2026 05 22 - Maths F5 - MCQ Session 1 - Jan 2022 P1

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[00:01:36]It has well pressure.

[00:01:40]Okay. So, I see still here.

[00:01:43]Kimora Kana and Shazari.

[00:01:52]Okay, let's get some water and we'll we have like a little two minute countdown. But yeah, Jan 2022.

[00:02:00]Yeah, I figured we'd warm up with the John papers and then we would sort out the May papers.

[00:02:11]Okay, so it's 12:08. So we start in just less than 2 minutes.

[00:02:27]Let me check something real fast.

[00:02:39]Right. So, that's that.

[00:02:44]No, I don't want to do that.

[00:02:47]Okay.

[00:02:51]Okay, that's fine. Um, contact live.

[00:03:06]Oh, I didn't label that one properly.

[00:03:12]All right, I have a few seconds again before I start.

[00:03:24]You guys should go ahead if you want.

[00:03:29]Okay, seems to be able to get back in now. Yeah, sometimes you just have to close up the browser and go back in.

[00:03:42]Sorry.

[00:03:55]Right. So there going on here.

[00:04:02]Right.

[00:04:04]Three, two, and we're off. All right.

[00:04:08]So, we saw this one a couple of papers ago. Sorry, let me just get my glasses back on so I make sure my eye is not under too much strain. Right. So, we know what to do to find what percentage of 40. 8 is, you put 8 over 40. You multiply by 100. So, you can knock off a zero here and here. Four goes into 8 two times and 2 by 10 is 20.

[00:04:32]So, you have 20%.

[00:04:37]Right?

[00:04:38]Next, uh, the number that is written to three. Okay, so to three decimal places mean you're going to knock it off there.

[00:04:44]But the digit on this side is a six, which means you have to you have to round this digit up by one. So you're going to have 3.141.

[00:04:54]All right. Um, we saw number three in the previous paper. So we said, right, so if it's 4.3 by 37, right? So to get to 43, we had to shift this decimal point.1 space that way. And this had to go one, two, three spaces to get there.

[00:05:10]So that's like a minus one shift plus a three. Minus one being one space to the left, the plus three being three spaces to the right. So you got two shifts. So this would shift twice this way. So you would have 159.1.

[00:05:26]Okay. A little bit.

[00:05:30]Okay. So all right. Number six, there are 40 students in a class.

[00:05:40]All right. Girls make up 60% of the class. 25% of them wear wear glasses.

[00:05:44]Okay. So, how many girls in the class wear glasses? So, that's 25% of the girls, which is 60% of the 40.

[00:05:56]So, as we should know, right? So, 25 into 100 is just four, right? and 4 into 40 goes 10 times. Knock off zeros, knockoff zeros, you're just going to end up with six, right? If the universal set U is 1 2 3 4 5 6 and H is 1 3 4 6 and H complement.

[00:06:19]So H complement means everything but H.

[00:06:22]So that's one two and five. So seven is B.

[00:06:28]Oh, thanks for the rose, Tasha.

[00:06:30]Appreciate it. Uh let's craft JA. This is the Jan 2022 paper one.

[00:06:37]Okay, scrolling down so we can see the rest of the questions on the page.

[00:06:41]Right. So let's go back to question four on the right hand side. So the first three common multiples of three, four and six. So what I would say to do is start with the biggest number, right?

[00:06:50]Start with six and do its um times table. Actually, hold on. I just remembered I need to to enlarge this a little bit, right? So start with six. So six. So six times tables are 6 12 18 24 um 30 36 right so all of these are already multiples of three cuz every six is a multiple of three so every multiple of six is automatically a multiple of three so it's really only four you're testing so that's this one this one and this one which means d is the answer here right 350 is shared in the ratio 2 to 5 the smaller share is right. So whenever we see a ratio, we add the numbers. 2 + 5 is 7. We'll then take each number and put it over the seven. Well, the only one the smaller one, the smaller between 2 and 5 is 7. And then you find 27 of 350.

[00:07:47]So seven goes one into that goes 50 times and 2 by 50 is 100.

[00:07:56]Right. Number eight. Which of the following statements describes the set of integers greater than three but less than six?

[00:08:04]Greater than minus three sorry and less than six. So D here is the correct option.

[00:08:12]Right? If X and Y are two finite sets such that the number in X is nine, the number in the intersection is four and the number in X union Y is 15, then N.

[00:08:25]Okay. Right. Soon.

[00:08:27]So x union y is equal to x + y - the intersection.

[00:08:37]So 15 is equal to 9 + well let's just put y - 4. So 9 - 4 is five.

[00:08:48]5 + y is that. So of course when you subtract five from both sides you get 10.

[00:08:57]Okay. So that's one to nine. So um Shari and Kimora, are we okay with page one?

[00:09:05]Okay. All right. Haley and Kana, let's give a thumbs up or a genie chat. Either one works. If you're good with this page, if if there any if there's any question or questions here, let me know how I could help. Okay, cool. No problems.

[00:09:20]Let's go on to the second page, shall we? Let's go.

[00:09:28]In the vin diagram above, right? X represents the factors of 12. Y represents the factors of nine. The shaded region represents all all the factors of okay. So the factors of 12, right? So 12 you have one by 12, 2 by 6 and 3x 4.

[00:09:52]And for nine is nine, right? So nine, you have 1, three and nine. And so it means that the common factors are 1 and three. Yeah.

[00:10:06]And those are all the factors of three.

[00:10:12]Okay.

[00:10:13]We saw 11, right? So in the 30 students in teacher May's class have either a dog or a cat or none. All the students who have a cat also have a dog. Okay. The number of people who own cats is 12.

[00:10:26]Number who own dogs is 16. Which of the following ven diagrams correct? Okay. So we know the answer is D because you saw it already, right?

[00:10:36]So the cat owners, there are 12 of them.

[00:10:40]They all own dogs. But there are 16 dog owners which implies that there are some dog sorry implies that there are some dog owners who do not own cats. If 12 people own cats and also own dogs, it means that okay 12 of those people own dogs. And if there are 16 dog owners split between a people who own cats as well and people who own only dogs, right? Okay. And then on top of that there are 30 people in total.

[00:11:09]when you minus 16 from that you get 14.

[00:11:14]So D is the answer here.

[00:11:18]And we've seen 12 on the past two papers today. Right. Is this a third paper? Uh no dear. Yeah. And I'll probably do a fourth one a little uh about 2:00. Yeah.

[00:11:29]So sorry what I was saying. Right.

[00:11:31]Disjoint sets. So disjoint sets are sets that have no common elements or no intersection. And that is option A. Even numbers and odd numbers. There are no numbers that are both even and odd.

[00:11:43]Either odd or even. It's binary. Okay.

[00:11:47]Sharan Kim, are we okay at page two here? Any questions at all? No. All right. Kitwana and Healey, let me know how we doing. If you have any questions at all. It's not a problem. Let me know.

[00:11:56]Good. Okay. On to page three.

[00:12:01]All right. So, we've seen question 13 already. We've seen question 18.

[00:12:06]Oops. Sorry. My bad.

[00:12:14]All right, I think that should be sufficient there, right? Okay, cool. So, one sec. Sorry, my bad. Yeah, number 13.

[00:12:21]If $2.50 is equivalent to$1 US. So, it costs it costs $ 250 to buy one of these and I have $20, how many can I buy?

[00:12:31]That's a division. 20 divided by 2.5.

[00:12:34]So, shift that. Shift that. So 200 / 25, right? So again that's 2 by 100 / 25.

[00:12:43]2x4 is 8.

[00:12:49]All right. Number 14. At a store 3 cents on every dollar spent is charged as sales tax. So that's 3%. Okay. How much is paid as sales tax on a costume costing 196?

[00:13:02]Okay. So 196 is almost 200, right? So check this. If you were to round that up to 200 and you multiply by 3%.

[00:13:13]Zeros will cancel. What's two by three?

[00:13:15]Six, right? So we know the answer has to be less than six. What's the only answer there less than six?

[00:13:21]>> 588. Right.

[00:13:24]Cool.

[00:13:27]Right. 15. The cash price of a television set is $350.

[00:13:31]When bought on higher purchase, a deposit of 35 is required followed by 12 monthly payments of $30.

[00:13:38]How much cash is save? How much is saved by paying cash? Okay, so higher purchase is 35 is the deposit plus 12 monthly installments of $30 each. 12 by3 is 36.

[00:13:50]So 12 by 30 is 360.

[00:13:53]35 and 360 is 395.

[00:13:57]So if I take 395 and minus 350 I get 45.

[00:14:10]All right. Number 18. A car presently valued at $12,000 depreciates at a rate of 10% peranom. What will be the car value of the car? Sorry, one year later.

[00:14:21]Right. So if you take $12,000 and you lose sorry 10% of that now 10% of 1200 12,000 is 1,200 0 that's 8 you borrow 11 is 10 right so 10,800 option A 19 a man's basic wage for a 40hour week is $160 he is paid $5 per hour for overtime. If he works six and a half hours overtime in a certain week, then his wage for that week is okay.

[00:15:00]So his basic so basic wage for a 40hour week is 160, right?

[00:15:06]He is paid $5 per hour for overtime and then he works 6 and a half hours.

[00:15:13]Oh, so 6.5 * 5 6 by 5 is 30. 5 by 5 is 25 and you shift the 0.1 space you get 2.5.

[00:15:27]So 3250 is the overtime and 160 + 3250 is 19250.

[00:15:38]Okay. Um I guess we could go down 20 and then jump back to the left. A salesman sells a car for 10,500.

[00:15:45]If he is paid a commission of 5% for the first 10,000 and 8% on the remainder, his total commission is I don't understand why these are multiple dress questions and you're not allowed to go and they don't have space to do the work in there. It's a test to see how small they could write or how strong your mental math is. Okay, so he's paid 5% on the first 10,000, right?

[00:16:11]So scratch off, scratch off. So five by 100 now is 500. And he's paid 8% on the remainder. So the remainder is 500.

[00:16:21]Scratch off. Sorry.

[00:16:24]Knock off the zeros. 8 by 5 is 40. And 500 + 40 is simply 540.

[00:16:32]All right. Althia normally saves X each month, but in June she saved $4 more than twice her usual. But we we saw this in the previous paper, right? Let's let her usual be $10.

[00:16:43]$4 more than twice her usual. So twice her usual be 20 and four more is 24. So it would be 2 * x then add four.

[00:16:56]Not 2 by x + 4 2x then plus 4. All right, let's shift back across to 16 and 17. A company employs 20 persons as gardeners and clarks. The mean daily wage of all employees is 2240. If each of the 12 gardeners is paid 26 per day, the daily amount paid to each cler is okay.

[00:17:23]All right. So, this is a ridiculous question for a multiple choice unless there's some secret thing. Emails. Okay.

[00:17:28]Emails. All right. Cool. No problem.

[00:17:30]Right. Um, what was I saying? Right. So first of all if it's 20 people in all and the mean is 2240.

[00:17:39]So 2240 by 20. Now 20 is 10 by two right? So if you multiply by 10 you shift this one one space to the right and then you multiply by two which is 448. So the total money paid to everybody is 448. Right? Each of the 12 gardeners is paid 26 per day.

[00:18:06]So 20 + 6 by 12, right?

[00:18:12]That's 240 + 72, which is 312.

[00:18:19]So when you minus 312 from there, you get 106.

[00:18:24]All right? And that's the total pay to each of the um the clarks. And now we have to divide that sorry by eight.

[00:18:36]Uh there's a trick for dividing by 8 guys. Um although hold on let me double check that. Isn't it 136? Sorry 48 minus is right. So 336 136 sorry.

[00:18:51]Right. So the trick for divide actually that that's not too bad. That that does give us 17. 8 into 13 goes one time remainder five which gives us 56 and 56 divided by is 7. So we have $17 exactly here. So some questions you could breeze through some of them you had to invest your time in. All right. Delano invests 5,000 for two years in an investment scheme. The investment earns compound interest of $8 perom. What will be the amount of Dano's investment at the end of a two-year period?

[00:19:24]Okay, so we have year balance at start plus the interest equal the balance at end.

[00:19:40]In year one, he started with $5,000.

[00:19:44]The interest is 8%. So 8% of if you knock off two zeros, 8 by 5 is 40. So 8 by 50 is 400. So he's going to get 5,400 for his balance at end. Now the balance at the end of year 1 becomes the balance at the start of year 2. And we find 8% of that which is 432.

[00:20:03]And when you add that together you get 5832.

[00:20:14]Okay. Okay, so that's the third page done and we are actually uh onethird of the way through the paper with the first 20 questions down. All right. Um Chazari and Kimura, we okay with this page?

[00:20:26]>> 17. All right. So Delano invests 5,000 for two years in an investment scheme, right? It pays compound interest. So it's not principal by rate by time for how many years? Right. What happens in compound interest is you add your interest to your principal at the end of the year. And when you in the next year now you're finding the interest on the new figure which is the previous principal plus the interest. Right? So in year 1 where he now started he started with 5,000 8% of that is 400.

[00:20:57]When you add that together you get 5,4 we okay with year one. Now the balance at the end of year 1 becomes the balance at the start of year two and we find 8% of that. All right. All right. So, you knock off two zeros and 8 by if 8 by 50 was 400. Now, we had to add 8 by 4, which is 32. So, 42. And then you add these two together to get 50 or 32.

[00:21:20]Make sense? All right. All right. Haley and Kimora, let me know how we go in there. Please, if you're good with that.

[00:21:29]Yeah. Okay. Cool.

[00:21:35]All right. So we we saw 22 already.

[00:21:41]Now let's let's let's go in about here.

[00:21:43]I feel like that should be sufficient, right? So we could do 22, 26, and 27 cuz if if if A, B, and C are not the answers, we know it's had to be D, right?

[00:21:55]Sorry, one sec. I collect something. Go ahead now.

[00:22:19]What is it?

[00:23:31]Hey, you go away. Go a All right. Sorry guys.

[00:23:50]Number 16. Did I do that earlier or not?

[00:23:53]16.

[00:23:58]Right. That one. That one have plenty layers. So they're telling you they have 20 persons employed. The mean wage of all 20 is this. So what you have to do is first multiply the the mean by the number of people. What I did is I broke up 20 into 10 by two which made it easy to multiply. So the total amount that everybody earns is 448.

[00:24:20]The 12 gardeners earn 26 a day. 26 by 12 is 312.

[00:24:27]Yeah. So I took I took 312 away from 448 to get 136. And that's how much the clocks earn. And then I divide the 136 by the 8, which is the number of clocks, and I get 17, right? Number 16 was ch. Yeah. Yeah.

[00:24:47]Yeah. I find it was a lot of work for a multiple choice question to be honest.

[00:24:50]It's a it's not a an an appropriate question for a multiple choice paper unless there's some secret technique to work it that makes it very easy. Okay.

[00:24:59]So m star n is the square root of m cubed - n^ 2. So that's 5 cubed - 2^ 2. So that's 125 - 4 which is 121. The square root of 121 is 11.

[00:25:24]26. We did this one. It was 11, right?

[00:25:28]11 - 2 is 9. 11 + 4 is 15. 5 by 9 is 45.

[00:25:31]Okay. But when you expand, so 5 by y and 5 by - 2. So 5 by y is 5 y. 5 y - 2 is - 10. - 3x y is - 3 y and - 3x 4 is - 12.

[00:25:44]That's equal to zero. Right? So 5 y - 3 y - 10 - 12. That's 2 y - 22. which means 2 y is equal to 22 which means y has to be 11. 22 divided by two.

[00:26:04]So we have the same answer for both of them. That's interesting.

[00:26:08]Both of them are d and both of them are 11.

[00:26:11]Okay. Right.

[00:26:14]So it's it's not the next one B. Okay.

[00:26:22]So which which number? Whatever.

[00:26:29]No. So, sorry. Right. So, what will be the amount of Delano's investment at the end of the 2-year period? So, not just the interest, right? I hope is that one you're talking about. So, no, it's not just the 832, it's the 5832.

[00:26:43]All right. Thanks for being so Yeah, Elijah, no problem. Happy to help.

[00:26:48]Right. This one. So, we saw this one already. Um, but we'll do it again. So p min - q will end up giving us 3 - - 2 and 7 - 5. 3 - - 2 becomes 3 + 2 which gives us 5 and 7 - 5 is 2. So that is option C.

[00:27:06]All right.

[00:27:13]Item 23 refers to the following diagram of a trapezium.

[00:27:19]Okay. So we have the height h and we have two parallel sides. Okay. Um the equation that may be used to find the value of x. Okay. So the area is x squ. Area is x squ. The area of a trapezium is 12 of the sum of the parallel sides. So people call it a. So let's say this was a and this was b multiply by h.

[00:27:49]Right? So what they're saying here is that it'll be x^2. So x2 is the area and that's equal to a half of 2 + x - 4 then multiply by h. So 2 + x 2 - 4 is - 2. So we have x^2 is equal to a half of x - 2 then by h and you could actually multiply the half by the h. So a half by h just becomes h / 2. So x2 would be equal to h / 2 by x - 2.

[00:28:32]All right.

[00:28:34]Yeah. Our next one that may not necessarily be as multiple as friendly as they think.

[00:28:41]All right. 24 we we've seen already.

[00:28:43]Okay. So when you're minus min - 2 q you just get positive 2q. And then you're minus 3 q. Uh 2 - 3 is minus one. So we just have minus q.

[00:28:55]All right. This one down here is pretty hard to see but we've seen it already, right? So this is 5 to the n + 1 * 5 to the n + 2. And when you multiply and you have the same base as in the fives, we simply add the indices. So n + 1 + n + 2. So n + n is 2 and 1 + 2 is 3. So I know I know you might not be able to see it, but that's option B. 5 to the 2n + 3.

[00:29:27]All right. and then across and also we get some vectors now. So 28 diagram of a parallelogram which means that the opposite sides are parallel and equal.

[00:29:36]So EF is parallel. So the total EF is parallel to HG right and then um sorry EH is parallel to F.

[00:29:47]So e H FG. So the implications are that K sorry HG is also K and FG is also M.

[00:30:00]Right? Opposite sides of a par of a parallelogram being equal and all that.

[00:30:04]Right? So EG represented in terms of K.

[00:30:08]So to go from E to G, you could go from E to F and then F to G. Or you could go from E to H and then H to G. Either way, you're going to be adding M and K, which is option A. 28 is A.

[00:30:24]All right, Kice. Very good. Okay. All right. In class people, are we okay with what's on the screen there?

[00:30:32]Yeah. Okay. Cool. How we going?

[00:30:41]We good. All right.

[00:30:46]All right. So, we're almost to the halfway point. Let's see how we go. All right. So, we've seen we've seen that one already. So, let me let me punch in a little bit, right?

[00:30:59]Okay.

[00:31:00]So So, we'll expand. So, five by if if five multipy is equal to 4x 10 20. So, let's go. So, 5 by is equal to 4x 10. So 5x is equal to 40 which means 4x is equal to 40 / 5. So x is 8 right. And then 5 by y is equal to 4x 20 and that's 80. So therefore y is equal to 80 over 5 y is equal to 16.

[00:31:34]So that's option b 8 and 16.

[00:31:39]Um, let's check out 32.

[00:31:46]And maybe we could try 30. No, no, no. I will come back to 30. Right. 32. The perimeter of the trapezium. So, the perimeter in millimeters. Okay. So, we could either scale everything up to to millimeters first or add everything up and then scale it after. So, let's let's add everything. Why not? So if we do zero, okay, let's scale up. So long story short, all these you're just going to shift the zero to the end. I mean, so you multiply each of them by a,000. So from the top you have 410. Going to the right you have 210. To the bottom you have 180 and to the left you have 120.

[00:32:26]So that's 630 plus 620 sorry plus 300 is 920.

[00:32:34]So 920 mm, right?

[00:32:41]Okay. So we're just about halfway through in about half an hour. Really?

[00:32:47]I may have to stop early then. I don't want to leave the paper unfinished.

[00:32:53]But yeah, I don't want to go late for my son and then start back late and then things be over. Anyhow, we'll figure it out. The matrix product AB. Okay, cool.

[00:33:02]So we saw this already. Let's do it again. Right. So you have to go row by column.

[00:33:10]So it's going to be 1 by 3 which is 3.

[00:33:13]3x 2 which is 6 minus 3 by anything by zero is zero. Right? So that's going to give us a nine. So we have a nine here and a nine here. So a and b are out.

[00:33:25]What about the first column by the second row? First row by the second column. One by zero is zero. 3x 1 is 3 2 over 32. Okay, just now right and - 3x 5 is -5.

[00:33:40]That will give us minus 12. So the answer here is d. We have we don't have to work on any of the others, right?

[00:33:46]Okay. 32. Oh, sure. Yeah. So like I said, each of these measurements here were in meters and they want the answer in millimeters.

[00:33:56]So you multiply all of them by a thousand and they'll all be like like in the hundreds 410 200 210 180 and and then 120 and you just add them up going around right is the perimeter the total distance around the edge of the ship.

[00:34:11]All right 31 but we saw 31 a few times.

[00:34:13]If it took a speedboat 9 hours to travel the distance of 1080 kilometers, what is its average speed? So average speed is total distance traveled divided by total time taken. So that's 120 kilometers per hour.

[00:34:33]Right? We saw a similar question with this um arc and stuff. Right? If the circumference of the circle is 15 cm, the length of the minor, right? So the length of the minor arc is theta in degrees / 360 multiplied by the circumference. circumference is 15. So we're going to put 120 over 360 * 15.

[00:34:57]That's option B.

[00:35:03]Cool.

[00:35:05]All right.

[00:35:12]All right. Shazar and Kimora, we okay with that page? All right. and k that page please and thanks.

[00:35:22]If you have any questions, please feel free to ask.

[00:35:30]Cool.

[00:35:31]All right, we're going again. 34.

[00:35:35]Okay, we saw this one already. 34 aircraft leaves at 1600, which is at 9:30, 19:30. So that's um 4:00 to half 7. So that's 3 and 1/2 hours traveling at an average speed of 550 kilometers/h. Okay. The distance. Okay.

[00:35:58]So speed is distance over time. Distance therefore would be equal to speed by time.

[00:36:08]So the speed is 550.

[00:36:12]And we have to multiply that by 3 and a half.

[00:36:17]Okay.

[00:36:24]So we multiply them separately.

[00:36:26]So 0 by 3 is 5 by 3 is 15 carry the one.

[00:36:29]5 by 3 is 15 plus the 1 is 1650. 550 by 0.5. So you could shift this point here.

[00:36:36]Shift this one back. So 55 by 5. 5 by 5 is 25. Carry the two. Five by is 25. Add the two you get 27.650 + 275 is 1925.

[00:36:55]Uh let's do 36.

[00:36:57]Right. Um cuboid we saw this just now.

[00:36:59]Right. So the volume of the cubid is 320 and the height is five. But it has a square base. So the bases are square which means that that this length here and this length here are equal even though it does not look so let's just call it um s and s right. Sorry it doesn't look like an s.

[00:37:17]So the volume is length by bread by height. The volume is 320 and we have s by s by five.

[00:37:31]So 320 is equal to 5 by s^2.

[00:37:38]So if you divide by five you get 64 and if 64 is s squared.

[00:37:49]It means that to find s you find the square root of 64 and the square of 64 is 8.

[00:37:59]Right.

[00:38:02]So we did it already.

[00:38:07]All right. Item 35 refers to the following diagram which shows a circle center O a set. Okay. But this the same one from just now right previous paper.

[00:38:20]The length of the major arc is 40. So this one is 40. And that's five times oops sorry.

[00:38:29]So the angle here of course would be 300 because the total degrees in a circle is 360 right? So if you have 60 on this side you have 300 next side. All right.

[00:38:39]So if you take 300 as a fraction of 360 you get 56.

[00:38:46]So five sorry 56 of the circumference is 40. Let's multiply by six first, right? To clear out the denominator. So that'll give us 240 and then we'll divide by five and that'll give us 48.

[00:39:15]Item 37. The area of a triangle is 60 square cm and its base is 12. What is the height? Well, we know it's 10, right? So base is 12 by height over two is equal to area 2 into that goes 1 and six.

[00:39:34]So 6 by h is equal to 60 which means h is equal to 60 / 6 which is what? 10.

[00:39:45]Right? A square has the same area as a rectangle with sides of length 16. Okay.

[00:39:51]So we kind of know this one already, right?

[00:39:56]So if you take the rectangle 9 by 16, right? So that gives us 144.

[00:40:07]And that's the same area of the square.

[00:40:09]So s^ squ is equal to 144.

[00:40:13]So to find s, we have to find the square root of 144, which of course is just 12.

[00:40:26]All right. Shazarian Kimora, we okay with this page here? Yeah. All right.

[00:40:35]37 is 10. That's correct. Yeah. All right. Divider. Yeah. Okay. Cool. Cool.

[00:40:41]Cool. All right. Next page. We're going again. Good. Big.

[00:40:48]All right.

[00:40:49]Items 39 and 40 refer to the following frequency distribution which shows the average mass in kilograms of a group of schooled children. Schooled children, right? The upper limit of the modal class.

[00:41:03]So the modal class is the class with the highest frequency. Highest frequency is here is the modal class. The upper limit is the number to the right hand side. So that's just 60.

[00:41:18]How many children have a mass greater than 40 kg? Right. So, we'll add the 24, the 40, and the 18. 64 is 82.

[00:41:38]Item 41 refers to the following table.

[00:41:41]The modal score. So, the modal score is the score obtained by the most number of students. All right. Right. The highest students students count is 12 and therefore the mode is eight.

[00:42:08]All right. Are you okay with this page with the stats? Yeah. All right. And let me know how you're going now. Please and thanks.

[00:42:16]Okay. All right. So, let's just do 42.

[00:42:20]Yeah. I mean, I'm hoping I don't have to cut it short, but I don't want to rush and you all miss something or don't understand something. So, item 42 refers to the following diagram of CF curve, which shows the marks obtained by 200 students. They want the median score.

[00:42:34]So, if it's a CF curve, the median is the halfway point. Uh half of 200 is 100. So, what we have to do is find 100 on the y ais.

[00:42:44]We then have to read across till we hit the CF curve.

[00:42:50]Let's try that again.

[00:42:58]Then we're going to be down about 37.5 because between 30 and 40, this is 35 here and that's half between 35 and 40. So that's 37.5 approximately.

[00:43:18]Can you imagine that?

[00:43:22]Okay.

[00:43:27]Some more stats here. Boy, we keep going. Nice. All right. So, item 43 refers to the following bar chart which shows Yeah.

[00:43:39]the ages of children who took part in a survey. How many children took part?

[00:43:43]Okay. So the four for four years there was three three kids. Um there were four kids age five, two kids age six, five kids age seven, and then one kid aed eight.

[00:43:58]All right. Sorry. Give me one second.

[00:44:01]I think I may have gotten a better copy of the um multiple choice. Let me see.

[00:44:06]So 1 + 2 + 3 + 4 + 5 is 15.

[00:44:13]Okay. Yeah, we got a better copy now.

[00:44:37]What is her name?

[00:44:40]Cool.

[00:44:50]All right. Lovely. Yeah. So 15 is the answer there.

[00:44:55]45. Which of the following equations represents a linear function? Well, that's item C because in item B and D, there's the presence of an X squar term.

[00:45:05]That's the highest power of X, which makes that a quadratic function. and x by y would not give us a linear function.

[00:45:12]Right? And you could rearrange this to get y is = 2x - 3 which is in the form y = m by x + c. All right? Okay. The set of ordered pairs below represents a relation is a function. So that means either a one to one or it's a many to one.

[00:45:35]If we want so which of the following points when added to the set would form a relation that is not a function. So that's either a many to many or a one to many. So what that means is the x value one of the x values has to be connected to a second y. And if you go through a list the answer is a because it has x equal to two. none of the others have an x value in any of the um ordered pairs before.

[00:46:08]Right? So it means that two would mark two would connect to seven and eight.

[00:46:11]That's so that's one value to many values. All right? And that's not a function. That's just a relation. So relation is not a function. Okay. Um item 44. 600 students write an exam. The probability of a randomly selected student failing is 1/5. Which means people who pass is four fifths. How many students are are expected to pass? So that's four fifths by 600.

[00:46:38]5 into 600. So 5 into 60 goes 12 times, right?

[00:46:43]So that's one and 4 by 120 is 480.

[00:46:48]All right. 47. The arrow diagram above describes the relation Y is a multiple of X. Yeah. Y is a multiple. So they they swap the positions here with the stuffer if you notice. Right. So eight connects to two and four. Nine connects straight to three and 10 connects to two.

[00:47:22]So right so the items in X are multiples of the items in Y.

[00:47:28]That's x is a multiple of that's t.

[00:47:33]Okay.

[00:47:34]Uh that's that page. Okay. Shazari and kimora. Are we okay with what's on the page there? Any questions? Anything?

[00:47:41]Anybody?

[00:47:43]All right. Um Haley and Kitwan, let me know how you all feeling with that one, please and thanks.

[00:47:48]Yeah. Okay, cool.

[00:47:53]All right. So, we're going again.

[00:47:57]What is the gradient of that straight line? Okay, so to put it to get it in gradient form, it needs to be in y = mx + c form. To get rid of that, we divide throughout by two. So you'll have -3 over 2 byx and then - 8 / 2, which is 4.

[00:48:14]And then -3 over2 is the coefficient of the x term, which is the gradient in this case. We saw this one in the previous paper. H of minus 6. So that this be 3 by - 6 - 2 all over 5. So that's -8 - 20.

[00:48:33]Sorry, minus 2. Sorry, I started to fall asleep, which is not a good thing cuz I go and pick up tren.

[00:48:42]So minus 20 over 5 is minus 4.

[00:48:48]All right. 52. Okay. The hold on.

[00:48:54]Oh, okay. So 50 the range of that function is okay. So when you plug in -2 into x^2 a minus by a minus is a plus.

[00:49:05]Sorry, my bad.

[00:49:15]So min - 2^ 2 is okay. Okay. So, if we square each of those values, you're going to get 4 1 0 1 4.

[00:49:25]Oh, wow. I missed something very important. There's a minus in front of it. There's a minus.

[00:49:37]So, no. Um, the values will be -4 -1.

[00:49:44]Well, 0 is neither positive or negative.

[00:49:47]Right. So -4 - 1 0. Okay. Cool.

[00:49:55]You guys are trying to slow down here.

[00:49:56]Bad. Bad. Bad. All right. All right. We have five minutes with the last 10 questions.

[00:50:02]All right. The par a line parallel to this line. Okay. What is the gradient?

[00:50:06]Okay. So we know parallel lines the gradients are equal. So we'll bring this across and then divide by five together in the form y = mx + c.

[00:50:21]All right. So that's part c.

[00:50:28]Okay.

[00:50:30]All right.

[00:50:32]The values of x are the points where that inter okay when it intersects y equal to zero. Those those are the roots. So you're going to let 4 x - x would equal to zero.

[00:50:47]So either x is zero or 4 - x is zero. In which case x is 4. So 0 and four.

[00:50:58]Yeah guys uh some of a problem. Uh we saw this translation as well. So again, if you check out the corresponding points, went from two to four, which is an a shift to the right of two. Five to six, a shift upwards of one. Let's confirm. Five to seven on the top plus two 5 to 8 below is minus one.

[00:51:20]Sorry, it's just one. My bad. That's the sleep talk. Plus one. So 2 one 2 one is a vector. My bad.

[00:51:27]option B.

[00:51:33]All right, I had to wrap up fast. Sorry.

[00:51:36]Okay, but we saw 54 and 55 on the previous um paper, right? So, we know that if you follow your lines, hold on. Sorry.

[00:51:54]You'll see. So we should and they tell us that P Q and R S are parallel which means what? Um Q and P are equal.

[00:52:08]Wow. Okay. A ship sailed 8 km due east from A to B. It has neither A nor B here. Right. And then 6 km due north to C.

[00:52:21]Right. A to B, 8 kilometers due east, and then 6km due north.

[00:52:26]Cool.

[00:52:35]Okay, ladies. Sorry. Are we okay with this page here?

[00:52:39]Any questions? Anything? No. All right.

[00:52:40]Clearly, Katana, let's give our feedback there, please. And thanks.

[00:52:46]Yeah. Okay.

[00:52:50]Okay. Okay, so we know 56. We saw it already, right? Um the angle at center is double the angle at circumference.

[00:52:58]So the answer there is 100 50 in triangle that triangle angle A is X angle B is that what's the size? I feel like we just just did this one, right? So again, the sum of the interior angles of a triangle is 180°.

[00:53:20]never been to like 55 55.

[00:53:25]Oh, that's just cardinal points. If we did geography, you could you could get that. But that's that comes in stuff like bearings, but it doesn't really involve bearings, right? Of course, x + 2x is 3x.

[00:53:39]And to find the unknown as simply 180 - 3x what go away 59 59 was the last question we were here Right? Angle of depression 35°. Which means that this angle down here because this line is parallel to that line.

[00:54:21]This is also 35° relative to the 38°. This is the opposite side and this is the hypotenuse.

[00:54:32]Sorry, that's the adjacent.

[00:54:35]Hey, guys. You sleep a real hard. So, we'll use tan. So, tan 3 is o. And to find that, you have to Yeah, there's only one option with tan here. So, we're going to go for it.

[00:54:51]Sorry. Yeah, guys. 57.

[00:54:54]Yeah.

[00:54:56]If y equal to x is rotated anticlockwise. So, anticlockwise means you're going this way. Sorry. No, no, no.

[00:55:06]All right. Is it going this way about Oh, right. 90°. This image will be sorry I fell asleep halfway through line.

[00:55:45]All right. Um, sorry. Haley Kim, are you okay with that one? All right. Um, Shazari. Yeah. And Helian Kana. Yeah.

[00:55:53]Okay. Cool. And then the last question.

[00:55:58]But we saw this too. This is sinx, right?

[00:56:01]So relative to the angle that's the opposite length relative to the hypotenuse sorry to the right angle that's the hypotenuse which the unknown angle unknown length already uply adjacent the trig ratio is this over.

[00:56:26]Okay. So it means therefore that that's opposite over hypotenuse which is sign. Yeah.

[00:56:36]Yeah. So sine x is 48.

[00:56:42]Sorry guys.

[00:56:45]Yeah.

[00:56:47]Okay.

[00:56:49]Guess I'm sleep. I had to go pick up my kids from school now and come back and do our next paper and then do a four to six class after that. then drop the babysitter up up the road to dance class, come back down and have dinner.

[00:57:04]But yeah, I I a folks, we're going to put a pin in there for um for now. Not today. I have one more session to do with y'all. Um which is 2 to half three.

[00:57:15]I'm going for my sons, drop them home, and then we're going to start back. So I would need about an hour. So it's just about 1:00 now. I check them back 2:00.

[00:57:25]All right. If anybody coming in person, let me know so I can print out a paper for you all. All right. Um, okay. Google Meet. I'm going to log off here because I don't want to leave it open for a whole hour, but I'll send back a signal when they're ready. Right.

[00:57:37]Later.

[00:57:42]Okay. Um, how it in the meantime? Yeah. Yeah. Do your thing. Do your thing. Okay. Cool. So anytime.