GRADE 8 MATHEMATICS COMPASS JS2606 EXAMS

[00:00:02]Greetings and welcome to STEM Smart Academy.

[00:00:08]We are discussing the compass JS2606 grade 8 mathematics 20 26.

[00:00:22]This is the exam we are discussing in preparation for the end of term two exams. So stay attentive till the end of the lesson for we are going to discuss the paper in detail. Allow I start by having a look at section A.

[00:00:40]Those who are asking my consultation number, you are free to reach out through the number 07 41 30 4311.

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[00:01:24]Mhm.

[00:01:26]Question number one of the discussion. Let us have a look at um question number one of this discussion.

[00:01:38]Ladies and gentlemen, we are being told the identification number of Machuka's number is 3 4 0 8 2 1 56. What is the place value of digit four? This is once tens hundreds thousands tens of thousands hundreds of thousands millions. So it is choice D for dog which is um millions. Choice D for dog. Mhm. That is how you respond to such like a question.

[00:02:28]Uhhuh.

[00:02:32]Question number two.

[00:02:39]Mhm. I'm seeing many people tuning in.

[00:02:47]I'm seeing many many people tuning in and following our live programs.

[00:02:56]That is great work. Ladies and gentlemen, this is great work. The temperature the temperatures of four cities were recorded 2°C that 1°C -4.8°C and 12°C.

[00:03:24]Which of the following is an integer?

[00:03:27]Remember an integer must be a whole number. Decimals and decimals and fractions are not part of it. Decimals and fractions are not part of the integers.

[00:03:57]Mhm.

[00:03:59]So they want an integer. 8.2 cannot be the answer because it's a decimal. 31° this one is correct is a whole number.

[00:04:09]-4.8 cannot be an integer because it's a decimal. This one is a mixed fraction.

[00:04:14]So the correct answer is 31 which is B for dog. Question number four. Number three. Four athletes were given number tags as follows. 75 77 83 and 81.

[00:04:31]Which one of the following is a prime number?

[00:04:35]A prime number is a number that is divisible by one and itself only and in this case it is 83.

[00:04:42]Question four.

[00:04:44]The temperature of a substance was recorded as -5°C.

[00:04:52]The temperature increased to 12°C.

[00:04:56]What is the rise in temperature? What is the rise in temperature?

[00:05:02]So in that case you can see the temperature of a substance was -5 and it increase to 12. So to get the rise in temperature you take the final temperature which is 12.

[00:05:18]Then you subtract the initial which is -5.

[00:05:23]So this becomes 17° C which is B for boy. Choice B for boy.

[00:05:33]Mhm.

[00:05:35]Allow I look at question number five we've been told in question number five a group of learners were given the expression 0.24 * 0.8 8 / 0.03.

[00:05:54]What is the value of this expression?

[00:05:57]So when you have 0.24 * 0.8 all over 0.03, you can decide to multiply both sides by a,000 to eliminate the denominator.

[00:06:13]Sorry, to eliminate the decimal points.

[00:06:16]So this will be like saying 24 * 8 over 3 * 10.

[00:06:23]So rear 1 year 8. So this is 64 over 10 which is 6.4.

[00:06:33]Choice is B for boy. That is how you respond to it * 1.

[00:06:48]So this is 64.

[00:06:51]>> Mhm. Allow I have a look at question number six where we are being told that um the cost of petrol is 299.08.

[00:07:03]What is the price written to one significant figure? This is a decimal number. To one significant figure it is going to be the one significant figure here is two. And because to the right we have nine, it will increase the value of two by one to make it three. Then the two nines here change to zeros to act as placeholders. So the value will become 300. The zeros here will act as placeholders. So that marks choice C for cut as the correct answer. Question number seven.

[00:07:35]There are 600 learners in a school. The ratio of boys to girls is 3 is to2. How many more boys are in the school than girls? So if the ratio is 3 is to2 get the number of boys it will be three over the total number of learners which is five * 600.

[00:07:58]So when you take um 3 over 5 3 over 5 * 600 this is 360 that school has 360 boys. To get the number of girls it will be now 2 over 5 * 600 to give you 240. But now they're asking how many more boys than girls are in that school. So it will be 360 minus 240 to give you 120 which is choice A for a question eight. The price of a calculator is 2,400 shillings. What is the price written in standard form?

[00:08:42]So when you have 2,400 shillings in standard form this will be 1 2 3. So this will be 2.4 4 * 10 ^ of 3 which is our number of steps. Choice B for boy.

[00:08:56]Question 9. A group of learners compared some numbers. Which of the following statements is correct? Mhm.

[00:09:05]3 over 4 is greater than 0.75.

[00:09:10]Uh-huh. Is it true? When you convert 3 over 4 to a fraction, you'll be getting 0.75. So this one is not true.

[00:09:23]4 over 3 is greater than is less than 1.3. So 4 over 3 in decimal form that is 1.333.

[00:09:33]So this one is also not correct.

[00:09:36]Choice B 1 9 is less than 0.9.

[00:09:41]1 / 9 is indeed 0.1.

[00:09:45]So 0.11 is less than this. This one also is not true.

[00:09:51]Choice B 2 is less than 0.5.

[00:09:57]Yes, because 2 over 5 is like saying 0.4 is less than 0.5. So this is true. So the [snorts] correct statement here is choice B for dog. Choice B for dog.

[00:10:11]Ladies and gentlemen, allow I make progress to question number 10.

[00:10:19]Mhm. Uni spent a half of her salary on food and a quart of the remainder on rent and saved the rest. What fraction did she save?

[00:10:29]You can see food alone she spent a half a quarter of the remainder on rent.

[00:10:40]So rent if you spend a half you are left with a half. So it's a half times a quarter.

[00:10:47]This becomes 1 / 8 on rent and save the rest. So the savings to get what was saved you take the total fraction 1 minus what was spent on food plus the rent.

[00:11:01]So when you take a half + 1 / 8 you're going to get 5 / 8 you less from one you get 38 which is choice C for cut.

[00:11:18]Question 11. A storekeeper donated 5 tons of sugar to some families in a village. Each family received 2.5 kg of sugar. How many families benefited? So first I have to convert the tons to kgs.

[00:11:35]I know that one t is equivalent to 1,000 kilog. What about five tons? You cross multiply this will be five. multiply this by a,000 to give you 5,000 kilogram. So this 5,000 kg we are going to divide it by 2.5 to get the number of families. So when you take 5,000 you divide by 2.5 in your calculator. What are we going to get? Mhm. I'm doing the division. And this is exactly 2,000 which is choice B for boy. Question number 12. Manuru deposited um 100,000 in a bank which paid a simple interest at the rate of 9% peranom. How much money was in this account after 3 years? Remember simple interest is given by the formula principle time rate of 100 time.

[00:12:44]The principle in this case is 1 100,000 multiply by the rate of 9 over 100 by time 3.

[00:12:56]When you perform this multiplication, when you take 100,000, you multiply by 9 over 100 uh by 3, you get 27,000.

[00:13:10]So this 27,000 is just the interest. But what is in the account is what is called the amount. Amount is given by principle plus the interest. So the principle is 100,000.

[00:13:28]plus the interest 27,000.

[00:13:30]So this gives you 127,000.

[00:13:36]Choice C for cut.

[00:13:40]Question number 13. I'm seeing so many people following through our live lesson. That is excellent. If you are following us for the first time, kindly make sure you subscribe, like and share.

[00:14:08]Mhm. Also you can share this link to your other friends so that um they can also enjoy these wonderful lessons.

[00:14:25]They can also enjoy these wonderful lessons.

[00:14:34]Mhm.

[00:14:39]Question number 13.

[00:14:42]Question number 13. Ladies and gentlemen, we are being told Jerro's farm is in the shape of a trapezium. The perpendicular distance between the parallel sides is 58 m and the parallel sides measure 73 m by 63 m 6 67 m. What is the area? So this can be the trapezium they are referring to.

[00:15:08]So that this is 8 uh this is 73 the top here is 67 and the perpendicular height is 58.

[00:15:15]Area of a trapezium area of a trapezium is given by the formula I have into a plus b h. So this is a half into my a 73 + 67 into our height which is 58.

[00:15:39]When you execute this 73 + 67 * a half mult* 58 this is 4,60 4,60 square m. But now because they want the area in hectares, you simply take 4,60 you divide by because you know that 1 hectare is equivalent like saying 10,000 square m.

[00:16:14]So you divide by 10,000. This becomes 0.46 which is choice B for dog in that particular case. in that particular case. Allow I have a look at uh the next question where we are being told Monica molded a cubicle container of side 30 square cm.

[00:16:41]What is the surface area of the container?

[00:16:44]If the container is 30 square cm, so that is of side 30 it will be 30 * 30.

[00:16:50]This is the area of one face.

[00:17:01]5400 choice A for apple.

[00:17:07]Question number 15. Mhm. You can see how enjoyable math is on this other side. I hope you are also enjoying it the same way I do from my end. I told you learners that math is fun but you need to have daily practice and consistency for you to get the best score.

[00:17:39]It is one of the easiest easiest subjects I've ever seen.

[00:17:48]Mhm.

[00:17:50]We are told the area of a square cardboard is 22.4 square cm. Use mathematical tables to determine the length of one side. So the length will simply be given by the square root of the area. So we need to get the square root of 22.4.

[00:18:12]In this case, we've been told to use mathematical tables. So we go to the uh to the mathematical tables and read the square root of 22.4.

[00:18:25]Ladies and gentlemen, I hope you see 22.4.

[00:18:32]22.4.

[00:18:36]Mhm. So this is 22 you come to 40 is here. So 4.7329 4.7329 4.73 29 which is exactly choice B4 sorry C for cut be very keen question number 16. MGO drove for 3 hours covering a distance of 270 km.

[00:19:05]What is his speed in meters/s?

[00:19:08]Remember that speed is given by distance over time. So the distance is 270 km divided by the time 3 hours. This is 90 kilometers per hour. But now when you look at the question they want the speed in me/s. You convert the speed in from kilome/ hour to m/s. You take your speed then you multiply by 5 over 18. So when you multiply this by 5 over 18 you get 25 m/s which is choice B for dog.

[00:19:44]Mhm. Again if you are interested in reaching out WhatsApp the number 0741 30 43 111 that is our consultation number you can reach out anytime then my team will be able to respond to you my team will be able to respond to you dear learnersh H question number 17. A vegetable garden is in the shape of a semicircle of a diameter 25 sorry 56 square cm.

[00:20:27]What is the perimeter of the garden? The best way to respond to such like a question is by representing it diagrammatically.

[00:20:39]This is the semicircle whose diameter is 56. They want the perimeter. Perimeter will be given by a half. When you substitute this will be a half * 5 which is 22 / 7* the diameter 56 then plus again the diameter 56.

[00:21:01]So when you execute this When you execute this, what are we going to get?

[00:21:19]management.

[00:21:20]You will realize in this particular in this particular context when I take a half * 22 / 7 * 56 this is going to be 88. So I have here 88 + 56. Now when I add 56 this exactly gives me 144 which is choice D for dog. Question number 18.

[00:22:06]Timothy was paid 9,000 shillings after working for 5 days. At what rate was he being paid per day? If 5 days is equals to 9,000, what about 1 day? We simply take 9,000, you divide by 5, and this is going to be 1,800.

[00:22:28]1,800 per day, which is choice C for cut.

[00:22:33]Question number 19.

[00:22:37]A phone's subscription plan charges is 12 M + 24 M. What is the factorized form of 12 m + 24? Look at the common term. What is common here? 12 is common. So I'll factor out 12. I'll be left with m + 2.

[00:22:59]That is a factorized form. 12 into m + 2. Looking at the choices, I have choice B for boy. Mhm. Question number 20.

[00:23:10]A carpenter made the design of a window in the form of a parallelogram.

[00:23:18]What is the size of the angle marked X?

[00:23:21]Angle X is what is called angle X and angle 110 are interior angles. And the interior angles add up to 180°. That means if I take X + 110, I'm going to get 180°. So when you collect like terms you have x = 180 - 110. Therefore x is 70°.

[00:23:48]Choice B for boy.

[00:23:53]Mhm. Section B of this great discussion.

[00:23:57]Ladies and gentlemen, remember our consultation number still remains 0741 30 4311.

[00:24:10]Muhammad imported um Muhammad imported Muhammad imported 2,45,763 electric bulbs. Write the number of bulbs imported in words. How do we write these in words? We are going to call this as 2 million.

[00:24:36]We are going to say two 2 million 45,000 45,000 763 700 and 763.

[00:25:14]Mhm. Part B. Determine the difference between the total value of digit 4 and digit 6 in the number 2,45,763.

[00:25:28]So first let me start by getting the total value of digit four which will be given by 4 * its place value which is once 10 100,000 t of th00and so times 10,000 to give you a total value of 40,000.

[00:25:47]Then also let's get the total value of digit 6 which is 6 * 10 to give you 60.

[00:25:56]So now they want the difference. The term difference means you subtract. So I'm going to take 40,000 you minus 60.

[00:26:08]This will be when you take 40,000 you less 60 you get 39,940.

[00:26:24]Part 22, part A. A teacher wrote the expression x 8 - 4 + 2 on the board.

[00:26:36]Use a number line to work it out.

[00:26:41]So this means mhm let me have maybe this as -21 0 1 2 3 4 5 6 maybe 7 and 8. So from 8 you move to -4.

[00:27:04]That 8 - 4 that's like saying from 8 move four steps to the to the left. 1 2 3 4 then now plus two. Plus two means from where you've reached now move two steps to the right. So that is step one.

[00:27:23]Step two. So my answer in this case is six which is positive.

[00:27:30]Question number B. A mobile money transaction was recorded as follows. A deposit of 3,000 shillings, a withdrawal of 2,500 shillings, and a deposit of 1,200 shillings. Determine the net balance of the mobile account balance.

[00:27:52]So, a deposit of 3,000, that means the account now has 3,000.

[00:27:57]A withdrawal of 2500. So you minus 2500.

[00:28:02]This means in the account when you take 3,000 and you withdraw, if you had 3,000 in your account and you withdraw 2,500, you will be left with 500 in your account. Then again you deposit, you add another 1,200. So from the 500 that was there, you are now adding 1,200.

[00:28:24]This means at the end you're going to have a net of 1,700 Kenyan shieldings.

[00:28:32]Part B of the question paper round the sorry the mass of a specimen was measured as 04 52 Mhm. kilogram. Round off the mass to two decimal points. Round off the mass to two decimal points. When you have 0.0 452 after the decimal point, you should have two uh two digits 1 two. So the last digit should be four. But now look at the digit to the right which is five. It will increase the value of this one by one as these ones here will vanish. So my answer will be 0.05.

[00:29:20]05 kgs.

[00:29:24]That is the final answer to that particular question.

[00:29:31]Part B, write the mass in standard form.

[00:29:35]Mhm. In standard form when you have um 0.0452 when you have 0.0452.

[00:29:46]So this is one two two steps. So this will be 4.52 * 10 ^ of -2 that is the mass in standard form.

[00:29:59]That is the mass in standard form. And now I have a look at part C. Write write the place value of digit 5 in this number. So when you have the number 0.04 04 52.

[00:30:18]This is once. After the decimal point, we do start with 10.

[00:30:23]Then four will be in what is called 100.

[00:30:30]Five will now be in what is called thousands.

[00:30:36]So because they want the place value of digit five, the most correct answer is thousands.

[00:30:44]with a T H S very very important.

[00:30:58]>> Mhm. Let us look at ratio number 24.

[00:31:04]Three bulbs PQ and R are set to flash after 18 minutes, 24 minutes, and 36 minutes respectively. The bulbs flash together at 10:48 p.m. Determine after how long will the bulbs flash together again? So here we are going to get the LCM. I want to get now the LCM of 18, 24 and 36.

[00:31:32]Mhm.

[00:31:34]Let us see how we are going to get this particular LCM.

[00:31:45]Let us see how we are going to get this particular LCM.

[00:31:49]So I'll start with two here.

[00:31:52]Two here 969 two here 939 3 here 313 3 here one 1. So my LCM will be 2 ^ 1 2 3. So 2 cubed * 3^ 2.

[00:32:20]That is like saying 8 * 9 which is 72.

[00:32:27]So determine after how long the bulbs will flash together again. The bulbs will flash together again after 72 minutes. After 72 minutes. Mhm. Which can be written as after 1 hour and 12 minutes.

[00:32:51]Part B. Determine the time.

[00:32:56]Determine the time they will flash at the same So determine the time they will flash at the same time again. So if they flashed at together at 10:48 p.m. They'll flash together again 1 hour 12 minutes later. So you take 10:48 + 1 hour 12 minutes. This is 60 0 112.

[00:33:27]So this is 1200 a.m.

[00:33:31]Be very keen. It was P.M. And now it is 12:0 a.m. Meaning K has spent a quarter of his monthly sorry a quart of his money on buying school uniform for his daughter, a third on books and 2/3 of the remainder on food.

[00:33:56]He saved the rest of the money.

[00:33:59]Determine the fraction of the money same.

[00:34:03]Mhm. So when you look at that particular question, when you look at Mhm. Determine the fraction of the money saved. So you can see on this a quarter of his money is used to buy school uniform. So to buy uniform this person spent a quarter of the money, a third on buying books.

[00:34:58]Purchase of books is a third and 2/3 of the remainder on food. First of all, let me get the remainder. It will be 1 minus a4 plus a third.

[00:35:13]So when when I calculate um a quarter plus a3 a4 + a3 I'm getting 7 / 12 you less from 1 you get 5 12 as your remainder.

[00:35:38]So they are saying 2/3 of the remained on food that means that food is 2/3 of what remained which is 5 / 12.

[00:35:53]So when you take uh 2 / 3 * 5 / 12 this is 5 18 on food 5 18 on food.

[00:36:07]Determine the fraction of the money saved. Now savings you can take the total fraction one you less a uniform is a quarter plus books a third plus food 5 18. So this is like saying 1 minus when you take a quarter plus a3 + 5 over 18 you get that 1 / 36 and when you less from 1 you get 5 over 36. So the answer here is 5 over 36.

[00:36:49]Mhm. Question number 35. The number of textbooks in a shelf is represented by the decimal 0.54.

[00:36:59]Express the decimal as a fraction in the simplest form. In that case, five and four are recurring. So I'll say let R be equals to 0 54 54 54.

[00:37:14]10 R will be 5.45454.

[00:37:19]Then 100 R will be 54 4.

[00:37:30]Let me see.

[00:37:33]54 54 54. When I subtract equation one from equation 3 100 R minus R, you get 99 R being equivalent to 54.54 - 0.54 is 54.

[00:37:56]So to get the value of r you divide through by 99 by 99.

[00:38:02]So you're going in this case to get r.

[00:38:05]We need our answer in simplified form.

[00:38:08]So 54 over 99 in simplified form is 6 over 11.

[00:38:16]Mhm. Question 27.

[00:38:20]A piece of land was valued at 2 million shillings. The value of the land appreciates at the rate of 5% perom.

[00:38:29]Determine the value of the land after 2 years. So what we are going to do here after the first year the land will be given by interest is equals to principal time rate * 100. So this will be 2 million multiply by the rate which is 500 * 1.

[00:38:56]So this means at the end of the first year at the end of the first year the land would have gained an interest of 100,000.

[00:39:13]So the amount at that at the end of the first year will be 2 million plus 100,000.

[00:39:26]So this is 2 million 100,000.

[00:39:31]So at the end of the second year the interest in the second year will be given by the principle which is now 2,100,000 multiply by the rate 500 * time 1.

[00:39:46]This will become uh when you execute this you get 105,000 105 uh 105,000 shillings. They want the value of the land after 2 years. So amount after the second year we will have 2,100,000 plus 105,000.

[00:40:23]So this is going to give you a computation of 2 million 205,000.

[00:40:36]Mhm. Part B. Determine the amount by which the land appreciated in value. So you take the final value which is 2,25,000.

[00:40:53]You less the 2 million.

[00:40:58]So this is going to give you and 205,000.

[00:41:06]Question 28.

[00:41:09]A rectangular tank is 2.5 m long, 1.5 m wide, and 2.0 m high. Determine the volume of the tank.

[00:41:21]Volume is given by length multiply by the width multiply by the height. So this is 2.5 * 1.5 * 2.0.

[00:41:33]When you do this multiplication, this is going to give you allow I do this multiplication. I see this is 7.5 cubic m as the volume. Then calculate the capacity of the tank in liters. You know that 1 c m is equivalent to 1,000 L. What about 7.5 m? So what do we do? We cross multiply.

[00:42:06]This will be 7.5 * 1,000 / 1 which is like saying 7,500 L.

[00:42:17]Mhm.

[00:42:18]Question 29.

[00:42:22]We are being told in question 29, Oeno invested uh 15,000 shillings in a financial institution. The institution paid a compound interest at the rate of 6% peranom. Determine the total amount of money or collected after the two years.

[00:42:41]So the interest during the first year will be given by principal time rate over 100 times time. So the principle here is 15,000 time the rate which is 6 over 100 * 1.

[00:42:59]So this is going to give us when you take 15,000 * 6 over 100 * 1 you get 900.

[00:43:12]So the amount after the first year will be now 15,000 + 900 to give you 15,900 shillings.

[00:43:28]The next you now go to in the second year now the interest in the second year will be given by the principal which is the amount of the after the end of the first year. So this will be now our new principle 15,900 multiplied by 6 over 100 by 1.

[00:43:46]So this will become 15900 * 6 over 100 that is 954.

[00:43:58]Now amount is equal to principle which is 15 900 + 9 54.

[00:44:11]When you do this addition, ladies and gentlemen, you're getting 16,000 854.

[00:44:23]Part 30 of the question.

[00:44:26]The perimeter of a rectangular curve board is 2 is represented by 2x + y into x + z. Determine the perimeter given that x = 2, y = 2 and z = 3.

[00:44:43]Remember that the perimeter is 2x + y into x + z. Let us substitute this will be 2 into the value of x which is 2 + y which is 2 into x 2 + z 3. So 2 * 2 this is 4 + 2 into 2 + 3 that is 5. Opening the brackets this will be 4 + 2 into 5 that is 10. So this gives you the perimeter is 14.

[00:45:18]Part B.

[00:45:20]The cost of the cost and the quantity of two similar items bought by two people from the same shop is given by 20x + 30 y= to 80 and 30x + 20 y = to 70. Use elimination method to determine the values of x and y. The question is very specific. Use elimination method. So when I have here 20 x + 30 y = 80 and 30x + 20 y = 70, I can decide to eliminate x by simply multiplying here by 30 and here by 20. So this will become 600 x + 900 y is equivalent to 2400.

[00:46:12]Then the lower equation will be 600x + 400 y is =,400.

[00:46:23]When you subtract 600x - 600x they will vanish.

[00:46:29]Then now in that case you are left with you are left with um 900 y - 400 y this is 500 y is equal to 1,000.

[00:46:49]So if 500 y is equivalent to 1,000, we get the value of y. What do we do?

[00:47:00]Um you divide here by 500 also here by 500. This and this cancel you get y is equal to 2.

[00:47:11]So if y is 2 to get the value of x you have here 20x + 30 y. So 30 into 2 is equivalent to 80.

[00:47:22]This means 20x + 60 is equal to 80. When you collect like terms, you're going to get 20x = 80 - 60.

[00:47:38]Mhm. So this will be 20x is equal to 80 - 60 that is 20. Get the value of x.

[00:47:46]divide here by 20 divide also here by 20 this and this vanishes x will be equal to 1 so x is 1 while y is 2 and the method I've applied there is what is called elimination method elimination method we are making progress to question number 31 still our consultation remains as 07 41 30 43 11 Mhm.

[00:48:32]A motorist drove for 5 hours and covered a distance of 540 km.

[00:48:37]Determine the speed part A in kilometers per hour. speed is given by distance over time.

[00:48:49]So the distance here is uh by 40 kilome divided by 5 hours.

[00:48:58]This will become when you take 540 / 5 this is 108 kilometers per hour. Part B the speed in m/s you simply take 58 * 108.

[00:49:23]Mhm. This gives you 30 m/s.

[00:49:32]Let us look at um the next question.

[00:49:38]Let us look at the next question.

[00:49:41]We are being told in the next question that um that uh six men can complete digging a shamba in 12 days.

[00:49:56]Two of them failed to turn up for the job. How many days the remaining men took to complete the work? So we have the number of men and the period in days.

[00:50:10]Six men completed digging the chamba in 12 days.

[00:50:15]If two of them failed to stand up, meaning 10 uh four showed up, how long will they take? So this will be 6 / 4 * 12. This will be 18 days.

[00:50:31]How many days the remaining men took to complete the job? They completed the job in 18 days. But B, how many more days did the remaining men took to complete the job? How many more days? To get more days, you take 18 days minus 12 days.

[00:50:49]This is six more days. Mhm.

[00:50:56]Question number 33. A cylindrical road of diameter 14 cm and height 20 cm. Part A. Calculate the total surface area.

[00:51:08]Look at it. This is how it looks like.

[00:51:12]It has the cross-sectional part. So uh total surface area will be given by 2 pi r² for the circular bottom and top plus pi dh for the curved surface part.

[00:51:30]So substituting into the formula we'll have 2 * 22 / 7 * the radius if the diameter is 14 then the radius will be 7 squared [sighs] plus 22 / 7 * the diameter 14 * the height of 20.

[00:51:52]So when you substitute this this will be 2 * 22 / 7 * 7^ 2 that is 308.

[00:52:06]Then you add these two 22 / 7 * 14 * 20 this is 880.

[00:52:17]When you add these together, you're going to get 1188 square cm as the total surface area of the road. Part B, the volume of the road. Volume will be given by the formula pi r²h.

[00:52:38]So this is 22 / 7 by the radius 7 by the height of 20.

[00:52:46]So this will be when you substitute you are going to get your height sorry your volume is 3,080 cubic cm.

[00:53:04]Question number 34. Alo had a vegetable garden in the shape of a square. The perimeter of the garden was 116 m.

[00:53:13]Determine the area of the garden.

[00:53:17]It is a square meaning that all it sides are equal and the perimeter is 114. How do we get perimeter of a square? It is 4 L. So the perimeter which is 114 is equivalent to 4 * length. So to get the measure of one length you divide here by four divide here by four. This and this goes. So it means one side of the garden measures when you divide 114 by 4 uh sorry this is 116 not 114 the perimeter is 116.

[00:53:57]So when you divide 116 by 4 you get 29 m. But now they want the area. I'll say now that area is side multiplied by side. So that is 29. You multiply that by 29 to exactly give you 841 square m.

[00:54:24]841 square meters. Question number 35.

[00:54:32]Tom, Mary and Dana shared 84,000 in the ratio 3 is to 4 is to 5. Determine the amount Tom got. Tom will have gotten 3 over the total ratio which is 3 + 4 + 5 that is 12 * 84,000 which will be 3 / 12. You multiply by 84,000 you get 21,000.

[00:55:11]Mary got uh Mary will be 4 / 12 * 84,000 which is going to give you 28,000.

[00:55:30]Then got this one will be 5 / 12 you multiply by 84,000 and this will be 35,000.

[00:55:48]Part D of the question.

[00:55:51]Determine how much Dana received than Tom. Dana 35,000 Tom 21,000.

[00:55:59]So this will be 35,000. You lease 21,000.

[00:56:08]So when you lease 21,000, you're going to get 14,000 shillings more. Mhm. Question number 36.

[00:56:21]When you look at the question, we are being told in the question, we are being told in that particular question that um Wamboo modeled a window in the shape of a triangle XY Z. Line XY is equal to line YZ = 4 cm.

[00:56:49]Angle XZ Y is equal to 75 cm.

[00:56:56]Construct the triangle and measure the angle Y X three marks Y XZ.

[00:57:08]Equation is 3.

[00:57:12]marks.

[00:57:13]Mhm.

[00:57:15]So when we are there, I hope you are gaining something, dear learners.

[00:57:24]It is my hope that you are gaining something, dear learners.

[00:57:35]Mhm.

[00:57:38]So let us respond to it.

[00:57:41]The first approach I'll draw the line XY which is 4 cm.

[00:57:51]So I'll draw a line X Y and ensure that um it is 4 cm.

[00:58:00]Then the line x zed is also 4 cm and the angle here is 75 cm.

[00:58:12]So first I love to measure the 4 cm from x is cutting there. Then 75 my protractor here 75 is somewhere here.

[00:58:24]Then now I join.

[00:58:29]Then now from this point I can join this back to Y. So this is the Z.

[00:58:37]Measure the angle X Y XZ. So when they say YX Z sorry let me check. Let me have this one corrected.

[00:58:50]X Z Y is the one that is 75.

[00:58:55]Mhm. There is I think there is something missing here. Let me fix.

[00:59:00]XY is 4. XZ is also four. So I'll have to make sure XZ is 4 cm.

[00:59:12]XZ is 4 cm. So from X 4 cm can be that way.

[00:59:20]Then the angle because um I want us to reason this way. A side that has a triangle that has two sides equal is an isocles triangle.

[00:59:35]Diagrammatically if this is my sketch this is what it means. If this is x y z if x if xy is 4 xz is four. So those are base angles. So meaning that this angle and this angle should be equal. So when they say the angle this angle is 75 it means also the angle at y should be 75.

[00:59:59]So this angle here should be 75. I stand here measure 45 75 75 is here.

[01:00:06]Then what I'll do that way.

[01:00:15]Mhm.

[01:00:17]You need to ensure that this angle here is also 75.

[01:00:22]The property you need to apply there is that um the base angles of isocles triangle are always equal. That is a rule. Mhm.

[01:00:36]Question number 37. The figure below is a design of a ladder made by a carpenter. You can see the diagram.

[01:00:46]Use the letters M, N, X, Y, and Z.

[01:00:49]Identify the which pairs of angles are corresponding.

[01:00:54]The pairs of angles that are corresponding.

[01:00:57]I can say Y and M.

[01:01:02]Mhm. I do. We have any other that is corresponding after Y and M. I can also talk about Z and N X and 70 all those are corresponding angles. Then the alternate angles alternate is very simple. I'll talk about um X and Y.

[01:01:32]Alternate angles are also called the Z angles. So X and Y.

[01:01:39]Mhm. Another alternating angle I can refer to is U M and 70.

[01:01:52]Yes, those are the alternating angles.

[01:01:56]Mhm. The remember this is JS2606 grade 8 mathematics.

[01:02:03]Coerior.

[01:02:05]interior we have X Z X and Z X and Z are point angles also N and 70 and so on calculate the values remember they just said using the letters so let me wrap the anything any one that involves a 70 here yeah this one is not correct Mhm. [clears throat] Calculate the values of my y z. So if this is 70, this is 110, this is 70, this is 110, this is 70, this is 70.

[01:02:48]So m is 70°.

[01:02:53]Y is sorry m is 70. Y is also 70 because they are corresponding and they must be equal.

[01:03:03]Z is um 110 because they are going like that based on that eight.

[01:03:14]Uh the area of a square hole is 77.64 square m.

[01:03:20]Using mathematical tables determine the length of one side. 77.64.

[01:03:28]So let me go to the<unk> 77.64 64 77 77.64 77.64 is here. 77.64.6 is here. Uh 8.891.

[01:03:50]We have 8891.

[01:03:54]77.6. Then four.

[01:03:57]For you have that 23. What do we do to go up and confirm? You add the 23.

[01:04:04]So when you add this 23, this will be 4 1188.

[01:04:12]So the answer is 8.8114.

[01:04:16]Question number 39.

[01:04:20]The table below shows the m the number of hectares of land four farmers head.

[01:04:27]Mhm.

[01:04:31]Use a scale of 1 cm represents two hectars to draw a bar graph to represent the information.

[01:04:43]Mhm.

[01:04:48]So I have um up to six. So it goes up to six. So this can be 1 cm to represent two hectares. So I can have here.

[01:05:04]So I can have here 2 4 6 or maybe let me just because let me just have 1 2 3 4 5 and six. Remember this is on the y- axis I'm going to have the number of vectors then on the x-axis I'll have the farmer name of the farmer.

[01:05:42]Mhm.

[01:05:44]I have musa musa six hectares. So for six he sectors.

[01:06:02]Mhm.

[01:06:06]Then Tina 4 hectares.

[01:06:10]Then Tina 4 hectares.

[01:06:14]We have Tina here.

[01:06:21]Tina is four.

[01:06:24]This is Tina.

[01:06:28]Then after Tina we have current six hectares.

[01:06:32]Current six hectares that is current six hectares. Then William 2 hectares.

[01:06:54]William.

[01:07:02]This is William.

[01:07:07]Two hectares.

[01:07:09]So this is the bar graph. Maybe I can just shade to make them visible or easily identifiable.

[01:07:23]So this is what we call the background.

[01:07:28]Mhm.

[01:07:30]It is my hope you all understood what I've done at that particular point. Let me have a look at the last question.

[01:07:39]Uh Roy bought a bed on higher purchase.

[01:07:42]He deposited 24,000 shillings. The remaining balance he paid in seven monthly seven equal monthly installments of 4,500 shillings each. Determine the total amount of money he paid for the bed.

[01:07:56]This is higher purchase which is obtained by taking the deposit plus the total monthly installments.

[01:08:03]So the deposit here is 24,000 plus how many months? 7 and each installment was 4,500.

[01:08:15]So this is 24,000 [sighs] multiplied by when uh not multiplied by added to this should be added to when you take 7 7 * 4500 you get 31500 our consultation number feel free reaching out anytime. time. Mhm.

[01:08:43][clears throat] I hope you've gained something throughout this particular lesson.