2026 05 24 - Maths F5 - P1 prep sessions - Jan 2025 P1

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[00:00:06]ugly.

[00:00:27]I had my Okay.

[00:00:37]>> Question.

[00:01:19]Hello. All right, I'm going to stick my rule real quick.

[00:01:51]Christina.

[00:02:15]This one a little green.

[00:02:27]I'm going to start. You guys could eat.

[00:02:28]Take your time.

[00:02:36]>> Well, we saw number one previous, right?

[00:02:39]Not many papers before. Hey, give yourself stop. What percentage of eight is 40? So 8 over 40 by 100.

[00:02:53]>> All right. So 0 is 0.

[00:02:56]4 into 4 goes 1 2 and then 2 by 10 is 20.

[00:03:01]>> The value of the digit two in this number. All right. So the two is in this position here which is two places to the right of the decimal point which means it's in the hundredth's place. So that's 2 over 10 squar. Okay, so this is the interesting way that they they did it.

[00:03:16]They didn't put 200, they put 2 over 10 squared. So watch out for that.

[00:03:20]Then this one is 17 squarus 15 squar then square. So if you know that 17 squar is 289 and 15 squar is 225 then that's a square root of 64 which is 8. If however you don't know that you can use a difference of two squares. 17^ 2 - 15^ 2 is the same as 17 - 15 * 17 + 15.

[00:03:48]That's going to give us 2 by 32 which is 64 and the<unk> of 64 as we know is equal to 8.

[00:03:59]Hey, you're back. All right. A bag of apples can be shared equally among six.

[00:04:03]Okay. So, we know the number of apples that is likely is 30.

[00:04:08]the minimum number, right? 60 could be there, 10 could 90 could be there. Sure.

[00:04:12]All right.

[00:04:15]Because we know so again if you want to do the kind of old old school kind of reduction thing to find the LCM, right? So two will go into this three times into this five times not into that.

[00:04:29]Three will cancel that not that but it'll cancel this one and then five one one and you multiply Right. Okay. Number six. 99 by 101 has the same. So that's 99 multiplied by 101 like 99 by 100 + one. Like 99 by 100 + 99 by one.

[00:04:58]Right. So that's option D.

[00:05:01]Uh which of the following sets is defined by X? So x is an element of z which is integers as whole numbers could be positive or negative and x um is greater than or equal to minus2 and less than equal to positive4 right so that starts from minus2 and goes all the way up to positive4 including all the numbers between all right then number four right so we've seen number four in quite a few papers in in a school the ratio of the number of pupils to the number of teachers is 20 to one If the number of >> Mhm.

[00:05:38]>> right so there so it means that 840 is 20 times the number of teachers. So if we divide by 20 we get 42 is D. Yeah very good N.

[00:05:53]>> Okay. All right. So Christine Kana and Zabi ask him a little feedback on his page. You figure with it cool. If you need a rework or anything no. Okay.

[00:06:02]Lovely. Thank you.

[00:06:03]All right. All right.

[00:06:06]Ranch area. How we feeling with this page? Good. All right. Ladies on this side. I know. But you okay with this on this page?

[00:06:11]>> Yeah.

[00:06:13]>> We go. Yeah. That was a really good one.

[00:06:16]>> So, this looks >> Yeah. I don't know how blurry on yours.

[00:06:20]Real clear on mine.

[00:06:26]>> It's kind of weird. Yeah. Well, just check on the board now. It's quite clear there.

[00:06:32]I don't know. Let's print this page out.

[00:06:34]I know. Okay. Item eight refers to the following van diagram. Hold on. Number eight. The number of elements in the shaded region. Okay. The shaded region is P union Q.

[00:06:45]So P union Q. So that's equal to P + Q minus P inter Q.

[00:06:54]So P so they give us P is five, Q is 9, and P intersect Q is four. So 5 + 9 - 4 that's equal to 14 - 4 which of course is 10.

[00:07:10]Okay.

[00:07:13]All students in our class play scrabble or checkers or both. 16% of the students play both scrabble and checkers. Um the number of students who play checkers only is twice the number of students.

[00:07:25]Okay, we need a diagram. Doing this without a diagram is an exercise in fully. I mean, don't get me wrong, you could do it. I just think it's better to do with a diagram.

[00:07:36]All right. So, Scrabble checkers. Scrabble checkers.

[00:07:42]16% play both Scrabble and checkers. We're going to put 16 in the middle here. How about that? Yeah.

[00:07:52]The number of students who play checkers only is twice the number of students.

[00:07:56]Okay. So let's say x students play scrabble only which will be 2x here.

[00:08:02]What percentage of students play checkers but not scrabble? So that's what is 2x. Okay. So all students in the class play either scrabble or checkers or both. So everybody right? If you add up those you get 100%.

[00:08:16]All right. So x + 2x + 16 is equal to 100, right? So that's 36 3x sorry 100 - 16 is 84. And therefore to find x, that'll be 84 over 3, which is 27. And if you want 2x, 27, sorry, no, 28, my bad, my apologies. 28 by 2 is 56.

[00:08:52]Yeah.

[00:09:00]>> Okay. Number nine. In which of the following pairs of sets is one set not a subset of the other?

[00:09:09]Factors of three are one and three and multiples of 12 is one set not. So a factors of six and factors of 12. So e is a subset or fully contain in f whole numbers and rational.

[00:09:27]Yeah. So whole numbers can be contained multiples of five. So multiples of 10 is contained here. So a >> all right item 11 refers to the following ven diagram which shows two intersecting sets. The number of students in each set is indicated 5 2 4 and then we have three. In the ven diagram we have students who play games right? H is hockey. V is volleyball. How many students play either hockey or volleyball but not both? Either hockey or volleyball.

[00:10:00]>> Yep. But not both. So five and four will just give us nine.

[00:10:05]Okay, cool.

[00:10:10]>> All right. So in class people, are you okay with this page?

[00:10:23]Right.

[00:10:33]Christine, are you okay with the speech?

[00:10:58]The set of positive integers that are divisible by seven is an example of an infinite set.

[00:11:07]Right? So the numbers just keep getting bigger and bigger.

[00:11:13]15, right? We saw 15 on Friday, right? So every time you exchange 260 EC for 1 US, you get charged a 10 EC tax.

[00:11:24]But think about it. If you exchange $1,1 US, right, and then they give you EC260, right? But they take out a 10 cent tax.

[00:11:38]What how much are you effectively getting? 250.

[00:11:44]So how many EC dollars will Leon receive if he exited 1,000 US?

[00:11:51]Yeah. So basically if you take a,000, right, and then multiply it by 2.5, you get 2500.

[00:12:02]So for every dollar he exchanged, he gets 250. So if he had $1,000, he'd get a,000 times the 250.

[00:12:10]Right.

[00:12:15]We saw 16 before a calculator which is marked 120 is sold with at a 30% discount. How much change would Susan receive if she pays with a $100 bill?

[00:12:24]First things first discount was 36. Next step, subtract your discount.

[00:12:41]Next up, find a change.

[00:13:09]Right. So they give us this table. Now >> we all want to do 718 first. Listen to that first. Now >> by selling a bag for 1140 we shall incur a loss of 5%. At what price should he have sold the back to gain a profit of 5%. Wow, this interesting.

[00:13:30]Okay, check this.

[00:13:50]Follow this. Right.

[00:13:52]If we make a loss of 5%. Right. When you lose 5%, what percent? Okay. Assuming you sell about 100. If you lose 5%, what percent you have left?

[00:14:02]>> So 95% of the the selling price, >> sorry, of the cost price.

[00:14:11]is equal to 1140. So, so this was the selling price. So, he sold at a loss which means the selling price was less.

[00:14:18]So, to find the cost price, what would we do? We divide because we multiplied, right?

[00:14:30]>> 0.95 >> or I mean you could always if it's 95 over 100, you multiply by 195, right? So to find the selling price we could do 1140 multip sorry by 100 over 95 because that's dividing by and then of course if you want to if you want to gain a profit of 5%. If you want to gain a profit of 5% the relative percentage is 105% right? So you multiply that by 105 over 100. So what will happen here is check it right the hundreds cancel 5 into 95 goes 19 times 5 into this goes 21 times so we still had to multiply by 21 by 19 that's so that's almost by one 1140 um >> but what we could do actually you know the better thing to have done was just to find 5% 1140 and add it on that was thing to do. No 114 that wouldn't make sense cuz 90 can't go into that. Okay. And we carry calculator. So what's the story with this 1140? Right. Define the selling define find the cost price and divide by the percentage. Right.

[00:15:51]Okay. If you had to guess, what would you choose? 1197 or 1254? Or does it seem like a 1256? I feel like it's 1285 cuz look at 21 over 19.

[00:16:04]I'm not going to give you a flush figure.

[00:16:07]Yeah. So here what we going So here we go. We're going >> We're going to treat a little bit, right? We're going to treat a little bit >> 114 by 21.

[00:16:21]>> Oh wow. It's exactly 1260. 1260.

[00:16:31]That's exactly six day. Really?

[00:16:34]>> Well, god damn.

[00:16:38]>> Yeah. Well, now you know, right?

[00:16:53]>> That's interesting.

[00:16:59]All right. So 18 >> cost of a machine is estimated to be decreasing at a rate of 10. Okay. So that's depreciation. It currently cost 6,000. What would be the s after after two years?

[00:17:13]We check it right.

[00:17:15]We have here one. So we have the um so we have years the value at the start minus the depreciation equal the value at end. We have two years worth of depreciation to deal with. Right? So it's probably going to be option C to be honest.

[00:17:35]Yeah. Is C. I'll tell you why. The value start is 6,000. You're depreciating at 10%. What's 10% of 6,000?

[00:17:44]No 600. Right?

[00:17:49]The value of the end of year one becomes the value of the start of year two. 10% of that is 540.

[00:17:58]So of course you can do 540 5400us.

[00:18:05]So 0 6 that All right. Yeah. So that that number 17.

[00:18:23]>> Yeah. That's very interesting.

[00:18:29]>> Okay. Um I want to scroll back to do 13 and 14.

[00:18:33]You okay so far?

[00:18:35]>> Okay.

[00:18:38]So 13 and 14 with the following diagram.

[00:18:40]Shopping bill. Okay. So let's scroll it.

[00:18:42]Zoom in.

[00:18:44]So we do have Q and we don't have we don't do have P QT so the correct value oh we have to find all is that three for one so 4 * P gives us 1240 so to find P it would be 12 40 / 4 right 4 goes into 12 three times and 4 into 4 goes one so well 4 10 times so 310 so we have two options with 310 for P okay 10.

[00:19:16]Right? Now the next thing to find would be t because look to get t you have to if you add these three things you get 40 and 40.

[00:19:25]So 1240 and 720 is 1960.

[00:19:29]So if you take 40 40 and you minus the 1960.

[00:19:35]So 196 1940 from that will give us 21 minus an extra 20 cent is 2080 right so so t is 2080 so t is 2080 which is woo so 310 310 20 80 20 so the the the deciding factor here is option B that's quite interesting right and to find that to find that would be 208 divided by 8. Well, it can't be six something for sure. 6 by 8 is 48. So, it had to be 260.

[00:20:12]>> Wow.

[00:20:15]>> Uhhuh. Is this accounts? Uh, no. Even though we're looking at a little bit um >> Okay. And then according to the to the bill, the amount paid for VAT would be So, you had to find 8% of the 4040.

[00:20:29]Okay. Cool.

[00:20:32]The VA percent is 8% of 4, right? Um, so what we could do here is you can multiply if you want. So 40.40 by 8, right? So 0 32 carry the three 0 by 8 is 0 + the 3 and 4 by 8 is 32 32 4 by 8 is 32 Christopher.

[00:21:06]Wow. Okay. And then if you divide by 100 it's going to shift this two spaces. So you're going to get 3.23 >> 3.23. Do I do individual? If I have space available I do. Yes. If you need to find out, you could always DM me and we could go from there. Oh yeah, evening melon. No problem. Yeah, even if I can't do it, I have many friends who are very good. Right. Um, >> you said >> yeah. So we didn't >> the end of today. So by half past 8 >> we we would have been that's the second one for 24 this is 25 and then by after this one we do 26 >> well I don't have May 226 and even if I did I wouldn't do it >> all right okay um Christine Katana just give a little gen or a thumb if if you're good with this page this page was a little challenging to be honest with a with 17 and a couple other things there.

[00:22:16]>> All right, ladies. So, um Kim Ranches, are you okay with this page? Ladies on this side, you okay with this page? All right, going again.

[00:22:23]Okay, so we are a little a little slower than previous, but that's okay. We're not behind. A man pays 60 cents. Okay, we know this one.

[00:22:32]So, we know the fixture is 1375, but we had to be able to show that, right? 60 cents for every 200 cubic meters of gas used plus a fixed charge. If he pays 17875 in total when he uses 55,000 cubic meters of gas, how much is the fixed charge? So first things first in if you have if you're using 55,000 cubic meters and your unit is 200, you have to divide that to show how many units you use, which you'll then multiply by 60 cents, which is 60 over 100, right? And then whatever you whatever you get there, you're going to add to the fixed charge and that's going to give you the 17875.

[00:23:10]Right? Now, if you're watching across to the next side, um the 165 might be a very good candidate because you have a 75 cents there and a 0 there, which if you add, you'll get this. But again, that's not necessarily Sorry, I mean the 1375. My bad. Yeah.

[00:23:28]So, that's not necessarily um the way to go after it. But if we if we look inside that bracket, what can we cancel along?

[00:23:34]Anything?

[00:23:36]Yeah. Uh we could do a zero here and a zero there. A zero here and a zero there. Two zeros there, two zeros there.

[00:23:44]2 into 6 goes three times. And 55 by 3 is 158 + 15 which is 165. So 165 plus the fixed charge is 17875.

[00:23:56]So now if we do 17875 minus 165 we will indeed get 137.

[00:24:15]All right.

[00:24:18]Okay. The compound interest on 12,000 for two years at 10% and I'm compounded annually is okay. So there's a formula.

[00:24:26]I prefer a little step by step, right?

[00:24:28]So just like with the depreciation, we'll do like a little table, right?

[00:24:36]So you're going to add your interest to your balance at start to get the balance. So in year one, you have 12,000.

[00:24:42]The interest is 10%. 10% of 12,000 is 1,200.

[00:24:47]When we add that together, we get 13,200.

[00:24:50]And the balance at the end of year 1 becomes the balance at the start of year two.

[00:24:58]10% of that now is 1320. Now we don't even need to add going across but we will. That's 145. But what they ask for is total interest. So when you add these two together you get 2520.

[00:25:19]All right, let's do number 21 and we'll scroll back up to the 22. Right. The product of a number P and its reciprocal may be written as the reciprocal of P is simply 1 / P. So that's option D.

[00:25:35]Okay. So we're about onethird of the way through the paper in about 25 minutes.

[00:25:38]So that's okay. That's not bad.

[00:25:41]Not the usual, but again we have some new questions here.

[00:25:46]So item 22 refers to the following.

[00:25:48]Okay, so back up to the right hand side.

[00:25:51]If the area of the rectangle, what did we No, we saw something similar with trapezium is x squ. The equation that may be used to find the value of x. Okay, so the area of our rectangle is length by breadth by that. So the area is equal to 2 by x - 4, which is option A. It's just staring at us right there.

[00:26:19]Okay, Altha, Bob and Chris collect shells. Altha has pa shells. Bob has twice as many shells as Ala and Chris has four more than the total number of shells that Altha and Bob have collected all together. The total number of shells they have. Okay, let's take it one at a time. Ala, Bob and Crease, right? Alsa has P shells. Bob has twice as many shells as out there. Chris has four more than the total number of shells. The total number of shells they have is P + 2 P, which is 3 P. And he has four more than that. So if you add these together, you get 6 P + 4.

[00:27:04]And if you factor out the two, you get 2 by 3 P + 2.

[00:27:24]See if you say anything.

[00:27:32]>> We don't live in reality.

[00:27:35]We don't live in reality when it comes to these things. It's whatever they decide.

[00:27:40]Anyhow, this SBA, so maybe there's some >> I don't I think that's the best.

[00:27:56]>> You need the only SBI was physics. That was enough. You don't need a P, SBA, POV. You need PE, you need sciences, food and nutrition, plant textiles, anything practical. Cool. I think for like >> yeah large practical right but a research project find an aspect of the syllabus you want to explore nothing cool no SBA good when when for POA was a simulation where you had you got transactions to do like a whole account cycle that made sense for POB business plan projections okay cool Now we got to go and talk to our company questionnaire do this and then for P diagrams with charts and statistics what are you talking about any just me right okay so 3 + 2 overx = 1 then the value of x is so just look at this equation for a second right 3 plus something is one.

[00:29:06]Isn't one less than three? How do we add something to three and get a number less than >> if the thing we add is negative? So think about this three.

[00:29:19]How do we how do we what do we have to add to three to get one? What do what do we do to three to decrease it to one? We have to minus 2 which means 2 /x has to be equal to minus2. So if you multiply by x and then divide by minus 2 you get minus one.

[00:29:54]>> All right kids want to let me know how you guys are with this page. This page was a little better than the previous page. It was full of repeats except for Alia, Bob and Chris, right?

[00:30:04]And the compound interest one.

[00:30:11]So the max one, the math a little more interesting with some of these little twists and adjustments.

[00:30:19]All right, so we kind of know 25 already. Wait, when n is Oh, look at that. I saying it's the same thing. It's not when n is so five. So we have 5 to the n + 1 * 5 to the n + 2 when n is minus1. So we know that this gives us 5 to the 2n + 3. If n is -1 that's 5 by 2 to the by sorry to the power of 2 by - 1 + 3. So 2 by - 1 is what? That's - 2 - 2 + 3 1. So basically you have 5 to the 1 and 5 to the^ 1 is if 40 students take 20 days to paint a wall.

[00:31:08]How many days will it take to paint the wall of 10 more students are added looking the same rate?

[00:31:13]So okay I see your question again boy.

[00:31:24]All right. Hold on.

[00:31:28]>> All right.

[00:31:29]>> All right. So, hold on. Before you before you skip it, quick question. If you have more people working, will it take more or less time? It take less time. Cool.

[00:31:36]>> Now, check it. Will it take as few? If it's 40 students taking 20 days, could it possibly be 10 days? No. Because 10 days means half the time, which means double the students. If we only add in 10 more people, right? Now check this.

[00:31:50]If you consider what 10 over 40 is, what's 10 over 40? That's our quote.

[00:31:55]Right?

[00:31:57]So what that means is now let's follow al right.

[00:32:04]So you you now have 50 over 40 students.

[00:32:08]Sorry, you're taking 50 over 40 as long sorry as 50 over 40 is the number of times the original. Right? So this is equal to 5 over 4.

[00:32:19]So when you get when you establish the number the the the kind of the fraction relative to the original you invert it.

[00:32:26]5 over 4 becomes 4 over 5. Right?

[00:32:29]>> Multiplied by 20. Five goes into 20 four times and 4x4 is 16. Right? So let me let me explain a little bit more. Right?

[00:32:38]So let let's let's imagine it was you added 40 students. Right? If you added 40 students don't don't mind our cross here. Right? Go forget that person.

[00:32:46]Right? If I added 40 students, I would have how many? 80. Right? If I took 80 over 40, that tells me I have double the number of original students. Right? And then if I were to invert that and multiply it by the 20, right? I would take half the number of days, which makes sense. If I have double the number of students, I take half the number of days. So what you want to find is well, not double whatever the fraction or number of times is. And then you you'll divide the number of base by that.

[00:33:18]Right? So you could you could talk about the inversion or whatever. When you divide by a fraction, you end up inverting.

[00:33:25]Okay? So for this one down here, so this means the determinant of P. So for the determinant, we multiply the two yellows together.

[00:33:34]Multiply the two blues together. And then we do product of yellow minus product of blue.

[00:33:42]So 2 by 3 - 5 by -1. 2x 3 is 6 - 5 by - 1 is a positive 5 and 6 + 5 is >> Yeah.

[00:33:59]>> All right. Item 29 refers to the following diagram of a par. Okay. We did this one already, right? Um so in a parallelogram, the opposite sides are parallel equal.

[00:34:11]So E and F are parallel and equal as EH sorry I mean EF EF and EF and HG are parallel and equal to each other as EH and oh is EH and E EF and HG are parallel and equal as are EH and FG.

[00:34:33]Okay. What the implication therefore is that the vector here is the same as the vector here and the vector here is the same as the vector there.

[00:34:45]So to go from E to G, I have to go from E to F and then F to G or E to H and H to G. Either way, I'm going to add M to K, which will give me D K plus F. So whether you have K plus M or M plus K matters. Now addition is commutated there. H.

[00:35:06]All right. So, we saw 30 already. So, we'll do it quickly. All right. 5 by X.

[00:35:11]Sorry, my bad. One second.

[00:35:17]All right. So 5 by X is 5X and that's equal to 4x 10, which is 40. So to solve for X, we will do 40 / 5, which is 8.

[00:35:29]And then right 5 by y is 5 y 4 by 20 is 80. So to find y we'll divide 80 / 5 which is 16.

[00:35:47]Um so what was the answer here? 8 and 16. That's option B. Nice.

[00:35:53]Um and 28. Now the order. So the order of a matrix is a way of referring to it by citing the number of rows and the number of columns. So this is a 3x four matrix. Yeah.

[00:36:08]All right. So we at the halfway point uh at 35 minutes or so. So that's not bad.

[00:36:13]Okay. Uh Christine Zavia and Kitan, let me know how this page was for you. If there's anything you want to go over or reexlain, let me know. All right. All right. Kazari, how are we with this page? Any particular one you have in trouble? Anything? No. All right. H.

[00:36:29]All right. Cool. Shift to next page. Do one more slice of pizza and then go.

[00:37:12]What else?

[00:37:26]So if the diameter is six that means that the radius is three.

[00:37:33]Volume of a cylinder is<unk> by R 2 by height.

[00:37:40]That's 22 over 7 by 3^ 2 by 21.

[00:37:45]So what's going to happen here is 7 will cancel with 21 three times and then you have 22 by 3^ 2 which is 9 and then 9 by 3 is 27.

[00:37:58]Okay.

[00:38:02]So you end up with 540 + 54 is 594.

[00:38:08]All right. Top right on a sec.

[00:38:24]The three lengths of a triangle are x, 2x, and 2x. And the perimeter is 20.

[00:38:29]What is perimeter? Total distance around the edge of the shape. We have x + 2x + 2x.

[00:38:37]Total there is 5x 5 x is 20. X is equal to 20 / 5 which is ah they come back here with the same trapezium but now they want it in millimeters.

[00:38:56]>> 1 meter is equal to a,000 mm. So in each case here you have meters. So to convert to millimeters you'll multiply each of these by a th00and. Oh divide you. See for number 31 here. So you'll have 120.

[00:39:12]So starting from here and going clockwise, right? So 120 + 410 + 210 + 180.

[00:39:21]So that's 920.

[00:39:24]That's deep.

[00:39:39]We've seen this quite a few times before.

[00:39:42]>> How long?

[00:39:44]>> How long?

[00:39:51]>> So time how long? Huh?

[00:39:56]So speed is equal to distance over time.

[00:40:00]So speed by time is distance.

[00:40:04]If they say hold on they want time. So time is equal to distance over speed. So that's 1080 over 120. Knock out the zeros. And 12 by 9 is 1080.

[00:40:35]A rectangular garden put 15 by 12.

[00:40:39]15 by 12 is 180. If 80 m is used for gardening, it means 100 m is not used for gardening.

[00:40:52]>> Right?

[00:40:59]>> Sorry. Divide 32 is B. B for 33.

[00:41:06]E for 33 is correct for 32 as well.

[00:41:20]This pageine let me know if you guys are page good again.

[00:41:34]Where's that way?

[00:42:04]Item 36 refers to the phone diagram.

[00:42:07]There's a circle centered at O. The major sector and minor sector are indicated.

[00:42:14]If the area of the major sector is 115.5, the diameter of the circle is okay.

[00:42:21]That's interesting.

[00:42:23]What does this symbol here mean? How many degrees?

[00:42:29]90.

[00:42:30]What is the total degrees in a circle?

[00:42:33]360.

[00:42:35]>> Which means that the remainder across here is 290. The area of a sector is the angle 270.

[00:42:43]The angle in the sector multiplied by the area of the circle that's 115.9.

[00:42:50]Now 270 over 360 is 3/4. So 3/4 of the whole circle 115.9. So if you multiply by four 440 20 460 plus a half is 462 and then we divide by 3.

[00:43:11]So that's 154. Now that is the area of the circle. They want the diameter.

[00:43:17]So area is equal to p<unk> pi r².

[00:43:22]So the area is 154 that's equal to 22 / 7 by r 2.

[00:43:31]So if you do a little marks 154 by say you multiply by 7 and divide by 22 you get r 2. So that goes 7 * 7 by 7 is 49.

[00:43:45]So to find r we square root 49 which we get seven. And to find diameter, we multiply that by two.

[00:43:55]Yeah. Why is this a multiple question?

[00:43:58]Is there is there an easier way to find it? I wonder though interesting.

[00:44:09]That one had some work in it.

[00:44:12]Okay, let's do 38 and then backtrack to 37.

[00:44:18]The 38. The distance around the lake is 8 km in real life. On a map, this distance is around the lake is represented by a length of 4 cm.

[00:44:28]The scale on the map. So 4 cm on the map represents 8 km in real life. So we could we could start off by dividing by four. So 1 cm on the map represents 2 km in real life.

[00:44:44]So if we scale up so kilometers to meters is a th00and right. So that and then meter centime meters is multip by 100. So you have 200,000.

[00:44:56]So yeah option D.

[00:45:03]Right. And now the surface area of the compound solid in the shape above.

[00:45:08]They're kind of wicked with this boy.

[00:45:10]All right.

[00:45:15]So we have we have five faces for the shape the cube in the bottom right we have the >> cm 200,000 cm Right. So the bottom the bottom face here is 12x 10.

[00:45:47]Right? So 12x 10 is 120. Right? Then you have the front face and the back face and those are both 10 by 10. Right?

[00:46:02]And we'll double that one time. 10 x 10 is 100. 100 by two is 200. And then you have the side face and then the other side face opposite. And that's 12x 10.

[00:46:13]So it's two of those 12 by 10. So 12x 10 is 120. Doubling that you get 240.

[00:46:19]Right? Now we don't have the top face here because the other shape is lying down on that. So those those so the the yeah those two faces are touching and not on the surface.

[00:46:32]So 1 2 3 20 that's 5 six so far right now we're not done right now on the top now we have two triangular faces here and here right so that's base by height so the height is 8 and the base is 12 so 8x 12 over 2x two so the the the over two and the by two will cancel so we'll just do 8 x 12 and that's 96 uh the face to the back face to the back here is 8 by 10, right?

[00:47:03]So the 10 corresponds to here and to here and to here, right? And it's just one face, one 8 by 10 face, right? So that's 80. And then the face on the front here is a rectangle and that's 13 by 10.

[00:47:22]All right. So 90 and 96, sorry. So that's a six. So it's either A or B, right? Um 90 and 80 is 170. 170 and 30 is 300. So it's 300 and 6 plus the 560.

[00:47:39]Well, that Okay, that's 866.

[00:47:42]Why is it so much working for a multiple choice question?

[00:47:49]>> Yeah, boy. Make it easy. Um Multiple choice for maths makes no sense and for ad maths makes less sense especially with some of the questions.

[00:48:04]Yeah.

[00:48:05]>> Yeah. On top of which you don't have a to use one in ad for sure but maths >> I don't mind you all not having to use a calculator but if that's the case then don't give youall some of these questions to actually >> no I don't mind having some calculation base. I don't mind that.

[00:48:30]I wouldn't I wouldn't say that. I wouldn't I wouldn't say that.

[00:48:35]>> Who wouldn't say that?

[00:48:38]>> All right. All right. Give more Russia.

[00:48:40]We give this page. All right. Christie and Zabi, talk to me. We all right with this page. This is some Russia. But I say more than usual, you know, not not a whole set, but it could bo Yeah, because we I want to I want to clock. I want to end this by seven. Um in the corner, you okay with this page?

[00:49:00]Okay, we almost to the 2/3 mark here.

[00:49:04]Um refer to the following table which shows number of words that a group of 60 students got correct. The mode of the number of words spelled correctly would be the number of words got correct by the most number of students. So seven 18 students got seven words correct.

[00:49:25]Seven is the most the median number of words spel. Okay. Right. So we're in a CF. So there's the frequency need a cumulative frequency. Right. So we add 3 and 18 gives us 21. 21 and 7 is 28. 28 and 16 is 44 and 16 is 60. Wow. But they give us right. So n + one. So 60 + 1 / 2 means 61 / 2. Which means that's the 30.5 mark. So we do have a 30 point. We need the 30th mark and the 31st mark. Well, 31st data point to find their average. Now, interestingly enough, both of those are nine because look after after data point 28, you have data point 29 and data points 29 to 44 are all nine. So, the median is nine. Okay, so we at the 2/3 mark. We uh 2/3 we are marking the paper. So, we have just 20 questions to go. We should be able to finish up by 7, take a little break by 7:15 and then finish by 8:30, provided Jan 2026 was not a serious departure from the the norm.

[00:50:37]All right.

[00:50:40]41. Item 41 refers to the pie chart which shows the popular games played by a group of students. Basketball, cricket, tennis, football. All right. So football is an angle. If 180 students play football, how many students are in the group? Okay.

[00:50:58]So, 30 and 35 and 36.

[00:51:11]Um, sorry, what am I am I confused? Because um I'm 35 and that's not 111%.

[00:51:25]I wonder if the adjustments cuz for if 180 >> Oh, no. You know what? Yeah. Look >> over 180 or 360, >> right? So, this is 90° here, right? So, if you have 90 out of 360, right, that's a quarter.

[00:51:49]So a quarter by the number of students is 180. So therefore n will be equal to 180 by 4 which is 720.

[00:52:01]Yeah.

[00:52:04]Okay. That's interesting.

[00:52:07]Item 42 refers to the following chart which shows the amount of fish bought in kilograms by the first 60 customers in a fish market. All right. Cool. Um right.

[00:52:17]How many customers bought at least six fish? So at least six means six or more.

[00:52:22]So if you read across you get 11 people buying six. 11 people bought six.

[00:52:30]Uh five people bought seven. Four bought eight.

[00:52:37]Uh seven bought nine.

[00:52:42]Hold on. No this number wrong.

[00:52:47]Five people bought seven.

[00:52:52]Four people bought eight. What? Oh, I was right. Oh, ow. I was writing the wrong number. Whoa. And then three people bought 10. My bad. My bad. My I don't care anyway. 514 is nine and is 20. 7 is 10. That's 30.

[00:53:09]So 30 student.

[00:53:13]All right. And add this page.

[00:53:16]All right. All right. Christine, Zavi, and Kitan, are you okay with this page?

[00:53:22]>> Let me know how we go there. All right.

[00:53:24]All right. Sharing with that page. Good.

[00:53:27]All right.

[00:53:29]Ladies in the corner here. Are we okay with this page? Yeah. All right.

[00:53:33]Again, water go, right?

[00:53:39]Item 43 refers to the following diagram and shows this the Okay, so it's a little wavy. The cumulative frequency curve of the height of 20 ceilings is semi- interquartile range. Okay. So semi interquartile. So a quarter of 20 is five. The 3/4 mark is 15. Okay. So five will go that line is a bit a bit too heavy on the weight there.

[00:54:04]Let's let's zoom in.

[00:54:13]Is that passing? No, that is passing through the halfway point there. Okay, cool. So 1.2 1.4 1.6 one. So this is 1.3 and if it 15 and then read down that's 2.6. Well, that's what I got.

[00:54:32]Yeah. And then 2.6 minus 1.3 is itself 1.3.

[00:54:45]Uh let's do 45 and 46 before we go down to 44 and the rest shall we? All right.

[00:54:51]Uh which of the following line graphs represents x is greater than minus2 but less than equal to? Right. So for the greater than you would have an open circle but for the less than equal to it would just be a closed circle. So, we're looking for an open to the left and a close to the right.

[00:55:10]>> That's option D.

[00:55:13]Cool. 46. Now, which of the following represents the equation of a straight line? That's option B. Right? Not just because it's in the form y= to mx plus c, but because c and d both have a highest power of 2, which means that they are quadratic and this is an x to the minus1, which is an inverse function, which is nonlinear, right? 44 and 47 600 students sit an exam. The probability of randomly selected of a randomly selected student failing. Oh, so now they give us the failing and actually pass. So if the pro >> Yeah. So we had a reverse. So if 1/5 fail it means four fifths do not fail.

[00:55:53]Four fifths of 600, right? Yeah. That's 48.

[00:56:02]>> She said yes in Spanish. Anyhow, Right. So to find the gradient here, we want to express it in the form y = m by x + c. So we'll divide by two throughout the equation. So y would be equal to -3 /2 by x - 8 / 2. The gradient being the coefficient of the x term, which in this case is 32, right? All right. Uh and Christina just never know.

[00:56:31]>> Wait, sorry. We had to go back. Where?

[00:56:34]It said semi-enterile range guys. It said semi interquartile range.

[00:56:42]>> Wow.

[00:56:45]>> Yeah.

[00:56:47]>> So we have to divide. Sorry. Thank you very much.

[00:56:53]So that point >> that is divider. No no sorry. Sorry. I really I really don't know. That's what you said. I really decay.

[00:57:04]Yes. Yes. Yes. Yeah. Me too. It should be a that is correct. That's correct. I stand corrected.

[00:57:14]And the good news, good part about that is that we're making it here. So we see what went wrong and what wrong is. We did not read the question properly. So what is the morning story? Read the question properly. All right. Cool. All right. Shazari and Kimar, you okay here with this page now?

[00:57:29]>> Ladies on this side. You okay here with this page?

[00:57:31]>> All right. Lovely.

[00:57:33]>> Right. So they bring back the diagram that they left in the previous um toilet paper. Your name is Josh. All right, Josh. Thank you very much.

[00:57:41]>> Thank you, Josh.

[00:57:42]>> We appreciate you. Yeah.

[00:57:51]>> Yeah, you just did.

[00:57:55]>> All right. So the maximum point is here, right? So if you read down to the X, it says two across to the Y, it says four, right? So we get 24 2 for the price of 1 and 49. According to the graph, the solution of the equations y = 4x - x^2 and y = 0. So y equal to 0 is the x ais.

[00:58:25]So what it's saying here is okay where on the diagram does the graph cut the x- axis and it does so at two points does so at zero and at four. So 0 0 and 4 0.

[00:58:40]>> So when x is zero and y is zero and when x is zero and y is sorry x is four and y is right. So yeah very weird we are saying that but okay cool.

[00:58:53]Yeah.

[00:58:55]Okay. Uh I'm I'm thinking as a 4x^2.

[00:59:00]So we want h of a half.

[00:59:04]>> Yeah.

[00:59:06]So 4 by - a half squared. When you square something, what are you actually doing? Multiplying it by itself. And a minus by a minus will give us a plus. A half by a half is 14. And a quarter of four is 1. 1 - 6 is - 5.

[00:59:24]The line L is perpendicular to this line. What is the gradient of line L.

[00:59:29]So, first things first, we're going to make Y the subject here by just cutting it across there. So, y would be equal to 2x - 8, which means the gra gradient of this line is two. So, of a perpendicular line means you're going to put minus one over that value, which will give us b.

[00:59:53]scrolling down. Okay. So, right lunch and cheese.

[01:00:06]>> Which of the following sets is? Okay, we know this one already this one before.

[01:00:10]So, basically all we doing here is substituting, right? So, if this is these are the x values you plug in one.

[01:00:17]So 0 2 is 0. 0 + 3 is 3. So when x is 0 and y is 3. Cool. Next 1 2 is 1 + 3 is 4. So there's only two of the possible options here. And then two. 22 is 4. 4 + 3 is 7. So 2 and 7, right? And then 3 2 is 9 + 3 is 12. So there's only one option with 32. So should have start with three.

[01:00:42]Okay. All right.

[01:00:44]All right. She's Arian Kim. Are we okay with this page?

[01:00:47]All right. Hold. You okay with this page? All right.

[01:00:50]>> All right. Kana Zavia and Christine, we okay with this one?

[01:00:55]>> Yeah. All right. Cool.

[01:00:58]Okay. We're in the last eight questions or so now. Hey, look at circle geometry, buddy. What the value of y is 61, right?

[01:01:08]Because that's the angle. The angle at the center is double. So the angle here is double the angle of the circumference. So 122 / 2 is 61, right? This would also equal 61 here, but it didn't ask for that. Uh this one across here. So we have two parallel lines, right? PQ and RS are mutually parallel, right? Which means that when the transversal cuts them they form they have Z angle being formed which which are X and Y. So X equal to Y. Long story short oh wait I didn't share the answer correctly. The answer is C. My bad.

[01:01:56]All right.

[01:02:04]>> All right ladies and ladies in class.

[01:02:06]You okay with this page? I was in two questions. Okay. Circle geometry and right. Cool. Christina Kana and Christine Kana.

[01:02:17]Good there. All right. Lovely. All right. We have a whole page for one thing. All right.

[01:02:24]Item 55 refers to the following diagram.

[01:02:27]It shows triangle ABC. Okay. Let me get some colors going here.

[01:03:05]She probably could somewhere.

[01:03:11]>> All right. So, green went to blue and then blue went to orange.

[01:03:17]I'm going to guess, not guess. So, if you look at the green and the blue, that is like a reflection, right? and to analyze where that that mirror line is.

[01:03:27]1 2 3 4 5 6 7 8. So the mirror line will be halfway between which would be here.

[01:03:37]So that's that's passing through. So if you look at the x axis now to find the coordinates. So zero. So four. So 4 3 2 1 right? So that's x equal to 1. So a reflection in the line x = 1. And then we went from blue to orange. So that's a translation.

[01:03:57]So we had to go how many places? So one, two, three to the left and then one, two, three, four down. So going three to the left is a -3 and four down is a -4.

[01:04:09]So reflection in the Oh, option A. Wow.

[01:04:13]Okay.

[01:04:15]This I don't recall ever seeing this question. I mean, we have we've had one with a double uh a composite track before, but not this one.

[01:04:25]>> That's the funny part. Some of the weird ones, the answers.

[01:04:32]All right. Okay.

[01:04:35]Everybody in class, we okay with this one here? All right. Google Meet, let me know.

[01:04:44]Yeah. Okay. All right. In the last five questions now, uh, in each of the following diagrams, A prime is the image of A. Which diagram shows a reflection in the X, right? So that's a reflection in the X means you're going to reflect down here, right? So the diagram that has that, I believe, is diagram D. Yeah, that's a reflection in the X axis.

[01:05:10]57. Okay, we saw 57 already, but I mean, we're going to do it, right? So let me do the thing.

[01:05:17]In ABC angle X is that and B is that what it says angle. Okay. So the sum of the angles in a triangle is 180. So if we have two of the other sorry if we have two of the angles to find the third one we'll do what? We'll add them together and then subtract from 180 and x + 2x is 3x and 3x - 180. 3x from 180.

[01:05:43]>> That's degrees.

[01:05:49]Item 58 refers to the following. Okay, so the angle of elevation. Oh, so they've actually given us the elevation now. Okay, interesting. If X is 15 m from Z, then the height YZ. Okay, this is interesting, right?

[01:06:10]How much?

[01:06:15]a half inch bound to wear heels.

[01:06:20]You guys saw that one on social media.

[01:06:22]This the tall girls met up on Tinder and she went to his house and she was like tall. He was even wearing like lifts and like >> Yeah. And she she she thought he was like like insulting her and like no and it went for coffee. But he was like down here any unnecessary.

[01:06:46]>> Right? So relative to the 35° angle, this side is opposite and relative to the right angle, that side is >> hypotenuse.

[01:06:56]>> So sin 35. So if it's opposite, so we know sign right. So that's option C.

[01:07:07]>> Do the full work, right?

[01:07:09]So sin 35 would be equal to y z over hypotenuse 15. So we'd multiply 15 by both sides to solve for y z.

[01:07:31]>> Sorry is c for which one? For 58. Yeah.

[01:07:34]Yeah. All right.

[01:07:36]level grade 11. Is that grade 12? Is that grade 12 or grade level six?

[01:07:43]All right. Okay. Um Christine Kan and Zabi all the feedback on this page on tanks. We good?

[01:07:51]>> Yeah. All right. Ranchers, are you okay with this page? All right, ladies on this side. You okay with this page? All right, last page now.

[01:08:04]Okay, so pair of similar triangles.

[01:08:07]Okay, so check this. Right.

[01:08:11]So this this side and this side correspond.

[01:08:16]The reason that they are similar triangle because look you have 31° here and 31 here. Right? You then have a 59 up. Sorry I was very sure I selected a different color. Right? You then have 59 up here and 59 here. And they both have a right angle down in the corner. Not so right. Boom. Boom. Cool. So, because the corresponding angles as in the angles in the same relative positions are equal, we know that they are called similar triangles, which means there's usually a scale factor element. And if we observe the six and the three, those are two corresponding lengths. Now what that means is that the corresponding length in the bigger triangle sorry are double. So these lengths are double the the corresponding as in the smaller triangle. So if you reverse that right that's correct. Yeah you get half. So if this is seven to find the corresponding you multiply seven by half and a half by seven or 7ide by two is 3.5. Right.

[01:09:24]And finally the last thing we have here.

[01:09:28]So under the translation minus 23 the image. Okay. So - 23 is the translation and you just add it to - 53.

[01:09:38]So -2 + - 5 >> and then 3 + 3 right? -2 + - 5 is - 7 and 3 + 3 is 6. So your answer here is - 7.

[01:09:52]Okay.

[01:09:55]Six to C and you said it was B. Yep. So, good. So, Joshua and divider on the wall, man. All right. Lovely. Lovely.

[01:10:04]Make it easy. Oh, easy.

[01:10:06]Okay.

[01:10:08]>> All right. So, Christine, Kana, and Zabi, are we okay with this last page here?

[01:10:13]>> Yeah. All right. Shar with ladies in the corner. We Okay. All right, folks. So, we'll take a break there for about um Yeah, man. No problem. We have one more to go for the day, but we take an actual break, right?

[01:10:27]So, let's So, it's 6:55 now. So, we'll take about a 50 minutes. Uh I'll print out some papers for those who need the papers. All right. So, virtual break, get a little dinner or something, right?

[01:10:38]So, it's 6:55 by my clock or just about.

[01:10:41]So, by 710, we logging on. So, by 7:50, we start. All right. We're hitting the 2026 jam.

[01:10:47]All right. So, what that means? So um but Google meet you can stay on right