GRADE 9 MATHEMATICS END TERM 2

[00:00:10][clears throat] Thank you. Thank you for joining this lesson. Today we're going to look at a grade nine paper that is a mathematics in preparation for the KGC. Some of you think that we are only focusing on end terms, midterm exams, open exams. Not really. We are here to prepare for the KG. That is our main goal. So please uh stay focused to shifting grades online school. Even as we prepare you for the national assessment, remember uh our number is already on the wall. Remember that we are organizing the best education platform that is the best platform that this country will ever have. So please take your time and join us for the neck examiners bench whereby we shall be preparing learners for KCC and KG. If you have a brother in form four you are free to invite them. We're going to invite neck examiners. These are the people that are going to handle your paper after you've done it. So they know everything that is required. They know the neck prediction patterns. They know what is expected of you. They know the marking trends. So kindly join us as we exhaust everything as you exhaust everything this holiday. Do not be left out. For KCC we are offering mathematics, the two languages, three sciences and the three humanities. So enroll and let us know uh the subjects that you are taking. In future we shall involve all the learning areas but allow us to start at some point. We're also having for KGC mathematics, the two languages, integrated science, pre-technical studies, social studies.

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[00:03:05]Otherwise, thank you so much. Let us now get into this paper. Today, we shall check the section A. A grade 9 learner is simplifying indices and gets the expression 5^ x * 5^ 3 equals to 625.

[00:03:26]What is the value of x? You will allow me use the you'll allow me use the working space here. 5^ x * 5^ 3 this is equal to 62 5.

[00:03:43]Uh-huh.

[00:03:45]One thing that you're supposed to know is that according to the laws of indices, whenever you have a base to a certain power multiplied by the same base to a different power, this one is usually solved by picking the base and you add the different indices. So on the left hand side we talk about five then x + 3. This is equivalent to 5 raised to the power of 4. So instead of 625, now we express it to the same base.

[00:04:24]Yeah. 5^ 4. Now that the bases are the same, we can equate the powers. X + 3 = to 4. to remain with x. 3 is to be subtracted on the right hand side. 4 minus 3 gives us one. Meaning that c is the right answer in number one. A very good question in indices. Can we check number two? A cubic water storage tank has a volume of 2743.

[00:04:56]What is the length of one side of the tank? Length of one side of the tank.

[00:05:03]2744. So we are already having a volume as 2744 cubic uh cm uh cubic m 744 m. So because we are given the shape of the container that this container is cubic then it means length cubed gives us volume.

[00:05:35]If length cubed equals to volume then length cubed is equivalent to 27 44.

[00:05:42]Meaning that for us to get the length then we obtain the third root of both sides cube roots of both sides. Can we now divide this one? 2744.

[00:05:54]We divide by two first. Uhhuh. 2744ide by 2 I'm getting 1372 again by 2 we get 686 and by two again we get 343.

[00:06:18]Uh-huh. We can now divide 343 by 343 by 7.

[00:06:26]By 7 we get 49.

[00:06:30]7 we get 49. Then by 7 once again get seven. So now we are having this volume as 2 by 2 by 2 then by 7 by 7 by 7. Now when we talk about the third root using the factorization method in every three similar factors we pick only one. These are sevens. So we pick only one seven.

[00:07:09]So 2 by 7 giving us 14 m. This is the length of the container. 14.

[00:07:20]The length of the container is 14. We have 14 m there. Meaning that number two. The correct answer is 14. Yeah. Correct answer is 14.

[00:07:35]Mhm.

[00:07:37]We can check number three now. In number three, we told that a jet flies at a constant speed of 900 km/ hour. What is its speed expressed in meters per second? 900 km/ hour expressed in meters/ second.

[00:07:59]900 kilometers per hour. You know it means 900 this is the kilometers has been divided by 1 hour. So we can multiply this by a,000 to get m and this one by 36 0 to get seconds. So precisely we now having 900 * 1,000 and this should be divided by 3600 0 giving us exactly 250 m/ second.

[00:08:37]m/s.

[00:08:40]250 m per