0862/02/March 2026-Part 3/ Lower Secondary Checkpoint Mathematics #checkpoint#pastpapers#ms

追加: 2026-05-20

[00:00:00]which is similar on the other side like the parallel. Okay. So, now we are given here that uh tick the column the correct column in the table for the volume of each prism.

[00:00:13]So, now we know that the formula of volume of prism volume of prism is equal to area of cross section area of cross section times height, right? Or the length. So, now here for prism A, let me uh do >> [clears throat] >> here for A and B separately. Uh so, for A I'm directly writing the uh substituting the values in here. Uh so, area of cross section uh now in prism A the cross section is this the upper part.

[00:01:00]Right, this one is the cross section.

[00:01:03]Because you have another parallel triangle and this is a right angle triangle. And if this is five, this is also five. So, area of cross section meaning area of the triangle that is half times base. Base is five. And the height is seven. And then the this is area of the triangle times height. Height is now here you can see is 3.5.

[00:01:29]So, this is for A only. So, when you calculate this, I got here 61.2 five. So, which is greater than 54. This was the question here. If the volume is less than, equal, or greater than. So, for prism A we will tick uh this part here. So, similarly we will do for uh prism B. Uh base base here is again right angle triangle here.

[00:01:54]We have here uh half times base. Base is four.

[00:02:01]And height is six of the triangle. I'm talking about triangle. And then the height of the prism, which is 4.5.

[00:02:08]Right? So, when you calculate this, I got here equals to 54. So, we will take this central part here, which is equal.

[00:02:17]Now, calculate the difference between the area of shaded face of prism A and area of shaded face of prism B. Now, we are just looking at the shaded part. So, shaded part if you see this is a rectangular. So, if uh Do we need to find out? We need to find out this. This is 3.5. So, one side this is going to be 3.5. But, we need to have the other side.

[00:02:48]Uh we need to find out this side here.

[00:02:51]And on Okay. So, let's do one by one. So, for this side, so this is a right-angle triangle here.

[00:03:00]You see?

[00:03:01]This one is a right-angle triangle that is shaded in green. Uh so, we will use Pythagoras theorem for that to find out the other side. Uh let's say its name I can give AB, right? So, AB squared is going to be AB is going to be square root of 7 squared plus 5 squared, which comes out to be 8.60 cm. Right? So, now we can find out the area of area of shaded part of A.

[00:03:41]Uh which is going to be 8.6 length and width was 3.5.

[00:03:49]So, this is 30.

[00:03:52]108 cm squared. So, that was part A for prism A. Now, for prism B, we have the shaded area here. This is 4.5.

[00:04:04]This one is 4.5. And then again, we will find out the same. Now, we have this is a right angle triangle here. So, we can find out this side. Let's say this is L.

[00:04:15]Uh LM, then we will find out LM similarly.

[00:04:23]Oh, sorry. Sorry. Sorry. Sorry. Sorry, guys. We do not to do that one.

[00:04:28]We are already having this shaded part.

[00:04:30]We have 4.5 and 4. So, you just multiply this 4.5 and 4. That will give you area of shaded part. So, area of shaded part is going to be 4.5 * 4. So, this is 18 cm squared. So, now the difference is going to be you subtract this 30.108 - 18. We can say 0 0.

[00:04:59]So, this is 12.108.

[00:05:02]We can round it to 12.1 as uh three significant figures, right?

[00:05:12]Now, number 22, the stable shows the information about masses of 50 chicks.

[00:05:19]Now, we have the mass here in grams and frequency. Write down the model class.

[00:05:23]So, the model class is a class having with my maximum frequency. So, maximum frequency is 24. And the class is going to be then 30 to 40.

[00:05:34]Right? Now, calculate the estimated mean. So, now you know that the formula of mean is sum of F frequencies * X. X is the midpoint and divided by sum of the frequencies. So, I'm adding here one column for X, which is a midpoint.

[00:05:54]Midpoint of the frequencies. So, meaning you add this one here. I'll show you one. 30 + 40 / 2. So, add these upper and lower uh this limit of this and then you add. 30 + 40 70. 70 / 2 it is 35.

[00:06:14]So, next is going to be similar way 45 55 and I'm getting here 65, right? So, you can add this here this column.

[00:06:26]Now, we are going to multiply this. This is our frequency and this is F. F * X.

[00:06:31]So, that is going to be then the mean is going to be 35 * 24 + 45 * 12 + 55 * 9 65 * 5 over the total. So, total of the frequency we are given uh 50. So, now you plug in everything and I got this one as 44, right? So, make sure you do the corrections properly uh calculations properly.

[00:07:03]Okay, number 23. Solve these equations.

[00:07:06]So, uh 5 over 1. We will cross multiply, so it will be 5x = 135.

[00:07:13]Divide by 5 divide by 5.

[00:07:16]So, 5 * 2 10. 5 * 27, right?

[00:07:22]Now, here also this is 16 over 1. Then you cross multiply, it will be 16 into Y minus 1. 8 * 1. This is uh expand the bracket equals to 8. Uh 16y = 8 + 16 which is 24.

[00:07:40]Y divided by 16. 8 * 3 8 * 2.

[00:07:45]So, it is 1 1 and 1/2 or we can say 1.

[00:07:49]5. Okay.

[00:07:51]So, now 24 uh two numbers are in ratio 3:5. One number is 4.5. Find the two possible values for this. So, two numbers are in ratio. So, meaning let's say the numbers are x and y. So, we have x ratio y is 3:5.

[00:08:11]So, there are two possible values. One number is 45. Let's say if x is uh 4.5.

[00:08:20]If x is 4.5, then we will put x here.

[00:08:25]I mean then we are looking for this one.

[00:08:27]So, then this number is going to be which we are talking about uh let's say this is y1. Let me write it down y1. Wait, huh.

[00:08:43]So, let's say this is y1. Now, you cross multiply. 3 y1 equals to 5 * 4.5. Then divide by 3. Divide by 3. Then our y1 is going to be uh 5 * This is 1.5. It is going to be 7.5.

[00:09:00]So, one of the numbers can be 7.5.

[00:09:04]Now, there is another possibility if x ratio y is 3:5.

[00:09:09]Maybe y is 4.5, right? Then we will have this number here x. So, now you cross multiply x times uh this we'll do the same calculation the same way.

[00:09:21]Divide by 5. This and this is gone.

[00:09:24]So, 5 * 0.9. 0.9 * 3 is uh uh 2.7. Sorry, it's 2.

[00:09:34]7. Right?

[00:09:37]So, I think yeah, there is last question here. So, I hope you guys are getting every concept clearly. Kindly take a moment, please, to give your feedback in the comment section and let me know which next paper or next video you want to me make for you guys.

[00:09:56]Okay, [snorts] so for the to simplify this one, we have to take common in the from the numbers first. Six is multiple of three. We can write down three times two y and this can be written times three times five x y. Right? Over three y. Now, you will see what is common here. If I see, the common part here is three and three and y. Right? So, that we are going to take out. So, three y inside we will have here then two plus five x over three y. So, this is cancelled. So, answer is two plus five x. So, that's it, guys. Good luck for your exams. Thank you so much what for watching and please share it with your friends. Be blessed, guys.