2026 05 25 - Maths F5 - P1 prep sessions - May 2019 P1

追加: 2026-05-26

[00:00:07]All right.

[00:00:09]I like going there. All right. Let's Let's staple up some hot Daniel, how you doing, Daniel?

[00:01:06]All right.

[00:01:09]>> All right, folks. Morning. Sorry for the slight delay in this time. So, we know the drill, right? Basically, you're just kind of running through and talking through these papers. We're not flying through them. We're discussing them, working them out, putting the work in, etc., etc. Right? So, let me just open up a little thing on this side here and we shall begin. Oh, hold on.

[00:01:38]No, I I hear in class. Um, she's home, but she might have gone back to sleep.

[00:01:44]Yeah.

[00:01:46]Okay. Bye.

[00:01:51]All right. So, you can go ahead and start if you want there with nobody. Not in the Olympics. I know. Reason I started but not this.

[00:02:17]Okay. Yeah. So, I had a B We'll cut the break between fish in terms of what we got to do and when.

[00:02:30]Okay. Um here's cool. All right. So with that, let's um start.

[00:02:47]>> Okay. So uh -3 all^ 2 + -2 all^ 2.

[00:02:54]So when you square something what are you actually doing? Multiplying it by itself right and when you multiply a minus by minus you get a plus. So - 3 2 is 9 - 2 is 4 and 9 + 4 is simply going to be 13 as option C. All right. Next question. What number when added to 1 and 1/3 gives two? So what number when added to one and 1/3 gives two. So basically you're asking well how many what do I need to add here right? So I mean you could do it like the regular transposition where by subtracting 1 and a3 from two that'll give you 2/3 right simple enough where now again remember you don't have calculators so if you need to do a fraction subtraction so of course 2 is 2 over 1 and a3 is 4 over 3 common denominator is 3 2x 3 is 6 4 by 1 is 4 and 6 - 4 is 2 all right number three we've seen before number three we've seen so 11.1 / 0 11.1 divided by 01. So you want to shift this point two spaces and how many ever spaces you shift that one? You have to shift the numerator the point in numerator the same number of spaces. So it's 1,110.

[00:04:08]All right. Uh we'll do six. So we saw six already in some of the January papers. The square root of 181. Okay. So if you know your square numbers, so we know 12 squared, right, is 144. uh 13 squared is 169 and 14 squar is 196. So 181 lies somewhere in the middle there.

[00:04:30]So that's between 13 and the square root of 181 lies somewhere between 13 and 14.

[00:04:36]Number seven. Number seven they like to back but which of the following sets is defined by so x is x is an element of z which is the set of integers as whole numbers which can be positive or negative. Um so x is greater than equal to minus2 but less than equal to 4. So that's option D right. If it was just the just the greater than sorry and less than it would it would be option C because it wouldn't include the minus2 and the four. But the presence of the equal means that they are included.

[00:05:08]Okay. Um next one. If a if equal to ABC how many subsets can be obtained? Okay.

[00:05:15]But there are three elements in Q and for any given set the number of subsets is always 2 to the power of n where n is the number of elements. So two and there are three elements. So 2 to the^ 3.

[00:05:28]Okay. So let's scroll down.

[00:05:32]Right? So we're on the right hand side.

[00:05:35]Right? 12% of a sum of money is four ts.

[00:05:39]Now if you don't know 12 1/2% is exactly equal to 1/8. So 1/8 by let's just say s for sum of money is equal to 40. So to solve for s what would we do? We would multiply by four.

[00:05:57]All right. So right so four by 8.

[00:06:04]Okay.

[00:06:08]One sec. I have to send them to print.

[00:06:14]It does say my only count is right, right?

[00:06:22]So print.

[00:06:37]Yeah. All right. A test was marked out of out of 80. The boy scored 60% of the marks. How many marks did he score? So 60% is 60 out of 100 by 80. Okay, cool.

[00:06:48]So of course, knock off for zero. Knock off for zero. Same thing here. And 6 by 8 is 48, right? If you find multiplying by 8 a little too difficult. Number eight is 2 by 2 by two. And people find multiplying by two a bit easier by eight. So that's a trick you could use, right? 6 by 2 is 12. 12 by 2 is 24. 24 by 2 is 48.

[00:07:10]All right. Item nine refers to the following ven diagram in the vendor. The number of elements in P is five. Number in Q is nine and the number in P union Q is 10. So if you lump together P and Q, you get 10. But you might say, but Chris, 9 and 5 is 14, right? So that's where the formula comes in, right? So P intersect Q is equal to the number in P plus the number in Q minus the number in the union. So 5 + 9 is 14, right? Then - 10 gives us hit me 24. Four. Wow.

[00:07:48]Hey, how you doing? Yes, that is correct.

[00:07:51]All right. So, okay. All right, ladies and gents in class. How are we feeling with the first page? Any questions, problem issues? Are we good? We good.

[00:07:59]All right. So, are you feeling it?

[00:08:03]>> Number six.

[00:08:06]Yeah. All right. All right. The following. Any questions? All right.

[00:08:10]Okay. Let's go to page two.

[00:08:15]All right. So, item 10 refers to the following prime, odd, even. Okay. Cool.

[00:08:20]Which of the following sets is empty?

[00:08:22]Well, that's um odd and even. The intersection of odd and even. That's Q intersect R, right? That means they have no common elements, no overlap. You could be there's one even prime number.

[00:08:32]It's a very small intersection, right?

[00:08:36]And then every every other odd number is prime.

[00:08:40]Okay. Uh 11. So P is 2357 as the first four prime numbers. Q is 236. Uh S is 245. So P intersect Q intersect S as in what is common to all three? Well, I'm only seeing one element there.

[00:08:56]The three is common there. Five is common there. Okay, cool. So just just two. This option A then put me on fire this morning. Good work, Mia. All right. If um so we we'll do 12.

[00:09:09]All right. Let's do 12. Let's do 12.

[00:09:12]V diagram. Okay. Um in the vin diagram, the shaded area. So everything except P is shaded and everything except P is P complement.

[00:09:23]Sorry. Yeah.

[00:09:25]Okay. So 13 14. Okay. So let's if if 6 TT is equivalent to one US, then 15 is okay. So how I tell people is $6 for a doubles which actually is true in most places right if I have $15 how many doubles can I buy to find that out I have to divide now 15 divide into six sorry 6 into 15 so the thing about it is you could divide by three you'll get two and you get five and then fiveide by two is two and a half so obviously we can't get two and a half doubles but it's US dollars you buy and you could get $250 2019 me yes web with me We we finished the January papers from 2020 to 2026. So now we do 2019 May to 2025 May. We're doing four papers today as funny. We'll probably finish tomorrow. Um I think unless we skip tomorrow and go straight to Wednesday cuz tomorrow as we could do tomorrow and skip Wednesday all they want. We'll ask in the chat or we could do over some papers or older papers. I don't mind. It's all they want to do.

[00:10:26]All right. If 7,000 is borrowed at a rate of 5% per year for 3 years, simple interest is so principal right by rate which is 5% which is five out of 100 by time which is three. I heard the gate there. So we knock off a couple zeros here and here.

[00:10:54]All right, not too far. We're now on the second page. The first page had some repeat some slightly new thing, but nothing overly difficult. And these questions were about the same.

[00:11:09]All right. Yeah. So here we 70 by 5 is 350. 350 by 3. Or you could do 7 by 10 by 5 by 3. Any how you want to do remember multiplication is commutative, right? So if we do 70 by 5 is 350. 350 by 3. Remember 300 by 3 would be 900. 50 by 3 is 150. When you add those two, you get 1050. Boom.

[00:11:34]A dress which costs $180 is being sold at a discount of 10%. The amount of the working 10% of 180 is 18. Right? This knock off a zero.

[00:11:47]And then the last question on this page.

[00:11:50]The value of a plot of land is $18,000.

[00:11:53]Land tax is charged at a rate of 70 cents per $100 of value. What is the total amount of tax paid? Okay. So you have $18,000 worth of land and you we charge based on $100 units. We have to divide and then we multiply that by um well 7 is that right? Okay. So we have plenty of zeros.

[00:12:14]We could knock off here, right? Knock off those. of that one of these two. So now it's just 18 by 7 which I think is 126, right? So 18 by 7. So 10 by 7 is 70. 8 by 7 is 56, right? Math Shamal is maths, right?

[00:12:36]Okay. So that's page two. All right. So ladies and gents in class, are we okay with page two? Any questions, problems, issues? Anybody? I know you're not jumping, but if you have any questions, let me know.

[00:12:46]Okay, cool. I don't see anybody online in the Google Meet, but I might just fill in the um but Kimora is here.

[00:12:54]All right, there we go again. Number 17. At the end of a year, any year, a car is worth 5% less than what it was worth at the beginning.

[00:13:07]If a car was worth 9,500 in December 2016 and its value in Jan Oh, so it's a backwards depreciation.

[00:13:15]So, so check it right. What they're saying here is that so the value value at start let's call it S right minus 5 5% of S right is equal to the 9500 ultimate. So S if you want to talk about percentages, S is what percent of itself? S is 100% of itself, right? So if you minus 5% from 100%, what we get?

[00:13:45]We get 95%.

[00:13:52]But 95% is 95 over 100. So to find S, you could divide by 95 over 100. And when you divide them by fractions was the protocol, ladies and gents, you change divide to multiply and you invert the fraction. So you'll have 100 over 95. Now the interesting thing here is 95 goes into 9500 100 times and 100 by 100 is 10,000.

[00:14:19]Yeah. So those backwards one.

[00:14:21]Yeah. Like depreciation here. Can I do over 60? I know the morning. Do over 16.

[00:14:27]Okay.

[00:14:30]All right. Check it real real quick.

[00:14:32]Right.

[00:14:33]So, a plot of land is valued at $18,000 and we pay 70 cents per $100 of value.

[00:14:40]So, the first thing to do is to take the 18,000 and divide by 100 to find out how many hundreds are there in 18,000, right? And then you multiply that by 70 cents, which is 70 out of $100. We cross off some zeros, we get 18 by 7. That's that's 126. All right. So, I hope that helps um audio.

[00:15:01]Okay.

[00:15:04]Oh, thank you, Gory. Right. A loan of 8,000 was paid repaid in 24 monthly installments of 400. The rate of interest was, so we know it's 20%, but we of course want to show you working for those who may not have been here before. So, how many months in a year?

[00:15:18]12. So, we have 24 monthly installments of 400, right? So, if you take your 400 by 24, so you put your two zeros there for the 100. 4x4 is 16 carry 1. 4x 2 is 8 + 1 is 9. So you paid back 9,600 in total after borrowing 8,000. That means you pay back 1 1600 extra which is the interest. And now if we take the interest as a percentage of the amount borrowed, right? So we could knock off some zeros there, knock off some zeros there, and then 8 into 16 goes two times and 2 by 10 will give us 20. All right.

[00:16:00]Okay. So maybe we could scroll down to finish off the um consumer arithmetic before we tackle the algebra. Right. A dinner at a restaurant was advertised as $60 plus 18% tax. The total bill for this dinner was okay. Well, obviously it's not going to be it's not going to be a right. Um it might be well any of the others. I don't think it'll be a flat 78. So to me B or D are the are the potentials here, right? All we find 18% of 60. So again you could do 60 by 18 right? So you put the zero. So 0 by that is 0 6 by 1 is 6. 0 by 0 6 is 48 right? So 0 um 8. So 1080. But then of course don't forget it's 18%. So you have to divide by 100. So of course 1080 divided by 100 means I'm going to shift that decimal point two spaces to the left. So 1080 is the tax. But don't forget we have to add that 1080 to the 60.

[00:16:58]60 + 1080 will just give us 7080.

[00:17:04]That's option B.

[00:17:07]Hear me here. Very good. Right. Uh number 20. At a sale. Each book was marked $3 off the original price. Daniel paid $46 for two books that had the same sale price. What was the original cost of one of the books? Okay, so he paid four, sorry, he paid $46 for two books that had the same sale price. So if you divide by two, you get the original, sorry, the sale price. And each book is $3 off. So you're going to add back three to get 26 because they ask for the original cost.

[00:17:45]Okay, take a very brief pause there. So we we just finished the first oneird of the paper, first 20 out of 60 questions in about 15 minutes, right? So that's pretty decent time. Again, if you need me to go back and rework or explain anything, please do let me know. It's not a problem. All right. Uh we will get to this point, ladies and gents. Any questions? Anybody anything? No. All right. Um I was going to ask nobody there.

[00:18:13]Hey, Alicia. How you doing? Thanks.

[00:18:15]Okay, so let's go back to the top.

[00:18:21]All right, 1 over 5x + 2 over 3x. Okay, so the easy way to do this is to multiply the denominators to get the common denominator. But if you want the LCM, it'll just be 15x. Question two, what number when added to 1 and a3 gives two? Just subtract one and third from two and you get two things or number 12.

[00:18:50]Yeah, the the shaded region is P complement. Everything but P is shaded.

[00:18:54]So it's just P complement, right?

[00:18:58]Okay. Yeah. So, um 5x 3x. So you could you could start off with 15x^2 if you want and then each numerator multiply by the opposite denominator. So you have 3x + 10 x. Well, that'll give us 13x over 15 x^2. I need to cancel the x and the x^2 just to get 13 over 15x.

[00:19:25]Which one? 20.

[00:19:31]You good? You sure? All right. You see it? Oh.

[00:19:39]Right. Number 22. When five is added to a certain number and the result is multiplied by three, the final answer is 29. 27. What is the original? So when five is added to a certain number, so a certain number plus five, the result is the result is multiplied by three. The final answer is 27. So check this. You could do the transposition, but look at what the statement is telling you.

[00:20:05]What's the understood operation between three and the bracket? Multiply. So 3 multiply by some number is 27. What's the only number we can multiply three by and get 27? 9. So you could also say, well, let's divide by three on both sides. So it'll knock out the three here. And 27 / 3 is 9. So the same the same result, right? Now look at what's done here. Some number plus 5 is 9.

[00:20:27]There's only one number to which you can add five and get nine. What number is that? Four. Or you could say, well, look, I'm going to subtract five from both sides of the equation.

[00:20:37]21 I multiply to get the common denominator. I have no idea. And then you multiply each numerator by the opposite denominator, right? So then x so x will be equal to 4. And think about it, what's 4 + 5? 9.

[00:20:53]9 by 3 is 27. So it satisfies the equation.

[00:21:04]All right. What is the value of x2 + 3 y all over x * y if x is 4 and y is 2? So x is 4. So 4^ 2 + 3x 2 all over 4x2.

[00:21:20]So that's 16 + 6 all over 8.

[00:21:27]22 / 2 11 / 4. So that will 2 * remainder 3. So 2 and 34.

[00:21:45]If x is an integer that satisfies the inequality, then x is. Okay, cool. So check this. So you have four is less than x 2x sorry and that's less than equal to 6. So we could divide by two throughout. If we do that we get 2 is less than x is less than equal to I know where the minus signs come from but um the only answer with all the minus sign is um a kind of made that one easy for right. Okay. Uh, ladies and gents class, we okay with 21 24? Yeah. All right. So, let's pitch it right over to the next page.

[00:22:30]The sum of two positive numbers P and Q is 32. The difference is 12. What is the smaller number?

[00:22:37]Quadratics.

[00:22:40]So, we're talking about the sum of two positive numbers. So, P + Q is equal to 32. Oh, no, it's not. Sorry, it's just simultaneous.

[00:22:51]All right, smaller number. Um, well, check what we could do, right? We could we could add these together or subtract them.

[00:22:59]They didn't say which one is smaller, right? Okay.

[00:23:02]So, let's add them together. Why not?

[00:23:04]So, in so doing, you'll get 2 P is equal to 44.

[00:23:09]So, P is 22.

[00:23:12]Right? Now if you were to subtract that might actually give you a small number. P minus P is zero. Now Q minus minus Q when you minus a minus I get a plus and Q plus Q is 2 Q and 32 - 12 is just 20. If 2 by Q is 20. To find Q we divide by two on both sides and we get 10. So 22 and 10. 22 + 10 is 32 and 22 - 10 is 12. Okay. Yeah. So those numbers.

[00:23:40]All right. 3x^2 by 2x cub. Okay. Cool.

[00:23:42]So what we do is we separate 3x2 by x^2 by x cub. 3x2 is 6. When you lose the indices, when you have the same base and you're multiplying, what do you do with the indices? You add them. So we have 6 by x ^ 5.

[00:24:06]Two matrices a and b are conformable for multiplication a by b. If the number of rows in A is equal to the number of columns in B. Number of rows and number of columns. No, no. Number of columns in A is equal to number of rows in there.

[00:24:22]That's the one there.

[00:24:26]All right. So, what the general thing um we to double check if the order of the first matrix. So, let me go on top. No, I'll go. Right. So, row one, column one.

[00:24:37]Well, let's say row A for matrix A, right? and column A and then row B by column B. If this number the number of columns in A is equal to the number of rows in B, then we're good to go because the number of it's really the number of elements along the rows in A and the number of elements down the columns in B. But what that matters up to is the columns in A and rows in B.

[00:24:59]All right. Um, if vectors P and Q are 3 2 and minus 1/4, then P min - 2 Q cuz last time they catch me. Last time I g it was Q minus 2 P. So make sure and read your question properly people. Right? So that'll just be 3 2 - 2 by -1 4. Right? So that's 3 2us.

[00:25:25]So 2 by - 1 is - 2. 2x 4 is 8. And when you match up the corresponding so 3 - - 2 and then 2 - 8 when you minus and minus you get a plus 3 + 2 is 5 and 2 - 8 is - 6.

[00:25:41]So that is d Okay, let's scroll down a bit to see 28 and 30. All right, so let's do 28 first.

[00:26:06]Now, the determinant of the identity matrix is one, I believe. Right. So, what is the identity matrix? 1 0 0 1.

[00:26:15]How do we find the determinant? Right.

[00:26:17]Well, you have to multiply the yellow items together and then multiply the blue items together and then subtract yellow product minus blue product. So 1 by 1 is 1. 0 by 0 is 0 and 1 - 0 is just okay we have a item 30. Item 30 refers to the following parallelogram wxyz. Okay. So with parallelograms the opposite lengths are parallel and equal right. So um x w and y z are parallel which means the vector along y r is also going to be the same v right. So um going down is yeah same v.

[00:27:02]Yeah. And then same thing for um the horizontals right XY and WZ are parallel and equal which is the vector along um WZ on the bottom here is also just going to be um U. Now WR now sorry I forgot a very important point here. R is the midpoint of YZ the midpoint is the exact what halfway point between the two end points right? So you want to go from W to R. Okay. So to me the easiest way to go from W to R is to go from W to Z and then from Z to R.

[00:27:36]So let's start there. So WR is equal to W Z plus Z R. Okay, WZ is just given by vector U. But ZR first of all if you go to go from Z to R, you're going in the opposite direction of the the vector on on which which lies on the line. The vector going down is this vector V. again because the opposite sides of a parallelogram are parallel and equal. Okay, which mean the vectors along them in the same direction. So, and on top of that, so so that's minus a half um y a half because you're only traveling half the distance to the well from one end point to the midpoint. And then y z is just v, right? So that's equal to u minus just a half as option a.

[00:28:29]Okay.

[00:28:32]So that's the page. So we officially halfway through the paper in just about 25 minutes which is pretty good time. A little less than a minute of question.

[00:28:39]Again we're not trying to speed through.

[00:28:40]We're doing the working. We explaining stuff because I want to understand how to do the questions because as we saw in the January papers sometimes things come back whole some as if they tweak something here and there. They change what they're asking you for. They change a figure. You have to know how to win stuff. Uhhuh.

[00:28:59]12 + 10.

[00:29:01]Uh-huh.

[00:29:04]12.

[00:29:11]Wait, what number? 25.

[00:29:25]The two numbers are 22 and 10, right?

[00:29:27]So, so 22 + 10 is 32. 22 - 10 is 12.

[00:29:37]12 + 10 gives 32.

[00:29:41]No, no. 12 + 10 is 22. You're correct.

[00:29:43]12 + 10 is 22. My bad.

[00:29:46]Yeah. What did I say? Okay. No, but there still the two numbers are 22 and 10. Sorry about that. My bad.

[00:29:53]Okay.

[00:29:55]All right. Um, ladies and gents in class, are we okay with this page and the first half of the paper? Anything still bugging you about the first half?

[00:30:02]No. All right. Right here. No idea. Kind of feeling can't be Yeah, you're trying.

[00:30:06]Yeah. Yeah. Well, let me want to go over anything.

[00:30:21]All right, cool. All right, let's go.

[00:30:25]So given that 1 millm is 1,000th of a meter, 2500 mm, right? So you're dividing by a,000.

[00:30:36]So that's going to shift the decimal point three spaces to the left. So, we're going to get 2.5 m.

[00:30:44]Um, okay. So, let's do 34 and 35, I guess, because Okay, I guess we 32, right? So, item 32 refers to the following diagram, which shows a sector of a circle A O B, right?

[00:30:56]A OB is 60 and that is R. The area of A O. Okay, cool. So the area of a sector is theta the angle in the sector over 360 multiplied by<unk> r 2.

[00:31:13]So 60 over 360 by pi r 2. So the zeros will cancel and 6 into 36 goes six times. So we have 16 p<unk> r^ 2 which sorry yeah which actually is option a right let's jump up to 34. Uh the perimeter of a square is 48 cm. What is the area? Right? So a square as we know has all equal sides and the perimeter is simply the sum of all four sides which in this case of course would just be four * s. So if 48 is equal to 4 * s to find s all we have to do is divide by 4 on both sides of the equation which will give us 12 and of course area now is the square side by side which is side squared and 12 squar is 144 right 30 is 30 is bold So there's not you're going backwards along the vector they had to invert it.

[00:32:29]All right, scrolling down 33. Now the volume on on the bottom left hand side the volume in cubic centimeters of a cube at three. Okay, so the volume of a cube is side cube side by side by side.

[00:32:47]That's why they call a cube because it's side by side by side. So 3 cubed is 3x3 by 3 which is not 9, it's 27. 3x3 is 9.

[00:32:55]9 by 3 is 27. Oh, go over 30. All right.

[00:33:02]Right. So right. So with a parallelogram the opposite sides are parallel and equal which means that if the vector from x to w is given by v means that the vector from y to z is also given by v right and similarly the vector from x to y is given by small u the opposite side here is wz so the vector along there is given by u as well now they want w r is the midpoint of yz which means you're going halfway along uh the vector. Okay. So or half along the line. So using half the vector. So to go from W to R, we have to first go from W to Z and then from Z to R. So W so you write that W, Z, and Z. Now WZ is just plain old easy U. Z to R is a little more complicated. So first of all, Z to R lies on the larger line YZ.

[00:34:02]And going from Z to R is only going halfway along. So to go from Z to R that's halfway right but also what happens right is you are going in the opposite direction of the vector along the line. So you have to invert the vector. To invert the vector all we have to do is put a minus sign. So we are minusing half of YZ.

[00:34:23]So that's u minus 12 V. So hope that helps.

[00:34:29]Okay.

[00:34:31]The answer is correct. Check it out. 22 and 10. to attend fit both of them.

[00:34:38]All right.

[00:34:41]So, which of the following figures not drawn to scale has an area equal to a half 5x 4 then by two, right? So, the area of a trapezium, right, is 1/2 of the sum of the parallel sides, right? Multiply by the perpendicular distance or height between them. So, a plus b. So, five and four.

[00:35:01]We're looking for a four and a five, right?

[00:35:04]But um the the perpendicular distance between them has to be two which this one down here.

[00:35:14]Right. So that one was nice little easiest question 36. The area of a rectangle is 53.6 square cm. If the length is multiplied by four and the width is half, then the area would be Oh, I've seen this one before, right? So the area of a rectangle is length multiplied by breadth and that's equal to 53.6.

[00:35:41]If the length is multiplied by four and the width is half, right? So if you if you focus on the algebra for a second, right, the two will cancel with the two one time and then into four. So 2 into two goes one into four goes two times.

[00:35:55]So when you simplify this, you're just going to get 2 * length by breath, which just means 2 * 53.6, which is 107.2.

[00:36:06]So it couldn't be a, couldn't be b, and d seems pretty big.

[00:36:11]Yeah. Okay. All right. Ladies and gentle, are we okay with this page?

[00:36:16]Any questions? Anybody? Anything? Any problems? No. All right.

[00:36:21]All right. again next sector. All right.

[00:36:28]Item 37 refers to the following diagram which shows a sector of a circle with center O. If the length of the minor arc is 8 cm, what is the length of the circumference?

[00:36:39]Okay. So the length of the minor ark is theta over 360 by the circumference. So that's equal to 8. And the angle here is 60.

[00:36:54]And we saw earlier that 60 over 360 is exactly 16.

[00:36:59]But to solve for C, we multiply by six on both sides of the equation. And 8 by 6 is 48.

[00:37:06]Princess Lisha. Uh this is the May 2019 paper. We finished the January 2020 to 2026 uh between Friday and Sunday. So yeah, we started May today. We were from May 2019 to May 2025.

[00:37:21]Right? The area of a triangle is 30 square cm and its base is 10 cm. What is the height? So area of a triangle is base by sorry by height all over two. So we'll multiply first of all by two to clear out the denominator. And then 10 by h is 60. 10 by 6 is 60.

[00:37:43]Of course you could show us 60 / 10.

[00:37:48]Right. Okay. So, we're into some stats now. Some data visualization.

[00:37:53]Right. So, item 39 refers to the following histogram which shows the number of children aged four, five, six, seven, and eight who took part in a survey. Okay. What is the modal age? So, the modal age is the age of the of um had by the most number of kids. So, the tallest bar, long story short, that corresponds to seven years in age, right? So five kids were seven years old. That was the most number of kids who had the same age. So yeah. So seven is the modal age, right? Had a frequency of five.

[00:38:27]Okay. Uh ladies and gentlemen, we okay with this page? 37 a short page. Yeah.

[00:38:31]All right. Go ahead again.

[00:38:35]Hey, a CF curve thereby. All right. Um, so we could All right, let's do that and then we'll scroll down a bit to the 41. So items 40 to 42 refer to the following diagram which shows the CF curve based on the marks of 200 students who took a driving test. Okay, cool. The median mark scored by the two. Okay, so median is the halfway point, right? For group data, which is what we base the CF curve on, you just divide by two, right? Um so divide by n so sorry n plus s is n divide by not so not n plus one right so we're looking for the hundth mark or the mark obtained by the 100th person so the 100 would lie right here between 80 and one okay that oh that line is too thick It does seem kind of halfway between the two physical lines, doesn't it?

[00:39:45]Right. So, between 80 and 120. Exactly.

[00:39:48]Right.

[00:39:53]I'm going to read down exactly halfway between those two vertical grid lines. So that's 30 that's 35 here. 36 37 38. So it's 37 and a2.

[00:40:09]Yep.

[00:40:11]So once you read carefully you'll get 37 and a2. Okay. Now what is the interquartile range of the mark? So the interquartile not semi-inquartile. All right. Okay. So, we need quarter way and the 3/4 way. So, let's see what those values are. So, for Q1, 200ide by 4 is the 50th and then you just triple that. So, 50 by 3 is 150, right? So, we need the 50th and then the 150th um data points.

[00:40:44]All right. So, let's let's see first of all what's going on here. Right. So between 40 and 80 the halfway point is 60.

[00:40:57]And then between 40 and 60 the halfway point is 50.

[00:41:03]So that should be like right here between those two.

[00:41:09]And then you read down and I get 29. So I've gotten 29 for the lower quartile. Looks like Yeah. And for the upper quartile. So again, we're looking at one what? 150.

[00:41:22]All right. So this is Hold on. Let me get a different color for that one.

[00:41:27]All right. Cool.

[00:41:31]So that's 140 here. Oops. That point is way too heavy. So right, we're going halfway between 140 and one now.

[00:41:41]160. Sorry.

[00:41:44]So that's around here.

[00:41:58]right? So, it looks like it looks like 42.5, but could be 42.

[00:42:05]Oh, let's see if 13.5 is an option. If it's an option or 12.5, no, 12.5. Yeah, there you go. So 40 42.5 - 29 here 42.5 - 29 I'm doing January. I did it yesterday.

[00:42:36]Just go on my channel, YouTube channel from Jan 2020 all the way to Jan 2026, right? Let's zoom out a bit.

[00:42:48]Um 40. Okay, so that's Let's go back to the top end.

[00:42:54]Oh, this one. Oh, okay. 42 also refers to this. Wow, so they kind of put three question. Okay. So if 38% of the students pass the test, what was the pass mark?

[00:43:07]Okay. So first of all, we're going to find 38% of 200, right?

[00:43:13]The 38% of 200 is 76.

[00:43:20]So we want to find the 76 person. Sorry, no. Yeah.

[00:43:28]8% of the students pass the test, right? Sorry.

[00:43:34]So the pass the people who pass would be in the upper the upper side of it. So if you take away 76 here, we'll find that 124 people failed.

[00:43:45]That's 62%. Right?

[00:43:49]So we want to find 124. 124 is and then basically just read up from there.

[00:43:55]Sorry, read across and read down. So what was the pass mark?

[00:44:03]That's fine. Great.

[00:44:08]So, it's 124 128 152 15. No, that's 140 there, right? 122, 128, 132, 136. Yeah. Okay. So, 124. So each of these little uh um minor grid lines horizontally that spaces 4 sorry not 4 is four.

[00:44:31]So 40 seems to be the pass mark.

[00:44:35]Okay there you go.

[00:44:46]Yeah, because after that 76 people Yeah. that be how the curve look for you is about that is about 30 somewhere about 13 and 36% of people pass mass in the Caribbean, right?

[00:45:08]>> Yeah.

[00:45:11]41 All right. 43. The following table shows the frequency of scores obtained by students in a test. Okay, cool. Uh, the range of scores. So, the range is the highest minus the lowest. So, the highest score is 10, lowest score is two. So, that's 10 minus two. So, the range is eight.

[00:45:36]Item 44 refers to the following two-way table which shows the mode of transportation. So not more is the most popular but the type right. Uhhuh. Okay.

[00:45:46]So you have male female going horizontally. Male totaling 108 female 92 total students is 200. Okay. Um bus taxi and walking going down. So 74 66 and 60 add across I get 200. Okay. A male student is picked at random.

[00:46:06]What is the probability that he does not walk to school? that. So does not walk means he either does what? Takes a bus or a taxi. So to me that's 80 out of 108, right? So if you divide by four, you get 20 out of 27. So that's option C.

[00:46:27]Okay.

[00:46:30]Jose.

[00:46:34]All right. Uh in class people, are you okay with the stats on this page? Any questions? anywhere anything.

[00:46:42]Okay. So, where does some functions?

[00:46:44]Okay. So, which of the following represents the graph of a function?

[00:46:48]Okay. Cool. So, a function is either a a many to one or a one to many. But there's something called the vertical line test that you could do.

[00:46:58]Right? So, check this. Right? So, first things first, let's um let's join these points. Right?

[00:47:11]If you were to draw a vertical line and it only hits one point on the function at every time you draw it, then it's a function. Right? If it hits more than one point at any point in time, then for sure it's a relation and not a function.

[00:47:30]Right? So for example here if we draw a line either here or here it hits two points. This one is only that is a vertical line. This one also has three verticals in a row. So the only item here that corresponds to a function is option A. Right? So the vertical line test. Right?

[00:47:55]All right. 46 now. So 46 if 2x^2 - 1.

[00:48:00]Right? So f of -3, right? So you're going to have 2 by - 3^ 2 - 1 - 3 2 is 9. 2 by 9 is 18. 18 - 1 is 7, right? Am I doing any 2015 to 2019? I'm focusing mainly on the more recent ones, but I mean we might run out of that soon enough, so we could probably go back.

[00:48:26]Yeah.

[00:48:28]Right. Item 47 refers to the following graph of a straight line.

[00:48:33]The straight line cuts the sorry the straight line AB cuts the y ais at here. So that's 0 minus 2. Remember anywhere along the y- axis the x coordinate is always zero 48. Now the equation of the line which passes through the point 05 and has gradient four. Right? So y = m by x + c 4 is the gradient and because this x value is zero that has to be the y intercept.

[00:49:10]So we have y is = 4x + 5 that's 48.

[00:49:34]Okay, ladies and gents, class, are we okay with this page?

[00:49:39]Uhhuh.

[00:49:44]Oh, for Jan 2019. Oh, I didn't do that one. But I have not yet. That's correct.

[00:49:53]Yeah.

[00:49:56]Okay. So there we go.

[00:49:58]If you can finish this by the plan 10 15 time the range is of f ofx to x cubed.

[00:50:09]Okay.

[00:50:11]So x cub so -2 cubed is a minus minus bar minus. So a minus minus is a plus.

[00:50:19]So when they multiply by a minus again it goes back to being minus. So the only option here with minus 8 is option D.

[00:50:26]Now if you were to cube minus1 you also get minus one. 0 to any power is 0 1 to any power is 1 and of course 2 to the^ 3 is 8. So option D right u 52. Which of the following pairs of lines is perpendicular? Right. So when they're perpendicular their gradients are the negative reciprocal of each other. So B is out cuz the gradients there are equal. So no.

[00:50:54]All right. Let's check option which we call it there. Um C. So this is already the M here. So to get y = mx + c here we'd have to divide by 4. So y would be equal to x over 4 + a4. Now x over 4 is 14 by x. So if we take the minus 4 from the first line equation, sorry, and multiply by 1 over4. Guess what happens?

[00:51:18]we get minus one. And that is how we know two lines are two straight lines are mutually perpendicular but the product of their gradients is minus one.

[00:51:27]Right?

[00:51:32]What's this?

[00:51:34]26 46. Oh, right. - 3 2 is 9. 2 by 9 is 18. 18 - 1 is 17.

[00:51:56]No problem.

[00:52:03]Right. Let's go down. Okay. So, we know this diagram 50 and 51. So, we have the function. Let's see if we could get slightly more pronounced.

[00:52:18]Right. Um so the maximum point as you can see is this point here. When you read down to the x you get two across to the y you get four. So x hold on sorry that's 51. The cocoordinates of the turning point are two four. Sorry I didn't read the question. See so again read the question. The values of x for which the function intersects y equal to so y equal to0 is the x axis and the intersection points are um here and here. Let's get that x-axis in a slightly darker color so it stands out a bit more.

[00:52:59]Right. So yeah, zero and four as option A. Right.

[00:53:05]Okay.

[00:53:07]Yeah. So intersects at 0 and four and the turning point is has two four right okay 53 with what transformation maps PQR on the up a reflection a line in the middle here as a mirror line right okay cool reflection all right ladies and gents in class we okay with this page any questions problems is all right so we're in the last seven questions or So right 54 refers to the following diagram of an isosles triangle.

[00:53:50]Right? And as we could see the the little strokes are here and here. So this angle down here has to be 30° as well. In the triangle the value of x is so the sum of the angles in a triangle is 180°. So if you subtract the sum of the angles that you have that you know you will find the value of the angle that you do not know.

[00:54:28]Item 56 refers to the following pair of similar trials. Okay. Um, you know what?

[00:54:33]Let's do 55. That That one is pretty easy, right? So, we have two transversals, right? Those are two straight lines. All right. No, sorry. We have two parallel lines, right? It says item 55 refers to the following transversal diagram, right? In which lines A, B, and CD are parallel, right? And the transversal is the um the diagonal line cutting both of them.

[00:55:02]And what that creates is F and Z angle.

[00:55:04]So we know X is equal to Y. That option is option E. Normally is option A. So as they say look before you leap, right?

[00:55:12]Okay cool. Um we know 56 is the length of M O.

[00:55:25]Right? Now we know that first of all these are two similar triangles. Why similar? Because the they have the same angles same the magnitudes of what we call the corresponding angles are equal.

[00:55:38]So the bottom left hand side is 31. The top angle is 59 and we have a right angle tri right angle down to the bottom right hand side. Sorry one sec. Cool.

[00:55:54]Geometry. Yeah. Yes. Yes. Yes. Some geometry going on here. Yeah. Right.

[00:55:58]Now, similar triangles have the same corresponding angles but different lengths. There's a scalar relationship.

[00:56:05]For example, this length AB and this length MN correspond. As we can see, this one is six, this one is three. So, it means that in the bigger triangle, each length is double or two times the smaller length in the corresponding triangle. And in the smaller triangle, um, it's a half by AB. So if they want M O and that corresponds to CA, that's simply going to be a half by 7. And a half of 7 is 3 and 12.

[00:56:35]That's option C.

[00:56:39]57. The image of a point2 under a translation - 5 - 4 is right. So 1 2 the x and the y coordinates -5 -4 are the horizontal and vertical components or of the transition. So 1 + - - 5 2 + - -4 1 - 5 is -4. 2 - 4 is -2.

[00:57:05]So b.

[00:57:09]All right. Ladies and gents in class, are you okay with this page here? Any questions, problems, issues? Anybody?

[00:57:14]Anything? No. Okay. All right. On the last page, we've seen some a couple of familiar things here. Actually, now 59 look interesting.

[00:57:26]Let's tackle 58 first, right?

[00:57:29]So, O A prime O A prime OB prime are straight line. So, what are they talking about here?

[00:57:38]O A A prime.

[00:57:42]Now OBB prime and OC prime lie on the same horizontal line. So we can't really distinguish them. But let's put an orange line just below for OC C prime.

[00:57:53]Right by an enlargement. Okay. So ABC is mapped onto A prime B prime C prime by an enlargement center. What is the scale factor? Okay. So all that just to ask the scale factor. All right. No problem.

[00:58:06]So what we'll do is compare corresponding size. So AC was two units in the smaller one and four units in the bigger one. So 4 / two is two. You want to compare the horizontals. You have one here and you have two here. So again a scale factor of two.

[00:58:24]59. A plane flying in a direction of 045° changes course in a clockwise direction to 135°. The angle through which the plane turned is 90°.

[00:58:37]Right? So if you 135 minus 045 it's 90 right photography by you're welcome right the coordinate really going up first then across x axis then y axis now for 51 yeah always x and y so from that point you have read you have to read down to the X then across to the Y right and then the last question on the page >> right so right item 60 refers to the following diagram not drawn to scale which shows that the angle of depression of X from point Z is 30° now what we also know is that this line here this line here are both parallel and then of course the transversal connecting them the hypotenuse in this case of the triangle creates the Z angles. So it indicates therefore that this angle here is also 30°.

[00:59:53]Sorry one sec.

[01:00:13]If XY is 10 mters, if X is 10 m from Y, the height YZ in meters. So height YZ is the orange, right? Okay. So relative to the angle, the orange side is opposite. This blue side is the hypotenuse, which makes this line down here the adjacent.

[01:00:37]Right? Now, if we're looking, we neither are looking for nor have the hypotenuse.

[01:00:42]So, it's opposite and adjacent. Right?

[01:00:45]So, if that's the case, we know we're using tan. And there's only one option here with tan, which is option A. But just to be very clearly working, tan 30° would be equal to the opposite length divided by 10. And then we would multiply by 10.

[01:01:04]So 10 * 30 which is option 8. Oops.

[01:01:12]Right. And there you go. So 2019 finished in just under an hour. So even though we had a bit of a late start, we got to sort it out. Ladies and gents in class, are we okay with the last page here? Yeah. Okay. Lovely. All right. So, what we're going to do, we're going to take a short break, like a 10 minutes or so, 15 max, but we're looking at Starbucks by half pass, right? So, you can get up, stretch your leg, use the bathroom, whatever the case is. All right? So, um, YouTube, I am popping off there for five for 10, maybe 15 minutes, right? So, check back in about that time.