:25:17]O A A prime O B prime and O C C prime are straight lines.

[02:25:26]A triangle ABC is mapped onto triangle A prime B prime C prime by an enlargement with the center zero.

[02:25:36]>> What is the scale factor of enlargement?

[02:25:39]>> 2 C 2 >> C.

[02:25:49]>> All right. And question 60 in the diagram item 60 refers to the diagram the following diagram. The diagram above not drawn to scale shows the angle of depression of a point X from Z is 30°. If X is 10 m from Y, the height of Y Z in meters is a >> A.

[02:26:29]Everybody say how she got a >> Oh >> no.

[02:26:36]Okay.

[02:26:38]So if this type Yeah, I'm going to explain it. So, if the angle of the pressure is 30° here, that means that this angle here is also 30°, right?

[02:26:52]We have a right angle triangle and we're trying to find this length.

[02:27:01]So, this would be my opposite and this is my adjacent. So therefore I am using the tan of that 30° is equal to my opposite over my adjacent. So if I am finding opposite it would be 10 by tan 30.

[02:27:30]See you in question 58.

[02:27:51]>> Question 58.

[02:27:53]>> Alpha but um >> okay >> believe this is about to finish now. I think there should be less people than >> so in question 58 we can see that between triangles A B C and triangles M N O the scale factor is two right you see a not >> yeah miss >> right so if the scale factor is two then that does not mean that the scale factor for the area of the triangles is two.

[02:28:33]The scale factor for the area.

[02:28:37]So area scale factor is the square which is 2^ 2 of which is four. Right? So think of it as whatever your scale factor is. When you're thinking of the length, the regular triangle is two. But for area, it is going to be 2^ 2. So if it was three, the area scale factor would have been 3^ squ, which is 9, right? Because the triangle the area of ABC is 20. To find the area of Mn O, we are not dividing by the two. We have to divide by the scale factor for area.

[02:29:22]So 20 / 4 will give us I >> Okay, thanks miss.

[02:29:32]>> No problem.

[02:29:37]>> Miss.

[02:29:38]>> Yes, love.

[02:29:39]>> The question paper we will be able to work out the questions on it or we can we are not writing up on the paper here.

[02:29:47]Yeah.

[02:29:48]>> Yeah. Write on the paper.

[02:29:52]Yes, you can write on the paper.

[02:30:00]Do you all have any questions?

[02:30:07]>> Miss didn't do 59 and 60.

[02:30:09]>> Yes.

[02:30:12]>> Really?

[02:30:14]>> Where you was?

[02:30:17]But right here 59 >> and I work on >> right.

[02:30:30]How are you all feeling? Are you all okay?

[02:30:34]>> Yes.

[02:30:35]>> All right.

[02:30:36]>> Feeling confident. Not feeling confident, but I'll get through. Who said not feeling confident? Why you not feeling confident? You want another paper? You want us to do another paper confidence?

[02:30:48]>> No.

[02:30:52]>> I don't know. I just >> look at papers we did. Look at how many repeats there were. Even in the papers where it wasn't straight repeats, it was the same questions kind of worded differently. You don't have anything to worry about.

[02:31:22]I could do one more.

[02:31:25]>> What? One more >> paper.

[02:31:29]>> A whole You're not tired. You don't want to go and sleep.

[02:31:33]>> No.

[02:31:38]See, how do you not sleep this morning?

[02:31:41]sending the um solutions in the group chat.

[02:31:44]>> Let me download them to send >> How come you didn't do 2026 >> 202 January >> January?

[02:31:52]>> Yeah.

[02:31:54]>> Oh, I really did focus on the June papers. That's why I start from 2025.

[02:32:00]The only paper that I did January 4 was 2020.

[02:32:07]Um, hold on.

[02:32:16]I am going to download the papers to send them for you.

[02:32:26]I wish you all all the best tomorrow.

[02:32:31]Please God, you all will be fine.

[02:32:34]Do not go and overthink it. Read what they give you properly. That's the biggest thing I have with you all. Read the questions properly. Do not see something that looks familiar and just answer what you remember. Actually read to see if the question changed at all. Okay?

[02:32:58]And guys, if you really can't answer the question, you really don't know what to do anymore. Eeny meenie miny, >> do not miny. Oh my goodness.

[02:33:08]>> That the best solution miss.

[02:33:14]>> It does not work.

[02:33:16]>> Miss, it work. I did it and get a question.

[02:33:19]>> Hey, that was one of the answers. See, you know, >> not no go with that. Most of the trying to frustrate me. Do not go with that.

[02:33:32]Most of the time, >> no, no, no. If you really look at the trends of CC fast paper answers, you actually sit down and you count them.

[02:33:41]They are usually miss.

[02:33:51]Okay, hold on.

[02:33:58]That's too easy.

[02:34:00]>> Wow.

[02:34:02]>> This all right.

[02:34:06]Do item 36.

[02:34:11]>> Now, you should be the one doing it, miss.

[02:34:14]>> No.

[02:34:19]I see. Wait.

[02:34:29]>> So, what is the answer?

[02:34:40]>> See, this question was this question wasn't the question that I given you.

[02:34:44]>> The answer is C.

[02:34:45]>> C. Yes. See miss. Yeah.

[02:34:47]>> Okay.

[02:34:49]It is an option that if you actually don't know the answer >> don't know the question >> number 30.

[02:34:58]>> Yes. When six is added to a number and the sum is divided by three the result is four.

[02:35:09]The answer is a better >> do not >> recording stopped.

[02:35:28]>> Okay.

[02:35:30]>> What do you recommend then miss?

[02:35:32]>> I recommend you work out the question.

[02:35:35]Read what they give you. All right. on the live are coming off now right >> mommy you don't know the question you don't know it best tomorrow please do not >> just pick analyze it >> thank you >> but imagine no but imagine you analy really don't know >> okay >> make sense of it intelligent >> all right so if you look at any multiple choice >> you have two questions at a real >> paper it could be mathematics physics anybody when examiners are when people are doing assessments for multiple choice it is done like this we have two answers that are definitely wrong >> the same thing she's saying >> two answers that are definitely definitely wrong the correct answer and an answer that would make you think it's the correct answer >> exactly that >> so if you definitely don't know what to do >> yes >> try to see how best you can figure out which two makes no sense at and the two that could be the possible answer work it out >> exactly that >> I going to say any me those two but don't do anymore at all please >> all right I told earlier I'm coming off the >> it is not proven that any me anymore works >> when this recording is ready I'll upload this recording I may record I may upload this live >> but when the full recording of the entire class is ready I'll upload that as All right guys, enjoy the rest of your night.

[02:37:09]>> Have a great night. Get some rest.

[02:37:11]>> All the best tomorrow.

[02:37:13]>> Say your prayers.

[02:37:14]>> Miss watch my message in the chat.

[02:37:17]>> I am not buying orchard. So you buy orchard for me. I tired.

[02:37:21]>> Wow.

[02:37:23]>> Miss orchard. I could >> enjoy your night too miss.

[02:37:29]>> Thank you love. All right, guys.

[02:37:39]>> Miss. Yes.