CSEC Math June 2026 Paper 1 23.5.2026 Part 1

Added: 2026-05-24

[00:00:27]Okay, ready to start. So, as I said, you have to write down um you know, you'll get the paper on the website and also in the folder. All right, so this going to be the latest paper. So, let's go straight to the whiteboard.

[00:00:43]Just let me know when you're okay with the working and you're ready to move forward. All right. So, you can see that this is the January 2026 paper.

[00:00:52]Okay. So, it's um this week I put it into the folder with all the um past papers. All right.

[00:01:00]So, let's go to the first question.

[00:01:06]All right. So, we have the number um you know 3.14 03 063 written correct to three decimal places. So you want to write this to three decimal places. So you know your first decimal, second, third after third decimal places are six. Therefore zero goes up by one and therefore my answer is supposed to be 3.14 and that zero will go up by one and everything behind it will turn into zeros.

[00:01:34]Now because we behind the decimal point these zeros don't matter and therefore my answer will just be 3.41. 4 1.

[00:01:45]Okay, so that's a So that's ready to move for my thumbs up.

[00:02:34]Okay.

[00:02:39]All right. Next question we have.

[00:02:46]All right.

[00:02:48]Yeah, I know that.

[00:02:50]Well, the rest of them go see the recording. All right.

[00:02:54]So, using the distributive property. All right. So we want to you know write this and we look at the options that we have here. They say use the distributive property. So when I think of the distributive property I'm looking at expansion. So I just want to show you on the side here what's on my mind when they say distributive property. You know if you have um let's say this is three here. Yeah. X + Y right? This is distributive. 3x is 3x and 3x y. So you see plus sign here and you put 3 y. So this is distributive property. All right.

[00:03:42]So when I look at this question now um notice this is 3 * x + 3 * y. I'm seeing 49 * 17 + 49 * 3. So you see how the three is um common to these two here with the plus sign in the middle. I'm seeing the 49. All right. Multiply by 17 and multiply by three the plus sign in the middle which would tell me that you know um we're going to add the 49 outside the brackets and it's going to distribute over the 17 + 3. If you already look at it, you going get 49 right by 17 plus 49 by three with the distributive property.

[00:04:28]So then I come here and I look and say okay um do I have anything like that? And the answer is no. All right, I don't have anything like that. So then I say hm um well I don't have anything like this 49 but 17 + 3 is 20 and I'm seeing 49 by 20.

[00:04:51]This is 49 by this in brackets right?

[00:04:55]So 49 by 17 + 3 would give you 49 by 20.

[00:05:06]Okay. So as I shown you how we move from this why this is equal to this. All right distributive property right and the 17 + 3 is the 20. So you see the 49 by 20 right here.

[00:06:16]I just ready to move forward. Let this give me thumbs up.

[00:06:21]I just want to make sure you go through the working.

[00:06:24]You understand what going on?

[00:07:22]Okay.

[00:07:26]All right. So moving on to number three, we have you know standard notation. So that's um standard form and you know the objective of standard form is to have one decimal point in well one nonzero digit in front of the decimal point. So what I need is 2.0806.

[00:07:47]Now we can see that I moved the decimal point. Put in red one two two places this way. All right. Remember I told you the direction you go opposite the number line. So on the number line going to the left is negative. So this could be the opposite. If I go to the left that'll be positive. So that you multiply by 10. So it's always multiply by 10. I power positive two. All right. So let's come here and see if we have that as option.

[00:08:16]And let's go through on the 10th side here. Negative -2. No one positive2.

[00:08:19]Okay, let's read. 2.086 2.0 sorry 806. Yep. By 10^ 2. So the answer is C uh if you go backwards the power will be negative.

[00:08:49]So yes, even if you had to go backwards to move the decimal points, but the power will be negative instead. All right.

[00:08:57]So forward power is positive. But it depends on what how how you look at it there cuz I might say this is backwards and this way is forwards. So I just think opposite the number line. So going to the left is um negative. Sorry.

[00:09:11]Going to the left is positive and going to the right will be negative.

[00:09:30]All right. Going this way. Positive.

[00:09:36]Going this way. Negative.

[00:09:39]All right. Right. So number four.

[00:10:11]So this is number bases. All right. I think I'm with the January 2026 paper 2.

[00:10:17]I went through a little bit of explanation on this. All right. So in base 10, the value of the digit two in the number here is so this is the two right here.

[00:10:28]And I want it in base 10. The value of the two in base 10. So this is base 8.

[00:10:33]So I'll split everything up. We counting um 8 to the^ 0 8 the power 1 8 the power 2 8 to the power 3. So this is going to look like this.

[00:10:47]4 2 3 1 in base 8 is 4 by 8 to the power of 1 2 0 1 2 3 so 3 + 2 by 8 to the power 2 + bring this across a little more anyway.

[00:11:16]All right. Then we have 3 by 80 ^ 1 + 1 by 8 the power zero. So that that's that's how you write out um in any base.

[00:11:29]This this number here will be the base right. Uh yes counting the first number here is to the power 0. This one to the power 1 power two power 3 exactly what you seen here. So the two the value of the two is 2 by 8 to the power two. All right. So the value of two is 2x 8 ^ 2 and once I work this out I'm going to get it in the answer base 10 then all right so 88 squar is 64 so that's 2x 64 um you could go and do a long multiplication here because you're my calculators but you should know that 128 but I still do it you know 64 by 2 so you know 2x4 is 8 and 2x 6 is 12 all All right. So 128 is B.

[00:13:53]All right. So, moving on to number five coming up here.

[00:13:58]All right. So, we got some stats here now.

[00:14:02]So item five refers to the following table which shows the relationship between the number of matches an umpire officiates during a T20 cricket tournament and the amount of money he earns. So on top here we have the number of matches, three matches, four matches, five matches, six matches, right? So the matches on top here this is the money he earns. So off three matches he earned $61.

[00:14:26]Four matches he he earned $73. five matches he officiates he earn $85 and so on. Let's see what I want to ask here now.

[00:14:39]If the pattern continues, how much money will he would the umpire receive if he officiates eight matches? So there's a pattern here, right? So we so this a pattern question.

[00:14:52]So basically I want to know when seven matches and then eight.

[00:15:02]Let's extend this a little bit cuz I I go and add this one.

[00:15:15]All right, that's what we want to know.

[00:15:20]how much money you going to earn for eight matches if this pattern continues.

[00:15:25]So I to figure out the pattern right now you have no calculator here. So I'm looking 61 to 73. Uh what what's what do I see? Let's just subtract it and see.

[00:15:36]All right. So 73 I mean you could do that. Um 9 to make 7 and then three. So 9 and 3 is 12.

[00:15:46]All right. Uh 7 85 to 73.

[00:15:50]uh 7 to make 80 and 7 and 5 is 12. So they go up by 12. But I'll just demonstrate here. 73 take away 61.

[00:16:00]2 1 12. All right. And then I say 85 take away 73.

[00:16:08]3.5 is 2 1. If I see um 97 take away 85, I get two one.

[00:16:20]So therefore the common difference is equal to 12. Okay. Now you don't need to find the nth term here because you know it's it's right here. So um 7 match is going to be 97 + 12. Okay.

[00:16:46]So if I put 97 + 12 um 9 and 2 sorry 7 and 2 is 9 and this is um 10 109. So I'll get 109 here. All right. And then I'll say you know 109 + 12.

[00:17:05]All right. 9 and 2 is 11.

[00:17:10]All right, take the one from here. 1 + 0 is 1 plus this one is 2 and 1. So 121.

[00:17:17]Okay, going up by 12 all the time. All right, so the answer is B.

[00:18:38]All right.

[00:18:40]So, going on question six now.

[00:18:44]All right. We have there are 40 students in a class. Okay. Girls make up 60% of the class and 25% of the girls wear glasses. I remember this question was in the the 2022 paper that will tell the questions repeat exactly. All right. So once you do enough add these past papers you'll see same you'll be seeing the same questions over and over. It don't matter what year you do. See 2022 2026 do a older year the same questions being recycled all the time. All right. So we have 40 students in the class.

[00:19:15]All right. 60% is girls and then you got 25% are the 60 that wear glasses. Right.

[00:19:20]So you'll take the photo you multiply it by 60%. So as 60 over 100 and this shall be the number of girls and from the number of girls you want 25%. So let's multiply by further 25 over 100 to get the glasses. Who wearing glasses? Right.

[00:19:40]So one big working. Uh we just start crossing out.

[00:19:47]I could um I mean I could go to a zero here and a zero here.

[00:19:52]I can leave the photo. It really don't matter how you want to do it. Cancel these zeros right here. It's just your choice.

[00:20:01]Okay. And then you know I could see you know 25 into 251 25 to 104.

[00:20:11]So this is one and four.

[00:20:16]All right. Um the 6 and 10 we could do something there as well.

[00:20:22]We could say um you know 2 into six and two into 100 2 into 10 sorry is five.

[00:20:31]And instead of saying five, you can go 5 into 40 is 8. Um, that could work. Or 4 into 40 is 10.

[00:20:40]However you want to do it. All right.

[00:20:42]So, let's go the um I'll go with um 5 into 5 1 5 into 4 to 8. And then I will do the eight and four. All right. So 4 into 8 is two.

[00:20:58]So 4 into 4 1 and 4 into 8 is two. So in the end all remains down here is just ones and here's just 2x 3x 1.

[00:21:09]So end up with a two by three which is six All right.

[00:22:30]Uh let's move forward here now. So seven uh we have Okay. So this is a six question.

[00:22:38]Um this is a standard formula. So this is called the power set. This means the number of elements in a m then the number of subsets of a can be expressed as. All right. Right. So, I just going to put um note if all right they use M here, right? Um so if n is the number of elements in a set the number of subsets is equal to 2 ^ n. So this is a general formula for the number of subsets 2 ^ n.

[00:23:37]Example, if a is equal to let's call this um p Q q r all right so there are three elements in the set then the number of elements in a is three because you have one two three elements in a then the number of subsets.

[00:24:13]Okay of a is equal to 2 ^ 3 which is equal to 8.

[00:24:26]So that that that that's the concept behind number of subsets. Um therefore if this the number of elements is m then the number of subsets of a is equal to 2 ^ of m because m is the number of elements in a see just like I had number of elements in a is three. All right, cuz you have three elements in the set. There's 2 to the^ 3. Well, the number of elements in A is M. So the number of subsets of A will just be 2 to the power M. Okay, so the answer is B.

[00:25:08]I mean, you can just watch this and write the answer one time, but I just want to explain why it's why I have two to the power M, right? This is standard formula for this um number of subsets.

[00:26:46]Okay. See. All right. So, going on to question eight, we have that given that A is equal to well all these numbers here. Okay. We have B. Which of the following statements is true about A and B? All right. So this is uh liqu processor elimination here because you don't know what to do with these two sets as yet.

[00:27:09]Um but what I could observe is that before I start answer anything you know um let's highlight some things I'll shade in here going on and I'll shade in this brown. I seen six here and I've seen six here. I seen nine here and I seen nine here. I've seen 12 here and I seen 12 here. So that I observe right which means all the elements of B is contained in A which tells me that B is a subset of A. All right.

[00:27:45]So since all the elements of B is contained in A.

[00:28:04]B is a subset of A. I write that.

[00:28:13]Well, you've seen it right here. B is a subset of A. That's how you write it.

[00:28:20]And that's your option right here.

[00:29:50]Okay. All right. So, let's move forward here. Next page.

[00:29:56]Question nine.

[00:30:03]All right. So we have a big ven diagram.

[00:30:05]Plenty things going on inside of here according to the diagram.

[00:30:11]Now this mean number of elements. Right.

[00:30:13]So and this is union and this is a complement. All right.

[00:30:19]So this is how I'm going to read this number of elements in X union Y complement.

[00:30:49]Now complement mean not. Okay.

[00:30:53]So X union Y means all the elements in X together with all the elements in Y. All right.

[00:31:03]So you see these two circles with X and Y that'll be X union Y. The two circles is X union Y. And then the complement mean not that. Okay. Not that. So not that will be everything outside. So we are looking at these numbers out here.

[00:31:29]Okay.

[00:31:30]So again I I'll explain all the elements in X together with all the elements in Y will be X union Y. The union between these two is all the elements in here.

[00:31:42]But complement means not. So then you're saying it's not the elements in these two circles. So if it's not the elements in these two circles, it will be the elements on the outside. Now number of elements means you have to count them up. So I say 1 2 3 4 5 6 7 8 9 10 11.

[00:32:02]Okay? And that's how I end up with 11 here.

[00:32:42]If I spell compliment correct means not.

[00:32:46]Let make sure I spell that correct.

[00:33:02]E L I M T. All right. Good.

[00:33:18]See saying I counted up.

[00:33:25]I counted up the numbers on the outside.

[00:33:28]The ones that shade in yellow. Those are count up to 11.

[00:33:32]Remember compliment means not. The little stroke I seen on outside the brackets mean not.

[00:33:40]So it's not the union.

[00:34:05]Right. The number of elements in X union Y complement.

[00:34:12]All right. Complement mean not not Okay. All right. So, next one.

[00:34:39]All right. Question 10. We have which of the following statements best describe the elements of the subset X intersect Y complement in the V vend diagram?

[00:34:52]Okay. So, we are referring to this vend diagram.

[00:34:57]All right. So this is X intersect Y complement.

[00:35:05]So all right thin red.

[00:35:38]Okay.

[00:35:39]Now I would just draw a little vend diagram here for your sake just to explain this before I go to the um you know the vend diagram above there smaller to circle inside of Yeah.

[00:36:10]Nice.

[00:36:13]All right. So, I'm going to put here as X and Y. Now, the intersection of space there, right?

[00:36:45]right? So the intersection right will be inside of here. All right. Now when I say X intersect Y those are all the elements that's common to X and Y but when I say X intersect Y complement think about it Y complement mean not Y.

[00:37:06]So all the elements that are common between X and not Y. All right. So this I don't if I space to write I'm going make cell bigger so I can write out small this will be all the elements that is Come on to X and not Y.

[00:37:53]All right.

[00:37:55]Now I know that's English X and not Y. I say you're thinking X alone. X and not Y. Not Y is something, right? Put not Y in brackets. All right. X and not Y. So I put X in brackets and not Y. So if you come back here now, not y is everything on the outside.

[00:38:15]Okay? Cuz this this is this circle here is y. So not y is on the outside here, including this part x here. And then what x have in common? What x have in common and not y would just be this portion alone.

[00:38:34]I don't know if you can visually see that.

[00:38:39]So I try and explain it again. Not Y is everything that's not in the circle Y.

[00:38:46]So that includes all out here and this part X. So everything that's not in the circle Y is not Y. But then you want what's common between X and not Y. And this part here is common to is common in X and also in not Y. So this is the intersection between the two. Okay. So with that in mind, we come up here now and we look this here will be X and not Y.

[00:39:15]Okay, the two one and four. So you have three elements here. I hope that makes sense. Okay, again think about it. Not Y will be all these elements out here together with these elements here. Everything inside the circle here will be Y. So not y is everything on the outside including these here cuz this is not in y. And then what does x have in common with that set? Well only these three elements cuz this this is an x as well. Okay. So that's how we're going to get well those three elements. Let's see that's uh 2 1 and four.

[00:40:03]So x intersect not y would be elements 1 2 and four.

[00:40:13]All right. And then you're asking you know which best describes that um factors of four because all these could go into four right factors of four is 1 2 and four only. So therefore the answer is a. These are factors of four.

[00:40:32]All right.

[00:40:49]I will try and make this all smaller.

[00:40:51]So, kind of want to see the vendagram as well. Let's see. I could bring this I hope you can still see there. All right. So, refer to that vend diagram.

[00:43:13]All right. So, moving forward here now.

[00:43:18]Question 11.

[00:43:20]All right. All right. So this have nothing to do with this vin diagram. So 9 and 10 was for that vin diagram. So we can just focus on question 11 here now.

[00:43:30]All right. So which of the following I realized with this 2026 paper they're asking a lot of questions on sets cuz look how much questions they ask so far normal the other past papers they didn't ask so much sets questions. So that might that might be a trend for this um multiple choice are coming up here that you know going to ask a good number of questions on sets because you know sets is not tested in the paper too. All right so I guess they're really testing it here in paper one normally just ask a few questions and not so much. All right so I just noticing that. All right.

[00:44:05]All right. So which of the following pairs of sets is an example of disjoint sets? So disjoint sets are sets that have nothing in common. Okay? So if you think about it, disjoint sets have nothing in common. I wonder if I could just borrow this from on top here.

[00:44:38]All right. So that that's just disjoint steps here.

[00:44:41]All right. Nothing in common.

[00:44:53]All right. So then you go through this list here and see you know which which one of these will have nothing overlapping. Right now whole numbers and rational numbers. Any rational number can be written as a whole number cuz rational numbers um numbers that can be written as a fraction. But I could write 5 over 1. 5 over 1 is a rational number cuz a fraction 5 over 1 but is also a whole number which is five. So you know x and y have a overlap. They have elements in common. Therefore they're not disjoint.

[00:45:24]Multiples of five and multiples of 10.

[00:45:26]That should be obvious cuz 10 is a multiple of five and 10 is of the first multiple of 10. So they have elements in common. All right. Multiples of two are like 2 4 6 but multiples of three are 369. So six is common to these two. So you have elements in common. So they're not disjoint. So I mean by process of elimination I eliminate a b and c. So obviously it had to be d. If you think about it if a number is even then it's not odd. I'm sorry it's it's not odd.

[00:45:55]Yeah. And if it's odd it's not even.

[00:45:58]Even and odd numbers have no overlap.

[00:46:00]All right. Even is 2 4 68. Odd is 1 357 going down like that. They don't intersect at all. They have nothing in common. So the answer is D. They'll be disjoint.

[00:46:19]And I could even put something here, you know, even.

[00:46:25]All right. Just to make it all better.

[00:46:27]Yeah. Um 2 4 6 remove let remove the um comma.

[00:46:37]All right 2 4 6 8 10 12 etc. Right. And here you are 1 3 5 7 9 11 you know 13 and so on. says C there's no overlapping between odd and even I believe in 2022 paper as well we had the same question okay I tell you questions Eight.

[00:48:31]All right, let's move on to Okay, 12 will be up here. All right, so 12 is a pretty big question in terms of size.

[00:48:39]You know, I might have to zoom out.

[00:48:41]Might things might look a little small, but let me see. All students in a class play Scrabble. So S is for Scrabble, C is for checkers. They're saying all students play Scrabble or checkers. All right. So they say no intersection yet, right? Scrabble or.

[00:48:57]All right. Or both. Okay. So both mean inter. So see this could mean intersection.

[00:49:03]All right.

[00:49:05]Now I would draw a vend diagram. So before I look at the options, I would um I want that packet borrowed. I'm going borrow from here.

[00:49:15]Okay, I'll do it fresh.

[00:49:18]All right, I'm just going to read the question and formulate my own vend diagram and then I'll look at the options that are available and see which one, you know, is that nice.

[00:49:48]All right. So, we have Scrabble. S is scrabble and C's for checks. And the reason I draw it intersecting is because they say both. All right.

[00:49:58]Now, if 36% of the students play Scrabble, I'll hold off cuz whenever I have an intersection, you're putting the intersection first. Okay. So I ain't going Russ and put 36% as yet. Oh you see this only. Okay. So this this changes things. If they say 36% of the students play Scrabble then the whole circle will be 36%. So I have to wait to see where the intersection is. But because they say scrabble only talking about this part here. So therefore I could come and put you know 36%. Here could scrabble only. That's with without the intersection there 36%. All right.

[00:50:40]Um then 48% of the students play checkers only. So that's without the intersection.

[00:50:48]All right. So that's 48%.

[00:50:51]So that doesn't include the intersection. All right. Uh which of the following vend diagrams is most accurately represent the information?

[00:51:00]Now the thing is they say all students play Scrabble or checkers. All that be 100% has to be in Scrabble or checkers. So everything inside of here must add up to 100%.

[00:51:19]So if I put here as X then what I'm saying is 36% plus 48% plus X must be equal to 100%.

[00:51:40]Okay.

[00:51:45]Okay.

[00:51:47]I'm going to erase that.

[00:51:51]All right. So, we could add that up quickly. Um, you know, 48 + 36. All right. 6 and 8 that is uh 12 13 14 4. All right. 3 and 4 is 7 + 1 is 8.

[00:52:09]That 84. So, you have 84% plus X is equal to 100%. Let's take that away. So x is equal to 100 take away 84.

[00:52:29]All right. Uh you can do that in your head. Um six to make 90 and then 10. So that's 16.

[00:52:35]All right. So that tells me x is 16%.

[00:52:41]Okay. So um yeah look for that 36 x 36 and 48 I seen that right here as 36 16 and 48.

[00:52:54]Yeah.

[00:52:55]So I go I go and look for the answer right here.

[00:53:13]So let's give a two seconds.

[00:55:02]All right. So, I'm back.

[00:55:22]So, don't forget to give me a thumbs up when you're ready to move forward.

[00:55:29]Right. Nice. So, okay. So, we didn't go through all these option cuz A was the answer.

[00:55:41]Okay.

[00:55:42]All right. Question 13.

[00:55:45]Okay. So, some consumer arithmetic here now. So, excluding sales tax, how much will be saved when a video which costs $12 is sold at 20% discount? Now, they never told you what sales tax is. So, this is just to throw you off. All right?

[00:56:06]Because this was never mentioned. So, yeah, explain sales tax. So, we just want to find, you know, something was sold at $12 at 20% discount. Now, think about it. The item was sold at 80%. All right. Um, let me explain that. So, the the cost price is 100%.

[00:56:30]All right. So the cost price would be 100%.

[00:56:38]Now because I discount the selling price it was sold at a discount right of 20%.

[00:56:52]Because this is the discount. So 80%.

[00:56:58]Where you know this is the discount.

[00:57:06]Now it means this $12. It means the 80% is the $12.

[00:57:17]Okay.

[00:57:19]So, oh, I reading this question wrong. How much will be saved when a video which cost $12 is sold at 20% discount? Okay, so the video is sold at $12.

[00:57:41]Then we have to find the discounted price and see how much will be saved.

[00:57:44]All right. So the uh the $12 is 100% the cost price.

[00:57:49]Okay. So 100% is equal to $12.

[00:57:56]All right. So what we want to do is find for 1%.

[00:58:00]Which means we got to divide this by 100.

[00:58:06]All right. And then the selling price which is 80% cuz 20% discount. Or we could have find 20% of 12. All right.

[00:58:15]And and see how much would that be saved. That that could have worked too.

[00:58:18]So you know approach this question in a longer way. Um the shorter way is just um cuz initially I read the question at the wrong time of mine. All right. So I just find 20% of $12 and that's how much you save. So you go through all this. Okay.

[00:58:39]cuz now I go and see okay now the um 20% or the 80% to get the selling price is um this by 80 to get the selling price but we already know what the selling price that's what um the amount save which is the 20%. Okay. So, you know what? I scrap all this.

[00:58:58]All right. And just put um discount is just equal to 20% of the $12. Okay. And let's work out that. All right.

[00:59:18]So, we can cancel the zeros right here.

[00:59:22]All right. We could say, you know, um, you know, 10 12, however you want to do it. Or 2 into 2 1. And you know what? I prefer to keep it. You see this money here? I prefer to keep the 10. All right. That that'll make things nice. So I I know this is not um how you put it, you're looking to cancel, but you see this 10 below here, I want to keep it.

[00:59:51]So I multiply 2 by 12 and get 24 / 10.

[00:59:54]And I'll show you why. All right. So 2x 12 / 10. So that's 24 / 10. And by keeping the 10 there, I just move decimal point one space to the left and get 2.4, which would give me uh $240.

[01:00:14]And that's why I kept the 10 below.

[01:00:16]Let's make life easy instead of canceling up and then trying to convert a decimal. Making life harder, right?

[01:01:17]We'll see. So, I believe that's it for this page, right? So, next page now.

[01:01:30]All right. So, we have a store. Uh, at a store, 3 cents on every dollar spent is charged as sales tax. All right. So, three cents on every dollar. Okay, we can work with that. How much is paid in sales tax on a costume which costs 196?

[01:01:49]Remember, it's three three cents on every dollar, right?

[01:01:53]So for sales tax all right is equal to 0.03 all right on every dollar.

[01:02:15]So we have $196.

[01:02:18]All right. We just multiply that by 0.03. 03. Okay, cuz 0.03 196 times. So sales tax is just equal to 0.03 * 196. Oh, that makes sense, right? Cuz is this amount for every dollar and you have $196. So you have this 196 times.

[01:02:43]Okay. Now when we multiply, we don't multiply with the decimal point. We add it in after. So you put the 196 like this. You multiply by three. All right.

[01:02:53]So 3 sixes are 18.

[01:02:56]All right. 9 3es are 27 and add the one 28.

[01:03:01]All right. And 3x 1 is 3 + 2 5. All right. Now the only thing with 5 88 is this one. So all right. See that this is the answer. But you know we had two decimal places here. So I come and put it back in. So you start here. icon 1 2 and that's how you're going to get your sales tax to be equal to 5.88.

[01:03:26]All right.

[01:03:28]So does Hey, All right. No All right. So, moving on here now.

[01:05:19]So, we have the cash price of a television set is $350.

[01:05:25]All right. When bought on high purchase.

[01:05:28]Okay. Okay, so cash price purchase price the deposit is 35 down payment 12 month payments are $30. Okay, how much is saved by paying cash? So what we want to work out is the higher purchase price.

[01:05:43]So would be the $35 down payment plus your monthly 12 monthly payments at.

[01:06:00]Now this one easy to work out cuz you can just multiply 12 by three and get 36 and add a zero. All right. So 12 by 3 is 36 and add a zero.

[01:06:10]And I could add that up easy cuz this could be 3.95.

[01:06:14]Okay, if you need to go do while working, no problem. So that's your higher purchase price and the cash price is 350. All right, so money saved would just be the 395 take away 350 cash price here. And you can see that that's uh $45.

[01:06:43]So the answer is D Okay. All right. So, question 16. All right. So, we have a loan of $8,000 was paid back in 2 years. Okay. The monthly payments were $400. The interest on the loan as a percentage was All right. So, breaking this down, the you're paying $400 for 2 years um monthly payments. So, 2 years is equal to 24 months. All right. So, 2 years that's 24 cuz 12 months in a year, right? So, that's 24 months.

[01:09:53]Okay. So, you're paying $400 for two years. So that's 400 by 24.

[01:09:59]So I'm going put um money paid back is equal to $400.

[01:10:27]by 24. Now, you can multiply this easy by just saying 4 by 24 and adding two zeros. So, I could just put 24 by 4.

[01:10:37]All right. Um, four fours are 16 and 4 2's are 8 + 1 is 9 and let's add two zeros.

[01:10:50]So, my interest will be the 8,000. Take away this amount. Okay? cuz this is the money paid back total.

[01:10:58]So they want the interest on the loan as a percentage was. So I get the interest as a percentage. So let me work out the interest 9,600 take away the 8,000 you borrow and that will be 1,600.

[01:11:20]Okay. So now that we had the interest of 1,600, you want the interest on the loan as a percentage. So you put the interest over the original amount you borrow, which is the 8,000. So we're going to have the interest over the original amount you borrow as a percentage. So multiply by 100 over one.

[01:11:43]All right. So that's what we're working out. Um I mean these these are stuff you can work out quickly but you know trying to teach so I write it out so that you can understand. All right so start cancelelling up um however you want to do it. Now if you want to take these two zeros here, one, one, two, close those gold and then I could take, you know, this zero here with this one here. So that's our 8 over 160.

[01:12:21]For teaching sake, I'll bring it out.

[01:12:24]All right. Right. So I have um 160 over 8 which could be broken down, right? Cuz 8 into 16 is two, right? So that's that's 20. All right. 20%.

[01:12:40]All right. If you need to show that, you know, 8 into 81, 8 into 16 2 add the zero there.

[01:13:02]Hey hey hey hey hey hey hey hey hey hey.

[01:13:29]The power of the power.

[01:13:48]Let your power All right. So, moving on to question 17.

[01:14:29]Let's see what we have here. We have a man pays 60 60 cents for every 200 m cube of gas used plus a fixed charge.

[01:14:40]All right. So let's see if he pays this amount when using this volume of gas.

[01:14:47]How much was the fixed charge?

[01:14:51]So is 60 cents for every 200 m cube. All right.

[01:15:00]So when he uses this amount, how much? All right. So I would say, you know, 60 cents is 0.60 for every 200 m cube. All right. So what I want to get is how much for 5,500 m cubed. So maybe I could write this the other way around and find for one me cube and then I could find for 55,000. All right. And we'll see what the price will work out to be. So, let's put the other way around. Not not that I write it wrong.

[01:15:43]All this one here.

[01:15:48]All right. Go ahead. Go ahead.

[01:16:15]All right. Okay.

[01:16:19]So, as I said, I write it this way cuz I want to find for 1 m cube first, right?

[01:16:22]So, the 200 m cube is equal to 60 cents.

[01:16:28]Um, so that's 0.6, which is a 0.6. All right.

[01:16:35]So 1 m cub going be dividing this by 200 to get one. So I divide this by 200. So I have um 0.6 / 200. Okay. Now I could um sort this out because um 0 0 before I multiply by 55,000, right?

[01:16:55]0.6 six. If you think about it, I'm write it like this. 0.6 / 200.

[01:17:04]So this is uh 6 / 10 as a fraction multiply by I put this is 1 over 200 inverse. Okay.

[01:17:13]So you know you get 6 over 2,000.

[01:17:20]So that's one me cube. So, if you want 55,000 m cube, I'll multiply this by 55,000.

[01:17:38]All right. So, that's what we're working out.

[01:17:45]Now, of course, you know, I want this as a decimal. So, should I have converted this?

[01:17:51]cuz we guess back in money, right? So, I come back to a decimal. All right, let's see how best we could do this.

[01:17:59]I was wondering if it was a good choice to convert this to a fraction.

[01:18:05]All right, seeing that working in money, maybe it's best I kept it like this.

[01:18:12]Divide by 2,000 and multiply by 5,500.

[01:18:20]I mean the same thing move the decimal point one space to get six and here. So you got six divided by 2,00.

[01:18:28]Okay.

[01:18:30]All right.

[01:18:32]You cancel I just thinking was the easiest way to do this. All right. So the thousands these three zeros here.

[01:18:43]We'll go with these three zeros here.

[01:18:46]All right. And we just um you can say 2 into six is three.

[01:18:51]Yeah, let's work with that.

[01:18:54]So 2 into 2 1 2 into six is three.

[01:18:57]So what I end up with is 3x 55.

[01:19:01]Okay. So this this working out where you know it's solid. That's 3x 55.

[01:19:05]Everything down here cancel up m cube. So this work out um 55 by 3.

[01:19:16]All right. So, three fives are 15.

[01:19:19]Three fives are 15 and one as 16.

[01:19:23]So, this is 165.

[01:19:25]Now, there's no decimal pointed at dollars.

[01:19:29]Now, the thing is he paid 178.75.

[01:19:36]This is the cost of the 55,000 m cuba gas. So, remember is the cost of the gas plus a fixed charge, right? They want to know how much is the fixed charge. So we just have to take away these two figures and we get the fixed charge.

[01:19:49]So I just going to put here bring this across a little more and I'll put this put this here.

[01:20:09]So I'm going to put here the fixed charge will be the 178.75 take away that's 165.

[01:20:34]So you just have work that out. um 178.75.

[01:20:38]I mean you could do that in your head as well. Um five to make 7 and then 8. So that is 5 and 8 is 13 and 75 cent. So the answer is 8. 1375. All right.

[01:20:53]I put 0 to take away um I get five 7 you get three 1 zero.

[01:21:04]Okay.

[01:21:36]Mhm.

[01:21:39]>> Yeah.

[01:21:46]Yeah. Um 0.6 as a fraction. Remember this is 6/10. So that's 6 over 10.

[01:21:54]Okay.

[01:21:57]So if you have 0.6 six divided by 200.

[01:22:07]All right. And I convert this to 6 / 10 cuz 0.6 66 over 10 / 200 right over one cuz that what 200 is you convert the divide to multiply inverted divisor and that's how I get that make sense remember 6 is 6/10 so that's 6 over 10 so 6 is 6 over 10 convert divide to multiply and invert the 200 100. So you get one over 200 Okay.

[01:24:06]Okay. All right. So, question 18. Now, coming up here, we have the percentage profit gained by shopkeeper who bought a football for $15.

[01:24:20]All right. So he that's the cost price and sold it for 18. So the cost price is $15.

[01:24:36]Uh the selling price is $18 and therefore profit is 18 take away 15 which is $3.

[01:24:53]Now, you want the profit as a percentage. So, it's always a percentage of the cost price. Okay?

[01:25:00]Percentage profits is going to be the profits over the cost price multiply by 100.

[01:25:20]over one. So that's 3 over 15 by 100 over 1. All right. Um I mean three go into 15 five times and I can cancel 15 with the um 100. So it depends on how you want to do this.

[01:25:37]All right. So 3 into 3 1 3 into 15 is five.

[01:25:42]And then I could say you know 5 to 5 1 5 into 10 is 2 and add the zero. So let's get 20 all right answer is 20%.

[01:27:26]All right. So, moving on to question 19 now.

[01:27:42]All right. So, we have a man's basic wage for 4hour week is this.

[01:27:48]So, that's without overtime, right? Uh that that basic wage means without overtime. He's paid $5 per hour for overtime. So that's Let's see. He works six and a half hours overtime in a certain week. Then his wage would be. So let's work out the overtime.

[01:28:09]All right. So 6 and 12. So I 6.5 at $5.

[01:28:13]So I'll put six and a half still by $5. Right. So six and a half hours by five.

[01:28:20]You could convert this to improper um I mean work with decimals.

[01:28:26]So I prefer to work with decimals and cuz decimals will be money instead of working with fractions.

[01:28:33]But um I have I'll have um two as the denominator. So it'll still work out. Um just depends. So I could put this at 6.5.

[01:28:43]Okay. By five. And as you know you multiply 65 by 5 and add back in the one decimal place. 5 by 5 is 25.

[01:28:53]All right. 5 by 6 is 30 plus the two 32.

[01:28:58]All right. And then add back in the one decimal place.

[01:29:03]Here you have one decimal place. So just come here and add back in.

[01:29:09]And we get $32.50.

[01:29:15]Now that's his overtime plus his so his wage going to be 160 plus this. Okay. So his total wage is going to be the 160 plus the 3250.

[01:29:31]I mean we can know 6 60 and it is 90. So it's going to be 19250. All right.

[01:29:41]And that's D.

[01:29:53]Heat. Heat.

[01:30:36]Yeah.

[01:30:38]which number 17.

[01:30:53]Yeah.

[01:30:57]Okay. Say good, right?

[01:31:02]Yeah.

[01:31:06]Go back to the question here now.

[01:31:14]All right. All right. I just do one more. All right. Continue on Monday.

[01:31:18]Right. So 20.

[01:31:24]We have the amount accumulated on 2500.

[01:31:28]Okay. So this could be your principal invested for 2 years. So this your time at a rate of so principal principal time rate but you want compound interest. So we work this two years at a time. I would not advise you use the big formula because you don't have a calculator here in the multiple choice. So we work it one year at a time. I believe in the 2022 paper we work something similar to this. All right. So uh for the first year the first year all right the interest is principal by rate over 100 and your principal going to be 2500 by rate which is 5% over 100. Okay. Uh the zeros will cancel.

[01:32:18]So you guess get 25 by 5 which is 125.

[01:32:23]Okay. So this is 125 the interest.

[01:32:28]Okay. So I'm going to put money at end of first year is the 2500 plus the interest which is 125. All right. So that is equal to I can add that up right here 260 2625.

[01:33:01]So for your second year for your second year your principle is 2625.

[01:33:16]Okay. So your interest here again is principal by rates over 100.

[01:33:23]So 2,625 by a rate which is 5% over 100. All right. So I don't have no zeros to cancel here.

[01:33:33]Um actually because it's money. So here I'm out to make life easy. I'll leave the 100 below here. I know I could cancel 105 or 100 with this, but you know, I want those decimal um places. If I multiply these two, whatever answer I get, I just move the decimal point two spaces in and I get the money. Okay, so I'll just for me life easier that that way. All right, let's multiply this by five. Uh five fives are 25.

[01:34:08]Okay, so put five here. Five twos are 10. Make that five a little better.

[01:34:12]Yeah, 5 2's are 10 and add this two is 12.

[01:34:17]Uh 5 six is at plus this one is 31 and 5 2's are 10 + 3 13 and all I do is just bring in two decimal I'm write it like this one 3125 over 100. So now just bring two decimal places in and I get 131.25 25 and that's why I left the 100 below. Okay, so I could do that.

[01:34:47]So now I just have to add this to the original principle and that's the money we're talking about. Okay, so at the end of the second year, I just want to add this principle 2625 to this 0 to 1 31.2 two five and we add in. So I get back five, I get back the two, I get six, I get five, I get seven, two, and that's your money at the end of the second year.

[01:35:28]money at end of second year.

[01:35:39]All right. So where we seeing that 27 56.25 27 56.25 Okay. Now see, so I'll end it there. Um, we'll continue this paper on Monday. All right. I believe Monday will be last class because the 28th is the multiple choice and that will be on Thursday.

[01:37:26]All right, so we'll make sure and finish this paper on Monday. All right, so I will see you on Monday. All right, I hope everything going well with studying and stuff. Just remember the multiple choice questions are repeated. So once you're going through the multiple choice pass papers, even if you do understand a question, read the question and watch the answer. Okay? So if it's something you don't understand, read the question, watch the answer. I know time kind of short right now because the questions are repeated. You're going to see at least 50 of the questions in the exam.

[01:37:57]You should know them because you see them already. So if you read the question and look at the answer event once you do enough past papers you know it will start staying your head all right and you could get through like that as well okay just try to understand the working and work it out but if you can't understand make sure and look at the answer and memorize it okay well you see the yeah but you see the book if it's not the actual past papers the questions would not be repeated yeah look at the actual actual past papers.

[01:38:31]All right, those are the questions that going to come back, not necessarily a textbook. Okay, so that's why I give you access to the real pass papers with the solutions because that's the ones you need to memorize. Okay.

[01:38:51]>> All right. So, I'll see you on Monday.

[01:38:52]Okay.

[01:38:55]>> All right, man.

[01:38:59]All right. So those on YouTube, this is the end of this class. Of course, you know, we didn't finish the paper, but we'll continue this paper on Monday evening from 5:00. All right. We'll try and finish it off as that'll be the last class before the multiple choice exam.

[01:39:14]All right. So, always nice having you all, man. Look forward to seeing you all on Monday. Okay. So, say goodbye and see you all on Monday.