END-TERM 2 2026 GRADE 7 MATHEMATICS | CODE 006 LEARNING AREAS | KJSEA REVISION

[00:00:02]grade seven. This is now the last paper I'm doing before you go and do your examination and take this question seriously the way I'm serious with them.

[00:00:10]So the first I'm I'm going to do section B which is 20 marks and don't blame me for doing for not doing section A. I can take you through the questions so that you can see what you need to understand.

[00:00:23]But the same questions in section A and section B are somehow related. The problem is these ones are having answers. So let us start. Work out the following problem.

[00:00:35]142 + 980 / 1 40 - 30 1 * 4. What are you going to do here? B mass.

[00:00:48]As simple as that. B mass. So what are we going to start with? Do we have bracket? No, we have division. So we going to start with 1042 plus solve this division. If you take 980 divide by 140 what do you have? 980 that's now just 98ide by 14.

[00:01:11]98 divide by 14 what are we having? 98ID by 14 I'm having 7. So this now 7 - 31 * 4. I'm done with there's no bracket, there's no off. I'm done with the division. Do you have multiplication? Yes. Here do multiplication. So it will be 104 2 + 7 - 31 * 4. This 124 124 as simple as that. Then you start with you move to addition next. So here 1042 + 7 that's now 1042 + 7 that is now 1049 1049 - 124 so our final answer will be 10 49 - 124 because of time my answer is 925 and that's how you got your four marks so what do you need to do you solve one operation per step to avoid confusing yourself. So because I'm also not perfect, please check for me the answers and if there's an error I've made, just let me know. I won't be mad at you.

[00:02:33]Next number 22. What do you have? What is the difference in the value of the value between the LCM of and the GCD of 36? So let us get the LCM of 8 and 12.

[00:02:46]LCM of 8 and 12.

[00:02:49]So we have 8 and 12. So the LCM is very simple.

[00:02:55]Two here, four here, six.

[00:02:58]Then two here, two here, three.

[00:03:03]Then uh two we have 1 3 then three. So LCM very simple. This is now 24. 2 * 2 4 8 8 * 3 24. That's the LCM. Then move to the GCD of 36 and 54. The greatest common number that can divide this two. Here we have 18 27.

[00:03:29]So can two divide 18? Yes. Can it divide 27? No. So we move to three. Can three divide 18? Yes. 27. Yes. 3 divide this one is uh six. 3 / this one is uh this nine. Then here we still have three. 3 / this one is 2 3. So gcd we have as 2 * 9 which is 18. So you what is the difference between the LCM of this and the gcd? So difference what does the what difference means?

[00:04:05]Subtract. Subtraction. So difference is equals to 24 - 18. 24 - 18 this now 6. Very very interesting.

[00:04:17]Now let us move to the next question number 23. What is the area of the rectangle below? So we have been told that this this rectangle meaning that this side must be the same as this side. So what what will you say first by saying that 2x + 6 must be equals to 4x - 4. So it will be 2x - 4x = -4 - 6. So this now -2x = -10. x alone is equals to uh 5. So x is 5. So when x is 5, let us substitute the value of x here. So 10 + 6 this now 16. So this now uh 20 - 4 16. So here we have x that's why this is 8. What are you being asked?

[00:05:06]The area. So area is always length time width which is 16 * 8. 16 * 8 what do you have?

[00:05:16]16 * 8 I have 128 m²ared for marks. So learn how to solve that.

[00:05:26]Work out the problem. So what problem do we have here? 3.64 * 7.2 because of time I don't want to waste any time again. So the numerator here is 3.64 * 7.5 3 64 3.64 64 * 7.5 I'm having 27.3 so denominator here is 15 so numerator our denominator we have 27 3 / 15 so divide by 15 I'm having 1.82 1.82 82 four marks. That's I'm getting my my four marks. Come to number 25.

[00:06:15]This now for all grade sevens.

[00:06:18]Uhhuh. What do you have?

[00:06:24]A circular there's something missing here with a radius of 36 cm made made. So it will be a circular wheel. Ah very simple. A circular wheel of radius 35 cm made 10,000 revolutions. How many kilometers did it cover? So how many kilometers did it cover?

[00:06:48]Let us let us get one revolution. So one revolution is equals to the circumference. So first step get the circumference of this circular wheel.

[00:06:57]Circumference is pi d or 2 pi r pi d. So it is just or 2 pi r. Let me use I'm given the radius. So let me use the right formula. Circumference is 2 pi r.

[00:07:12]That's now 2 * 22 over 7 * 35. This one here 5. So 44 * 5 4 * 5 that is 220. So circumference is 220 cm.

[00:07:30]So 10 this now cm one revolution 10 cm one revolution is equals to 220 cm. So what about 10,000 revolution?

[00:07:42]It is 22 * 10,000 that is 2 million.

[00:07:50]So we have 2 million 200,000 cm. So convert this one into kilome.

[00:07:58]What do you do? divide by 100,000.

[00:08:01]So to convert we divide by 100,000.

[00:08:05]Divide here by 100,000.

[00:08:08]So 100,000.

[00:08:11]So answer divide by 100,000. What do I have? I have 22 kilometers covered. So because of time I will explain later if you have a problem. Number 26. Katana bought tea plates at 50 shillings each.

[00:08:28]He spent not more than 1,200 buying all the plates formal inequality. So t t plates the number of plates t. So t plates will cost 50 t shillings and this 50 t is we that it is not more than 1,200.

[00:08:53]So it is either less or equals to 1,200.

[00:08:56]So we have 50 t is less or equals to 1,200. That is two marks. Solve the inequality to find the value of t. So we have 50 t is less than or equals to 1,200.

[00:09:12]So divide by 50 / 50. So t alone we have 120 / 5. So t alone is less than or equals to 24.

[00:09:29]So t is less than or equals to 24. I've gotten the value of t. Simple number 27 you're being told that in the figure below the diameter of the semicircle is 21. So this is now 21.

[00:09:49]And uhhuh what are we being asked now?

[00:09:54]What is the perimeter of the figure?

[00:09:56]Perimeter is the distance all around the figure. Perimeter is the distance all around the figure. So perimeter of this one I can get from here to here is 21.

[00:10:05]Meaning that 40 + 40 + 21 give us the length from here up to here. This downer length. So 40 + 40 80 + 21 that's 180 + 21 that's 101 but confirm with me for the sake. So this now 101 perimeter is the distance the figure. So this semicircle I'm going to get the cve length. The curve length is now half pi d. So I'll start with that. So I say area the length of a semicircle that's now circumference that's now a half pi d that's now a half * 22 / 7 *<unk> 21 so this one goes here one this one goes here this is 11 this now three so that's now 33 cm is it centm or m it is 33 what cm now add all the length so this one is 90.

[00:11:07]So I'm going to have 90 + 33 plus.

[00:11:15]So the other lengths are 101.

[00:11:19]So 80 + that's now 80 + 101. So have I added everything? So 45 + 45 that's already 90. So this length this now 90 this one plus this one forms 80. Then this one we got as 303 then 101.

[00:11:46]So I have everything 90 + 33 + 80 + 101 what is the perimeter now? So 90 plus that's now the two sides two widths plus 33 that's now the circumference of that arc or the length of that half a circle.

[00:12:10]Huh? then + 80 + 101 I'm having 30 4 what 304 cm 304 cm so this one is giving me 304 cm very very interesting so 304 cm next work out the circumference of the circles. Work out the circumference of the circles. Work out the circumference of the circle. Circumference of a circle that's now pi d when given d or 2 pi r when given uh the radius. So circumference is equals to 2 pi r. We been told to take pi as 22 7. So it will be 22 / 7 *<unk> 2<unk>i r * 2 * r which is 14. So this one goes here. This one goes here.

[00:13:14]Seven. So 44 44 * 7.

[00:13:24]So this now 38 cm. Confirm with me that is four marks. Come here. the same circumference 2 pi r that's now 2 * 22 / 7 * 4.2 m so there what we having cm so check the units 7 goes here 1 7 goes here 0.6 so we have 44 * 0.6 44 * 0.6 6 we have 26.4 is now m that's the circumference.

[00:14:07]Wow. Number out the problem. Indeed this is a problem. So we told to work out the problem. What do you have as far as problem? This problem is concerned.

[00:14:18]Square root of this. So convert this one into improper fraction. So it will be 44 4 * 4 * 4 84 + 89.

[00:14:37]So I'm having 20 25 over 484. So this the same as square root of 2025 over 484. So get them. So square root of I don't need to waste time here. This is 45 over 484. 484 I'm having as 22. So 45 45ide by 22 5 / byide by 22.

[00:15:18]So um it is going there how many times?

[00:15:21]Two times bringing 44. So it is two times bringing 44 remainder two remainder one remainder 1 out of 22 remainder 1 out of 22. Very very simple square of this 40 + uh this is 40 + 1 that's now 41 out of 4 squared this now 41 out of 41 squared it is uh 1681. So this now 1681 over 4² now 16.

[00:16:02]So I'm having here 105 105 and one out of 16.

[00:16:18]Very very simple. So that one you get another four marks because of time. Come here. 30. What do we have as 30 area of a trapezium? This now garden is a trapezium. We calculate the area.

[00:16:41]So area is always a half into a + b h and I've asked somewhere in grade 8 what is a + b? So this now a half into a that's now 50 + 100 * 48. So this is now a half * 15 * 48. So 15 half of 15 that's 75. So I have 75 * 48 that's now 3,600.

[00:17:12]This is now me squared. That's the area of injuries farm. Then a publishing company sold books worth this amount 721,875.

[00:17:26]If one book falls to the front, how many books did the company sell? So this is very simple. Say one book is equals to 385.

[00:17:37]Uhhuh. Then 721,875 books will be uh ceilings will be how many books? So just cross multiply meaning that we're going to divide. So it will be 721,875ide by 385 divide very simple 721 this now 3 875 divide by 385.

[00:18:12]So this company sold in now books.

[00:18:17]How many how many books are here? 1,8 75. These are books were sold. Four marks. Very simple. Come to question number question. This what do we need to do? We open the bracket. So quarter times this one is now 6 x plus a quarter this one.

[00:18:40]Now 7 y plus third of this one is 3x minus a third of this one is now 2 y.

[00:18:50]That's the first step. Open the bracket by multiplying everything inside the bracket by whatever you have outside the bracket. Then collect the like terms. 6x + 3x + 7 y - 2 y. So this now 9x + this now 5 y very simple four marks come here come here we have this one also multiply 73 we've multiply this one * a third what are we going to have 7 * this now 9 m plus this now 42 2 6 18 n plus this now 15 m. This three out of five. This now minus uh this now 3 15 15 m. So 9 m + 18 n + 15 m - 15 n. So 9 m + 15 m collecting the like terms + 18 n - 15 n.

[00:20:12]So here what do I have? Uh I have here this plus this we have 24 m + 3 n. Very very simple. Come back to number 33. Number 33 here. What do you have?

[00:20:35]Find the measure. Find the measure of the side marked letter Y. Letter Y. This now I follow Pythagoras theorem. Very simple. So what does Pythagorean theorem say? C² is equ= to A² + B² where here is C A B.

[00:20:55]So I have C and B. So I say now a^ 2 = c^²us b^ 2. So I'll say this now uh a^ 2 is = 26^ 2 - 10^ 2. So 26^ 2 - 10^ 2 I got now a² = to 576. A alone is equals to square root of 576.

[00:21:29]So square<unk> of 576 that's 24. So what do we say? Y is equals to 24 cm.

[00:21:37]Very very simple. Come to number 34. The distance between Jared's home and school is uh 7 heto 8 decameters and 6 m. Jared goes to school in the morning and returns in the evening. What the distance he covered in 5 days?

[00:21:58]Okay, very very simple. This four marks not for a reason. So these are 7 8 6 this now ectometer.

[00:22:12]This now he ectoometers.

[00:22:15]So what will I say?

[00:22:18]7 HM 8 D M and 6 M* 2 because two and four.

[00:22:27]So this is now 12 * this one is 12 m* 16 diameters time this now 14 heto. So I've gotten the distance in what in uh in hecto decameters and meters to and fro. So for 5 days it would be 14 he 16 and 12 m * 5. So this one what I'm going to have 60 60 m 16 * 5 I'm going to have 80 diameter and 70 ectoometers that's now in how many days 5 days very very simple number 35 we have a and b a circular fish pond has an area of this one a circular fish point has an area of 13,00 1386 m square 1,386 m square square find the radius of the fish point fish pond. So area is always p<unk> r² so assuming that they use 22 7 I'm going to say 22 / 7 * r 2 is equ= to 1 1386.

[00:23:57]So here r² alone is equals to I multiply both side by 7 out of 22 by 7 out of 22.

[00:24:05]So I'll have 1386 / 22 then * 7.

[00:24:17]So r 2 is = to 441.

[00:24:24]So r alone is square root of 441. What do you have? Square root of answer is 21 cm. So very very simple. Once you get you have the area you can get the radius. Find the area of the shaded part. 14. So from here to here is also 14. So what do I do? The area of the square minus the area of the circle. I get the area of the shaded part. What will it be?

[00:24:51]Area of a square is side time side which is now 14 * 14 14 * 14 14 squar that is 196 m² area of a circle is<unk> r² pi r² area so<unk> * r radius is the d r r is the 14 / 2 that's now 7^ 2 so it's 22 / 7 * 7 squared.

[00:25:23]So 157 1 this now 7 squar is 49 7 / 49 7 * 2 this now 154 this now cm m squared it is m squared m squar now shaded area is 196 cm m squared minus 50 154 m squared what do you have - 154 So we have 42 m squared. Confirm because of time. Uh the last question here you're being told that what are we being told here? A cube a cube has a volume of 2.7 m cube.

[00:26:14]What is the volume of the cube in cubic cm? So we have how many? 1 m cube 1 m cube is equals to 1 million cm cube. 1 m cube is equals to 1 million cm cube. Mhm.

[00:26:37]What about 2.7 m cube will be cross multiply. So it will be 2.7 * 1 million.

[00:26:48]So this one we'll have to remove this.

[00:26:50]So we have 27.

[00:26:54]So let me write it properly.

[00:26:58]27.

[00:27:00]How many zeros? Five zeros. Now 1 2 3 4 5 cm cube. Very very simple. So because of time that is I have to stop there. Uh let us meet for other revision materials towards the next term. See you in the next video.