CSEC Maths - Jan 2026 Paper 3 (Terry David)

Added: 2026-05-14

[00:00:03]Hey guys, uh good night everybody. Um, just let me know if you guys can hear me uh before I start, please.

[00:00:33]All right. So, what I'm going to do in this video here, I'm just going to run through um the Jan 2026 paper tree. All right. Um we're going to start with this first question here.

[00:00:46]So, Plaxton owns and operates a small business. He does plumbing mostly in the countryside out of a well stocked mobile unit. He does not have a fixed way in which he calculates the cost of a job.

[00:01:04]Plaxton's clientele has increased. So he needs to develop a model that he can utilize to quickly determine the cost of a job. So we have some information here pertaining to the job. Uh basically we have hours and we have the cost. Okay.

[00:01:20]So this is what he's using right now to I guess calculate the cost of the job.

[00:01:24]Let's read what they are saying here. to develop the model uh you must answer the following questions based on the information provided. Okay. So let's read what what's happening to Plaxton here. Plaxton must carry out an inspection for each job and must discuss the findings and options with customers before he begins. The inspection cost is fixed and is included in the final payment. Okay. So here's what's happening here. He does an inspection, right? Right? So he does an inspection but there is a cost for this and that's a fixed cost and this cost is included in the final payment for the job. Use the information provided to plot a graph of cost versus time. Right? Cost versus time on the grid shown below where t represents the time taken in hours to complete a job and c represents the total cost for the job in dollars. So what we have here, we have a table that shows total cost here.

[00:02:26]So what we're going to do here, I'm going to draw a graph because that's what they want, right? They want a graph, right? So this is my data here.

[00:02:39]And we want to draw a graph of cost.

[00:02:42]Make sure I'm reading this correctly.

[00:02:44]Right? So the graph of cost versus time.

[00:02:46]So that means we're going to put cost on the y- axis. So this here has to be your cost on the y- axis and this here is going to be what are they calling it here?

[00:03:00]Time right time and t. So this here is going to be time and this is going to be t. This is cost and this here is going to be c.

[00:03:10]So I don't have the actual graph paper that they would have given the students.

[00:03:13]But what I can do I can do my own graph.

[00:03:16]So in this case here, this here is going to be on your x axis and this is going to be on the y axis. So if you look at the times here, we're going from 1 to 7.

[00:03:24]So let's see if we can go. Now you're trying to maximize the scale here. So I'll probably use 1 2 3 4 5 6 and 7.

[00:03:37]Okay, so that's my time in hours here.

[00:03:40]And on the y- axis, we're going up to 610. So you could probably go in terms of cost, we could probably go 100, 200, 300, 400, 500, 600 and we could stop here, right? So this could be our cost here, right? So if you are drawing this graph in your exam, you need to label your axes, right? So we have this here, right? So that's our time axis. And then we're going to draw a vertical line here to represent our y-axis, right? right or the cost taxes. Okay, so this is what we have here and what we need to do, we need to plot a graph of uh cost versus time. So in this case here, the first one is 1 against 130.

[00:04:44]So this is 110 20. This here is 30. So that's our first point. The second one is 2 against 210.

[00:04:54]So 2 against 210 is going to be here.

[00:04:59]Next one is 3 against 290.

[00:05:02]So this is going to be 290 here.

[00:05:07]Next one is going to be four against 370.

[00:05:10]So this is 350, 360, 370.

[00:05:15]And then we have five against 450, right? And then we have six against 530.

[00:05:25]5 10 20 30.

[00:05:30]And then you have 7 against 610, right?

[00:05:34]7 against 610.

[00:05:37]So that's going to be here, right? So what we're going to do, we're going to plot a straight line here.

[00:05:45]So in this case here, let's draw our straight line.

[00:06:01]Right. So, it's kind of looks like all our points kind of passing through, right? So, this looks about right. So, that's our straight line to represent our cost versus time. Okay. I hope that that makes a little sense. All right.

[00:06:27]um see what else we need to work out. So that's that's part one of the question, right? They only gave them three marks to draw in this here and that represent the total cost. Now in part two here they said the equation of the line represents the model to be used to calculate the cost of the job. So this um model here is a straight line model y is equal to mx + c. Now based on what we have here, this is a straight line but we just plotted here. So this y here is actually your cost right and this x here is your time. So the first thing they want um the equation of the line is represented by this model here and we want to determine the equation of the line. So first of all, right? So this is right this is what we have here.

[00:07:22]Okay. Now our equation is going to be y is equal to mx + c. That's the model that we're using. We're using a linear model here to represent this total cost.

[00:07:33]Okay. Um what we need to do we need to work out first of all well from the graph you can determine the y intercept.

[00:07:39]So the y intercept is simply right it is simply going to be this value here that's your y intercept. So just off the bat c is actually going to be equal to 50 right from the graph that's your y intercept. So that's c. So all we need to do now is to work out what is the slope of this line here. So to work out the slope m, we're going to be using the formula m= y 2 - y1 all over x 2 - x1. That's the formula we're going to use to work out the slope. So you just need to select two points on the line, right? Any two points on the line. So for me, I could probably use this point here, right? So I know this point is 050.

[00:08:24]That's one point I could potentially use. And we could select another point here on the line, right? Um because it's a straight line and all the points technically passes through, right? All the points technically passes through. What we could do, we can just use one of the points that we already have. Okay? So you can use six and maybe 530 if you want. Okay. Now, in order to work out the slope, all you're going to do, you're going to label these points.

[00:08:50]So you're going to say x1 y1 and we're going to say x2 y2. Once we do that, the next thing we're going to do now we are going to substitute into our gradient formula. So in this case here our y2 is 530 subtract y1 which is 50 in my case here all over x2 - x1 which is 6 - 0. And when I work this out here, I'm going to get a slope that is going to be so 530 minus 50. I'm going to divide that by 6 and I'm getting a slope of 80. Okay? So our gradient, that's M is going to be 80. So our cost equation is going to look like this. C is equal to your gradient, which is 80 * T. Now T in this case here is time plus 50. So this here represents the cost equation that Plaxton is going to be using, right?

[00:09:50]That's his cost equation, right?

[00:10:00]Okay. So that is that's part two. Uh the third part, use your graph or otherwise to determine Plton's inspection cost. So your inspection cost is you haven't worked at all, right? So your duration for the job is zero. You haven't actually started the work. It's an inspection. So therefore, it is actually this 50 here. All right? So the fixed cost or the inspection cost is going to be $50. So that's the answer there. We just need to see that the inspection cost is $50. All right, that's the inspection cost. Okay.

[00:10:42]All right. So, that is third part. Let's see what else we have here. Now, Plaxton received $490 for a job. Determine the number of hours worked um hours he spent on the job. Right? So, he received $490. So, what we could do, we can go directly to the graph and we can just read off, right? We can just read off this here. So to do that all I'm going to do right so you receive 490. Now you can use the equation equation if you want right or you could just come to the graph and read it off right. So that's um right. So that's 490 there. And all I need to do is to read what time that corresponds to.

[00:11:35]So according to my graph here, that looks like about 5 and 1/2 hours of work. Okay? So according to the graph, you're going to get 5 and 1/2 hours of work.

[00:11:44]Right? So for this part here, we can get t is equal to 5.5 hours. So that's one way of working the problem. Or you can use the equation here where um C is equal to 80 * T + 50.

[00:12:02]And what we can do we can put um 80 T + 50 is equal to the cost which is 490.

[00:12:11]So therefore 80 T is equal to 490 - 50.

[00:12:19]So therefore 80 t is equal to 440.

[00:12:24]So therefore t is equal to 440 over 80.

[00:12:30]So therefore t is equal to and we'll get 5.5. So you can get your answer of 5.5 hours directly from the graph or you can actually use your linear equation to work it out. Okay. Um right. So that is part B.

[00:12:50]Now, Plaxton and Leela are working jointly and they must settle on a common model to be used to calculate the cost of the job. Now, Leela charges $50 for inspections. So, she's charging $50, which is the same price as this guy, um, and $90 per hour to do the job. Unlike Plaxton, she refunds the inspection to to the customer once she's given the job.

[00:13:18]Plaxton wants to compare the two models using the same pair of axes. So that mean we're going to draw it on the same graph. Draw the line to represent Leela's model. Assume that she is given all jobs and that she inspects.

[00:13:34]So what's happening here is that even though she has an inspection cost of $50, if she is given the job, then what's going to happen is that she is going to give them back that inspection cost. Okay? and she's being she's charging $90 per hour. So what that means is that her cost function is simply going to be 90 multiply by t. So once she gets a job, she's actually just going to charge him $90 per hour. So if you work 1 hour, you're going to pay $90. If you work 2 hours, it'll be 90 by 2, which is $180. So this is the model that we're going to use here in order to draw a graph. Now, here's the thing. C is equal to 90T. that is a straight line that passes through the origin. So what you're going to do um so C is equal to 90T and we want to draw this graph here. So first of all let's plug in some values. So when T is equal to 0, it means that the cost is going to be 90 ultiplied by 0. So that corresponds to 0. So this point that we could use to plot is 0 0. And we could probably try one of the other points on the graph. We could probably try um maybe five. Yeah, we could probably try five.

[00:14:55]So we can say that when t is equal to five, right, the cost in this case here will be 19 multiply by 5. So 95 are 45. So that's going to be $450. So that means the point here that we can plot is 5 450. Okay. So these are the two points that I'm going to use to draw this new model here. So in this case here 0 0 and 5 450. So let's use a different set of colors for this one. Right? Um maybe green I guess. So 0 0 that's this point here. Right. And then we have um five against 450. So five against 450 is actually here. Wasn't that one of the points? Yeah, it's same point. One of the same points that we plotted.

[00:15:47]So let's draw a straight line to represent that model.

[00:15:59]Right.

[00:16:09]So that's our that's our new model there. That green line there represents that new model. All right. And we know for a fact that it's going to pass through five and 450. So based on what I'm seeing here, the two lines actually intersect at that point 5 450.

[00:16:25]Okay. I don't know if that's part of the question too. Maybe it is. All right. So that's part two. So we've drawn um we've drawn the graph. We've drawn this graph here. The next part we want to do here, determine how long a job that returns the same cost for both Paxton models and Leela's models. Well, based on what we just worked out there, we can tell that this point here is a point in common. That's um five against $450. So what that means is this. You see this here? This here for 5 hours is how long both models are going to agree on. So if you use both models, if you work for 5 hours, you're going to be paid the same $450. So this part of the question here, how long? They said how long the job. So you're going to say your time here is going to be five hours. Okay.

[00:17:24]So this takes care of question one, right? Um yeah, some people ask asking what what is paper tree? Paper tree is the paper that is done by students who are writing maths as a private candidate meaning that they don't have any SBA marks. So this paper is what they're going to use to compute a mark and give you out of 20%. That's what it is.

[00:17:53]All right. So that's question one. So these quest is basically two questions.

[00:17:56]First question is 10 marks. Second one is also 10 marks. Now Ella wanted to determine the characteristics of a great teacher that are important to a group of 30 fm students at her school. Right? She asks the students to rate the importance of each of the following five criteria using a scale of 1 to 10. 10 representing the characteristic that is most important.

[00:18:23]One representing a characteristic that is least important. Okay. So we have most important characteristic least important. But you have a scale here from 1 to 10. Now we are rating this in terms of entertainment, communicative, knowledgeable, caring and easygoing. The students ratings. So what they focusing on? They're focusing only on entertaining right now. Right? So the students rating for entertaining as follows. You are required to write a description of how the investigation would be conducted. Right? By using the headings provided and answering the questions that fall. Okay. Again I don't have the answer sheet. I just have the paper. So the first part says state the data collection method. Right. So, steady data collection method that Ella most likely used for the investigation, right? What is what did she use um for this investigation? Okay. Um but this one here, some of you all have done an actual SBA in school. Some of you all may may not have. So, basically what we can do here, we can do a survey, right?

[00:19:37]And we can do a survey here and we can use a questionnaire in order to collect that data. Right?

[00:19:47]Right? So that's the answer I would give for this part here. We use a survey or question here. So you're basically asking the 30 people to fill out this form. Right? And you just read them.

[00:19:58]Now B part one, we want to determine the range. So they want range of the ratings for the data recorded. So let's go back to the data. So if you all you all need to know that range right is simply maximum minus minimum of your data set. So if we look at the data set here the maximum is actually 10 right and the lowest value here is seven right any one of the sevens. So it's going to be the max minus the min. So it's 10 minus 7. Now some students what they do when they when they try to work out range they leave it like this when you all calculate range you're going to get a single number you know so 10 - 7 is going to be three so the range is actually going to be three in this case here okay um so that is part one they want the range for one mark next thing we want to do we want to complete this table here using the data okay so they fill out one of it for us so So let's look at the rating for seven and let's count it. So for seven we have 1 2 3 4 5 6 7 we have seven sevens. Right? So this is going to be seven. So let's write the tally for seven here. 1 2 3 4 5 6 7.

[00:21:24]Right? So that's our tally for seven. We need to check for um nine now. So to do this nine here, let's use a different color. So in the first row, we have no nines. Second row, we have no nines. But then we have one, two, three, four.

[00:21:40]Right? I'm only seeing four nines here.

[00:21:44]So in this case here, this would be four. All right? And this would be 1 2 3 4. Okay? Now, if I were you, the first thing I will do is double check to make sure that when I add up your frequency here. All right, I'm going to get um 30, right? So, 7 + 18 + 4 + 1. All right, and I am getting 30. So, I know that I am correct. Okay.

[00:22:22]Right. So that's part two. So so far this paper, honestly, this paper is pretty straightforward. I don't see anything off key with it so far. Right.

[00:22:31]So that's part B. We just have to fill that up for this part here. Now the table below shows this. feel miss.

[00:22:52]Yeah, I'm missing a piece of the question here that I didn't um copy across.

[00:23:02]All right, there's the third part here, right?

[00:23:08]Okay, so using the table, determine the for the 30 students, the median, right? We want to calculate the median. Now remember, when you want to calculate median, you have to arrange your data in ascending order and then pick the middle. Now these here represents our ratings 7 8 9 and 10.

[00:23:31]Okay. So what I'm going to do here I'm going to use that in order to figure out what the median is. Now to calculate the median we just need to know how many data set points do we have. We have 30 is 30 um students who are asked these questions. Okay. Now generally what I do I will do a simple diagram like this here. So we have 30. N is equal to 30.

[00:23:55]Now 30 is an even number. So when it comes to finding the median, there is no exact middle. So on this line here, I'm going to put my first student and I'm going to put the 30th student. All right. Now, what's going to happen here now is that we can divide our data into two equal parts. Right? Right, we're going to divide the data into two equal parts where I have 15 students here and I have 15 students across here. So I've divided the data up into two equal parts here. So once you have an even data set, there's no exact middle. So what's going to happen here? So this here represents our median or what we call Q2. So in the first half of the data you have up to the first 15 and then in the second half you start from 16 and then you go up to 30. Now if you want to get the um if you want to get the median what we need to do we need to figure out what did the 15 person say and what did the 16 person say. So you have to go to the table right now let's look at the frequencies here. So the first seven people right they would have said seven right? Then we're looking to see where does 15 and 16 lie. Based on what I'm seeing here, the 15th and the 16th person would have would have selected a rating of eight, right? So both the 15th and the 16th person would have selected eight as their rating. So therefore for this here, the 15th person actually had a rating of eight and the 16th person also had a rating of eight.

[00:25:31]So your Q1, which is your median, is simply going to be you're going to add those two numbers. So it'll be 8 + 8 / 2. So that's going to give you a rating of 8. Okay? And by the way, there's only one mark for this.

[00:25:50]The next part here, they want the average rating. When you all see average, I want you to think mean, right? So if you want to work out the mean here, let's we had to use the table to do that. So first of all, these are your ratings. So let's call that X and this is your frequency. So when you want to work out mean from a table like this, what you're going to do, you're going to first create a new column that we're going to call XF. So you're going to multiply your rating by your frequency.

[00:26:18]So 7 by 7 is going to give you 49.

[00:26:22]Then we have um 8 by 18 that's going to give us 144.

[00:26:29]Then we have 9 by 4 that's 36. And then we have 10 by 1 you're going to get 10.

[00:26:34]So what I need to do I need to add this up here. Okay. So this column here is what we call sigma xf. You need to add up this column here. So that's 49 + 144 + 36 + 10 and you're going to get 239.

[00:26:54]Okay. So when they ask you for the mean or the average that's Xbar that is equal to sigma XF all over sigma F in which case this will be 239 / 30 and I'm going to get about 7.97 right so that's our our mean for this data set here 7.97 Right.

[00:27:26]Right. Some of you asking what paper this is. This is John 2 2026 paper.

[00:27:43]Right. So that's the third part. Right.

[00:27:46]So so far this question honestly it has not been that bad.

[00:27:51]Now we have a a table here. Now the table below shows some statistics for five character characteristics under consideration. Most of the statistics for entertaining is missing. Now remember we have the entertaining data here. So they want the minimum rating and the maximum rating. So you have to go to the table. So the minimum rating here will be seven and the maximum is going to be 10. So all we need to do we just need to put uh minimum uh seven and the max here is going to be 10. Okay. Uh the next thing we want to write in the mean. So the mean here we had gotten 7.93.

[00:28:29]So this here is 7.93.

[00:28:33]So we just getting information here just to fill this out. Right. Now, fill in the missing information in the table above and use the data in your finalized table to complete the sample analysis and interpretation of the data below.

[00:28:48]So, let's see what they have here. So, they're calling this section here analysis and interpretation of data. In order of importance to the students, the five characteristics are ranked from one to five with one being the most important. So one is the most important and five being the least important.

[00:29:08]Given that easygoing is ranked at two and knowledge is ranked at four, rank the remaining qualities. Okay, so let's bring this table a little closer.

[00:29:39]All right. So this is my table here. All right. Let's try to understand what did they use to read this thing here. So if we were to look at let's say the mean.

[00:29:50]All right. If we were to look at the me would easy going be next?

[00:29:55]Possibly.

[00:29:57]Possibly.

[00:29:59]Um what else we have here? We have knowledge being fought, right? So one entertaining, easygoing, caring.

[00:30:13]Okay. So based on what I'm seeing here, if we were to follow just the mean, okay, um we could probably say that entertaining should be here, right? because that average there had the highest rating. Okay, so the highest rating for this whole thing was entertaining. So therefore, we put that first. Now then they put easygoing as 6.97.

[00:30:40]But you'll notice that Karen is also at 6.97. Well, since they already put easygoing, the only option we have here is Kierin and we have knowledge coming.

[00:30:51]Knowledgeable coming next. So this has Okay. So this is next in line in terms of uh mean. So that's fine. So then what you're left with here is communicative.

[00:31:09]Right? So I can't believe they just gave them three marks just to put this in order here. All right. um with respect to standard deviation, standard deviation basically gives you an idea of the spread of the data about the mean. That's what standard deviation is. So if I were to compare two sets of data, right? And let's say this here represents let's say this represents where the mean is. So this is Xbar and we had some data that did this, right? That's one set of data. And let's say we had a second set of data and this is our mean Xbar.

[00:31:49]But this time you add something like this, right? If you notice something here, the second data is narrow around the mean, right? Or is closely spread about the mean. Whereas the first diagram, that's this one here, the data is spread out more from the mean. So in terms of standard deviation all you all need to know for the exam is that the smaller the standard deviation the smaller the spread of the data. So if I look at those two diagrams here the one on the right hand side will have a smaller standard deviation. The one on the left because the data is more spread out is going to have a larger standard deviation. Okay. For ccmat we don't need to know how to calculate the standard deviation but we need to know how to interpret the standard deviation. Okay.

[00:32:40]Right. Uh some people are asking. No, this is the second question I'm doing here. The first question I already did it. Okay.

[00:32:47]All right, guys. So, I know some of you all wanted to um wanted to look at some more paper trees, but just do a quick search on my YouTube channel here and you will find additional paper trees that you can practice. Uh some people wonder about um what is the content of paper 3. The thing is the syllabus is exactly the same right the syllabus is exactly the same for the paper two. All they are doing is that they are selecting questions or creating questions that allows you to apply our maths to a real life scenario. That's essentially what they're doing. Okay. So what I want you all to do when you go to the exam tomorrow read the questions carefully.

[00:33:33]Read the questions carefully. Um all I want to say is oh people ask what do I think is bring honestly based on um this Jan paper they can basically bring anything. In the past they would have brought a lot of questions on measurement. So there would have been uh things like area volume right painting a building calculators. No calculators allowed for this paper. You can't use a calculator for this paper.

[00:34:00]Um, somebody want to know about the calculator. No, I don't have a video about the sharp calculator, right? Uh, at least not not now, right? Um, right. So guys, um, I just want to wish you all good luck in your exam tomorrow.

[00:34:22]Right. Hopefully you get a good paper.

[00:34:25]All right. But this is all the time I have for tonight. So, good luck in the paper and you guys can let me know how it was. All right.