2026 05 25 - Maths F5 - P1 prep sessions - May 2021 P1

追加: 2026-05-26

[00:00:01]All right.

[00:00:07]So, So I said okay.

[00:00:36]So I said okay we'll do it any previous I'll put Okay. Right folks, let's do the same thing.

[00:01:37]I don't know.

[00:01:40]Right. Left down. Select stop.

[00:01:44]I see. Sorry. Should have put the question under. Go down.

[00:01:51]Right. So, we on 2021.

[00:01:55]Let's see the people take.

[00:02:10]So, Okay, cool. Yeah.

[00:02:37]All right. Um heat on the fast speed and you have to go right.

[00:02:52]All right. So, we'll start very very soon.

[00:03:03]Right, let's go.

[00:03:06]- 3^ 2 + - 2. So, when you square something, what are we actually doing?

[00:03:11]multiplying it by itself. So when you square minus 3, you're multiplying minus 3 by which is positive 9 and -2 by itself is pos4. 9 + 4 is 30. What percentage of 8 of 40 sorry is 8. So 8 over 40 * 100 over one. So sort out 4 into that 2 by 10 will give us 20. All right. 235 by 48.7 is that what is 23.5 by 487. Okay. So in each case we move the decimal point back to the left. So one space there and then two spaces there for a total of three spaces. So 1 2 3 that will put the point between the one the four. So that means 11.45.

[00:04:03]Okay let's scroll down to do four and five. Then we'll go to the next column.

[00:04:07]Right. So using the distributive property. Okay. So that's distributive law. So if you put brackets to kind of make it look like that, right? So if you factor out the 49, you get 49 by 17 + 3.

[00:04:21]That's 49 by 20 basically, which is option A.

[00:04:28]A test was marked out of 80. A boy scored 60% of the marks on the test. How many marks did he score? So 60 out of 100.

[00:04:37]by 80, right? So, knock off a zero.

[00:04:40]Knock off a zero. Same thing. 6 by 8 is then 48. Uhhuh. What's this?

[00:04:53]Right.

[00:04:55]Yeah. So, number six was an interesting one. We saw on the previous paper. Damn.

[00:05:01]Sold four 40 tickets in five days. Each day he sold three more tickets than the previous day. So let's say it was Monday. Monday, Tuesday, Wednesday, Thursday, Friday. So on Monday he sold x tickets. Tuesday he sold three more. So that's x + 3. Wednesday he sold three more. So that's x + 6. Thursday he sold three more. X + 12. And Friday he sold x sorry x + 9 and then x+ 12. My bad. My bad. My bad. 6 + 3 is 9. Then 9 + 3 is 12. So if you add going down, you have five x's and 3 and 6 is 9. 9 and 9 is 18. 18 and 12 is 30, right? So you have 5x + 30 is equal to 40. So if we subtract 30 from both sides, we get 5 x is 10.

[00:05:53]And if 5 by x is 10, x is 2. Now they wanted the number of tickets sold on the third day. So we're not done. Don't just jump and put sorry um two right because that's not even an option right the number of tickets he sold in the third day right so that is actually x plus 6 2 + 6 is equal to 8 which of the following set is defined by x an element of so x element of z is integers, whole numbers both positive and negative and it's greater than or equal to minus2 but less than equal to four. So it means minus2 and four are included. So all the whole numbers from minus2 all the way up to four inclusive of those two numbers.

[00:06:47]Right number eight if how many subsets? So right so if the number of elements is three right the number of subsets is two to the^ three.

[00:06:57]So for any any given set if there are n elements in the set the number of subsets is always 2 to the^ n.

[00:07:04]So that's option D. N the set of positive integers is an example of an infinite set. So positive whole numbers start from one and go up till well it never really ends. So as that's what we call an infinite set. Number 10. If the number of elements in the universal set is 25, number in A is 14, number in B is 15 and the number in A union B in the complement. All right. So the little formula that we supposed to know is that A union B is equal to A + B minus D. The intersection 14 + 15 - 6. So 14 and 15 is 29. 29 - 6 is 23.

[00:07:53]All right. And with that, the first 10 questions are done. All right. So, ladies and gents, how are we feeling with page one here? Any questions, problems, issues, or so far so good?

[00:08:03]Yeah. Okay.

[00:08:08]>> We have two questions on this page. Um, so item 11 refers to the following ven diagram. What is shaded? That's P complement. So P is the only thing unshaded and everything outside of P is shad.

[00:08:22]Everything outside of P is P complent.

[00:08:26]Tammy. Tammy. Very good. Tammy. Uhhuh.

[00:08:31]Okay. Cool.

[00:08:35]Okay. We've seen teacher me and the um dogs and cats. So the 30 students in the class have either a dog or a cat or none of the two. 16 students have dogs, 12 students have a cat, and the remainder have neither a cat nor a dog. So, this looks like D.

[00:08:53]Yeah. In the on the January papers, they would tell you that um every student who has a cat also has a dog, but that's not what they said here. So, so here it looks like D is the answer. 16 and 12 is 28. If 30 is the total number of students, it means two people have neither car.

[00:09:11]>> Yeah. 12 is D. Little simmers. Yeah.

[00:09:14]Very good. Mhm. What was the answer to 10?

[00:09:18]Uh 10 was C 23.

[00:09:23]>> All right. Uhhuh.

[00:09:27]All right. So, folks in class, we okay with 11 and 12?

[00:09:30]>> Yeah. All right. Cool. Lovely.

[00:09:34]So, we'll do some consumer things. Give me one second. I'm going to check some messages here real quick.

[00:10:08]Okay, so we saw this one in the giant.

[00:10:10]as well. So at a bank EC 260 is equivalent to one US and for every one US exchange you deduct um 10 cents as a fee. So if you bring in one US right so if you bring in one US dollar you'll you'll get back 260 but minus 10 cents. So effectively how much EC you get $ 250 right? So if you bring in a hundred US dollars you're getting 100 by that. So 100 by 2.5 will give us 250 right.

[00:10:54]>> Um sorry Adrian morning.

[00:11:03]Yeah one.

[00:11:07]Thank you.

[00:11:13]Right. So where was I? Right. If 7,000 is borrowed at a rate of 5% peranom for 3 years, simple interest. So simple interest is principal by rate by time. So knock off two zeros there and there. So 70 by five >> is 350. 350 by 3. So that's 900 + 150 + 0.

[00:11:38]which is just 1050.

[00:11:43]Okay. A dress which costs 180 is being sold at a discount of 10%. The amount of the discount is well 10% of 180 is 18.

[00:11:51]You're not knock off the zero and you're good to go there.

[00:11:56]An article bought for 125 was sold for 175. The profit as a percentage. Okay.

[00:12:02]So first things first, profit is equal to selling price minus cost price and then 50 over 125 by 100.

[00:12:15]Okay.

[00:12:20]Hey Jonathan, how you doing? Good to have you on. We're doing 2021. We did two papers already for the date. So we're on paper three now. What I say a third paper any we are a little more than a quarter way through already. Right. So 25 into 50 goes how many times? That's two times.

[00:12:41]25 into that will go five times. And then 5 into 100 goes 20 times. And 2 by 20 is 40.

[00:12:52]Right.

[00:12:53]Let's scroll down and oh wait hold on.

[00:12:55]Oh scroll back up for 17. Oh yeah, right. The value of a plot of land is 18,000. Land tax is charged at the rate of 70 cents per $100 value. What is the total amount of tax paid for the land?

[00:13:10]So if your land is valued at $18,000, but the units you're charged on is every 100, you have to divide to find out how many hundreds are in 18,000. You then multiply that by the 70 cents, which is 70 out of 100. Uh, you know, I've got plenty zeros here.

[00:13:29]Dot dot. So, 18 by 7.

[00:13:33]So, sorry. Yeah.

[00:13:44]So, 10 by 7 is 70. 8 by 7 is 56. That's 126, right?

[00:13:52]If the simple interest on 900 for 3 years was 108, what is the rate of interest? So check, I'll give you a slightly different. So for 3 years, the interest was 108, right? So if you take your 108 and divide by three, you'll get $36 per year. And then you take the 36 over 900 and multiply by 100. Knock off the zeros. 9 into 36 goes four times, 4%.

[00:14:21]Right? Or you could use your regular formula and transpose. But either way, you're supposed to get four. And you could always cross check it. 4% of the 900 is 36. And then 36 by 3 will give you back 108.

[00:14:37]Right? At the end of any year, a car is worth 5% less. So we've seen this on both papers so far. All right? If the car is worth 9500 in December, what was the value at the start of the year in January? Okay, so we said if you take your value at start and you minus 5% of the value that's going to give you the 9500 the value at end. Now the value at start is 100% of itself. So if you're minus 5% from 100% you have 95%.

[00:15:09]So 95% of the value at start is equal to the value at end. Which means to find the value at start you take 9500 and divide by that and what's the protocol when you divide it by fractions change divide to multiply and invert the divisor before you go out 9500 by one no 95 into 9500 is 100 and 100 by 100 is 10,000 I could always cross check 5% of 10,000 is 500 500 from 10,000 is 9500 Okay.

[00:15:46]All right. We saw this question in previous paper too. A man's regular pay is $3 per hour up to right. Math math dad is live. No, not not 1.05. Yeah, it's you you're deducting. So it's 95.

[00:15:59]So 095.95.

[00:16:02]Sorry, I said the wrong thing. Eight there.

[00:16:07]>> So you're dividing by 0.95.

[00:16:10]Right. So a man's regular pay is $3 per hour up to 40 hours. Okay. Overtime is twice the payment for regular time. So 2 * 3 is six. If he was paid 216, how many hours of overtime did you Okay, so hold on. So first thing is he was paid 216.

[00:16:26]The regular hours is 3x40 in total.

[00:16:29]That's 120.

[00:16:31]So 216 minus 120 is 96. And now if he's paid $6 per hour for overtime, right? So again, if you want, you can do 2x3. 3 into 96 is 32 and 32 / 2 is 60.

[00:16:56]All right, ladies and gents in class, are we okay with this page?

[00:17:02]Any questions? Anybody? Any problems?

[00:17:03]Anything? No. All right. Okay. So, we're about onethird of the way through the paper in about 70 minutes. That's pretty decent, right? Again, if you have any questions, limited reex anything is not a problem. That's why we here.

[00:17:30]Okay. Next page.

[00:17:39]So we could kind of do everything here.

[00:17:42]Okay. 1 over 5x + 2 over 3x is okay. So again when you're adding or subtracting fractions within a common denominator, right? Now let's say the LCM. You don't have to use the LCM, right? Or redo 20.

[00:18:01]All right. So regular pay is $3 per hour up to 40 hours. Anytime you work over 40 hours, you get overtime.

[00:18:09]Overtime is twice the payment for regular time. 2 * 3 is six, right?

[00:18:15]If you was paid 216 for the week, how many hours of overtime work? So 216. So first of all, the regular pay is 3x40.

[00:18:22]That's this piece here, right? 216. So 3x40 is 120. 216us 120 is 96. as the overtime payment. The overtime rate is $6 which is 2x3 and I just I just divide it 96 by 6 is 16, right? Okay. So back here now.

[00:18:44]So 5x 3x will give us 15x^2 and then multiply each numerator by the opposite denominator.

[00:18:54]So we'll get 13 x over 15 x^2 and the x will cancel with the x^2. So we're left with 13 over 15x.

[00:19:08]Okay. 22 sorry. Yeah. 7 times the product of two numbers a and b. The product of a and b is ab and 7 times that is just 7 ab um 23. Then what is the value of x^2 + 3 y / x by y? So x is 4. So we have 4^ 2 3x y is 3x2. x by y is 4x 2. 4 is 16.

[00:19:43]3x2 is 6. 4x 2 is 8. 16 + 6 is 22 / 8.

[00:19:49]That could cancel to 11 / 4. That is equal to 2 and 3.

[00:20:01]All right. Okay. We've seen 24. 24 is 5 by 2x - 1 is. Okay. So check it. You could do this the regular transposition way if you want or ask yourself five. So five multiply by something is 35, right?

[00:20:14]What is the only thing I can multiply by five and get and get 35? Seven. So 2x - 1 has to be equal to 7 or you can say divide by 5 on both sides and 35id 5 is 7. Next. So if 2x - 1 is 7, I'm going to add one to both sides, right?

[00:20:33]And then I'll divide by two.

[00:20:38]So I'll just get four.

[00:20:43]John has x marbles.

[00:20:48]Max has twice as many as John.

[00:20:51]Okay. So Mark John Max Mark Max Mark Max Mark Max Mark Max Mark Max Mark Max Mark Max Mark Max Mark Max Mark Max. So twice as many is 2x, right?

[00:21:03]Max gives John five of his marbles. So Max gives John five. So John now has X + 5 and he gave out five. So x + 5 right if a is equal to 3 and a is equal to 6. Okay so if a is 3 and a * b is 6 it simply means that b had to be equal to 2. Then a^2 minus b ^ 2 is 3^ 2 - 2^ 2 which is 9 - 4 which is 5.

[00:21:43]Right. In the order of this matrix.

[00:21:46]Okay. So, number of rows. So, we have one, two, three rows and then 1 2 3 four columns. So, 27 is C.

[00:22:01]All right. People in class, are we okay with 21 to 27? Right. All right.

[00:22:06]Jonathan, how about you?

[00:22:08]Uh Jaden, this is Matt for now. Admat will start possibly on Friday and see.

[00:22:22]All right, cool. Okay, next page. There we go.

[00:22:29]All right, so we saw 28, 29, 31. Oh, we didn't see 32. Oh, that one is interesting. That one is Let's forget that one. I think that one is C. Anyway, um the determinant of the identity matrix, right? So, 1 0 0 1. So, again, you're multiplying the yellow items together and you're multiplying the blue items together and then you're doing yellow product minus blue and 1 minus 0 is just going to give us one.

[00:23:02]All right. 29. If the vectors P and Q uh that and that respectively. Then P minus 2 Q. So P so again that's 3 2 - 2 Q. So so if you multiply two by this you're going to get -2 and then 8 and you're going to have 3 - - 2 and then 2 - 8. So when you minus and minus you get a plus 3 + 2 is 5. 2 - 8 is - 6. That was option D.

[00:23:43]Bela, how do you recommend I study given that C6 pulling out random topics this year?

[00:23:49]Are we talking about next year? Are you in the next year? Brea or talking about the multiple choice? Does the multiple choice is just repeats? But you had to do enough papers to get all the repeats.

[00:24:00]All right, let's tackle 31 before we scroll down for the matrices. Right. So given that 1 millm is 1 1,000 m, right?

[00:24:09]So long story short, we're just going to divide by a th00and neat. So what I do is I get a PDF and then this is one note. So in one note, you could import the PDF, right? So basically when you import it you get a little file and a print out. I just I just cut and paste the pages and put them on a separate page each >> and then you can write on them at your heart.

[00:24:37]Right. So sorry. So you're going to shift that decimal point one two three spaces to the left. So we're going to end up with 2.5.

[00:24:44]All right. So we at about the halfway point there. Let me see how long we took to that point. About 25 minutes. All right. Not bad. It's pretty cool.

[00:24:53]Sorry. Okay. 32. How many kilograms are there in one ton? That's a th000.

[00:24:58]If anyone want to double check that, please do it. But I'm I'm very sure it's a th000. Okay. Scrolling down now with 30 and 33 and 34.

[00:25:09]Vectors in the middle. Everything. Okay.

[00:25:11]Item 30 refers to the following diagram of triangle OM. R is the midpoint of O.

[00:25:21]So R is the midpoint of the man Phillip.

[00:25:29]R is the midpoint of O L and T is the midpoint of O M. So that's the halfway point.

[00:25:38]Further O R O R is given as vector A. The vector from O to R is A. And if that's halfway along the whole line O L it means that the vector from R to L is also going to be A. Similarly, right, if the vector from O to T is given by B and that's the halfway point, the next half will have the same vector because there are two equal halves. So to go from R to M expressed in terms of A and B. So to go from R to M, you go from R to O and then O to M.

[00:26:15]Let's start there.

[00:26:29]Yeah. No circle theorem. No functions.

[00:26:31]Yeah.

[00:26:33]Hard M. Not to worry about that one.

[00:26:36]Just what you replace on this channel and you'll be fine. Real. Yeah. I don't worry about people, right? going to see a neat. All right, cool. So, check it out. Right. So, we going from R to O. R to O is the inverse of O to R. All right. So, you put a minus sign minus O R and O M is OT + TM. Right? So, that's minus A + B + B, which is minus A + 2 B, which is the same as 2 B minus A, right?

[00:27:13]Yeah, vectors way. All right, cool.

[00:27:17]33. Um, diagram trapezium. The area, so the area of a trapezium is 1/2 of the sum of the parallel sides. So the parallel sides of the two yellow sides there multiplied by the perpendicular distance between them.

[00:27:41]So yellow plus so half of yellow plus yellow then multiplied by the green that's so area is equal to 12 right 8 + 18 then multiply by 5. So 8 + 18 is 26. A half of 26 is 13. 13 by 5 is 65.

[00:28:10]Really? Very good. Okay. At a party, we deserve a party. Any um a number of guests will serve 15 lers of champ. So they doing it backwards, right? Normally we'd have to find out the 15, right?

[00:28:24]Each guest had two glasses of champagne.

[00:28:26]Each glass held 150 ml. Assuming it was a village, how many guests? I think it's 50, right? Okay. So, let me work backwards. Backward, right? Going backwards, right? So, each guest had two glasses of champagne and each glass held 150 milliliters. So, 2 by 150 is equal to 300 ml. So, each guest had that and you had 15 sorry, you had 15 lers. If you multiply 15 by a th00and, we'll convert from liters to milliliters. And then we'll take the 15,000 and divide by the 300 each guest got. Knock off that, knock off that. So 3 into 15 goes five times. So 50 guests.

[00:29:15]Uhhuh.

[00:29:20]Working too, but you're bad. Nice. Nice.

[00:29:26]Okay. In class people, are we okay with this page here? 28 to 34. Any questions, problems, issues? Any of them? No. All right. Jonathan, talk to me. We good there?

[00:29:41]You awake?

[00:29:44]Step away. All right.

[00:29:48]All right. No worries. All right. Going again.

[00:29:53]The perimeter of a square is 56 cm. What is its area in cm squared?

[00:30:00]No problem.

[00:30:02]So a square has four equal so four sides of equal length. So the perimeter is well the total distance around the edge that's side plus side plus side plus which is four times the side. Right? So 56 is equal to four * side length. So 56 / 4 is side length. If you have trouble dividing by four, just divide by two twice.

[00:30:27]So you'll get 14, right? That's equal to s. And now area is equal to s^2, which is 14^2 and that's 196.

[00:30:39]Okay. The circumference of a circle is 154. What is the diameter? So circumference is equal to p<unk> * diameter. So if you divide by pi you'll find diameter that's equal to 154. Now if you're dividing by pi when we're dividing by fractions the protocol change divide to multiply and invert the divider. So 22 goes into 154 seven times and 7 by 7 is 49.

[00:31:12]>> Huh? Yes.

[00:31:15]196 what?

[00:31:18]Yep. Yep. I agree. Get a bus.

[00:31:21]All right.

[00:31:23]Who's that? Cash King. Yeah. All right.

[00:31:25]There you go. On leaving Trinidad, the time on a pilot's watch was 2300 hours.

[00:31:29]That's 11 p.m. at night as opposed to him paying the day. Anyhow, uh when he arrived at his destination in the same time zone on the next day, his watch showed 3:00 a.m. How many hours did the flight take? All right, cool. So, he did 11 p.m. to 12:00 a.m. That's 1 hour.

[00:31:48]And then 12:00 a.m. to 3:00 a.m. is three more hours. So, that's 4 hours in total.

[00:31:56]Cash King. Very good.

[00:31:58]Miss Clark arranged the 15 test scores of her students in order of size and selected the eighth score for reporting purposes. Right. Which of the following statistical measures did Miss Clark obtain? Well, we know it's the median, right? To explain why the median cuts the data set into two equal halves. The half before and the half after you might say, well, how we gettingif how we get half of 15. So, if you take the first seven, right? So, one to seven, then the eighth, and then 9 to 14, you would have seven of um data points before and seven after. That's two equal halves, right? Mhm.

[00:32:36]28. Yeah. The exam was under pressure.

[00:32:40]Yeah, no circle here, no functions here.

[00:32:42]And they brought that first question six. They bring that thing with flour, butter and trigger, which is five C people, you know. And then they bring they brought transformations twice in a row. Yeah. So anyhow, I I like to say very very inappropriate things, but anyhow, before I get cancelled.

[00:33:05]>> Huh?

[00:33:08]Whoever things come into my mind sometime is you know automatic thoughts say psychology. So you have to control those impulses. Yeah. I want to insult them very bad you know.

[00:33:22]>> Anyhow anyhow item 37 refers to the following diagram which consists of a triangle. Okay we saw this right?

[00:33:28]Triangle on a square. If the total area is 63 what is the value of h? Okay cool no problem. So the area of the triangle is base by height over two. So the base here is seven cuz it's part of the side of the square. So 7 by h over two and we got to add 7 squared which is 49, right?

[00:33:47]Okay, cool. So where am I going with this?

[00:33:52]So yeah, so 7h over 2 + 49 is 63. So the first thing we're going to do is we're going to subtract the 49 from both sides.

[00:34:04]So we're going to get 14. Now we're going to multiply by two on both sides.

[00:34:08]Right? So that's 14. Then by two, which is 28.

[00:34:13]And last but not least, we're going to divide by 7. So h is equal to 4.

[00:34:20]There you go.

[00:34:23]Right. This is Yeah, there you go. Very good. Yeah. Really handy. Nice. Nice. Thank >> Okay. in class people are we okay what's on the screen yeah oh okay cool all right Jonathan let me know if you're clear if you're awake if you understand let me know what's up let me know what go hey have a cumulative frequency diagram going based on 200 students going okay median marks scored by the 200 students okay so that's the 100th person. So when you're doing group data, you don't have to worry about n + one, right? Just take the 200 n / two and that'll give you what the 100th, right?

[00:35:13]So what we're going to do, so you'll notice that we don't see 100 outright.

[00:35:18]But here, check it. We have 40, but two blocks, two two sets of big blocks. So clearly the 100 has to be here. What we're going to do, we're going to read across from that 100 across the line till we hit the graph, the CF curve, and then we're going to read down.

[00:35:43]Hey, be yourself now. Not supposed to go exactly, right?

[00:35:47]So that so yeah, and then between the 30 and 40, it has 10 little blocks and 10.

[00:35:51]All right. So 31, 32, 33, 34, 35, 36, 37, 38. So be between 38 and 37. That's 37.5.

[00:36:00]Yep. There you go.

[00:36:06]There you go.

[00:36:10]You just guess. All right. Well, hopefully you pick up the highest mark score in the test was um we'll discover the the 200 student.

[00:36:19]So if you read down from from here so straight down is 60 not so yeah looks to me okay Q1 is a quarter we had yeah that's correct Q2 is a half there you go all right ladies and gents in class you okay with the answers on this page all right so we have about 23 of through the paper. Take a little time check.

[00:36:52]>> 37 minutes. That's pretty good.

[00:36:56]>> Okay.

[00:36:58]All right. Now we go again.

[00:37:01]42. In a box, there are eight red, seven blue, and six green marbles. One marble is picked up randomly. What is the probability that is neither blue nor green? Well, if it's neither blue nor green, there's only one color left, which is what? Red. So that's eight out of. So 8 and 7 is 15. 15 and 6 is 21.

[00:37:21]So the the answer here is a right. Um we'll scroll down just now to do 41. Let's do 44. Right. Um right. A two-way table shows the mode of transport. Let me try me transportation.

[00:37:35]Transportation to school on a particular day. 200 students. Right. So 200 is down here. So you have male, you have female and if you add up 108 and 92 you get 200. Then you have bus, you have taxi, you have walk and then if you add up going across, you also get 200. Okay, a male student is picked at random from the group. What is the probability he does not walk that day?

[00:38:01]So if he doesn't walk, he either takes a taxi or rides a bus. So that's 80 out of 108.

[00:38:11]Now if you divide by four, you get 20 out of 27, which is option C.

[00:38:18]All right, over to YouTube. All right, no problem. How did I get 21?

[00:38:25]Oh, I added up. 8 and 7 is 15. 15 + 6 is 21.

[00:38:31]Sorry. Yeah, cash king.

[00:38:36]Yep, there you go. Real. Very good. All right, cool. Um, yeah, Q1 would be 50. That's correct.

[00:38:44]Melanin Queen, how you going? Me and Triny, how you going? You good? Good to see you online today. Right. Item 43 refers to the following pie chart which shows the popular games played by 720 students. Okay. So, we have degrees, a percentage, and a right angle. How many students play cricket? All right. So, check it. You have 36° here. You have 90 here. 30% of 360.

[00:39:14]Knock off a zero. Knock off a zero. 3x 36 is 108°, right? So, that's 108°.

[00:39:22]So, let's add up those three answers, right? So 36 + 90 + 108.

[00:39:32]Um that's 126 + 108 is 234.

[00:39:39]And then what we'll do is we'll take the 360 minus the 234 and get 126.

[00:39:50]Right? So now we could take 126 over 360. by 720. And here the good news, 360 actually cancels perfectly into 720 twice.

[00:40:03]126 by 2 is 252.

[00:40:10]Very good.

[00:40:13]Right. Number 45. The point where a linear function crosses the horizontal axis as the x intercept. The horizontal axis is the x axis where the function crosses it is the x intercept. The equation of the line which passes through the point 05 which is on the y ais and has a gradient of so so the four is the m this is the x and y which means that five is the c value when you put in the form y = m by x + c right so y is equal to 4 by x which is 4x and plus c is + 5 right cool.

[00:40:49]So, option C.

[00:40:52]All right. Okay, guys. So, we 3/4 of the way through the paper.

[00:40:56]Um, are we okay with this page? Any questions, problems, issues? We good?

[00:41:01]All right. No, let me know how we go with this page.

[00:41:11]All right. So, just two question. Which of the following a linear function?

[00:41:14]That's option A, right? C and D are out.

[00:41:17]Those are when they say linear straight line function. Now you might say, "But Chris, B is a straight line." Yeah, but it's not a function. Why? Because if you were to do the vertical line test, it'll pass the entire thing. A vertical line test should only pass through one point at a time on the line.

[00:41:35]So a hey, look your favorite one.

[00:41:40]So the coordinates of the turning point of the function, right? Let me see if you could just kind of make it look a little right. And then we have the X. Sorry.

[00:41:56]Right. So this is what right that's the turning point. So you read down to the X axis you get two.

[00:42:04]Across to the Y you get four.

[00:42:07]So two four.

[00:42:09]Right. That's 47 and 48.

[00:42:13]All right.

[00:42:15]Need. Yeah. Looks so Well, we good. But yeah. All right. Okay. We okay with 47 and 48?

[00:42:23]Okay. Right. 49 to 54. Okay.

[00:42:28]A line L is parallel to the line that what is the gradient of that line L? So we need to put it in the form y is equal to m by x + c to extract the gradient.

[00:42:39]Right. Okay. Um so what we could do first of all is let's carry across the minus 7 y. So 7 y would be equal to 3x - 9 and then we just divide by 7 on both sides of the equation. So 37s is the gradient there. That's option c. All right number 50. If g of x is 7 x - 3 all over all over 5, right? g of - 6. So 7 by - 6 is - 42 - 42 over -3 will give us - 455 and - 45 is - 9.

[00:43:19]Uh that's correct. Yeah. 37s. Yeah.

[00:43:23]Right. So - 9.

[00:43:27]Okay. Okay. All right. So that's question fifth. This is now in the last 10 questions on the paper. Right. The do the range for f of x to so that's an x cubed. It's a little blurry. Right. So min -2 cubed is -2 by -2 by -2 which is - 8. A minus by minus is a plus. But then when you multiply that by a negative you're going to get back a negative. Minus one cub is -1. 0 to any power is 0. 1 to any power is 1. 2 cub is eight. So option D here.

[00:44:02]Item 53 is a reflection, right? We don't need to know what what the line is or the axis is. We just know, hey, it's a reflection, right? 51 and 54. So we saw 51 already.

[00:44:17]Um that's just x + 3, right? 2 + 3 is 5.

[00:44:21]5 + 3 is 8. 8 + 3 is 11. 11 + 3 is 14.

[00:44:30]Okay.

[00:44:35]Right. So, y is equal to x + 3.

[00:44:38]All right. In which of the following polygons does the sum of the measures of the interior angles equal the sum of the measures of the exterior? Okay. So first of all you have to know that the ex the exterior angles of a plane figure always adds up to 360.

[00:44:57]And if the interior is also 360 what what shape what straight edge shape has the as the sum of the interior angles are 360? A square >> quadrilateral square rectangle quadrilateral.

[00:45:17]>> All right. Okay, folks. Are we okay with 49 to 54? Any questions? Anything to reexlain? Right. How we doing?

[00:45:30]52 is a reflection.

[00:45:37]real after learn how to do reflections.

[00:45:40]Check my previous post. You'll see some stuff.

[00:45:44]Well, my lines, but we know 55. So, what what is the image of y equal to x, right? If it is rotated 90° anticlockwise about the origin, right? That's line y = - 6.

[00:46:17]Okay. Um, but we know what this this one is. Um, the usual thing, right? So, we have the blue line. Sorry, one sec.

[00:46:25]Right?

[00:46:31]And it was translated shifted to the orange. So it's just it's just a shift. It's a translation. So was the vector. So to go from 2 to 4, that's an increase of two. Same thing for 5 to 7 as an increase of two. And then vertically 5 to 6 is an increase of one.

[00:46:47]7 to 8 is an increase of one. So it corresponds. There's a translation with vector 21.

[00:46:55]Correct. Y minus.

[00:46:56]>> Oh, you read it wrong. Yeah. Yeah, that's happening. So, make sure I read it properly. Yeah.

[00:47:03]Okay, ladies and gents in class. How are we feeling with 55 and 56? You okay with those?

[00:47:09]>> Yeah. All right. Going again. 57 and 58 now.

[00:47:14]Okay. So, we've seen both of these already. So, but let's play them the respect. Um, we have a right angle triangle. Angle 30, hypotenuse is 40.

[00:47:23]Um, the length BC. Okay, cool. So relative to the angle given to us 30° that length across there is the opposite side. This length across here is opposite to the right angle which makes it the hypotenuse.

[00:47:38]So opposite and hypotenuse require sign to be used. So sine of 30 is equal to B C over 40. So when you multiply by the denominator to solve we get that BC is equal to 40 by sin 30 which is option A.

[00:47:55]Okay, item 58 refers to the following diagram of an enlargement. Okay, what is the scale factor? So all we have to do is compare the corresponding length. So for example, sorry one sec. Yeah, the vertical here and the vertical here.

[00:48:12]This was one, two units. This was one, two, three, four units. So that's a scale factor of two. If you want to just confirm and frustrate just in case, compare the horizontals.

[00:48:23]That's just one horizontal one two. So the scale factor in the scaling up is two cash king. Very good. Very good. Right.

[00:48:35]Uhhuh. Right. Okay. Ladies and gents in class, are we okay with 57 and 58? Yeah.

[00:48:44]Okay. And so a plane is flying in a direction of 45° changes course in a clockwise direction.

[00:48:53]Uh the angle through which the plane turns is 90. Right? So if you were flying at a 45° angle and then it turns to 135 you increase by 90° in triangle PQR. P is X Q is 2X was the size of angle R. Right? So, if you have two of the angles in the triangle and you want to find the third, you're going to add those two angles together and then subtract from 180.

[00:49:25]That's just going to give us 180 - 3x.

[00:49:29]Okay.

[00:49:33]Okay.

[00:49:36]59 is 90. Very good. Okay. So, we did 60 questions in about 50 minutes.

[00:49:44]Not bad.

[00:49:49]So folks, we'll take our next break there. Uh about maybe about 12 minutes or so. Try and start back about 12:45.

[00:49:55]All right. So 12:45 with various 45 or so. Yeah, I'll cut it close after reaching St. James 4 to get the kids.

[00:50:04]Anyhow, all right. Um