GRADE 9 MATHEMATICS | COMPASS EXAMS JS2606 | SECTION A

[00:00:06]Greetings and welcome to STEM Smart Academy. Hope you are doing fine wherever you are. Today we are here to look at the grade 9 mathematics the compass JS2606 to help us in preparation for the end of term two exams and also for our upcoming KGA exams. We are going to have focus in section A. So stay tuned till the end.

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[00:01:11]>> So ladies and gentlemen, before we dive deep into this particular question paper, allow I take you through our August holiday tution program. STEM Smart Academy offers August holiday tuition program where we handle both that is grade 7 to grade 9, senior school grade 10 and high school currently from four form four and form three. We offer mathematics, physics, computer studies, pre techchnical studies and integrated science. Both online and physical classes are available at as low as 500 shillings per hour. Mhm. You can contact us via the number 07 41 30 4311.

[00:02:07]Having said that, having said that ladies and gentlemen allow I dive deep into the paper. This is compass grade 9 mathematics JS2606 a very predictive paper in preparation for the KGA exams.

[00:02:27]Question number one. Let us have a look at question number one. It reads, "The temperature of Pritoria was recorded as 3° C at 5:30 a.m. After some time, the temperature dropped by 2°C.

[00:02:46]At midday, the temperature had increased by 4°.

[00:02:51]Which one of the following represents the minimum and the maximum temperatures of Pritoria that day?" Uhhuh. So initially the temperature was at -3°C -3°C and then it dropped by two. So when it dropped by two you less again two. This becomes -5°.

[00:03:18]So the minimum temperature here is -5°.

[00:03:26]Then from this°C ladies and gentlemen at midday the temperature increase by four. So when you add four this becomes -1°C.

[00:03:38]So this1°C becomes the maximum temperature.

[00:03:44]So the maximum temperature here is -1°.

[00:03:51]So the question is they want an expression or the values that represent the minimum and the maximum temperatures respectively. The minimum is -5 and the maximum is -1. That is exactly choice A for a in that particular question.

[00:04:11]Choice A for a question number two. Five grade nine learners played a first a number game using number cards. The first three learners picked the cards numbered 41, 43, and 47.

[00:04:27]Which of the following set of numbers should should the next two learners pick to continue with the pattern? Mhm. So when you look at the pattern, we have 41, 43, 47.

[00:04:45]When you look at it, we need to get get the trend in use here. All these three numbers are prime numbers. That is what we can easily tell. So the trend here is picking the next prime number. After 47, ladies and gentlemen, the next prime number is 53.

[00:05:08]Then after 53, the next prime number is 59.

[00:05:13]So the hidden secret here was concerning the prime the prime numbers picking the prime numbers which is exactly choice D for dog. Question three a school organized the fundraising to get money to build more classrooms. A total of a total of um 3 million 30,030 shillings was collected. What is the amount collected written in words? I've said this is 3 million 30,030.

[00:05:49]So this is 300,000. No 300 uh no start with 3 million. 3, 30, 30. Very correct what I've said 30 million. No. So the most correct answer is choice D in question three is C for cut. Question number four.

[00:06:08]Mono refuels his car after every two days. Nariki refuels his car after every 4 days while Nasula refuels a car after every 8 days. If they all refuel their cars on 3rd of May 2026, on which date will they refuel their cars again? A very beautiful question that needs the application of LCM. So amuno 2 days after every 2 days. Mhm.

[00:06:40]After every 4 days refuel after every 8 days. So we are going to get the LCM of these numbers.

[00:06:56]We are going to get the LCM of these numbers.

[00:07:01]I'm going to start with the 2 into 2 1 2 into 4 2 2 into 8 4 then we go to two we are one one two then two one one one so the LCM will be 2 * 2 * 2 which is 8. So this means these people will be refueling their cars again together after every 8 days is when they'll refuel it together.

[00:07:32]Now when you look at this they are saying they all refuel their cars on 3rd of May 2026 on which day did they refuel their cars again? They will refuel their cars again together after 8 days. So when you take um 3rd + 8 + 8 days we are going to get this as now 11 11th of May 2026 because on that you have to add the 8 days because they do refuel together after every 8 days. So this becomes 11th of May. Mhm. Question number five. Mumba had a small container full of grapes.

[00:08:18]She decided that each day she will eat half of what the contain what was in the container. If she started eating the grapes on Monday, what fraction of all the grapes did she eat on Tuesday? A very simple question. So each day she will eat half of what is in the container? I want we have an agreement here. So meaning we have Monday.

[00:08:43]This person had how many grapes? Uhhuh.

[00:08:46]Let me see.

[00:08:48]She had um a container full of grapes.

[00:08:52]So the total fraction was one. So when I divide that by two to get what she ate.

[00:08:56]So on Monday this mumbo ate half. Then what remained? Half remained.

[00:09:03]On Tuesday she ate a half divided by two. Meaning she ate a quarter on Tuesday.

[00:09:14]She ate a quarter on Tuesday. she eats um a half of what was on the container.

[00:09:21]So if she ate a quarter on Tuesday and she had eaten a half. So let me get first the remaining fraction. I'll take 1 minus a half plus a quarter. So meaning this person is left with a quarter.

[00:09:38]Then on Wednesday she's going to eat a half of what remains. So she will eat a a half of their quarter.

[00:09:46]When you divide this by 2, this will be 1 / 8.

[00:09:51]Meaning she ate 1 8 on Wednesday. Then let me get what remained again. To get what remained, I'll take she had a quarter and now she has eaten 1 8.

[00:10:03]Meaning the remainder is when I take a quarter minus 1 8 I'm going to get 1 8.

[00:10:13]1 8 is what remained.

[00:10:16]Then on Thursday she ate again a half of 1 8. So 1 / 8 when you divide it by 2 we get 1 / 16.

[00:10:28]So this is what this person ate on Thursday. So the question is what fraction of all the grapes did she eat on Thursday? She ate 1 / 16 which is choice A for apple. I want you to take note of that question with the seriousness it deserves.

[00:10:50]Let us look at question number six.

[00:10:53]The price of a book was 299 shillings and 8. Melissa wrote the price of a book to two significant figures. Which of the following is the price to two significant figures? So when you have 229.08 08 to two significant figures. You can see uh to two significant figures.

[00:11:18]What happens here? 1 2 this first significant figure is um two. Then the next is two. Then this is the third one which we should get rid of. But because 9 is greater than five, it will increase the value of two by one. So this will become 23. The 9 itself will become a zero to act as a placeholder. So that is 200.

[00:11:43]Sorry, this was um it was 299.

[00:11:50]This was 299.

[00:11:53]So when you add this will become 300.

[00:11:57]As simple as that. Choice C for cut.

[00:12:01]After the decimal point, the digits do disappear.

[00:12:06]The decimal part has to vanish.

[00:12:09]Question six. Question seven. Now, Mind worked out a question on indices and got the answer as M^ -2. Which of the following will result into M^ -2?

[00:12:21]Looking at this m² * m power 4. This one we going to apply. You know we have a law that says a power m * a power n.

[00:12:32]This is like a power m + n. We add the powers. So here because you are multiplying so this will be m^ 2 + 4 this will be m^ 6 in then we have another law that says we have another law ladies and gentlemen and the law is very specific that um the law is very very specific that a power m - a power n we are going to get a ^ of m - n when we apply that law to to see here because we are dividing this will be m^ 2 - 4 this is -2 then we have another law that says a power m power n will be like saying a power m so when I apply it here m^0 -2 will become like saying m to the power of zero then this one here we don't have a law supporting that mhm so the most correct answer here is c for cut applying the laws of indices question number eight says ki drew two parallel lines L1 and L2 the equation of line one is 2 y + 3x = 6. What is the gradient of line 2?

[00:14:11]So when you have that equation in form of I want to write this equation in form of y = mx + c. So I'll have this as 2 y = -3x + 6. To get the value of y, I'll divide each term here by two by two. So my y will be equivalent to -3 / 2x + 3. So my gradient one here will be -3 / 2. Remember whenever you have the equation in form of y is = mx + c. The coefficient of x which is our m here is usually our gradient. So in this case y =3 / 2x + 3. Our gradient is -3 /2. But now because the two lines are parallel, what we know about parallel lines is the gradient one should be equivalent to gradient 2. So this means also the gradient 2 is -3 /2 which is choice A for apple. Question number n. A vegetable garden is in the shape of a square. The area of the garden is 2578 square m. Which one of the following can be used to [clears throat] determine the length of one side of the garden? So to determine the length of one side of the garden, we are going to square root 2578.

[00:15:36]And if we have to use log tables in its evaluation, then this will be obtained by getting the square root of we have to express this number in standard form.

[00:15:47]But it must be in such a way that the power of 10 is an even number. So this will be the square root of 25.78 * 10 ^ of 2 which is uh when you look at the choices choice A for apple the power of 10 must be an even number and not an odd number. That is one important thing.

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[00:16:18]Karesa, Amanda and Aaliyah imported motorcycles, bicycles. The number of motorcycles and bicycles bought by each of the persons was represented by the matrix below. P 437 892. What is the order of the matrix? What is the order of the matrix? Ladies and gentlemen, whenever you are stating the order of the matrix, you simply take the number of rows multiplied by the number of columns.

[00:16:51]So in this case, how many rows do we have? This is row one, row two, row three. So we are having three rows.

[00:17:03]So this will be three multiplied by how many columns?

[00:17:06]This is column one. This one going downward is another column two. So two columns. So the order of the matrix is 3x two which is a choice B for boy.

[00:17:18]Remember it must be the number of rows multiplied by the number of columns.

[00:17:22]Don't reverse the process. Question 11.

[00:17:27]Muma had five acres of land. He sold 2 acres. The number of acres he was left with was less than 11. Which of the following inequalities represent the value? So if she had five and she sold 2x, what remained is 5 - 2x. This is what remained. And this is what remained. We are being told it is less than 11. So this one should be less than 11.

[00:17:55]That is less than 11. But now because they saying which of the following inequalities represent the value of x. So if I have if I'm having 5 - 2x being less than 11, I can collect the like terms. I can have here 5 - 11 being less than 2x. So 5 - 11 is 6. So -6. So this will be -6 is less than 2x. So if I have -6 being less than 2x get the value of x I divide by 2 I divide by 2. So this means -6 / 2 is -3. It means -3 is less than x. -3 is less than x. Or if I have to begin with um the value of x, I'll say x is greater than -3 because I'm seeing the choices they begin with the value of x. Remember it is the same thing when I say -3 is less than x and x is greater than -3. They mean the same thing. Looking at the choices, choice B for boy is the correct one. Question number 12. Melanic bought a TV for a TV set for 48,000 shillings after being allowed a 20% discount. What was the mark price of the TV? If she bought it at a discount of 20%, meaning she bought it at 80%. So this 80% is equivalent to 48,000.

[00:19:31]What about the multiplies which is usually 100%.

[00:19:35]We cross multiply. This will be 100 m* 48,000 divided by 80. Mhm. And this when you look at it well um this and this will go this is equivalent to 60,000. So the mark price here is 60,000 which is choice B for dog. For question number 13, in Washira's compound, there is a rectangular flower loan. His son walked around the loan and covered 57.98 m.

[00:20:16]Mhm.

[00:20:18]The length of the shorter side is 9 8.6 m. What is the length of the longer side? What is the length of the longer side? Remember it is a rectangular loan.

[00:20:32]So here you need to think the best way to answer this question.

[00:20:39]Let us have the rectangular the rectangular compound drawn first.

[00:20:47]So it means it if you walk around it the distance is the perimeter 57.98.

[00:20:57]The length of the shorter side is 8.6.

[00:20:59]So I can call this 8.6 m. The length of the other side I can call it a.

[00:21:05]But now the big question is how do we calcate perimeter? Perimeter is given by 2 into length plus width. So our perimeter is 57.98 which should be equivalent to 2 into the length k plus the width 8.6. 6.

[00:21:28]So this is 57.98 is equal to 2k + when you have 8.6 * 2 you get 17.2.

[00:21:44]Then you collect the like terms 57.98 you minus 17.2 to give you 2k.

[00:21:54]So when you take 57.98 ladies and gentlemen 57.98 you less 17.2 2 you get 40.78.

[00:22:05]So this is 40.78 is equivalent to 2 K. To get the value of K, you divide here by two. You divide here by two. So this means K will be 20. Um when you divide this by two, K will be 20.39.

[00:22:26]20.39.

[00:22:28]That is the length of the longer side.

[00:22:29]So they asking the length of the longer side. The answer is 20.39.

[00:22:35]Question number 14.

[00:22:37]A container had 4,500 cm of water. During a science practical, Moses dipped a cube of mass 500 g into the container. If the water rose to 4,65 cm, what is the density of the cube in kilog?

[00:22:59]One thing I want you learners to understand is that the cube resulted to a volume. So let me first get the volume of the cube.

[00:23:09]Volume of the cube here will be given by 46 25 you 4500.

[00:23:19]This gives when you take 4625 you less 4500 this is 125 125 cm.

[00:23:32]You know that how do we get density?

[00:23:34]Density is given by mass divided by the volume. So the mass of this is 50 g divided by the volume of 125 cm.

[00:23:48]This will be when you do that division, you're going to get 0.4 0.4 g per cm. But now here they want it in kilogram per m. So to convert g per c cm to kilog per m, you simply take your density 0.4. Then you're going to multiply this by a,000. You have to multiply it by you have to multiply it by a,000. So that you get it. So times 1,000.

[00:24:21]So this becomes 400 kilogram per meter which is choice B for dog. Question 15. A vehicle attained a velocity of 180 km/h from that 6 km/h in 5 seconds.

[00:24:38]Find the acceleration.

[00:24:41]Acceleration is given by final velocity v minus the initial velocity u over the time taken t. So the final velocity here is 108 kilome/ hour. Let me convert it to m/s. How do you convert it to me/s?

[00:24:57]You simply kilome/ meters/ second. You take your speed 108. You multiply this by 5 over 18. So when you take 108 * 5 / 18 uh * 5 18 I'm going to get 30 m/s.

[00:25:21]Mhm. Then 36 also 2 m/s I multiply by 5 / 18. So this is 10 m/s. So the final veloc the the final velocity is 30 minus initial 10 / the time 5 seconds. So this is um 4 m/ square as our acceleration choice B for boy.

[00:25:46]Belinda Belinda's farm is in the shape of a square. She used two equal pieces of wire to divide the farm into four equal parts along the diagonals. Which of the following statement is true?

[00:26:00]This is a square. Mhm. Let us first have the square.

[00:26:06]A square is a figure that has all the four sides being equal.

[00:26:12]And let's have this as our square that way.

[00:26:15]Now, she used two pieces of wire to divide it into four equal parts along the diagonal. So, it was divided diagonally twice this way. And when you divide this way, you're going to get four equal parts.

[00:26:32]All the sides are equal. Which of the following statement is true about one part? Just one part. The one part can be this one here.

[00:26:44]The one part can be that one here.

[00:26:52]All the parts are equal. All the angles are equal. One angle is 60°.

[00:26:59]One one angle is a right angle. Mhm.

[00:27:05]Let me have a simple example.

[00:27:08]If I have this one is a um 8 by 8. So what will be the diagonal will be 8 square * 8 2 8 2 * 8 2. This will be Mhm. Then you square root. This is 64. The diagonal will be 64. Meaning that if you divide 64 by 2, this will be 8. This will be 8. And because diagonals are equal, this is 88 88.

[00:27:37]So when you look at the sides of one side, they are all equal. 8 88. So it is true to say that all the sides of one part are equal. So this is the correct one. I just picked eight as an example to make you learners understand.

[00:27:54]Question 17 which is our third last. In a grade nine class there are three 33 learners. The learners who chose their desired pathway follows 15 chose them.

[00:28:04]11 chose social sciences. Seven chose arts and sports. If one learner was picked at random. What is the probability that all the learners that the learners chose STEM or social sciences? First of all the total learners are 33.

[00:28:20]Probability of choosing STEM or social sciences. Probability of choosing STEM is 15 / 33.

[00:28:29]The term or in probability means plus.

[00:28:32]The probability of choosing social sciences is 11 / 33.

[00:28:39]When you add 15 over 33 + 11 / 33, we are getting 26 over 33.

[00:28:51]is our answer.

[00:28:53]Mhm. Question 18. Kibbrrono wanted to construct a ladder. He arranged two pieces of timber in parallel position.

[00:29:02]One piece of timber across them. The three pieces of timber were formed formed angles as shown. Which of the following angles is equal to K RH?

[00:29:13]K RH. This particular angle.

[00:29:16]this particular angle SR let me see S RH this being equal to this no those ones um supplements they cannot be equal G R K G R K and this one here no because those ones are angles on a line or supplementary angles they should add up to one a SJ E SJ this angle and this one let me Okay.

[00:29:48]Yes. Yes. Because one thing I need to know that this angle corresponds to this angle. They must be equal. And this angle is vertically opposite to this one. So they must be equal. So this is correct. Let me look at choice D also.

[00:30:02]JSF. JSF.

[00:30:05]This one and that one. No. No. No. No.

[00:30:07]No. So the most correct answer here is C for cat.

[00:30:11]Question 19. Our second last. Masai walked from his house to the water point covering an angle of 1.5°.

[00:30:19]The diagram below shows his movement.

[00:30:22]What is the compass bearing of Masai of Masai? They're very specific the compass bearing of Masai.

[00:30:30]He walked from his south to the water point from here to the water point here.

[00:30:35]So what is the compass bearing of Masai?

[00:30:38]The compass bearing of Masai is now The compass bearing of Masai is now south from 90. When you take 90 125 you less 90 what do we get? Let me see.

[00:30:55]125 you less 90 you should be getting 35.

[00:31:00]So it is south 35° east. Yes, that is from the house in relation to the house. It is south at 5° east is it? No, this is there is a typo here.

[00:31:20]It cannot be south. South south.

[00:31:25]Mhm.

[00:31:27]Yes. So the most correct answer this should be east not south. I think there is a typo there. It is south at 5° east.

[00:31:35]Question number 20 which is the last question of discussion.

[00:31:39]The mass of a newborn baby was estimated by to be 3.5 kgs. The weighing balance read 3 kgs. What was the percentage error? First of all let me get the error.

[00:31:51]The error will be 3.5 minus 3. So this become 0.5.

[00:31:57]Now to get the percentage error you take your error which is uh 0.5 over the actual value that has been found in the weighing balance which is three then you multiply this by 100%.

[00:32:12]So when you take 0.5 uh over 3 * 100 this exactly gives you 16.67%. 67%.

[00:32:28]16.67%.

[00:32:30]That is how you should have answered the section A of this wonderful paper. If you feel you've gained something, don't forget to drop a comment saying I am learning. Remember our consultation number is 07 41 30 4311.

[00:32:49]Thank you for participating. See you in the section two in the section B of this paper shortly.