2026 05 25 - Maths F5 - P1 prep sessions - May 2022 P1

Added: 2026-05-26

[00:00:12]Yeah, I think you should go.

[00:00:21]>> All right, I will start starting momentarily.

[00:00:26]>> Give you all some time to Everything keeps looking so Okay, I'll see you tomorrow.

[00:01:02]>> All right.

[00:01:29]I don't have to open this chat. So, okay.

[00:01:40]All right. All right. All right. All right.

[00:01:48]Music.

[00:02:27]Hey, are you done?

[00:02:30]very soon.

[00:02:33]Okay, cool. Right. So, >> okay.

[00:02:50]- 3^ 2 + like that question for the start of the paper boy. It's the same um question two as well. Looks like yeah so it's a little bree - 3^ 2 is 9 - 2 2 is 4 9 + 4 is 13. What is the value of the digits in two in that number there? So that is in the hundreds column. So that's two hundredths. So two over 100.

[00:03:20]What number when added to one and 13 gives two?

[00:03:25]So when added to one and 13 gives two.

[00:03:30]So that's just 2/3, right? When you subtract 1 and 1/3 from that, they get two things.

[00:03:48]>> Okay. Um I guess we could scroll down and tackle four and five the next sequ.

[00:03:53]Okay. So we have to analyze the change.

[00:03:55]Okay. From 1 to six has an increase of five, right? So you add a plus five here. From 6 to 13, you had to add seven. From 13 to 22, you had to add 9.

[00:04:06]22 to 3, you had to add 11. 5 7 9 11 are odd numbers. So to go to the next one, you're going to have to add 13. And 33 + 13 is 46.

[00:04:21]If 30% of a number is 45, what is four fifths of the number? All right.

[00:04:29]So check this, right? So 4 fths is 0.8 or 80%.

[00:04:37]So what you could do to scale it up, all you have to do is take the 80%, put it over the 30, and multiply by the 45.

[00:04:46]Zeros will cancel.

[00:04:48]3 goes into 45 15 times.

[00:04:53]8 by 15 is 120.

[00:05:01]Right? You could always do 45 /.3 you get 150 and you find four fifths of 150 which is 120. Yeah. Okay. That's the first five six and seven. A certain amount of money is shared in the ratio 2 to 3 to 9. If the difference between the first and second shares is 4 and the amount of money shared. Okay, check it.

[00:05:27]What do we do with numbers in the ratio?

[00:05:29]We add them together. 2 + 3 is 5 + 9 is 14, which means we have we have 2 9ths, 3 9ths, sorry, two 14s, huh? 314s and then 94. Right? Now the difference between the first and second shares. So that's between 314s and 214 which is 114. So 114th of the whole is equal to $40.

[00:05:59]So to find the whole we'll multiply 40 by 14, right? Which gives us 560.

[00:06:13]2022.

[00:06:17]>> Yeah. Well, I'll send you obviously, right? Unless you all unless after this session you all don't want to go, >> we do that. But if you're here till 4:00 or just before that, then yeah, we'll do it next week. Right. If P is that, Q is that, S is that, then P intersect Q intersect S. So intersect means a common element. So common to all three is only two.

[00:06:48]Yeah, there you go.

[00:06:51]Item eight, what the shaded region represents? A comp P component. Sorry.

[00:06:56]Okay, so that's the first page one to eight. Ladies and gents, how are you feeling about one to eight? Any questions, problems, issues, anyone or ones you want me to go over or reexplain or we good? Good. Okay.

[00:07:09]>> Yeah.

[00:07:09]>> All right. Going again. 9 to 14 now.

[00:07:13]All right. So, the elements of the set that it's that's very okay. So, x is between six is greater than equal to x but less than 10. So, that's 6 7 8 9.

[00:07:25]So, I'll give you these because they're little they're not very legible. So 6 7 8 9 6 7 8 9 right but not 10 because it's less than 10 and I said x is an integer right item 10 refers to the following info m is pq and r n is p and q which of the following statements is true m is a subset of n intersect n is n yeah m union n is n intersect n is an empty set no right so this is b Right. The intersection of M and N is itself N. Item 11.

[00:08:04]Right. Um we have prime odd and even.

[00:08:06]Which of the following sets is empty? So we've seen this multiple times. That's Q intersect R which is odd intersect even.

[00:08:13]There are no elements in the set odd intersect even because there are no numbers that are all that are odd and also even at the same time. So that's an empty set or as they said in the other the January papers the disjoint sets.

[00:08:28]Uh item 12 refers to the following ven diagram. It shows the universal set and two sets T and C that represent the students in a class play tennis and chess.

[00:08:38]How many students play exactly one game?

[00:08:40]Well, as one, two, three, four people. So far a dress costs $180 and is being sold at a discount of 10%. The amount of the discount 10% of 180 is just 18. Uh the cost of a refrigerator is $1850. If a sales tax of 5% is paid on the cost price of the refrigerator, a buyer who purchases the refri cash will pay.

[00:09:12]So first of all the cost is that the sales tax is that so it'll be more right. So if you were to add 5% onto $1850 would you get a value greater than or less than $1850?

[00:09:33]If you add a 5% sales tax onto the cost you pay more or less than $1850. more was the only option there more than 1850 option D. So we have no calculations to do just have to apply some common sense.

[00:09:46]Well since we hope it's common if you want to work it out you could do that too.

[00:09:54]All right. Any Okay, ladies and gents in class, are you okay with page two?

[00:09:58]Right. All right. Going again.

[00:10:06]Salesman sells a car for 11,000. If he is paid 4.5% for the first 10,000 and 7.5% on the remainder, then the commission he receives is So that's probably good. Let's see. Let's see.

[00:10:19]Let's see. Let's see. Okay. So 11,000.

[00:10:22]So it's 10 it's 4.5% on the first 10,000 right? So 10,000 you get a commission of 4.5%. That's 045. Yeah, not45.

[00:10:34]Don't make that mistake. Now that's going to shift the 1 2 3 four spaces to the right which is $450 and then a,000 cuz 10 + 1 is 11,000 right? And that's the selling the um the price that's multiplied by 7.5% which is 075. So you're going to shift that three spaces that's going to be 75.

[00:11:01]So that's 525 ops on B.

[00:11:09]Okay.

[00:11:10]All right. We've seen 16 already. Let's check it out. Um the value of a plot of land is $18,000. Land tax is charged at a rate of 70 cents per $100 value. What is the total amount of tax paid for the land? Right. So your land is valued at $18,000.

[00:11:28]How many hundreds are in that? Because it's on that that we pay 70 cents which is 70 out of 100. Right? So knock out the zeros. Knock off the zeros. Knock off those. So we end up with 18 by 7.

[00:11:41]So that's 70 + 56 which is 120.

[00:11:54]All right. 17 man's basic wage for a 40hour week is 160. He is paid overtime at a rate of one and a quarter times the hourly rate.

[00:12:04]If he works six and a half hours overtime in a week, what is his wage for the week? So they change the question.

[00:12:11]So a man's basic wage 40 hours for a 40hour week is 160.

[00:12:17]So 160 divided by 40 will give us $4 per hour.

[00:12:24]If you take that and multiply it by 1 and a4 you'll get $5 per hour for the overtime.

[00:12:32]So if he is if he works six and a half hours overtime in a week 6.5 by five. So we've seen this question before. is phrased differently I guess 6x 5 is 30.5 by 5 is 2.5 so we have 32.5 so now the total wage would be the 160 plus the 32.5 which is 192 option D at the end of any year a car is worth 5% less than what it was worth it well we saw this one just now it's10 Right? We know it's 10,000, right? So again, right, if you find if you take the value at the start and you minus 5% of that value, you get the 9500 at the end of the year.

[00:13:27]Right? Now the value is 100% minus 5% that's 95%.

[00:13:33]Right?

[00:13:34]So 95% of the value at start is 9500.

[00:13:41]So to find the value at start you divide. So 9500 divided by when you divide by fractions is the protocol change divide to multiply and invert the divisor. 95 cancel with that 100 times. 100 by 100 is 10,000.

[00:14:00]A loan of 8,000 was repaid in 24 equal monthly installments of 400. What was the interest rate? So 24 by 400 is 9,600.

[00:14:15]>> 9,6us the 8,000 borrowed is 1,600.

[00:14:20]1,600 as a percent of 8,000 will give us 20.

[00:14:30]At a sale, each book was marked $3 off the original price. Daniel paid $46 for two books that had the same original price. What was the original? Sorry, had the same sale price. What was the original cost of one of the books? So, two books that had the same price together cost 46. 46 by 2 is 23. If we add back the $3 discount, we get 26.

[00:15:02]Right. So this is not very legible or visible but I will give it to you.

[00:15:09]So it was 3 x cubed * by not sorry 3x^2 by 2x cubed.

[00:15:18]All right. So 3x 2 will give us 6 and then x^2 by x cq we're going to add the indices you get 6 x to the^ 5 which I I'm thinking is a um c looks like I don't know.

[00:15:35]So it could be either a or c based on this the presence of the six. I'm going to go with a right. Um right and then this one 5 by 2x - 1 is 35. Right?

[00:15:48]If we divide by five first we get a 2x - 1 is = 7.

[00:15:54]If you add one back to both sides we get eight. And then we divide by two get x= Okay. So that's page three. So we about onethird of the way through the paper.

[00:16:13]Uh ladies in class are we okay with this page? Any questions, problems, issues, anything?

[00:16:28]All right.

[00:16:35]All right. So, when twice a certain number is subtracted from seven and the result is multiplied by three, the answer is 33. What is the original number? So when twice a certain number is subtracted from 7 minus twice a certain number and then is 3 to get 33.

[00:16:59]So we'll divide by 3 first to get 11.

[00:17:03]Then what we'll do is we'll minus 11 from both sides. Add the 2x. So we're going to get - 4 = 2x.

[00:17:17]US.

[00:17:23]All right. Tomorrow. Yeah. All right.

[00:17:26]Let's see what we have left to do.

[00:17:33]All right.

[00:17:50]Right. One sec.

[00:18:12]What's up, guys?

[00:18:51]All right. Cool. So given that three star 6 is 12, two star 5 is 9, a star b may be defined as. Right. All right. So we saw that this was option D but you can check them one by one. Right. So we do have that time. Right. So so if we go with option D. So 2 A. So obviously the 3 is in the A spot as the B is in the six spot. So 2x 3 is 6 and 6 + 6 is 12.

[00:19:16]Same thing here. 2x 2 is 4. 4 + 5 is 9.

[00:19:24]Let's scroll down. Okay. So this one's a little difficult to see. So I'm going to I'm going to write it out again.

[00:19:29]Right. So x is -2, y is 3, and I think it's a t. Right? So that's equal to 2.

[00:19:39]So they want um x over y to the power of t.

[00:19:48]Right? So um that's equal to -2 over 3 then squared. Right? Right. So of course when you square something, what are we actually doing? Multiplying it by itself.

[00:19:59]minus that minus is a plus.

[00:20:05]Yeah. Any Yeah. After this one, I'll take a I'll take a break to let me turn and then come on. So So this one is real rough to see. I'm I'm just going to kind of guess as to what it says. I think it says 3 2x + 1 is = 9 to the by 3 to the x.

[00:20:28]Right.

[00:20:30]Okay. So then in this particular case now on the right hand side that's 3^ 2 * 3 ^ x when you're multiplying and they have the same base you add the powers. So what this means is that if if 3 to the 2x + 1 is equal to 3x + 2 it means 2x + 1 is equal to x + 2.

[00:20:55]So what we'll do is we'll subtract the x from both sides and then subtract the one which means x is equal to one.

[00:21:25]All right.

[00:21:28]So, so that how we did this one in previous paper. We do it again. Obviously, three by A. So, you multiplying three by each element. So, what what's going to happen? You're going to get a three, a 9, a minus 9, a 9, a zero, and a 15, which is option A.

[00:21:51]the determinant of a 2x2 identity matrix. Right? So we know that the 2x two identity matrix is 1 0 0 1. So we multiply the one by the one and then minus 0 by 0. 1 - 0 is just one.

[00:22:09]All right. So P minus Q for number 29 that's 3 minus - 2 and then 7 - 5. So 3 - - 2 becomes 3 + 2 which is 5 back and 7 - 5 just so that's it for this page ladies and gents in class. Are you okay with this page?

[00:22:48]All right. So, >> right. So, so we halfway through the paper practically.

[00:23:14]Right.

[00:23:16]Right. Uh-huh. So, parallelogram WXYZ.

[00:23:20]So, XY this is the U here, right? And then the V across there, >> right? Um R is the midpoint of YZ. So WR so the opposite sides are equal and parallel. So this side is opposite to so to go from W to R, we'll go from W to Z and then Z to R, right? WZ is the same as U because they're opposite sides of a paralle which means they're parallel equal. So u now ZR is going up. The vector we have is going down. First thing is the inverse of YZ on top of which we're only going halfway up cuz we're going to the midpoint.

[00:24:26]So that's U - 12 P which is up in E.

[00:24:37]All right.

[00:24:39]34 trapezium. Right. So the area of a trapezium is 1/2 of the sum of the parallel sides multiplied by the perpendicular distance between them. So a half by yellow plus yellow then multiply by blue.

[00:24:58]8 + 18 is 26. A half of 26 is 13.

[00:25:03]13 is 65.

[00:25:10]How am I doing?

[00:25:20]Um probably at most 10 minutes to 35 minutes again it will be it will be um posted. Yes.

[00:25:33]Okay.

[00:25:35]So given that 1,000. Well, 1 millimeter is a thousandth of a meter, right? So, it means that we're dividing by a th00and to go from millimeters to meters. It's going to shift the decimal point three spaces to the left. We're going to get 2, right? The volume in cubic cm of a cube of edge three. So, volume of a cube is side multiply by side by side, right? So, that's 3 cubed 27.

[00:26:06]Perimeter of a square is 48. What is the area?

[00:26:14]>> Same size, right? So, perimeter perimeter is equal to 48.

[00:26:26]Four times the length of each side. So, side is 12. So the area therefore is side by side side by side is 12 by 2 which is 14.

[00:26:47]All right. And for this one here.

[00:26:51]All right. So sector of a circle a o is 60. The radius o is r. The area of a o.

[00:26:58]The area of a sector is the angle in the sector / 360 * pi r 2. That's 60 over 360.

[00:27:11]So six option B challenge now fall asleep boring ones just asleep is a premium for me. All right, ladies and gents class.

[00:27:36]Are we okay with this page up to 35 here? Any questions, problems, issues, anything on this page I want to rework or reexlain?

[00:27:43]No. Okay.

[00:27:45]Uh, no, you can't. You can't carry your calculator in the paper one. Sorry.

[00:27:52]You can't pressure.

[00:28:01]All right. Item 36 refers to a compound shape made up of a rectangle and two identical semicircles, one on either of the short sides. The perimeter above, right? Okay.

[00:28:12]So, two identical semicircles gives us one circle 32 side by side by side. 3x3 by 3 is 27.

[00:28:30]Okay. Okay. So the perimeter. Okay. So check it. Right. So perimeter. So um this piece is 15.

[00:28:38]This piece is 15.

[00:28:47]Right. And blue. That's just 2 pi r.

[00:28:49]Right.

[00:28:52]Right. So right. So if if you cut out the 15 in the middle, you're left with 12.

[00:29:02]So it'll be 15 + 15 plus the two half which is a whole that's two I r sorry so that's multip divide by 12, right?

[00:29:33]And you had to add 15 and 15.

[00:29:41]So, we'll get 30 + 6, sorry, 12 pi. How about you pull out six and get 5 + 2 pi?

[00:30:04]38 um form diagram triang. Okay, cool.

[00:30:08]So we know this side here is 5 cm as well.

[00:30:14]If the height of the triangle is 4 cm, what is the total area? Okay, so the area of the triangle is base by height over two. So base by height is 20 / 2 which is 10. The square is side by side.

[00:30:29]So that's five by five which is 25.

[00:30:31]Right? They have 35 squares as the area of a rectangle is 53.6. If the length is multiplied by four, the width is half then the area would be right length by breath which is 3.6 right the length is four with his heart.

[00:31:08]Sorry literally.

[00:31:17]So four by a half is two6 107.2.

[00:31:34]Okay.

[00:31:36]Right. 37 to 38.

[00:31:38]36 to 30. Are you okay with this page, ladies and gents? Yeah. All right. I'm going to finish the next um next two questions and take a little walk cuz I am knocking out. Not a good thing.

[00:31:52]All right. So, item 39 and 40 refer to the frequency distribution of the average mass in kilograms of a group of school children. The number of children who have a mass of of less than or equal to 40 right less than equal to 40. So that's these two here 28 and 40 is 68 the upper boundary of the media. Okay.

[00:32:18]So first of all to find the median class we need to get a CF CF cumulative frequency 28 plus 60 sorry 68 + 12 is 18 + 34 that's 130 check that again 68 80 114 and 132 All right so the upper boundary the median class So to find the median I just end with two. This is the data right that's 66.

[00:32:54]So the 66th data point would lie here.

[00:32:59]Upper boundary class is 40.5.

[00:33:03]Wow catch.

[00:33:11]All right you post solution files. files, just the replace links to this on YouTube.

[00:33:29]Mrs. Clark arranged 15 the 15 test scores the first students in order of size and the eighth. What did she do?

[00:33:36]She used the media.

[00:33:38]Why is it the medium? Because the first seven are there and then 9 to 14 which also seven.

[00:33:46]So you have the same number of data points before it as you have after it, which is by definition the median, right? Pie chart drawn to scale. Drawn to scale shows how students use 12 hours of study, right? So the amount of time spent. Okay, so math looks like 90°, right? So 90 over 360 multiply by 12. They studied for 12 hours, right?

[00:34:13]So that's a quarter by 12 which is three.

[00:34:22]All right.

[00:34:23]All right ladies and gents in class. Are we okay with 39 to 43?

[00:34:28]Any problems? Any questions? Anybody?

[00:34:29]Anything?

[00:34:36]Wait, is a 43? I didn't do 43.

[00:34:40]If the mean of four numbers is that an X is okay cool is 12. So X + 24 right. So by four is deep.

[00:35:31]There you go. All right. I'm going to put up 44 to 40.

[00:35:36]I had to take a little walk.

[00:35:40]We almost 3/4ers. Can I do this already?

[00:35:42]We are 3/4 of the way through. All right.

[00:35:47]So, we saw this already. So, P and R you have 100 respondents. A respondent is selected at random. What is the probability that he has a positive attitude towards math?

[00:35:59]So, positive is 37 out of a total of 100. That's 37.

[00:36:05]The point where a linear function crosses the horizontal axis that's the x intercept. The equation of a straight line which passes through 05. So that's x and y coordinate and the gradient is 4. So if y is = mx + c, right? So again y = 4 px 45 is correct 47. Okay, we know it's a none of the others pass the vertical line test.

[00:36:57]You doing this in class? You okay with 40 4 to 47?

[00:37:14]So what what is your hair here?

[00:37:34]A line parallel to that. What is the gradient? So parallel lines have the same gradient. So we want to put it in the form y = mx + c 7 y = 3x - youide by 7.

[00:37:57]If I make mistakes, tell me because I am not myself here. So I did very well doing rubbish off and 50 now.

[00:38:10]All right. Simple substitution with functions. G of X is 7 X - 3 over 5. So G of - 6 7 by - 6 and - 3.

[00:38:22]That's going to give us - 42 - 305 - N. Why is it over 45? So, right.

[00:38:54]Okay, sorry if I speeding through. I'm trying to finish this before I fall asleep. Prove to be difficult, right? So that's why that's x cubed, right? f of x is x cubed. So we said -2 cub is -2 by -2 by -2 minus by is a plus 4 by -2 is - 8 - 1 cubed - 1 0 cubed is 0 >> 1 cubed is just one cub So the solution set here is what?

[00:39:43]D.

[00:39:48]Which of the following pairs of lines is perpendicular?

[00:39:52]Right? So when they're perpendicular, the product of their gradients is minus one. So we could automatically eliminate E because the gradients are actually the same.

[00:40:01]Let's check out C. Here if by four= sorry remember right so if you take minus four and one what what yeah see is the answer here.

[00:40:54]If the sum of the interior angles of a polygon is four right angles, then the polygon is a so four by 90 is 360°.

[00:41:04]Right?

[00:41:06]That's a quarter.

[00:41:12]All right. Seven questions to go. Let's see if you could just finish this and then we'll take a a break.

[00:41:23]All right. So, we know 54 is a reflection.

[00:41:34]Come to mind yourself 55. So, that's 30 30 x. So, we know the isocles triangle, right?

[00:41:43]Come to man that 180 - 30 + 30 which is 60°.

[00:41:52]180 - 60 is 120, right?

[00:41:59]56. We know it's 3.5, right? So again, we know that the two the two triangles have the same angles or magnitude for the angles in the same corresponding positions.

[00:42:12]makes them similar. So the angles may be the same between the triangle but the lengths are not. Matter of fact, if we examine this and this we will see what the bigger is two times smaller or the smaller is one sec. Yeah.

[00:42:39]So to get the smaller value here we multiply by half of this point after it under goes a translation.

[00:43:00]Right? So we have one two plus >> sorry 1 + 2 + I guess from a four - 2, >> right? Plane flying through an angle of 45 changes to 135. The angle through which it travel is 90°.

[00:44:03]We okay with this page.

[00:44:05]All right, last two questions here.

[00:44:12]All right, look. Let me do 60 first.

[00:44:13]I'll back up on the 59. Right.

[00:44:19]>> Okay. So, we're going to drill. All right.

[00:44:23]These two lines are both parallel because they're both perfectly horizontal. we have a transversal cutting them which is the um the hypotenuse basically of the triangle which means therefore that we have Z angles being formed because that was the implication thereof mean that this angle here is also 30° right so if X is 10 m from Y the height of Z want the height right so that that's opposite to the angle that's adjacent sorry So we need tan. So tan theta tan 30 is equal to the opposite which is y z by 10. So 10 m* 10 30 sorry 10 30 right cool only option with tan by the way and then across here right so surveyor sets up his instruments 12 m from the foot of a building and records the angle of elevation to the top of the bit so that looks like to me like 40° right now he's 1.6 6 m in height and you have 12 m from that. So an estimate of the height of the building can be obtained by well you got to add back the 1.6.

[00:45:49]So to me that's going to be either option A or B, right? So this 12 here is the same as this 12 here.

[00:46:05]Right? So what that means therefore is that this is opposite and yellow is the adjacent.

[00:46:16]So tan 40 is equal to the height 12. So 12 by tan 40 and then you're going to add the 1.6. So that's option B.

[00:46:41]Okay, so that was about 46 minutes.

[00:46:49]All right, so we finished the plan for the day, but I mean we here advertised time was still 3:30, but I I will be running away now to go and pick up my kids and come back. So we might start back near to 2:30 but given the pace we moving at I think we'll still finish by 3:30. All right. All right guys. So you have a all the chill or whatever if you're going cool. If nobody going to be here this parents lost the lock. I need to.