GRADE 8 MATHEMATICS | COMPASS JS2605 (2026) | LIVE SOLUTIONS & MARKING SCHEME

[00:00:08]Thank you for joining this lesson.

[00:00:11]The great and smart academy.

[00:00:15]We are going to live stream the compass 005 series grade eight mathematics 20 26. This is the paper we are going to discuss.

[00:00:30]You can see it is the J S 2605.

[00:00:35]Mhm.

[00:00:36]And we're going to discuss the paper in detail.

[00:00:39]So, sure you are ready with um all the necessary tools to aid in the process.

[00:00:47]So, straight away we're going to question number one of the paper.

[00:00:54]It reads, the temperature of four cities were recorded as 23.8° 24.5° -4.8° and 21°.

[00:01:07]Which temperature represents an integer?

[00:01:10]The main thing here is you knowing what an integer is.

[00:01:13]This is something you learned in grade eight.

[00:01:16]When you talk about an integer, this must be a whole number whether negative or positive.

[00:01:23]Decimal numbers and fractions are not a part of the integers. So, anything that is a decimal we rule it out. So, 23.8 is a decimal, therefore we rule it out.

[00:01:35]24.5 is a fraction, we rule it out.

[00:01:38]-4.8 is a decimal, we rule it out.

[00:01:42]21 is a whole number, then this is correct.

[00:01:45]So, the correct answer for question number one is choice B for boy.

[00:01:50]That um an integer must be a whole number.

[00:01:56]An integer must be a whole number. That is what you must be knowing.

[00:02:03]Allow I make progress now to question number two.

[00:02:07]I make progress to question number two.

[00:02:10]I'm being told in question number two that um the age the ages in years of some learners are 14 16 13 11 and 15.

[00:02:23]Which pair of numbers is is the prime numbers only?

[00:02:27]When you talk about prime numbers these are numbers that are only divisible by one and itself.

[00:02:34]Mhm?

[00:02:35]That means So we're going to look at numbers that only that are only divisible by one and their itself. The first prime number Let us look at 14. Is 14 a prime number?

[00:02:58]No, it has more than two factors.

[00:03:00]Therefore, we rule it out.

[00:03:02]16, no, it has more than two factors.

[00:03:05]13, yes.

[00:03:07]11, yes. 15, no.

[00:03:10]So, the pair here that is made up of prime numbers are just 11 and 13. Then we look at the choices we have B for boy.

[00:03:20]We have choice B for boy.

[00:03:24]Allow now I have a look at uh question The length of a road is 4,085 4,085 km. What is the length written in standard form?

[00:03:38]So, when you have 4,085 in standard form it will be 1 2 3. I've moved three steps to the left.

[00:03:48]Therefore, it will be 4.085 * 10 ^ 3 where n represents the number of steps moved.

[00:03:57]Looking at the choices, I exactly have choice C for cat.

[00:04:02]I exactly have choice C for cat as my answer. Choice C for cat.

[00:04:11]Mhm.

[00:04:12]Let us look at question number four, dear learners.

[00:04:16]David divided David dived 2 m below the surface the water surface in a swimming pool. He moved down 5 m. He then moved up 4 m.

[00:04:27]What was his final position in the swimming pool?

[00:04:30]Because he dived 2 m below the surface of the water, so these 2 m we're going to treat it as -2.

[00:04:37]Because it is below the surface of the water, so that's why we put a negative.

[00:04:42]He then moved down. He He moved down 5 m, meaning he went again 5 m deep.

[00:04:49]So again, because he's proceeding downwards, we're going to put again minus five.

[00:04:55]He then moved 4 m up. So because we are now moving up the opposite direction, it will be [clears throat] now plus four.

[00:05:03]Mhm.

[00:05:04]Plus four, that way. What was his final position?

[00:05:08]So -2 + -5 -2 -5 that becomes -7.

[00:05:14]Plus four.

[00:05:16]Aha.

[00:05:17]And if you have -7 + 4 then the final answer becomes negative 3 m, which is exactly choice C for cat.

[00:05:25]Exactly choice C for cat.

[00:05:28]Let us look at question number five.

[00:05:30]Majong bought 5 1/3 kg of rice.

[00:05:34]He cooked She cooked 3 3/4 kg of the rice.

[00:05:39]The following day, her neighbor added her 2 1/4 kg of raw rice.

[00:05:44]How many kilograms of raw rice does Majong have now? Hm?

[00:05:49]She bought 5 and a third.

[00:05:52]She cooked 3 and 3/4 of the rice. What remained? First, we're going to take 5 and a third.

[00:06:00]The total kg this person bought minus what was cooked. She cooked 3 and 3/4.

[00:06:08]Mhm?

[00:06:09]So, how are we going to achieve this uh subtraction? We're going to convert them into improper fractions.

[00:06:16]These will become 16 over 3.

[00:06:20]Minus this will become 15 over 4.

[00:06:24]And this will be When you take uh when you take 16 over 3 minus 15 over 4 this exactly will become 19 over 12.

[00:06:39]19 over 12. 19 over 12.

[00:06:45]Then after that, the following day, the neighbor added uh 2 and 2/4 kg of rice.

[00:06:50]So, from this what what was remaining, again they were added this amount. So, we are now going to take 19 over 12 plus what the neighbor added. 2 whole number 2 over 4 is just like saying 9 over 4.

[00:07:05]So, this is like saying plus 9 over 4.

[00:07:08]And this will become when I add here 9 over 4 uh when I add here 9 over 4 I'm getting um I'm getting 23 over 6.

[00:07:20]And 23 over 6 is just like saying it's just like saying 3 whole number 5 over 6.

[00:07:26]3 5 over 6, which is choice A for apple.

[00:07:30]That is how we are going exactly to do that particular computation.

[00:07:36]Allow I go to question number next. That is question number six.

[00:07:41]Question number six. A teacher had four number cards as shown.

[00:07:47]Which pair contains recurring decimals?

[00:07:49]Recurring decimals are decimals that do not end.

[00:07:53]Let us convert each fraction to a decimal.

[00:07:56]The first is 2/5.

[00:07:58]To a decimal, when you divide 2 by 5, 2 / 5 from the calculator, 2 / 5, I get 0.4. So, this one is a terminating decimal and not a recurring decimal. Therefore, this one we rule it out. 7/15.

[00:08:16]In decimal form, 7 / 15, you get 0.6666.

[00:08:23]The six is recurring. It is continuing without an end. Uh-huh.

[00:08:28]Let us look at 8 over 9 over 8.

[00:08:32]In decimal form, 9 over 8 becomes 1.125.

[00:08:38]125 that has an end.

[00:08:41]Then, 4/12.

[00:08:43]In decimal form, 4/12 becomes Uh-huh. If they're saying 4/12, yes, 4/12 becomes 0.33333.

[00:08:57]Three is continuing without an end.

[00:08:59]So, when you talk about recurring decimals, these are decimals that do not end. The recurring decimals now I'm having, the ones that are continuing without ending is 7/15 and 4/12.

[00:09:10]7/15 and 4/12 are our answers.

[00:09:13]Therefore, choice D for dog is the correct answer.

[00:09:17]Question number seven.

[00:09:19]The length of a square farm is 108 m.

[00:09:22]Use mathematical tables to determine the area.

[00:09:25]Remember, it is a square farm.

[00:09:28]Meaning that all the sides are equal.

[00:09:31]Mhm.

[00:09:33]So, how do you get the If the length is 108, area of a square is given by side multiplied by side.

[00:09:40]Therefore, the area will be given by 108 squared. In short, they want we use mathematical tables to get the square of 108.

[00:09:52]We have to use mathematical tables here so that we get the square of 108.

[00:09:58]Dear learners, hm?

[00:10:00]This is again something we learned in grade eight. So, we should not struggle. We should not struggle at all.

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[00:10:43]So, when you want to square 108, first you express it in standard form. This will be 1.08 times 10 to the power of two.

[00:10:53]Squared. Mhm.

[00:10:55]So, what is the square of 1.0 then eight? We go to the tables uh to the square tables.

[00:11:01]Let me go to the square tables.

[00:11:04]Uh-huh.

[00:11:06]1.0 then eight.

[00:11:09]1.0 is here.

[00:11:12]Then eight is here.

[00:11:14]The number is 1.

[00:11:17]166. 1.166.

[00:11:19]So, here we have here 1.1 66 times 10 squared becomes 10 to the power of four. Mhm.

[00:11:29]So, that now becomes 1.166.

[00:11:32]I have now 1.166 * 10 ^ 4. This exactly becomes 11,000 660.

[00:11:43]11,000 660 sq meters as the answer.

[00:11:50]11,000 660 sq meters. Looking at choices, we don't have the correct answer. The correct answer should be 11,000 660 sq meters.

[00:12:03]That is what you get when you square 1.08.

[00:12:09]1.08 1.0 then 8.

[00:12:14]Let me hope I've read 1.0 then 8. Yes, 1.0 then 8. Mhm.

[00:12:20]That one is well taken care of.

[00:12:23]Allow I look at now question number eight. In a class, the fraction of boys is 3/5.

[00:12:29]What is the fraction of the ratio of girls to boys? So, if boys in a class is 3/5, then girls in that particular class can be obtained by taking Remember, the total fraction should add up to one.

[00:12:47]So, you take the total fraction one minus that of boys 3/5. So, we going to get the fraction for girls is 2/5.

[00:12:58]And now, when you talk about the ratio of girls to boys, this is the ratio of um girls you have now 2/5 is to 3/5.

[00:13:11]We can eliminate the denominator by multiplying by the LCM 5 by 5, where they'll be canceling out. Then you get your answer as 2: 2:3.

[00:13:21]It should be 2:3, not 3:2. So, that gives you the correct answer is C for cut.

[00:13:29]C for cut. Uh-huh.

[00:13:32]Allow I look at question number nine, ladies and gentlemen. The price of a pen increased from 150 shillings to 200 shillings. What was the percentage increase? Before getting the percentage increase, let us first compute the increase.

[00:13:49]The increase you take the final value 200 minus the initial value uh 150. So, this gives you an increase of 50 shillings.

[00:14:00]After getting that as the increase, now we can apply the formula that percentage increase is equal to the increase over the original value times 100%.

[00:14:12]Our increase here is 50, so this will be 50 over the original value. Initially, it was 150. So, it is over 150 times 100%. Mhm. [clears throat] So, when you have 50 over 150 50 over 150 multiplied by 100, this exactly gives you 33 and a third percent. Mhm.

[00:14:36]33 and a third percent.

[00:14:42]We are having 33 and a third percent as our answer.

[00:14:52]Now, I hope that has well been solved.

[00:14:56]Allow now I have a look at question number So, this one gave the correct answer as B for boy.

[00:15:04]Let us have question number 10.

[00:15:07]The perimeter of a figure is represented by the expression 7 into 3x + 4y + 6 into 2x - 3y.

[00:15:18]What is the simplest form of the expression?

[00:15:22]When they say the simplest form, we are going to open these brackets.

[00:15:27]7 * 3x will be 21x.

[00:15:32]7 + 4y, that will be + 28y.

[00:15:37]6 + 12x so + 2x This will be + 12x.

[00:15:44]6 - 3y, that will be - 18y.

[00:15:49]21x + 12x, that will be 33x.

[00:15:57]Positive 28y - 18y, this will be + + 10y.

[00:16:04]So, the simplified expression becomes 33x + 10y exactly giving you choice A for apple as the most correct answer. Mhm.

[00:16:18]Allow I look at now question number 11.

[00:16:23]Question number 11.

[00:16:24]The length of a playing field is given by the expression 2ax + bx all over 2ay + by.

[00:16:35]Factorize the expression. Factorizing the expression here means we factor out the common factor. Look at the numerator.

[00:16:42]When you have 2ax + bx, what is common here? The common factor there is uh x.

[00:16:49]We can factor out x in the numerator and you'll be left with 2a + b.

[00:16:58]Over the denominator, when you have 2ay + by, the common factor here is y. We factor out the y, you'll be left with 2a + b.

[00:17:10]Mhm.

[00:17:11]After that now, I can say 2a 2a + b and 2a + b will can out.

[00:17:16]Therefore, my answer will become x over y.

[00:17:19]That is now the simplified expression, which gives you choice A for apple as the correct answer. Mhm.

[00:17:27]Question 12.

[00:17:29]Amina earned a total of 4,800 shillings after working for 5 hours.

[00:17:34]At what rate per hour was she being paid?

[00:17:38]If 5 hours if working 5 hours someone is paid 4,800, what about working for 1 hour? You cross multiply.

[00:17:47]This will be 1 times 4,800 divided by 5.

[00:17:53]So, when you divide 4,800 by 5, you're exactly going to get 960 shillings.

[00:18:00]So, this means this person is being paid at at a rate of 960 shillings per hour, which is choice B for boy. Mhm.

[00:18:11]Question number 15 13.

[00:18:14]The The cost of a machine is 4,950.

[00:18:17]What is the cost to one significant figure?

[00:18:20]So, when you have 4,950, remember the zeros at the end of a decimal number is not Sorry. The zeros the trailing zeros or the zeros at the end of a whole number are never significant.

[00:18:37]They're just placeholders.

[00:18:39]Then any non-zero digit is a whole number. So, it is a significant number.

[00:18:46]So, when you look at this number 4950, it has three non-zero digits. Therefore, it has automatically three significant figures.

[00:18:56]Then the zero in it is a trailing zero, meaning it is at the end. And because this is a whole number, then the zero there is not a significant figure. It is just a placeholder.

[00:19:06]Converting this to uh to one significant figure, the first significant figure is four. Look at the digit to the right of four, it is nine.

[00:19:15]Because the digit is more than five, it will increase the value of one by one of four by one to make it five.

[00:19:24]Then these other digits will become zeros just to act as placeholders. In this case, the number becomes 5,000 so that we don't lose its value much.

[00:19:34]So the zeros at the end are just placeholders. So the correct answer is 5,000.

[00:19:39]Not five and not 4,000 or four.

[00:19:42]Mhm.

[00:19:44]Question number 14.

[00:19:46]A vegetable garden is in the shape of a semicircle.

[00:19:50]The diameter of the garden is 63 m. What is the distance round the garden?

[00:19:56]It is assumed that the garden looks like this. It is a semicircle.

[00:20:03]Whose diameter is 63 m. They want the distance around the field. The distance I'll move from here towards the semicircular part.

[00:20:15]This is a half pi d.

[00:20:18]But because I started here, I have to come back to where I started from. That is the diameter.

[00:20:24]So the formula here will be uh perimeter is given by a half pi d for the curved part plus d because they want the distance around the garden.

[00:20:36]So this will be a half times pi 22 over seven times the diameter 63 plus that diameter of 63.

[00:20:45]Mhm.

[00:20:46]So this will be when I take a half times 22 over seven times uh 63, I'm exactly getting 99.

[00:20:58]Then now I have to add the 63 here.

[00:21:01]This becomes when you add uh when you add the 63 you are going to get 162.

[00:21:12]As now your final answer. Be very keen.

[00:21:14]You can see the first choice you have given 99 to trick you or to make you get tempted to that as the answer. The final answer should be B for boy for that particular question.

[00:21:26]Question 15, Walter made a pattern as shown below.

[00:21:31]What is the length of the arc? They are asking the length.

[00:21:34]The formula for getting the length of any arc is given by the theta all over 360 to pi r. That is the formula for getting the length of the arc.

[00:21:46]So this will now be the 120 all over 360 being multiplied by our by two then by the pi 22 all over seven by the radius 21.

[00:22:01]Mhm. Use your calculator.

[00:22:04]120 over 360 by two by 22 over seven by 21, you exactly get 44 centimeters.

[00:22:14]Mhm.

[00:22:15]44 centimeters is the length.

[00:22:18]This particular distance here.

[00:22:21]44 centimeters, that is the correct answer.

[00:22:26]Mhm.

[00:22:27]Question number 16.

[00:22:29]A tank is in the shape of a cube. The sides measure 4 meters each. What is the surface area?

[00:22:37]Mhm.

[00:22:39]The best way to analyze the question is by first drawing something that looks more like a cube.

[00:22:46]That is my cube.

[00:22:48]4 4 4.

[00:22:51]A cube has how many faces?

[00:22:54]A cube has a It's a tank in the shape of a cube. Mhm.

[00:23:00]They have not specified. It has six faces.

[00:23:05]It has six faces.

[00:23:07]Let us calculate the area of one face.

[00:23:09]It is a square side The area of one face will be four times four which is 16.

[00:23:16]Now, this 16 you multiply by six to get the total area for all the faces.

[00:23:20]This becomes 96 square meters.

[00:23:24]96 square meters. Because they have not specified whether it is open or closed, we assume it to be closed. Could it be opened, they could have stated that clearly and told us that it is an open tank. Mhm.

[00:23:39]Allow I make progress to question number 17 now.

[00:23:43]The temperature of a liquid is 52°C.

[00:23:47]What is the temperature in Kelvin? To get To change the temperature from degree Celsius to Kelvin, simply add the 273. So, I'm going to take 273 plus my temperature in degree Celsius now 52.

[00:24:03]This expression should be sufficient enough to give me my temperature in Kelvin. It should be addition, not division, not multiplication, and not subtraction.

[00:24:13]Mhm.

[00:24:14]Question number 18.

[00:24:16]Peter drove a distance of 80 km/h. What was the speed in meters per second? To change speed from kilometers per hour to meters per second, you take your speed in kilometers per hour 90, you multiply this by five over 18. As simple as that.

[00:24:33]So, when you take a 90 * 5 over 18, you're exactly going to get 25 m/s.

[00:24:41]25 m per second.

[00:24:44]Choice C for cat.

[00:24:46]Question number 19.

[00:24:49]Leo drew the parallelogram below.

[00:24:52]What is the size of the angle marked X?

[00:24:55]This and this one here. Mhm. We call [clears throat] them the co-interior angles, and co-interior angles add up to 180°.

[00:25:04]What that means is when I take the angle 108 plus angle X, they add up to 180°.

[00:25:12]Collecting like terms, then it will mean X is given by 108.

[00:25:17]So, 180 - 108.

[00:25:21]180 - 108 exactly to give you 72°.

[00:25:29]Choice A for apple. Mhm.

[00:25:33]Question 20.

[00:25:35]An interior angle of a regular polygon is 120°. Interior angle. How many sides of the poly- How many sides does the polygon have?

[00:25:45]If the interior angle is 120, what is the exterior angle?

[00:25:49]Remember, interior angle plus exterior angle should add up to 180°. So, if the If the interior angle here is um If the interior angle here is 120, I'm going to have 120 plus the exterior angle to give me 180.

[00:26:09]Then it will mean that the exterior angle is equivalent to 180.

[00:26:13]You less 120. This exactly gives you 60° as the value of the exterior angle.

[00:26:19]Then to get the number of sides n of any polygon, we do take 360 divided by the exterior angle.

[00:26:27]So, this will be 360 divided by 60 to give you six sides.

[00:26:35]Six sides. This is um a six sided polygon. Mhm.

[00:26:43]That marks the end of section one.

[00:26:46]Allow me to look at now section B in brief.

[00:26:49]Question 21.

[00:26:50]During a rainy season, we are looking at section B.

[00:26:55]We are looking at section B. During a rainy season, Mazingira Club planted 59,000 845 tree seedlings. Fadhili Club planted 976 less tree seedlings.

[00:27:09]Write the number of tree seedlings planted by Fadhili in words. Fadhili planted um 976 So, we are first going to take 59 845 You subtract 976.

[00:27:31]When you subtract this, we are going to get the number of tree seedlings planted by Fadhili.

[00:27:40]Uh-huh.

[00:27:41]This is a 58 869.

[00:27:48]So, that is um 58,000 58 thousand 58,000 800 800 and 69.

[00:28:17]69, that is the value in words.

[00:28:22]Mhm.

[00:28:23]Part B Round off the number of the tree seedlings planted by Fadhili to the nearest hundreds of thousand. So, when you have 58,000 869 to the nearest hundreds of thousands ones, tens, hundreds, thousands, tens of thousands hundreds of thousands. Uh-huh.

[00:28:46]Is it to the nearest hundred thousand?

[00:28:52]Once, tens, aha.

[00:28:55]I can make Mhm. Is it making some sense?

[00:29:02]Round off to the nearest 100,000.

[00:29:07]Once, tens, 100,000, tens of thousands.

[00:29:10]If I assume we had a zero here, then this will increase this value by one.

[00:29:21]Mhm.

[00:29:22]This question is a bit complex and I want to find the best way of making my learners to literally understand that particular bit.

[00:29:37]Let us reread the question once again for our own consumption.

[00:29:43]We have to reread the question once again for our own consumption. The question is round off the number of seedlings planted by Fadhili Mhm. to the nearest hundreds of thousands.

[00:30:00]To the nearest hundreds of thousands.

[00:30:07]Aha.

[00:30:11]To the nearest hundreds of thousands.

[00:30:15]So, I've placed a zero here.

[00:30:17]And now we are going to look at um how we are going to approach it. Why did I place a zero there so that to make the digits to match exactly what the question is asking. So, the digit to the nearest hundred hundreds of thousand, the digit in the hundreds of thousand position is zero. To its right we have five. Because five is five is equal to five, it's to increase the value of zero by one to make it one. Then the others change to zeros. 0 0 0 0 0.

[00:30:50]So, you get your final answer as 100,000.

[00:30:54]So, your final answer becomes 100 thousand. Mhm.

[00:30:59]Part C, write the number of tree seedlings planted by Fadili to two significant figures.

[00:31:05]Fadili planted Remember they planted 58,869.

[00:31:11]To two significant figures, the first significant digit is five then eight. Look at the digit to the right. It is eight, so it will increase the value of this one by one.

[00:31:20]Then these ones will change to zeros as placeholders.

[00:31:23]So, the answer becomes 59 thousand.

[00:31:28]59 thousand will become the answer at that particular case.

[00:31:35]The question paper is so much interesting.

[00:31:38]Allow I look at Now, question number 22.

[00:31:42]Question number 22. The area of a square garden is 5125.

[00:31:46]Write 5125 in standard form.

[00:31:51]So, when you have 51 25, so this will be 1 2 3. So, this becomes 5.125 times 10 to the power of three.

[00:32:04]Like that. That is the value in standard form.

[00:32:07]Mhm.

[00:32:09]Part B, use the mathematical tables to determine the length of one side.

[00:32:13]The length of one side, if area is given by side times side, and this is the area, to get the length of one side, we are going to get the square root of the area.

[00:32:24]So, let us get the square root of um 51 25.

[00:32:32]We are going to express this number in standard form such that the power of a of 10 is an even number.

[00:32:39]So, this will be the square root of 51.25 * 10 ^ 2 Mhm.

[00:32:53]So, let us read it.

[00:32:55]The square root of 51.25 from the log table.

[00:32:59]We are going to the square roots table.

[00:33:02]51.25 under square roots table.

[00:33:06]51.25 51 is here. 51.2 is here. 7.1554 We have here 7.15 54 50 51.2 then 5. Proceed along the same row to 5. You get the value is 35. What do we do to 35? We are supposed to add. So, let us add here 35.

[00:33:37]This will become 9.

[00:33:39]8 5 1 7.1589 7.

[00:33:48]1589 * 10 ^ 2 when you square root it becomes 10.

[00:33:53]So, this becomes 71.

[00:33:57]5 89 m 71.589 m Then, determine the perimeter of the garden.

[00:34:07]Perimeter is given by 4 * the measure of one length.

[00:34:13]So, this will become When you have 4 * the measure of one length, this will be 4 multiplied by 71.

[00:34:22]5 89 Mhm.

[00:34:27]Let us see. 4 * 71.589 exactly gives you 286 286.3 56 m 286.356 m mhm Question number 23 ladies and gentlemen keep subscribing liking and sharing this video with your other friends.

[00:34:59]mhm A story building has a basement for parking vehicles.

[00:35:04]Muriuki's office is on ground floor. He climbed to fifth floor to park a pile and further three floors up to pick his car keys. He then went down 10 floors to the parking. Write this expression write an expression to represent this information.

[00:35:22]He climbed up five up to the fifth floor that is five.

[00:35:27]And further three floors up so plus three.

[00:35:31]He then went down. Look at this down.

[00:35:34]The opposite direction 10 floors so minus 10. So this is like saying uh eight write an expression to They just want an expression huh. So this is the expression.

[00:35:47]5 + 3 - 10 is the expression for that particular question. Remember they want an expression not the final answer.

[00:35:56]Part B use a number line to determine the position of the parking. So it means let us solve this expression using a number line. mhm This must be so much interesting.

[00:36:10]I'm going to start from uh-huh let us see.

[00:36:16]I can have here -4 -3 negative uh 2 -1 0 1 2 3 4 5 6 7 8 and so on.

[00:36:39]Maybe 9.

[00:36:43]So, starting from positive from positive 5, yeah. Move three steps to the left to the right because we are adding. So, this will be 1 2 3 I've arrived at 8. Then move now 10 steps to the left because he's moving down.

[00:37:02]10 steps to the left, we are now going to have 1 2 3 4 5 6 7 8 9 10. So, the final answer here is -2.

[00:37:23]We found our final answer is -2. That is by use of a number line.

[00:37:31]That is by use of a number line.

[00:37:35]I'm seeing many people appreciating the work we are doing. That is great work.

[00:37:40]Make sure you support us by subscribing.

[00:37:43]Wambua spent 3/4 of his salary on food, a quarter of the remainder on rent, and other bills, and saved the rest. Determine the of the salary that he saved.

[00:37:55]Food alone, food alone is 3/5.

[00:38:01]A quarter of the remainder on rent.

[00:38:04]First, what is the remainder?

[00:38:06]The remainder will be 1 - 3/5 to give you 2/5.

[00:38:11]Then, a quarter of it on rent, meaning rent alone.

[00:38:16]Rent took a quarter of the remainder, which is 2/5.

[00:38:21]This becomes 1/10. That is what the rent took.

[00:38:26]on rent and other bills and saved the rest.

[00:38:29]Now, to get the savings, we're going to take the total fraction one minus what has been spent on food 3/5 plus what has been spent on rent and other bills 1/10.

[00:38:46]When you add the two and subtract from one, Mhm. 3/5 plus 1/10 then you subtract, you get 3/10.

[00:39:02]The fraction for savings is 3/10.

[00:39:05]Mhm.

[00:39:06]His total salary I determine his total salary if he saved 36,000.

[00:39:12]So, this 3/10 is equivalent to 36,000.

[00:39:16]What about the total salary represented by a fraction of one?

[00:39:21]You cross multiply.

[00:39:22]This will become one times 36,000 divided by 3/10.

[00:39:30]Mhm. So, that is just like saying 3/ 36,000 uh divided by 3/10 exactly gives you 120,000 shillings.

[00:39:43]120,000 shillings.

[00:39:47]Mhm.

[00:39:48]Question 25.

[00:39:50]The fraction of cups in a cupboard of utensils is given in decimal form as 0.16.

[00:39:57]Express the decimal number as a fraction in the simplest form. You can see the six has a dot on top to mean that that six is recurring.

[00:40:10]So, in decimal form, we are going to relate it this way. We can say let R be 0.1 6666. This six is recurring.

[00:40:22]Then 10 R will be given by 1.6666.

[00:40:29]Mhm.

[00:40:30]Then uh 100 R will be given by 16.666.

[00:40:37]In that case, when I subtract equation two from equation three, that is 100 R minus 10 R gives you 16.66 minus 1.66.

[00:40:51]Mhm.

[00:40:52]100 R minus 10 R, this becomes exactly 90 R is equal to 16.66 minus 1.66.

[00:41:01]This becomes 15.

[00:41:03]Dividing through by 90, you get R is given by 15 over 90.

[00:41:10]But now, because they want your answer in simplified form, 15 over 90 is exactly 1 over 6.

[00:41:20]So, the answer becomes 1 over 6. Mhm.

[00:41:25]Question number 26.

[00:41:28]We are going to question number 26.

[00:41:31]Um thank you all for following deeply.

[00:41:36]In a bookshop, the ratio of textbooks, exercise books, and pens is 2:3:5.

[00:41:42]There are a total of 720 exercise books, textbooks, and pens.

[00:41:49]Determine the number of textbooks. Mhm.

[00:41:52]So, this total number of exercise books should be equal to the total ratio. 2 plus When I take two plus three plus five, this gives you a total ratio of 10. So, the total ratio of 10 is equivalent to the total number of uh all the books and pens, which is 720.

[00:42:13]They are asking determine the number of textbooks. Textbooks are being represented by two in the ratio. So, if 10 is equals to 720, what about two which represents the number of textbooks? You cross multiply.

[00:42:24]This becomes two multiply this by 720 then divided by 10.

[00:42:31]This exactly gives you 1 44.

[00:42:36]That exactly gives you 1 144 as your answer. Mhm.

[00:42:43]Part B.

[00:42:45]Determine the total number of exercise books and pens.

[00:42:49]So, if uh exercise books and pens Let me see.

[00:42:54]Exercise books and pens.

[00:42:57]Uh-huh. Exercise books and pens.

[00:43:00]It is very simple. I can say if 720 In fact, even I can say because the textbooks is this one. But, let me say if 720 is being represented by 10 as the total ratio.

[00:43:15]When you talk about exercise books and pens, their ratio is three and five. The total ratio 3 + 5 is eight. So, what about eight? You can cross multiply.

[00:43:25]This gives you 720 times eight divide this by 10.

[00:43:31]Mhm.

[00:43:32]So, 720 * 8 / 10 gives you 576.

[00:43:41]Or another method you could have just taken. Because the total of the three items is 720.

[00:43:49]And already uh ex- uh textbooks alone is 144. So, when you less 144 720 you less 144 exactly gives you 576.

[00:44:03]This method is also correct depending on how you will relate it. Mhm.

[00:44:09]Question number C.

[00:44:11]The total number of exercise books and pens was increased in the ratio of 3:2.

[00:44:17]What is the total number of items in the bookshop after the increase?

[00:44:21]It was increased in the ratio of 3:2.

[00:44:25]The total number of exercise books and pens. What is the total number of exercise books and pen? 576. Now, this 576 got increased in the ratio 3:2. So, to get the new number, it will be 3/2 multiplied by 576.

[00:44:43]This will give you when you take 3/2 times 576, you get 864.

[00:44:54]So, from this 864, we can get what we call the increase. What is the increase?

[00:45:01]It has increased from 576 to 864 minus 576.

[00:45:08]So, the new increase here will be 864 minus 576 gives you 288. There is an increase of 288.

[00:45:18]So, from the total 720, we expect an increase of 288.

[00:45:26]Therefore, the final number becomes 1,008.

[00:45:32]1,008.

[00:45:36]So, the answer becomes 1,000 and 8.

[00:45:43]Question number 27.

[00:45:47]Mungaru and Anyango work for the same organization.

[00:45:51]Each of them earn a monthly salary of 4,000.

[00:45:55]Anyango's salary was increased from from 40,000 to 50,000, while Mungaru's salary increased by 20% determine the percentage increase in Anyango's salary.

[00:46:08]First B, for us to get the percentage increase, we need to get the increase.

[00:46:13]To get the increase, you take 50,000 minus 40,000.

[00:46:19]This gives you an increase of 10,000.

[00:46:23]Now, to calculate percentage increase, we're going to take the increase, which is 10,000 um the increase is 10,000 all over the original salary or as the initial salary which is 40,000 times now 100%.

[00:46:44]So, when I take 10,000 over 40,000 times 100, this gives you 25%.

[00:46:56]So, that means Anyango's salary increased by 25%.

[00:47:00]Part B, Mugeru's new salary. Mhm.

[00:47:06]Mugeru's new salary, if it increased by 20 by 20%, the new salary will be 120% of the original. So, 120 over 100 multiply this by 40,000.

[00:47:18]This gives you when you take 120 over 100 times four um mhm times 40,000 you're going to get 48,000.

[00:47:36]Mhm.

[00:47:37]The difference in their new salaries you take 50,000 minus 48,000.

[00:47:46]This exactly gives you a difference of 2,000.

[00:47:52]Mhm.

[00:47:53]Issue number 28.

[00:47:55]Aluso had is cardboard of diameter as shown below.

[00:48:00]We cut out a circular part. Determine the area of the shaded part. First of all, allow I get the area of this area of the semicircle.

[00:48:10]Area of my semicircle This will be given by a half by r squared.

[00:48:19]So, this is a half multiplied by the pi which is 22 over seven.

[00:48:25]If the diameter is 28, then the radius is 14. So, times 14 squared.

[00:48:30]My semicircle now will be giving me ahem I'm I'm keying in.

[00:48:38]This gives me 308 square centimeters.

[00:48:43]That is the area of the semicircle.

[00:48:47]Ahem.

[00:48:50]Mhm. 308 square centimeters. We need now to calculate the area of the circle.

[00:48:57]And I want to be borrow this knowledge.

[00:48:59]If I divide this semicircle into uh two halves this way This is 14.

[00:49:08]This is 14. It means also going up this will be 14. That 14 now means we are going to have a circle whose diameter is 14. And we need now to calculate the area of that circle.

[00:49:21]Area of the circle will be now given by pi r squared. So, this is 22 over seven.

[00:49:29]If the diameter is 14, its radius now will be seven.

[00:49:32]Times seven squared. Mhm.

[00:49:35]So, this will become 22 over seven times seven squared become 154.

[00:49:42]1 54 square centimeters.

[00:49:46]Now, to get the shaded area we are going to take the area of the semi-circle, which is 308 - 154.

[00:49:59]This exactly leaves you with an answer of 154 square centimeters.

[00:50:06]Square centimeters. Mhm.

[00:50:09]Question 29.

[00:50:11]Ali and Wambua are sales people in different companies. Ali is paid a basic salary of 35,000 and a commission of 8 per cent of all the value of sales.

[00:50:22]Wambua is paid a commission of 13% on all the sales.

[00:50:26]In 1 month, they each sold goods worth 800,000.

[00:50:31]Determine part A, the total earnings of Ali. Mhm.

[00:50:36]We need to determine Ali's total earnings. Remember, to get the total earnings, you take the basic salary plus commission.

[00:50:43]So, let us get first his commission.

[00:50:47]Commission, you take percentage commission for Ali, which is 8%. So, it is 8 over 100 times his value of goods, which is 800,000.

[00:50:59]800 thousand. Mhm.

[00:51:02]So, this cancel off.

[00:51:05]When you take 8 over 100 times 800 thousand, you're going to get a commission of 64,000.

[00:51:16]This is just commission.

[00:51:19]64,000. Then now, to get the total earnings, the formula is the basic salary plus the commission.

[00:51:27]The basic salary is 35,000 plus a commission of 64,000.

[00:51:35]When you add this, this exactly gives you 99 thousand shillings.

[00:51:45]99,000 shillings. Part B, the commission for Wambua. Mhm. Wambua is paid a 13% commission. So, this will be um 13 over 100 times 800 thousand.

[00:52:02]And this gives you a commission of When you have 13 over 100 times 800 thousand, this gives you 104,000 commission.

[00:52:15]104 thousand as the commission for Wambua.

[00:52:19]Mhm.

[00:52:20]The difference in their total earnings.

[00:52:22]Let me get first Wambua's total earnings.

[00:52:25]Mhm.

[00:52:27]Uh the total earnings for Wambua will be given by the commission 104,000 plus Wambua's basic salary.

[00:52:38]Wambua earns uh-huh. In 1 month, they each sold goods worth this.

[00:52:45]Alice paid this and this reason. Wambua is paid on all sales.

[00:52:49]Mhm. Does Wambua get uh basic a basic salary? Alice and Wambua are sales people in different companies. Alice is paid a base salary of this and a commission of this. Wambua is paid a commission.

[00:53:02]So, Wambua is just getting a commission, huh? So, this basic salary is just like the commission.

[00:53:08]This commission of Wambua is the basic salary.

[00:53:12]So, that is the her total earnings. So, the difference now, you take Wambua's uh amount 104,000.

[00:53:21]You less uh you less you less Alice's earnings 99,000.

[00:53:31]So, this gives you a difference of 5,000.

[00:53:34]A difference of 5,000.

[00:53:37]Mhm.

[00:53:38]Question number 30.

[00:53:40]The following table shows the mobile money transaction charges for a mobile service provider.

[00:53:47]Gordie had 7,500 shillings in his mobile money account. He sent 2,800 to his daughter and withdrew 3,000 shillings. Determine part A, the cost of sending and withdrawing the money that Gordie paid.

[00:54:03]So, she had this. She sent the cost of sending. They just asked the cost of sending.

[00:54:10]Okay. You're getting the point? The cost.

[00:54:13]Sending 2,800. 2,800 lies here.

[00:54:18]Sending fee is 45.

[00:54:22]And withdrawing.

[00:54:25]And withdrawing money that Gordie paid.

[00:54:28]She withdrew 3,000, which falls here.

[00:54:31]The withdrawal fee is 48.

[00:54:35]This gives you a total of 13 93 shillings. So, that the cost spent on those transactions is 93 bob.

[00:54:45]How much money are remaining Gordie's account?

[00:54:51]So, she sent 2,800.

[00:54:54]This 2,800 she has to add here 45 shillings for sending. So, in total, the amount deducted from the account is 2,845.

[00:55:07]She withdrew 3,000.

[00:55:09]And in order to withdraw 3,000, you need a transaction of 48 bob.

[00:55:14]So, the amount that 38.

[00:55:19]3,048.

[00:55:23]Uh-huh.

[00:55:23]After getting that, now we can get what we the total amount deducted from the account.

[00:55:30]And to get it, you take 3,048 plus 28 45 Mhm?

[00:55:43]30 48 plus 28 45 So, when you take 30 When you take 30 48 plus 28 45, this gives you 58 93.

[00:56:03]58 90 3 Then, how much remained?

[00:56:08]You now take 7500.

[00:56:12]You less 58 93 When you less it uh you are exactly going out to get 16 07 shillings.

[00:56:27]As what remained, 16 16 uh 07 shillings 16 07 shillings Question number 31 Uh use elimination [clears throat] method to solve for the values of x and y. 2x + 3y = 8 3x + 2y = 7 Mhm?

[00:56:48]In this case when you have 2x plus 3y is equal to 8 and we had here 3x plus 2y is equal to 7 And they are specific we use elimination. I want to eliminate my x. I can multiply by two here by three.

[00:57:10]This becomes 6x plus 4y is equal to 14 then 6x plus 9y is equal to 24 When you subtract, 6x - 6x disappear.

[00:57:25]4y - 9y you get -5y is equal to -10 So, when you have it that way, then it will mean that Y will be given by -10 / -5.

[00:57:38]So, the value of Y is equal to 2.

[00:57:41]And if Y is 2, to get the value of X, you substitute.

[00:57:44]This will become 2X + 3Y, so 3 into 2 is equal to 8.

[00:57:53]So, this will become 2X + 6 = 8.

[00:57:59]Collecting the like terms, you get 2X = 8 - 6.

[00:58:07]2X will be equal to 2.

[00:58:09]Therefore, the value of X is equal to 1.

[00:58:12]So, Y is 2, X is 1.

[00:58:15]Do it that way, you'll have your five your four marks.

[00:58:22]Question number next.

[00:58:26]Given that A is equal to 3, B is equal to 2, and C is equal to 1, evaluate this. 2A - 2B plus all over C plus 1.

[00:58:36]So, 2A will be 2 into the value of A, which is 3.

[00:58:41]- 2 into B, which is 2.

[00:58:45]All over C, which is 1 plus 1.

[00:58:49]This will become 6 - 4 over 2.

[00:58:53]And this will become 2 over 2 which evaluates to 1. 2 over 2 evaluates to 1.

[00:59:03]Question number >> [clears throat] >> 32.

[00:59:07]Adam bought meat. The meat was more than 4 kg, but less than uh 7 kg. Write the inequality.

[00:59:16]This means 4 was more than So, 4 is less than X but less than 7, which is also this X is also less than seven.

[00:59:30]Mhm, because here we have two inequalities. The meat was more than 4 kg, meaning X was greater than four.

[00:59:39]And the meat was less than seven, meaning that this X was less than seven.

[00:59:44]When you combine them into one, this is what you're going to get.

[00:59:47]Illustrate this inequality on a number line. Mhm.

[00:59:51]I can have here four, five, six, seven.

[00:59:58]Mhm. This is a number line that way. We are done.

[01:00:02]Solve for the value of X in 6 into X + 1 is equals to 18. When you open the brackets, this will become 6X + 6 is equal to 18. Collecting like terms, this will become 6X is equal to 18 minus 6.

[01:00:18]Therefore, this becomes 6X is equal to 12. Dividing through by six, you get X is equal to two. The value of X there is exactly two.

[01:00:30]Question 32.

[01:00:33]A water tank is 5 m long, 4 m wide, and 3 m high. It contains water to a height of 2.5 m. Determine the volume of the tank in cubic meters.

[01:00:43]Uh-huh.

[01:00:45]Volume of this tank is given by length times width times height.

[01:00:51]The length is five times the width of four times the height of three.

[01:00:56]Mhm.

[01:00:57]Let us multiply that. 5 * 4 times three exactly gives you 60 cubic meters.

[01:01:05]60 cubic meters. They wanted now in centimeters.

[01:01:11]So, this will become 60 times 100 times 100 times 100.

[01:01:19]Mhm.

[01:01:21]So, becomes 60 L.

[01:01:29]60 million cubic centimeters. Part B, evaluate the capacity of the tank in liters. The capacity of the tank.

[01:01:42]Uh-huh.

[01:01:43]Sorry. Uh-huh.

[01:01:45]It that means the volume of the tank.

[01:01:47]Our water tank contains water to this capacity. Find the capacity of water in the of water in the tank. Uh-huh.

[01:01:53]Now, here you need to be very keen. Now, they want the capacity of water in the tank, not the capacity of the tank.

[01:01:59]We are going to still to say volume is given by length times width times height.

[01:02:05]Uh but here we need to be very keen.

[01:02:09]Our length is five times our width which is four times our height. Water fills up to 2.5.

[01:02:19]So, times 2.5.

[01:02:21]This will become 5 * 4 * 2.5 gives you 50 cubic meters.

[01:02:31]Now, you to convert it to liters, you multiply it by 1,000. Because you know 1 cubic meter is equal to 1,000 liters. What about 50?

[01:02:40]Mhm.

[01:02:41]So, this will become 50 multiplied by 1,000 to give you 50,000 liters.

[01:02:50]Question number 34.

[01:02:52]A motorist covered a distance of 180 km in 2 hours.

[01:02:56]Determine the speed in meters per second.

[01:02:59]Speed is given by distance 180 over time two.

[01:03:03]So, this gives you 90 km per hour.

[01:03:08]But now, because they want it in meters per second, you take your speed in kilometers per hour, that is 90.

[01:03:14]Then you multiply this by five over 18 to exactly give you 25 m/s.

[01:03:22]Mhm.

[01:03:23]Question 20 35.

[01:03:25]The temperature of ice was -18°C.

[01:03:29]What is the temperature in Kelvin? To change from degrees Celsius to Kelvin, take your temperature in degrees Celsius, which is -18, then add 273.

[01:03:39]Mhm.

[01:03:40]When you take -18 + 273, you exactly get 255 Kelvin.

[01:03:53]Mhm.

[01:03:55]Question number 36. Construct a triangle such that X is equal to Y is equal to Z is equal to 6 cm.

[01:04:03]Then bisect that particular angle.

[01:04:06]Mhm.

[01:04:08]I'm just going to give a sketch.

[01:04:09]So, let me say XY is 6 that way.

[01:04:13]This is XY. I've measured it to be 6 cm. Again, I'll measure another 6 cm making arc.

[01:04:21]Come also to X, measure another 6 cm make another arc.

[01:04:25]Then now I'm going to join.

[01:04:28]Mhm.

[01:04:32]So, this is our Z.

[01:04:34]So, each side here is 6 cm. So, this is an equilateral triangle. This one automatically becomes equilateral triangle because it has all the sides equal.

[01:04:47]And once you've gotten it that way, it means equilateral triangle has each side being 60°.

[01:04:52]Um what is the size of the angle after bisecting? Let us bisect this angle.

[01:04:56]Stand here, make arc, make arc. Come here, make arc, make an arc.

[01:05:01]Then measure this angle.

[01:05:07]The angle should be exactly 30°. So, if you bisect 60 into two, question 37.

[01:05:14]Mulimi joins the Question 37.

[01:05:16]Mulemi joins some lines as shown.

[01:05:19]I write the size of the angles marked X and Y. Mhm. When you look at the triangle it's it's an isosceles triangle.

[01:05:26]So, if this angle here is X, it means also this angle here is X.

[01:05:32]It means also this angle here is X because all those all the triangle has got all sides equal, meaning also all its angles will be equal.

[01:05:41]If this angle is X, by the property of alternating angles, there is this angle also here will be X because they are alternating. This angle alternates with this one here.

[01:05:52]Mhm.

[01:05:55]And if that is the case, this is 60 because it's an isosceles triangle by common sense.

[01:06:01]This is also 60. Therefore, the value of Y here will be 120 - 60, which is Sorry, 180 - 60 to give this as 120.

[01:06:10]So, they want the value of angle X.

[01:06:13]Angle X is 60°.

[01:06:17]Angle Y is 120°.

[01:06:21]That one is done and dusted. Mhm.

[01:06:24]Question number 38. Remember the paper goes up to question number 40, so we have something here.

[01:06:31]Sum of the interior angles of a regular polygon is 540°.

[01:06:35]Determine the number of sides of the polygon.

[01:06:38]How do we get the sum of interior angles? The sum of the interior angles is given by 2 n - 4 into 90.

[01:06:54]So, the sum which is 540 is equal to this becomes 180 n - 360.

[01:07:02]Collecting like terms, I'm going to have this as 540 + 360 is equal So, when I have 540 + 360 + 360, I'm going exactly to get 900.

[01:07:16]So, 900 is equal to 180n. So, to get the number of sides n, it will be 900 divide this by 180.

[01:07:27]So, my n will be exactly five sides.

[01:07:32]Five sides. That is the number of the polygon.

[01:07:37]Five sides. And then, the number of sides of the polygon.

[01:07:43]Mhm.

[01:07:44]A group of learners discuss the properties of rhombus. Write the two properties of rhombus. Property number one, all sides all sides are equal.

[01:08:00]Number two, diagonals are not equal.

[01:08:10]Number three, you can talk about diago- diagonals intersect at 90°.

[01:08:22]Or what we call perpendicularly. Those are the properties of a rhombus. You can pick any two, then you will should be good to go.

[01:08:30]Question number 40. The diagram The graph below represents a journey by a social worker to different villages.

[01:08:38]What is the distance between Q and S?

[01:08:41]Q and S. From Q, this is um the distance. Q is at 1.5 and S is at three.

[01:08:54]So, the distance between the two is 3 - 1.5 exactly giving you uh 1.5 km. Mhm.

[01:09:06]At what time did she leave Q?

[01:09:09]At what time did she leave Q? She arrived at Q at 9:00, stayed up to 10:00, so she left at 10:00 a.m.

[01:09:17]She left Q at 10:00 a.m. Mhm.

[01:09:22]Oh, that marks the end of the paper.

[01:09:24]This is the time she left Q for R, remember, and it was 10:00 a.m. That marks the end of this paper.

[01:09:31]That is the JS 2605.

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