2026 Stage 9 Mathematics CAMBRIDGE LOWER SECONDARY PROGRESSION P2 | Year 9 Checkpoint 2026

Added: 2026-05-24

[00:00:00]What's up everybody? This is teacher Ivan from NextGen Academy. Our goal in this channel is to help you achieve your highest potential and to help you understand subjects in the easiest and the most efficient way. If you like to get more tips and tricks on how to achieve a star in your IGCSE, don't forget to like, comment, share, and subscribe to this channel. Lastly, if you need any help in your studies, you can always head on to our website link in the below or our Instagram. Drop us a DM and we'll be able to help you. Enjoy this video and I wish you all the best.

[00:00:33]All right, let's start today. Okay, we are going to go through the 2026 progression test.

[00:00:42]Okay, this is a calculator paper. So, everyone take out your calculator if you haven't done it. We'll do it together.

[00:00:48]Okay, so allocate 1 hour for it. Okay, allocate 1 hour because uh I want you all to train.

[00:00:58]Okay, I want you all train to to make sure that y'all can finish it within the the time frame.

[00:01:10]Okay, let's look at question number one.

[00:01:12]Okay, by the way, this is a progression test. So, please don't go and share with other people. Your friends may not get this. This one actually cannot get right. Okay. All right, let's look at the first question.

[00:01:24]1 over 5, 2 over 5, 3 over 5, 4 over 5, 1. This is a sequence type of question.

[00:01:29]So, what will be the next term in the sequence? Okay, so 4 over 5. Can we see the pattern? All of it is at 1 over 5. Okay, this one is also adding 1 over 5 because it becomes 5 over 5. So, the next value will be + 1 over 5, 6 over 5. Okay, you don't need to write any working. This one normally like one mark one you all just uh Okay, just write the answer. Okay, what is the nth term of the sequence?

[00:02:00]Okay, do you all know this? What is the n term of the sequence? How do we express this?

[00:02:11]Okay, n + 1 over 5. Okay, why n + one?

[00:02:16]Why n + one?

[00:02:19]Okay, you look at the the top here first. Okay, normally for fraction, we don't look at the whole thing as one.

[00:02:24]Now, if you all see here, we should recognize that this is called a linear sequence or arithmetic sequence, right?

[00:02:31]Not because it's adding a fixed value.

[00:02:33]Okay, so this one we all recognize this first is called a linear or arithmetic sequence. Okay, if a fraction comes out, typically when we do linear arithmetic sequence, teacher teach you all the formula for the num is a + n minus 1 d. Okay, but for this one, you don't need to make it a little so complicated because you just look at the the values, right? It's actually quite simple. On top it is 1 2 3 4 5 6. At the bottom, the denominator is fixed, right? The value five five5.

[00:03:10]Okay. So normally for fraction you look at your numerator and your denominator separately. Okay. You all don't look at it together. Okay. So for the top can we say that the value is just equals to n because when n equals to 1 then here is one. When n equals to 2 here is two. So can we say the numerator is n and the bottom is 5. Okay. So your formula for this one don't need to write do any working. You just write n / 5. But I want you all to take note when we do for fraction normally you look at it separately. Okay. This is a pattern for um sequence in IGCSC.

[00:03:49]Okay. No n plus one. When will it be n plus one? If this one starts with two.

[00:03:53]Okay. This one 2 3 4 5 because your first term here is one. The value here is also one. Okay. Number one. All good sequences. Okay. You need to know at least for linear sequence. Sometimes you may use this formula a + n minus 1 d.

[00:04:07]Okay. Second question. Here is a polygon with some interior and some exterior angles given. Find the value of x. Okay.

[00:04:14]What is value of x? What formula can we use over here for angles?

[00:04:23]Okay. What formula can we use?

[00:04:32]Okay. Can we say that the exterior angle is 360° since they gave us a lot of exterior angles here, right? Except this one. Uh, no, no, not 360 overn. You only use 360 /n if this one is a regular polygon. This one is not regular. They just say this one is a polygon. Okay, 360 /n is the formula for exterior angle for regular polygon. Okay, we'll write that down somewhere. For this one, you must know that the total exterior angle for any shape is equals to 360°. What is exterior angle? The angle outside. Okay, so I want you to find this value here first.

[00:05:18]Okay, let's call this a. A will be 180 minus 80, which is 100°.

[00:05:27]So this is a pentagon. It doesn't matter how many sides that you have, the total exterior angle for any shape will always be 360°. So, we need to add this all up.

[00:05:37]This plus this plus this plus this plus this. Okay, so let's write down an equation. X + 90 + 100 + 71 + 50 1 2 3 4 5 is equals to 360. Okay, go and calculate for this side. Okay. On the left hand side, what will we get? 90 + 100 + 91 + 50, we get three.

[00:06:07]Uh, okay. Correct. 90 + 100 + 71 + 50. Okay.

[00:06:15]Total how much should we get here?

[00:06:20]Okay. Anyone got the value here?

[00:06:24]Okay. We will get 311. Do you get 311? x + 311 = to 360.

[00:06:32]Okay. Then x is equ= to 360 minus 311. We'll get 49° here.

[00:06:42]Okay. So your answer for question two is 49°. Okay. I'm looking at some of your papers that you submitted. Just double check your double check your working to make sure that that is correct. Okay.

[00:06:56]Number two, all good understand how exterior angle works. Okay, you can make a remark just now you say okay 300 and 60 / n only applies for regular. Okay, if they mention the word regular polygon, this one is not a regular polygon. The meaning of regular means your interior and exterior angle all the same. The site the length of the sides also is the same value.

[00:07:29]Okay, let's go to number three.

[00:07:34]Indices 4 ^ -3 is equals to 1 / 4 ^ of n. Okay, the power of negative means this is n inverse. Okay, you can write down inverse means upside down. So this one is just equals to 1 / 4 cub. So n is = 3. Okay. So for 10 / x = to 2. This we can write as 10 / 2 = to x. This is just a simple algebra question. x is equals to 5.

[00:08:04]Okay. Number six. This is on the concept of bearing. Here is a map showing the positions of town A and town B. Carlos says the bearing of town A from town B is -100. Explain how you know that Carlos is not correct.

[00:08:21]Okay. Yeah, it's a progression paper.

[00:08:23]Yeah, correct. Okay. So, how do we measure bearing? We have learned this chapter before, right? Bearing. Okay. We need to understand that the concept of bearing, there are few things that we need to take note.

[00:08:35]Number one, it is measured from north. Okay, that means you will start from north here. then you will get you will measure a clockwise direction from north.

[00:08:53]Okay, one more thing is that it needs to be presented as three digits.

[00:09:02]Okay, I want you to read the sentence properly also. They always upside down the the sentence, right? Okay, the starting point and the ending point. A lot of you will read out the bearing of town A to town B. But often they put the starting point at the end. They can they can say town A to town B also but this one they normally put it at a at a behind. This is just IGCSC way of testing your Okay. So the starting point is town B. This is the start. Okay.

[00:09:26]Where is the bearing that we want to measure over here? Okay. What is this angle? They gave us here 80. They gave us here 100.

[00:09:37]Can we say that this part is 360 minus 100°?

[00:09:43]Okay. And also bearing can it be negative? Is there such thing as a negative bearing? Okay. Noah is only from positive from 0 in between 0 to 360°. Okay. In between 0 to 360°. Okay.

[00:09:58]So what we can say over here? Um okay. We can start by saying okay I'll just write down a few points whatever that we we just say we say bearing can not be negative.

[00:10:16]Okay needs to be between 0° and 360°.

[00:10:26]We also mentioned this. It needs to be measured clockwise from north.

[00:10:40]Okay. And the final one just now we if we want to calculate okay the bearing over here the value of the bearing it should be 360° minus 100° okay actually these are one mark I just write down all the points uh you can actually just write down the final one okay this copy this uh can as well you can say it's a can it must can never be negative means it must be a positive number same meaning okay so the first sentence you can say it must always be a positive okay but the safest way actually is to make sure you you just do the calculation. Okay. So they wrote over here in the mark schema all of it is acceptable.

[00:11:37]Okay. First five question if you're good can you just type five.

[00:11:43]Any question anything to clarify please ask me otherwise type five in the chat.

[00:11:53]Okay let's go to the next one.

[00:11:57]Number six. A straight line has the equation y - x = 4. Find the gradient and the y intercept of this line. Okay, straight line equation. What is the form that we want to rearrange to for a straight line equation?

[00:12:13]Okay, we have learned this many times already.

[00:12:16]y = mx + c. Right? Okay, so we want Okay, very good Joshua. So y = mx + c. Okay, why we want to rearrange into this form?

[00:12:26]This form is called a gradient form.

[00:12:30]Okay, if it's not in gradient form, this is also still a straight line equation.

[00:12:35]But the information here not very useful. Okay, so we want to always rearrange the form into making y as a subject. Then you put all the other terms on the right hand side. Reason being is here we can get gradient and this one will be the y intercept. Okay. So from the question here y - x = 4 we rearrange to y = x + 4. So the gradient here okay gradient m this one is equals to 1. Then this one the y intercept is equals to four. You don't need to do any calculation. You just rearrange the value.

[00:13:21]Okay, let's go to number six.

[00:13:26]Okay, number seven. Naomi wants to construct the perpendicular bis sector of line A using a ruler and a pair of compasses. Here is her attempt. Okay, explain why Naomi's construction is not complete.

[00:13:41]Okay, what else? What else do you does she need to to sketch out for a perpendicular bis sector?

[00:13:52]Something is missing, right?

[00:13:58]Okay. Anyone knows how to sketch a perpendicular bis sector? The bottom crosses, right? Okay.

[00:14:06]What what do we call that? What do we call the intersection point?

[00:14:17]Okay, we can say um okay you you can say the ax okay to draw arcs okay from bottom top and bottom okay you know what's an arc all right so we can use this this term here um to complete this okay you need to sketch the intersecting arcs from A and B at the bottom also okay so basically is this this over here to make sure that it is perpendicular. So you know how to to sketch this. You will extend your compass to one length like this. Then from here like this. Okay. Then here also the same thing at the bottom. And here also at the bottom. Okay. So you say that she needs to sketch the intersecting arcs from A and B at the bottom of the line.

[00:15:27]Okay? Or something along these points.

[00:15:30]As long you got you got the main points to mention that you need to sketch some sort of arcs at the bottom.

[00:15:41]Okay. Uh okay. One thing right that I have observed also you all need to make sure you prepare your compass your projector for your exam. Uh they have been asking quite a bit on sketching in your in the official exam also. Okay.

[00:15:55]Okay. So, I need y'all to make sure that that you okay that you actually practice your sketching of drawing. Okay. What what are things that you all need to practice? Perpendicular bis sector sketching of 60° 30°.

[00:16:08]Okay. So, whatever that you all have learned from from last time.

[00:16:16]Okay.

[00:16:20]Okay. Let's go to the next one. Question eight.

[00:16:27]A car costs $9,000.

[00:16:32]The value of the car reduces by 10% each year. Take to show which expression represents the value of the car after 3 years.

[00:16:41]Okay. Which one is the answer? After 3 years, what is the value of the car?

[00:16:50]Which one do you think is the answer?

[00:16:55]Okay, very good. Uh Haley, okay, Haley say the fourth one, right? Okay, why is this the fourth one? How do we understand this value here? Okay, reduces by 10% means now it becomes 90%.

[00:17:08]90% is also equivalent to 0.9. Okay, so how do we read this? This is called a continuous percentage change. Okay, you remember this one or some of you all remember as like a compound interest formula. Again you can remember continuous percentage change. Okay. So what it means over here is that every year it become like that 9,000 time 0.9 because 90% to the power of three because power of three means your number of years every every year you will multiply 0.9 * 0.9 * 0.9. Okay.

[00:17:45]So this will be the answer.

[00:17:49]Okay. Okay, let's look at question number nine.

[00:17:53]Make x the subject. Okay, this I just rearrange. First step, multiply both side by 7. So 7 y = 3x + 2. We subtract 2. 7 y - 2 = to 3x. 7 y - 2. We divide both side by 3 = to x. Okay. Normally we will put the subject on the left hand side. If you want to write this down also. Okay.

[00:18:27]Okay, let's go to the next one.

[00:18:32]The distance time graph shows the journey of a train between A, B, and C.

[00:18:39]Find the speed of the train when traveling between point A and point B.

[00:18:44]Okay, this is also one of the graph that often comes out which is your kinematics graph. We need to know distance time graph and speed time graph. Do you know what it represents? Distance time and speed time graph.

[00:19:02]You don't understand number nine. Which part?

[00:19:08]Just rearrange the the thing.

[00:19:13]7 y - 2 over 3 just algebra rearrange okay show me your working okay later later we we discuss what to do with numerator and denominator you show me your working then I I can see okay distance time graph what can we find I want you to write this down when we got a distance time graph we can line. Number one, the gradient represents the speed. Okay, we need to remember this definition because speed is distance divided by time. Distance over time. This is what we learned in our physics also.

[00:19:59]Okay, if a speed time graph comes out, okay, this one very rarely will come out but I think they might slowly introduce you all. This one is a famous IGC.

[00:20:08]Okay, speed time graph we need to know you can find two things.

[00:20:14]Number one, your gradient will represent the acceleration of the object.

[00:20:24]Number two, the area under the graph represents the distance. Okay, you just write down the definition first just in case you all come across this one. But I I think speed time uh lower chance to come out. Normally it's distance time that they will test you on. Okay. So you need to learn how to read the distance time graph.

[00:20:55]Okay.

[00:20:58]The speed of the train from A to B. We need to find what is the gradient over here. How do we find the gradient?

[00:21:05]What's the definition of gradient?

[00:21:07]What's the formula of gradient? Okay, we learned this in straight line graph.

[00:21:11]So, you will need to use these two points. Okay, you all write down the the coordinates of these two points first.

[00:21:17]This is 0 25,500. Okay, you know how to read the the points on the graph.

[00:21:23]02,500. So, you need to find your X and Y coordinate. Your point B, this one is 100 and 5,000.

[00:21:35]Okay. Formula of gradient because this one we are trying to find the speed gradient.

[00:21:43]The formula is y2 - y1 over x2 - x1.

[00:21:49]Okay. The difference in y over the difference in x. This is one of the formula that you need to memorize.

[00:21:57]Difference in y over difference in x.

[00:22:14]Okay, we take point B as X2 and Y2. So we can write 5,000 - 2,500 over 100 - 0 Okay, the answer here will be equals to U.

[00:22:39]Okay, how much is the answer here? We will get 25 m per second.

[00:22:59]Okay, need to memorize gradient actually all the straight line graph questions, right? You all make sure that you all memorize it. All the all the formulas.

[00:23:10]Okay, let's move on. Next one.

[00:23:13]Okay, here is a triangular prism. Find the area of the largest face on the triangular prism. Okay, which one is the largest face? How do we know?

[00:23:25]Okay, how do we know which one is the largest face? Okay, we have to check right. Okay, we over here. Okay, we have here we have the bottom. We have here then we have here. Okay, which one is the largest face? Can we just look at the diagram and then say the largest face is the triangle? Do we know? No, no. Right. Okay. So, we have to check.

[00:23:46]Okay, let's start with this part here.

[00:23:47]Okay, let's we just sketch it out. 6 8 Okay, this one this area is half * base * height. So half * 6 * 8 6 * 8 this one will be equals to 24 cm² okay so the in front is 24 okay I want youall to find here okay because we want to find this this part here also so what is this this uh part okay let's call this uh hypotenus no maybe not h let's call this uh a okay a square = to 6 square + a square. Okay, we are using pythagoras theorem. A square = to 100. A is equ= to 10. Okay, so let's find find the slanted part.

[00:24:38]Okay, the this is the the sl 4 and 10. So 4 * 10 this one is 40 cm².

[00:24:49]Okay, 40 cm square.

[00:24:55]Okay, where else we need to calculate?

[00:24:57]Okay, you look at the bottom part. Okay, bottom is just 6 * 4 here at the back 8 * 4 32. Okay, so don't need to calculate. So the the biggest one is what? 40, right? This part here. Okay, so this is the biggest side.

[00:25:14]The bottom one, the bottom and the back one. You all can just use your mental calculation.

[00:25:24]Okay. So, here is 40 cm square.

[00:25:32]All right.

[00:25:36]Okay. Let's go to number 12. Okay.

[00:25:38]Triangle A has vertices 0 0 66 and 32.

[00:25:44]Triangle A is reflected in the line Y = to X to give triangle B. Draw a ring around each of the three vertices of triangle B.

[00:25:55]Okay, anyone got this answer here?

[00:26:00]What is Y equals to X? Okay, if it's reflected, do you all know this definition?

[00:26:08]Okay, of reflecting or reflection.

[00:26:13]Okay, diagonal. Okay, anyone knows knows what's the the meaning of this this question? Okay, now you see they really asked a little bit more tricky already.

[00:26:22]Okay, what would happen if a shape is reflected on the y equals to x line?

[00:26:34]This is actually more of a IGCSC question really, but they start introducing to you all in year 9 right now. Okay, I want you to write this down first. When a point or a shape is reflected. Okay, let's let's look at a point because since this is a point.

[00:26:50]Okay, write this down. When a point is reflected on y = x line. Okay. What would happen is that X will become uh okay you just remember like that X will become Y and the Y coordinate will become X. Basically what will happen is that they will interchange the coordinate. Okay. So this is something that we need to remember. Okay. What is this concept?

[00:27:23]This one later on we'll learn in year 10, year 11. It is on the concept of inverse.

[00:27:28]Okay. Okay, this one is actually inverse.

[00:27:33]So when it is reflected on the y = tox line, the meaning is inverse.

[00:27:39]Okay. So you look at these three points here. Okay. Let's start with this 0 0.

[00:27:43]Okay. 0 0 both x and y are zero. So this one will still maintain at 0 0 6 also still 66. Okay. So these two points doesn't change but 32. What will 32 become? It will become 2 three. Okay.

[00:28:01]So, we got these three points 0 0 66 and 23. Got it? Okay. This is one of the facts that we need to remember until year 11.

[00:28:21]Okay, let's go to question 13.

[00:28:30]Okay, users draw a van diagram to show the hierarchy of quadrilaterals. Write each of these words in the correct place to complete his ven diagram. One has been done for you. Okay, quadrilateral.

[00:28:41]So you got the word here rectangle, quadrilateral, square, parallelogram.

[00:28:46]Okay, do you all understand what this vin diagram means? Okay, that means they're asking you on the definition.

[00:28:52]This is part of this. These two is part of this circle and then all these three consist of the bigger side.

[00:29:02]Uh so van diagram this one is teachers diagram I v diagram. Okay what will be the most uh okay what will be the we start from the outside. What will be the most outside what is the general one for the name for all of this? What's the the big idea or the big definition?

[00:29:22]Rectangle, quadrilateral, square, parallelogram.

[00:29:25]We start from the d side. Can we say that this is the hierarchy of quadrilateral? Right? So any polygons that have four sides, we call it a quadrilateral. Correct? All these are some form of uh quadrilateral. So we we will put the most outside one the definition as quadrilateral because this is the generic name for any polygon with four sides. Okay. The second layer they say is a parallelogram. Okay. Why parallelogram? Because square and rectangles they are technically paralle parallelogram, right? Both square and rectangle they have two sets of parallel sides. Okay. Which one do you think will be the next layer?

[00:30:08]Rectangles or square?

[00:30:11]Okay. Rectangles or square?

[00:30:14]Rectangles. Okay. Why? Okay. Let's let's put rectangles as you all mentioned.

[00:30:18]rectangles and squares.

[00:30:23]Okay. So the question to ask right now is can square be a definition of a rectangle can. Right? Okay. Because we can say that square is a rectangle with all four sides that are the same length. But we cannot say that a rectangle can be a square.

[00:30:42]Got it? Because rectangle.

[00:30:46]Okay. square because square needs to be all four sides they are the same. So a square can be a rectangle but a rectangle cannot be a square. Got it?

[00:30:54]That's why we put rectangle then square.

[00:31:01]Okay let's go next one. Another definition. For each shape in the table take to show if it is always sometimes or never a parallelogram. Okay. A rhombus.

[00:31:12]What is a rhombus?

[00:31:14]Is it always, sometimes, or never a parallelogram?

[00:31:20]Okay, what do you think? Okay, first of all, you all know what's a rhombus.

[00:31:25]This is we learned this in uh when do we learn this? Year seven. What's a rhombus? Okay, what's the definition of a rhombus?

[00:31:34]It's like a square. All four sides that are the same. Okay, all four sides they are the same. And then there are two parallel sides. Okay. So we can say something like this. Okay. This is a a rhombus.

[00:31:49]It's like a square.

[00:32:01]Okay. So hard to draw. Uh okay. Wait. Do an easier way.

[00:32:16]Okay, something like this. Okay, this is not exactly a nice rhombus alone.

[00:32:20]Okay, trapezium is what can be like this. Okay, it's a quadrilateral with one pair of parallel sides. Okay, these are trapezium.

[00:32:30]Okay, first definition, what is it? Rhombus is it always a parallelogram?

[00:32:37]Money is must it always be a parallelogram? Okay. Parallelogram means it must always be parallel side. Always, sometimes or never.

[00:32:46]Okay. What do you think?

[00:32:49]Parallelogram all four sides. Sorry. Two pairs of parallel sides.

[00:33:00]Okay. So, this one always.

[00:33:04]Okay. or brus is always a parallelogram.

[00:33:09]Okay. Trapezium. Is it a parallelogram?

[00:33:12]Is any form of trapezium?

[00:33:15]You have two pairs of parallel side.

[00:33:19]Okay. Definition of paralle trapezium.

[00:33:22]There's always one pair only. Okay. This only one pair of parallel sides. It will never be two pairs. So the definition here is never.

[00:33:38]Okay, draw it out then understand the definition. Actually all this right they they got give you in the textbook but got too many things to memorize. So you may need to sketch it out then understand the definition. Okay, then you that's how you answer.

[00:33:54]Okay, are you 13? Are you all good? Are you here? Okay, let's move on to 14.

[00:34:09]Okay, how many questions are this paper?

[00:34:11]Okay, 25. Okay, almost there already.

[00:34:13]Okay, let's look at 14. Samira asked 31 children how long their journey to school took that day. Here are her results. Okay, do you not read this?

[00:34:21]From 10 to 20 minutes, there are three of them. 20 to 35 of them, 30 to 48, 40 to 50, 50. Okay. Drawing around the model class. Model means mode. Mode means the one with the highest frequency. This is under the topic of statistic. Okay. Which one is the highest frequency? The 40 to 50. Okay.

[00:34:43]Draw around a ring around the class that contains the median. Okay. How do we know which one has the median? So, we first need to find the position of the median. Okay. So, where is the position of median? the the formula we'll take n + 1 / 2. Okay, you all have to remember this formula. So if you got 10 values, let's say you got 10 values, it's not 10 divided by two to find your middle value because the middle of 10 values is the fifth and the sixth value.

[00:35:11]Okay? So we will take 31 + 1 / 2. We want to see where exactly is the 16th value. Okay, it's not in between here. You cannot look at the table then read. Okay. So what we need to do right now is we look at the frequency. Okay. What we need to do is we need to add the frequency up. How do we interpret it? This thing we are going to use is called cumulative frequency.

[00:35:40]Cumulative frequency means you will keep adding on the frequency. One of the way to do it or the the use of it is to find the position. So the first three numbers. Okay. This is the first group.

[00:35:52]First three numbers the student will take the time from 10 to 20. Okay. What we going to do for cumulative frequency?

[00:35:57]You keep adding the next frequency.

[00:35:59]Okay. So 3 + 5 8. Okay. How do we interpret this data? From the fourth position to the eighth position, it will be in this group.

[00:36:09]Understand how to interpret? Okay. The last value over here, this value is the last position of the of the group. Okay.

[00:36:16]Then you add again 8 + 8 will be 16.

[00:36:19]Okay. So we just need until 16 because we want to find where is the 16th position. The 16 position value will be over here because from the 9 value to the 16 value will be in this 30 to 40.

[00:36:31]Okay. So this is how we get the answer 30 to 40.

[00:36:40]Okay. The next one. Calculate the estimate of the mean. Okay. What is the formula for estimate of mean? Okay. We need to remember the the formula.

[00:36:51]Mean is the sum of f_sub_x over the sum of f. Okay. So you this symbol is called sigma. Sigma is sum of. Okay. So we need to find what is the midpoint. This is the x. How to find midpoint? Okay. You can write down the the working here. 10 + 20 / 2. 20 + 30id by 2. It's not necessary to write the the working. But let me just show youall. 40 + 50 divided by 2 15 25 35 45 Okay. Then we'll take midpoint frequency. So this one will take 15 * 3 25 * 5 35 * 8 45 * 15 Okay, use your calculator. Calculate this. 45125 280 675.

[00:37:49]Okay, this is your FX value. Okay, in exam I want you to write down the working. Don't straight type out in your calculator because sometimes working also got B side. Okay, so this one I want youall to write 45 + 125 + 280 + 675.

[00:38:07]Okay, what is the total? Okay, the total we go back to the question is equals to 31. So over 31.

[00:38:17]Okay, so type 45 + 125 + 280 + 675 1125 over 31.

[00:38:33]Okay, if you type in the calculator, this value is not a nice value, right?

[00:38:38]Okay, it's 36.2932258.

[00:38:42]So, we will just round it up to three significant figure.

[00:38:47]Okay, 36.3 minutes.

[00:38:57]Why do we take 31 and not 50? There's only 31 children.

[00:39:05]the first quest. Okay, only got 31 children. No, 50 children. Okay, all good. Are you here? Can do. Okay, we take a short break first. Um, for those of you who have not done it yet, I want you to try the next few question. Okay, we take a short 5 minutes break. Uh, when you come back, we'll continue doing it. Okay, because the next few one I think is got quite good questions for youall to to try and then got quite a bit on shapes also. Okay, we'll come back at 8:29. Okay, I'll see you all in 5 minutes.

[00:39:32]Okay, let's continue from question 15 to uh onwards. A cylinder has a base diameter of 6 cm and a height of 14 cm.

[00:39:41]Find the curved surface area of the cylinder. Okay, what is the curved surface area? Okay, so every time when you do shapes, I want you all to sketch it out. Okay, do a rough sketch out so we can see clearly. Okay, one cylinder like this.

[00:40:01]Okay, this is a cylinder. The curved surface area is this part here. Okay, what other information they give us is the diameter is 6 cm. The height is 14 cm. Okay, what is the curved surface area?

[00:40:21]The formula curve surface area. Okay, which is this part here. This one you all have to have to memorize the the formula. Okay, the side side part here.

[00:40:32]Okay, the formula is 2 pi r which is the circumference of the circle multiply by the height. 2 pi r height.

[00:40:44]Okay, what is the r? Okay, let's calculate what's the the r here first. R is your diameter divided by 2. So, which is three. So, 2 pi 3 40. Okay, time in the calculator.

[00:41:00]This is 84 pi. Okay. But we don't leave it in 84 pi. Let's write type in the calculator since this on calculator paper. So we'll get 263 9. Okay. If you want to write to one decimal place 263.9 you can write 264 also can. Yeah. 2 pi radius height.

[00:41:20]Correct.

[00:41:28]Okay. Okay. Do we always need to sketch it out? You sketch it out easier for you to see. Okay. Shapes as if to your the best of your ability. If you can see anything that you can sketch out, normally you sketch out will be easier for you to to visualize it. Okay. Don't keep it everything in your head. Okay.

[00:41:43]Number 16. The distance DKM between two towns is 16.0 correct to one decimal place.

[00:41:50]This is called an upper bound lower bound type of question. Complete the inequality to show the bounce between the ts. Okay. Do you all know what's lower bound upper bound? When they say 16.0 correct to one decimal place. Okay.

[00:42:02]This is the formula that you need to remember. You will take 16.0 plus minus. Okay. They say correct to one decimal place. So 0.1. You take half * 0.1. Okay. You always take half times whatever they correct to.

[00:42:20]Okay. This is the the rounded up value.

[00:42:22]So for this question your lower bound okay we use LB is 16 minus 0.05 your upper bound which is what they give you 16 0.05 okay so this one will become 15.95 this one will become 16.05 05.

[00:42:46]Okay. 17. Here is a sequence 5 91 131 17. Oliver says 131 is a term in this sequence. Take to show if Oliver is correct or not correct.

[00:43:01]Okay. Give a give us a reason for your answer.

[00:43:05]Okay. How should we check for for this side?

[00:43:08]Is he correct or not? How many marks is this two mark question?

[00:43:14]Okay. What what should we check for first? 5 9 13 17. Okay. Are we going to keep adding adding four four? No. Right.

[00:43:22]Okay. Will take quite quite long. You can but it will take quite long. Okay.

[00:43:24]What we should do is let's find what is the nth term of these sequences. Okay.

[00:43:28]So I want you all to write down n's term.

[00:43:32]This is a linear sequence. So + 4 + 4 + 4. Okay, we will use this formula. A + n -1 d a is your first term. Okay, a is 5.

[00:43:47]D is equals to 4. Okay, this one is your first term. The value of the first term, this one is called your common difference. So what do you add or subtract?

[00:44:00]Okay. So this one will be 5 + n - 1 * 4 5 + 4 n - 4 which will get 4 n + 1.

[00:44:10]Okay. We need to have this formula first. 4 n + one. Okay. If you don't write the working 4 n + one, however you find it, it's up to you. Okay. Now we need to check is n part of this or not.

[00:44:23]Okay. We we solve for this 4n + 1 = to 131. 4n = to 130 and 130 / 4. Okay, your n condition it needs to be a positive integer. Okay, for this case n is 32.5.

[00:44:47]Okay, so this one is wrong. So we can say not correct because n is not a positive whole number or positive integer.

[00:45:05]You need to show some sort of working.

[00:45:06]So your n can only be 1 2 3 4 5 6 whole number. Cannot be a decimal. Cannot be a negative value and cannot be zero also.

[00:45:21]Okay.

[00:45:25]All right. Let's go to question 18.

[00:45:32]Okay. All copy down already.

[00:45:35]Okay. Question 18. Draw a ring around each of the two expression that are equivalent. Okay. So, we just need to open up the bracket. First one. Multiply multiply like this. This will be 6 P minus 2 PQ and then 6 P - Q multiply multiply 6 P minus 2 Q. Okay, so the first one. Okay, this one and this is the saber. So we just circle this, this, and this.

[00:46:06]Okay, number 19. It takes four people 30 minutes to restock the shelves in a shop. Find how many people would be needed to restock the shelves in 20 minutes.

[00:46:16]Okay. What type of question is this?

[00:46:19]Four people 30 minutes. Now you need you want to restock in 20 minutes.

[00:46:27]Okay. This is as an inverse proportion type of question, right? Okay. We need to know that this is a proportional but it is inversely proportional because you have to use your logic over here. You got more people means less time. Right?

[00:46:40]You can write this. More people means less time. This is called an inverse proportion. Like what a mentioned inverse proportion question.

[00:46:52]Okay. For this what we can do? Okay. We can write like that people and uh okay we write time here. Time and people 30 minutes need four people. Now we want 20 minutes. Okay. How should we calculate for this?

[00:47:16]Okay. Any idea or any method that you all use for this question?

[00:47:23]30 / 4.

[00:47:26]Okay. 4 * 30 divided by 20. Okay. Why 4 * 30 divided by 20?

[00:47:34]Why do you use that that method?

[00:47:39]4 * 30 / 20.

[00:47:45]Okay, anyone got a different different way? But okay, we or we can see Sean Sean Irish Chu. Okay, he wrote wrote 4 * 30 divided by 40. Okay, normally this method we do like this. This one is like a more of a direct proportionate type of question. Okay. So you Okay. Let me see if we can do this way. Okay. We can find this first. We can find 10 minutes first. Okay. That means this one if we divide by uh three. Okay. This one will be 10 minutes.

[00:48:23]Okay. Let me just see is this a good method or not. Okay. Here you need to time three. Okay. So here will be equals to 12.

[00:48:32]uh this way actually you can do also okay this inverse proportion if you use this way you divide three here you have to times three here so now we times two here means here you need to divide by two got it because it's inversely proportional one you will increase the other one will decrease so this will be 12ide by two the answer will be equals to 6 okay do you get the same answer should I ru 4 * 30 / 20 I think same also right you also get six okay the other way that we can do is you use Sean's way. Okay. 4 * 30 then you get 120 then 120 divided by 2 60. Okay. I'll teach you all one more way. This one is later when you all do your your IGCSC papers normally we'll use use this one.

[00:49:22]Okay. The relationship between time and people is inverse. So this is how we we write that time and people inverse like that. T is inverse of 1 / P. We can write like that T is equals to K over P.

[00:49:37]Okay. What is K value? K is a constant.

[00:49:40]Okay. So this one a bit longer longer way but you can just copy down for to prepare your for year 10 year 11 this constant. Okay. The time right now is 30 minutes for four people. Okay. Actually this one is uh quite similar to what Sean Sean Arishu is using. Okay, what you're calculating the first one is actually a K value. K is 4 * 30. You see here right we are finding the relationship between time and people. So 30 * 4 is equals to K. K is 120. Okay.

[00:50:14]So the relationship between T and P is T equals to 120 / P. We construct an equation. Got it? This is the relationship based on this question. So now if we want to find time of people, right? We can just sub in the the value.

[00:50:30]Okay. They say now we want time is 20, right? Okay. T is equals to 20. So 20 = to 120 / P. P is 120 divided by 2. You see he's working 120id by 2. So this one is equals to 60. Okay, this method later on in the IGCSC paper, year 10, year 11, we will be using a lot of this. Okay, because in IGCSC the proportion type question not so straightforward anymore.

[00:50:55]They give you some very weird value.

[00:50:56]They'll give you like find the relationship between let's say P and square root T. They will introduce some other elements inside.

[00:51:10]Okay, let's go next one. Draw a ring around each of the rational numbers in the list. Okay. What is the definition of rational numbers?

[00:51:20]>> That means that you can change into a fraction.

[00:51:23]>> Okay. Can be written as a fraction. That also means it can be written as a whole number. So can Okay. The proper definition can be written as fraction. Okay. So the first one yes 43 also can be written as fraction.

[00:51:40]Technically it's 43 over 1. Okay. Set three. This one cannot be changed to a whole number. So no7 yes pi okay pi is not a rational number it's actually it keeps going on and on square root 100 this one is actually equals to 10. So you get these four answers.

[00:52:01]Okay let's go to question 21.

[00:52:08]Work out the parameter of the shape.

[00:52:12]All right, this one actually not that hard even though it's a three markup question. So let's look here. The shape consists of two semicircles which has a radius of 3.25 cm. So two semicircles add up together will be equals to one circle. Okay. Then plus here 15 15.

[00:52:38]Okay. So let's calculate the circle first. Okay, we say like this two semicircle is equals to one circle. Okay, circle is 2 pi r which is 2 pi 3.25.

[00:52:59]Okay, this is equals to 6.5 pi. We leave it in pi first. Normally you okay if you see got irrational values in the middle of the equation try not to expand the the value first okay so the total parameter we will take the two blue one so 15 * 2 plus 6.5 pi 30 + 6.5 pi okay we just round it out to 3 SF 50.4 Four.

[00:53:45]Okay, let's go to 22.

[00:53:48]A right angle triangle has a base 4 y and a height that is 5 cm more than the base. Find an expression in terms of y for the area of the triangle. Okay, let's draw it out. Your right angle triangle. Base is 4 y. Height is 4 y + 5, right? Because it's five more. What is the formula? Half * base * height.

[00:54:16]So, we get half * 4 y * 4 y + 5. If we multiply this, half * 4 y will be equals to 2 y * 4 y + 5.

[00:54:29]2 y * 4 y this will be 8 y 2 + 10 y where I get the square from y * y will be y² indices do you Okay, previous question later you ask. I move on already. I don't want to go to the previous.

[00:55:07]Okay, let's go to 23. Any question until here?

[00:55:13]Okay. Three children's shares of money in the ratio 258. One child receives 180 more than one of the other children.

[00:55:22]Find the two possible amounts that the children share. Okay, this one is an interesting question. Okay, so they say that this one child receives 180 more than one of the other children. Okay, so we need to find this part here. Okay, this part here. Which one does it represent? There are two possibilities.

[00:55:43]Okay, which one is it?

[00:55:48]We can say the difference is either two and five or we can say it's two and eight. Got it? Okay. Because we don't know what which who and who got the difference. Okay. First let's understand this the possible difference. Okay. Uh okay. We can write down possible difference in parts of ratio. Okay. It can be either scenario 1 which is 5 - 2 = to 3 or 8 - 2 = to 6. Okay. So that means your 180 can represent three parts of the ratio or six parts of the ratio. Okay.

[00:56:34]Everyone understand this part first?

[00:56:36]Okay. So now we want to find okay total parts got how many? Okay. total parts of the ratio or total shares 2 + 5 + 8 okay 2 + 5 + 8 this one will be equals to 15 parts okay let's base it on three parts first okay so the difference in three parts if let's say three parts is equals to 180 one part will be equals to 180 divided by 3 this will 37. Okay. 0.30.

[00:57:14]So your total parts we have 15 parts. We will take 0.3 multiply by 15.

[00:57:25]This will be 450.

[00:57:27]Okay. This is scenario number one.

[00:57:36]It's 0.6. Thanks. Uh going. Sorry. Hey, did you write wrong already? Uh 6 * 15.

[00:57:43]Okay, my bad. $9.

[00:57:49]Okay, if is six parts. Okay, I accidentally divide by six. That's why.

[00:57:54]Okay, six parts. Let's say six parts is 180. One part we'll take 180 divided by six.

[00:58:02]Okay, this one this one is 0.3. So if we base it on six parts difference then it'll be 30 cent for one part. So 15 parts will be 0.3 * 15 which will be equals to $450. So, it's either $9 or $450.

[00:58:42]Okay, this an interesting question.

[00:58:43]Okay, let's go to 24. Okay, this one is about you, Eva. Eva, are you there?

[00:58:51]Okay. Eva thinks of a number n. She doubles the number, then adds 12, then divides by five. Eva Eva knows that her answer is the same as the number that she first thought of. Okay, write an equation and solve it to show there's only one number that Eva could have been thinking of. Okay, Eva, what were you thinking about? So, how do we write an equation out first? Okay, the initial number that she was thinking of is represented by n. Okay, so what did she do with n? n she doubles the number. So 2 * n, we write 2 n then add 12 then divided by 5. So it's 2 n + 12 over 5.

[00:59:33]Then she say that the this answer is the same number that she first thought of which is equals to n. Okay, because the original number that she was thinking of is n. 2 n + 12 over 5 = to n. Okay, so let's solve this. Ainas, just now you are asking how to solve this type of question. What's the first step that we should do? 2 n + 12 over 5 = to n. Okay, so think of it as remove denominator.

[01:00:00]Okay, so how do we remove the denominator? Okay, think of it as what do we need to do to the entire equation on both side. Okay, don't don't think of it as uh move here and move there.

[01:00:14]What do we need to do to the entire equation? To remove the denominator, we want to multiply by five, right? Because on the left hand side we want multiply five, right hand side also we multiply by 5. So this will become 2 n + 12 = to 5n because many of you right you all have a habit from young or and technically ply is actually not your fault. Your teacher will always say if on the bottom you just throw it up. Not always the case. What we are doing this is a shortcut method to think about but what we are doing is we are multiplying both side by five. Okay. Then the next thing we want to get rid of this, right?

[01:00:46]So we will subtract 12 on both side. So 2 n = to 5 n - 12.

[01:00:54]Okay.

[01:00:56]Sorry. Sorry. Sorry. Wrong already.

[01:00:58]Okay. Sorry. We want to move the n both to one side. Okay. So I want to put the 2 n on the right hand side.

[01:01:07]Okay. So here will now become 12 = to 3 n. Okay. What should we do? The last step here to get rid of the tree. Okay, if you like if you don't like to see the 3 n on the right hand side, you move like that first. You just switch the position. 3 n equ= to 12. Normally, we put the the unknown that we want to solve on the left hand side. Okay, the last step now is 3 * n. To get rid of the three, we divide three on both side.

[01:01:33]12 / 3, which is equals to 4.

[01:01:39]Okay, n is equals to 4. This is the only possible value.

[01:01:57]All right. Okay. One last question.

[01:02:01]The diagram shows a rectangular garden with a circular pond. The shaded area of the garden is 95.1 m square. Find the diameter of the pawn.

[01:02:14]Give your answer correct to three significant figure. Okay, this one doesn't look shaded, right? Okay, but I will assume that the shaded part is everywhere except the pawn. Okay, let me see. Let me just double check. Okay, very funny.

[01:02:30]Yeah, this one. Why no shader? Okay, I think it is here.

[01:02:39]This is a shaded part.

[01:02:43]Okay, what's the diameter of the pond?

[01:02:45]Okay, so first thing we need to find the area of the pond first. Okay, what's the area of pond?

[01:02:53]We will take 12.3 * 8.5 minus the shaded area of the garden. Okay. So 12.3 * 8.5 this will be 104.55 - 95.1.

[01:03:10]Okay. Here will be equals to 9.45 m².

[01:03:15]Okay. Then to find the pod. Okay. What will be the formula of the pod? Area of pod and we say is p<unk> r².

[01:03:26]Right? P<unk> r² r² is 9.45 45 /<unk> r is square t 9.545 over pi.

[01:03:41]Okay, this one will be 1.7344.

[01:03:47]Okay, this one you write a little bit more decimal place first. But I'll keep this value because the last value that they want is a diameter. Okay, so diameter is 2 r. So 2 * 1.7344.

[01:04:00]Okay. The final answer we round it to three significant figure. 3.4687.

[01:04:06]So here is 3.47.

[01:04:10]>> Isn't it 3.46?

[01:04:13]>> Okay. So 3.47 is the final answer.

[01:04:18][clears throat] All right. Can this paper? Okay. I think this one easier than the paper one, right? Okay. The paper one a bit more more tricky. All right. If you are good for this paper two, 20 26. Okay. 25 questions here. I want you to type seven.

[01:04:39]This one much much easier. Okay. You all got any question? Please ask me. I'll stop this recording verse.