JESMA 006 GRADE 9 MATHS END OF TERM 2

[00:00:02]Hello. Thank you for joining this lesson. We're going to do a grade nine paper actually a continuation. The other time we were here, we discussed number one. It is a question on indices and we said what you need to do in a question like this is that you're supposed to ensure that this composite number has been expressed to a base of five or other the least common base according to the question. So in a question like this you should talk about five power x multiplied by the other five which is power 3. This is equal to 5^ 4. You see then with this now according to the multiplication law of indices it says with the base and a power multiplied by the same base and the different power you simply take the base and you add the powers. So on the left hand side it should be the summation of the powers.

[00:01:08]Yeah. Then now you can equate them. X + 3 is equivalent to 4. Meaning that to remain with X, three should be subtracted on the right hand side making the value of X 1. That is what we said.

[00:01:24]Then here we told that a cubic water storage tank has a volume of 2744. What is the length of one side of the tank?

[00:01:34]If it is cubic, all the sides are the same. So one length times itself three times will give us volume which is equivalent to 27 44. Meaning that to remain with the length then we need the third root of 2744.

[00:01:52]The third root is also called the cube root. So shift power three in the calculator 27 44 giving us exactly 14.

[00:02:03]Now 14 makes B to be our correct answer.

[00:02:07]Then we can now check number three.

[00:02:10]Right? In number three, a jet flies at a constant speed of 900 km/ hour. What is its speed expressed in meters/s?

[00:02:20]Now when we talk about m/s, it means we convert these units from kilometers and also the time which has divided the distance into seconds.

[00:02:32]So 900 should be multiplied by 1,000 to become m per hour. 1 hour should be multiplied by 3600 to make it seconds. When you divide this, you get exactly 250 m/ second. That becomes our that becomes our speed or our velocity. Looking at number four. But before then guys, be reminded of our August program here. If you're a candidate and you're following us, whether KGA, whether KC, we got you covered, KJS and KCC. So, we're going to have a one onone interaction with neck senior examiners. you may not have an idea of what kind of information that you need to know for you to sit perfectly and successfully for your national assessment. So please join us over the August holiday and any other August holiday that will ever come.

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[00:04:44]You may reach out anytime so that you may get enrolled to our serious programs. Number four, simplify. The first thing that you're going to do is to open brackets. So four should multiply everything inside the brackets.

[00:04:58]That makes it 12 x - 8. Then -2 should multiply everything giving us -2x. Then -2 by -5 makes it a positive 10. Should be very careful there. It is a -2 not just two.

[00:05:16]Uh-huh. Grouping of terms. 12 and -2 makes it 10 x.

[00:05:22]Is that okay? The8 and positive 10 makes it positive2. So 10 x + 2 becomes our most simplified answer in number four making b the correct choice. Number five ladies and gentlemen in number five a farmer harvested wire bags of men. The wheat harvest was 15 bugs more than the maze and Bali was triple the maze. If the total harvest was 100 bs, which equation is correct? Uh-huh. Can we get the first harvest? Maze is why uh wheat 15 bags more.

[00:06:16]Y + 15 that is 15 bs more than maze. All right. Then Bali triple the maze. So Bali triple three times the maze. Now which equation shall be correct?

[00:06:30]Mhm. Your the total is 100. So y + y + 15 then + 3 y this should give us 100.

[00:06:40]So we should look for such an idea now in the equations presented here and I can see why uh option a is the most correct. The other thing we could have opted for is a grouping of terms. When they say y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y and 3 y making it 5 y then positive 15 and this is equal to 100 that can be another relevant equation. Yeah, it can be a relevant equation and you can also further group terms together you end up solving the equation but for now they just wanted the simplest equation.

[00:07:21]Mhm. In a 3x3 number six matrix representing sports scores, an element is at position A23.

[00:07:33]Oh, sorry. Element A is a 2 three.

[00:07:38]Position 2 three. Where is it located?

[00:07:41]When you talk about 2 three, the first mentioning is about the row and the second one is about the column. So it's located in second row but the third column second row but the third column. So row two and column three number seven. A regular polygon has an interior angle of 140. How many sides does this polygon have? One. We're going to understand the principle about polygons and angles that is supposed to be applied here. The first one is that interior plus exterior gives 180. Meaning that this 140 plus a non exterior should give 180. Meaning that the exterior is exactly 40°. The other one should be you see when we take an exterior angle times the number of angles or sides we should get 360 exterior angles times okay the sum of exterior angles should be 360.

[00:08:48]So each exterior angle times the number of sides we have we should get 360. So to remain with n we divide by 40. This will give us exactly 9. Meaning that in number seven the final answer is nine.

[00:09:05]The final answer is nine. Can we together check number eight? Now the price of a smartphone decreased from 2,000 to 17 20,000 to 17,000. What was the percentage decrease? We should talk about the decrease itself. from 20,000 to 17,000 3,000 out of original 20,000 then this we express as a percentage.

[00:09:33]Yeah, this we express as a percentage.

[00:09:36]So 3,000 thousands can cancel like that and so this one zero. Uhhuh.

[00:09:44]So this is going to be 15% uh decrease. 15% decrease. Remember you can compute using the calculator very quickly and you arrive at your answer. We solve this one or simply we simplify to remain with 3x here less than or equal to -4 becomes positive on the other side making it a 15. Right? So x less than or equal to 5 less than or equal to 5 making to be the most appropriate answer. The most appropriate answer. Now a student evaluates 3^ 3 +<unk> 64 the roo<unk> of 64. What answer should they obtain? Okay. And depending on how you approach this question, you might get two different answers. One -3^ 3 gives us -27.

[00:10:42]Then we are adding the square root of 64 which is 8. So now this becomes a 19 that becomes a 19. Similarly if somebody says that if somebody says that the square root of 64 is either plus or minus 8 because in case you square8 you will get 64. And in case you square 8, you still get 64. So both of them are two different integers and they are both being squared to give us 64. And therefore and therefore the final answer can still be argued using 8 which is also a valid square root. So we are having -27us 8 you know this will take us to -35.

[00:11:44]which is option D. So according to the level of math that you have those two answers are valid.

[00:11:54]Very very valid. Yeah.

[00:11:58]Square root of a number is either plus or minus the value that should be squared to give us uh the number. Yeah.

[00:12:09]Squared to give us the number like that.

[00:12:15]Number 11 writes, a straight line has equation 2 y + x + 3. Another line is drawn perpendicular to it. What is the gradient of the new line? Now, first we can express this gradient to know its equation. To remain with y on one side, we divide both sides by two making it half x plus 1.5 or rather 3 /2. Meaning that with an equation at this format, half is the gradient and 1.5 is the y intercept. So gradient of the first line equals to ah the coefficient of x about perpendicular lines it's a concept you're supposed to know that gradient 1 * gradient 2 should give us a -1.

[00:13:09]Yeah.

[00:13:11]Therefore now we can talk about f * a non gradient to give us -1. And how will you remain with a non gradient? You multiply both sides by two. Multiply both sides by two so that the half is eliminated. So this becomes a two. C is the right answer in number C is the right answer in number number 11. I hope we are together in such a case. Can we check number 12 ladies and gentlemen?

[00:13:51]Can we check number 12? In number 12, we being told that a milk container shaped like a cuboid measures 28x 10 by 15 by 10. What is the capacity in liters? First, can we find volume before we go to capacity?

[00:14:07]Length * width * 8. Length * width time a height means that a length of 28, a length of 15 and a height of 10 to give us what?

[00:14:25]28x 15 by 10 giving us 420 0.

[00:14:32]Mhm. Now cubic cm. Now to make it liters we divide by a th00and because for every liter there's 1,000 c cm. So 4 2 lit 4.2 L becomes the answer.

[00:14:50]4.2 L becomes the the only correct answer in number 12. Uh 13 together calculate the area of the regular pentagon. Regular pentagon. This is grade nine work. Regular pentagon.

[00:15:09]Regular what? Pentagon. You can see h it's measuring 10 by 10. And now the sides are measuring 12. So we supposed to know that a pentagon can be divided into five. It can be partitioned into five equal triangles. Then we deal with one triangle times the area of the five of them times five to get the area of all of them. So here we should first talk about vertical height here. After dividing like that you get six and six. So then there's a 10 here. How about the vertical height? It shall be 10^ 2 - 6 2 then the square root. Are we not getting exactly 8? Yes. 8 cm. Meaning that we need half time a base of 12 and a vertical height of 8. Then this we multiply by the five equal now. Mhm.

[00:16:10]48 by 5 giving us exactly 240.

[00:16:16]240.

[00:16:18]So you should be able to follow through a question like that. You deal with one triangle then now times the number of triangles. Remember, when dealing with an hexagon, you partition the hexagon into six equal six equal triangles. Then you interact with the one until you find its area.

[00:16:41]Then you multiply by six, which is the total. Now for you to get the total, what is the least number that can be added to to make it divisible by 11? Can we first make it? Can we divide it by 11? 48 96 511 divide by 11. I'm getting I'm getting as a fraction as [clears throat] a fraction.

[00:17:15]Just a minute. Let me divide 48 96 51 divide by 11.

[00:17:26]Mhm.

[00:17:28]48 96 511.

[00:17:37]Mhm. So I'm getting 445 137 and what?

[00:17:55]H remainder 4 over 11.

[00:18:00]Yeah, remainder 4 11. Remainder 4 11. So if when we divide we get 445, 137 and 4 11. That's after dividing this number by 11. After dividing it by 11, this is what you get. 445,000 137 and 4 11. What is the least number that can be added? So to add means what can we add to four to make it a divisible to make it divisible by 11?

[00:18:32]It's only a seven.

[00:18:34]Now in case it was what should be subtracted.

[00:18:38]In case it was what should be subtracted it would have been this four because it is what remains.

[00:18:47]But now that we need what should be added then you examine now 4 against 11.

[00:18:53]How can we make it divisible?

[00:18:57]Number 15. Calculate the area of the square plot whose perimeter is 600.

[00:19:03]Perimeter of square is given by one length multiplied by 4 to give us a perimeter of 600. Meaning that we can get each length you know all the lengths are equal. So you divide 600 by 4 you find that each length is 150. And now that we want area it should be 150 squared.

[00:19:25]So you square this value you get 22 2 5 0 0 making a the most appropriate answer in number 15. Can we now check number 16? A chocolate bar was enlarged from a length of 35 to 50. If each wing remained as 24 cm but the triangle-shaped sides were 25 each.

[00:19:56]Calculate its area. So this was enlarged from 35 to 50. Enlarged from 35 to 50.

[00:20:09]Uh-huh. Its w remained 24.

[00:20:13]All right.

[00:20:15]And the triangle shaped sides were 25 by 25. Calculate its area. So the area of this chocolate, the area of the shape, you can see let's say the cross-section.

[00:20:33]Uh-huh.

[00:20:37]So if we subdivide here, what are we getting? 12.

[00:20:44]by 12. Yeah. Instead of 24, 12 by 12. So now we pick 25^ 2 - 12 2. Then we pick the square roots.

[00:20:59]Mhm.

[00:21:04]Look at that. 25 - 12^ 2. Then we pick square roots. I'm getting 21.93.

[00:21:16]Mhm. Like that. So now for us to get area you need to talk about 24 by 50.

[00:21:26]Okay.

[00:21:29]24 * 50 this is a 12 0 0. Then the triangular portion shall be half * a base of 24 * a vertical height of 21.93.

[00:21:45]So this is a you multiply this.

[00:21:50]Mhm.

[00:21:53]263.16.

[00:21:56]So when we add for us to get total then we are adding this to 12 0.

[00:22:03]So I'm getting 1463.16 square cm.

[00:22:13]I can't see a correct answer here. Let me check whether maybe we are misinterpreting something. Maybe we are misinterpreting something but I don't think but I don't think Mhm.

[00:22:27]a chocolate bar was enlarged from 35 to 50. Okay. So it has been stretched. It is now measuring 50 on the length. The width remains 24. But the triangular shaped sides were 25 each. 25 each.

[00:22:47]Calculate its area. Yes. So I think I have done it in the right in the right way. So that is how the question is supposed to be approached. 17.

[00:22:59]The sum of two numbers x and y is 56 and the difference is 16. What are the two numbers? When we add x and y we are getting 56 and when we subtract the two numbers we get uh 16. Can we use elimination method to solve the two simultaneous whereby y cancels out then 2 y = 2. The difference here is 40, right? So, y is equivalent to 20.

[00:23:37]Yeah. Y = to 20.

[00:23:40]Mhm.

[00:23:43]56 - 16 40ide by 2ide by 2 we get 20. Meaning that x shall be x + 20 = to 56. How do you remain with x? 36.

[00:24:02]Uh-huh. Can we confirm the sum of the two numbers?

[00:24:06]36 and 20. 56. The difference between the two numbers 36 and 20.

[00:24:13]36 and 20 you will get a difference of 16. So it's okay. We can also argue that x + y = 56.

[00:24:26]Then because we've been told they difference can be either way that it can be this way to give us 16. So now to rearrange the first division y + x = 56. Then we should be able to talk about subtraction again.

[00:24:46]-x - x -2x = -40. So x is becoming exactly 20.

[00:24:56]Yeah, x is becoming 20. What about y?

[00:25:01]y - x = 16. So y = to 36. So they can interchange. It can be the y which is 36 and the x 20 or the y which is 20 and x 36. But at least we have 20 and 36. So again in this one I'm not seeing an appropriate answer.

[00:25:28]I cannot see any appropriate answer. 36 and 20 are not here like that. Then now we can check number eight. Right? A mathematician finds that the logarithm of 64 2= to 6. How do we write this in index form? To write in index form, it means 2^ 6 = 64.

[00:25:56]2^ 6 = 64.

[00:26:00]So you're supposed to know that a statement can be changed from logarithm to index notation. When you have a log of b to base a= to c, it implies that in index notation a power c is equal to b.

[00:26:18]a power c is equal to b. A power C = to B.

[00:26:26]A power C = to B. We together in that if yes type then 19. In 19 a piece of sugar cane 150 cm long is shared in the ratio 2 is to 3. What is the length of the largest share? Now the bigger proportion here is a three. We sharing it into two proportions. Three out of the total proportions which is five. So we get a fraction 150. So we divide 150 into two proportions. Three out of the total and also two out of the total. Uh-huh.

[00:27:07]13 we get 90 as the final answer. 90 as the final answer. Then ladies and gentlemen we now at number 20. In number 20, you're being told that in an election, 48 voters were spoiled.

[00:27:25]752 were for candidate A and 400 for candidate B. Find the probability of picking a spoiled vote.

[00:27:37]When we talk about probability, it means the number of favorable outcomes out of the total possible outcomes.

[00:27:46]So uh-huh probabilities point it means spo 48 out of total possible 48 7 52 + 400 Let me work out that sum. 48 + 752 + 400. Uhhuh. So this is 48 out of 12 0 0 48 / 12 0 0 we get 0 04 making a the most appropriate answer. So that is how the section A of this paper was supposed to be done. A good good question. So thank you for following.

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