Live GCSE Maths Past Paper

Added: 2026-05-24

[00:00:04]Are we live?

[00:00:07]Haha, I think we might be.

[00:00:11]Oh, we are live, guys. Let me know.

[00:00:16]Can you hear me?

[00:00:21]Hello Emily. Hello, it's me. Hello Porsha.

[00:00:24]Hello Zayn.

[00:00:26]Hello Ali Zayn.

[00:00:29]Hey guys.

[00:00:30]How is it going?

[00:00:33]How are we?

[00:00:38]Ah, fantastic. Hello Maria. Hello Vincenzo. Hello Theo. Hello Gammon says hello. Let's go.

[00:00:45]Hello Carmel.

[00:00:48]Oh guys, yeah, how was chemistry today?

[00:00:52]Talk to me. Talk to me.

[00:00:53]Um, I need to just quickly check if we're running up over on the talkers.

[00:00:59]We might be, but they do have a habit of shutting us down over there.

[00:01:04]So, let's see.

[00:01:08]I'm expecting a little bit of a quieter session today um, cuz of course you guys have got literature tomorrow. We're only going to be live for an hour. I know that you want to revise for your other subjects, of course.

[00:01:20]Um, but I also know that a lot of people are were expecting the live today because we go live every Monday half five to half six. So, I just wanted to make sure that we uh that we kept the uh the pattern going and that nobody was let down.

[00:01:38]Ah, fantastic Zayn.

[00:01:40]Okay, so the Okay, so the opinions on chem look pretty good, actually.

[00:01:46]Sounds like it wasn't too bad. Mary's saying it was better than bio.

[00:01:50]Um, Ali Zayn says chem was beautiful.

[00:01:53]Very nice. As always, different opinions.

[00:02:06]The plan for this evening, guys, we're going to be going through some paper two questions and focusing specifically, of course, on those ones that need the calculator and the topics that didn't come up in paper one.

[00:02:20]Ooh, doesn't look like I'm actually the stream is up on the talkers.

[00:02:26]It should be.

[00:02:28]But I can't Ah, okay, it is. Fantastic.

[00:02:32]My connection was just taking a bit of time to get it looking good, get it set up.

[00:02:37]Um How's the connection looking, guys? Have you got me clearly? Is everything nice and smooth?

[00:02:50]Just want to make sure because for some reason it's not looking so smooth when I look up my own stream. But there's a few different things that can cause that.

[00:02:58]So, before we get going I just want to check we're all good.

[00:03:02]Nice. Al Izain says smooth as butter.

[00:03:06]Zane says, "Yep."

[00:03:08]Carmel said everything's perfect.

[00:03:10]Fantastic, Carmel. Um guys, exciting announcement today.

[00:03:15]A very exciting announcement today. I'm going to save it for the end of the stream. We're going to be live for 1 hour from 5:30 until 6:30 focusing on the questions from the June 2022 paper two, which you can see that we've got up here.

[00:03:27]Um and then I'm going to make an exciting announcement on this stream that is going to be made officially on social media at the back end of the week and I'm going to ask for your guys' opinions.

[00:03:38]Um on something very important which is going to inform how I help you guys over the next couple of weeks.

[00:03:46]So, let's see. How many of us are engaged, guys? Can we get a quick W or lightning bolt emoji in the chat for me if you're interacting, if you're engaged?

[00:03:56]And then we can get going.

[00:03:59]Quite a few people saying that they can't um join today because they have to revise English. Guys, honestly, honestly, that's all good. If you want to keep the stream on in the background, you can just for the community revision element. If you want to leave the stream and go and revise English, that's also fine.

[00:04:15]Um but you absolutely can also um just do one little hour of maths, treat this kind of kind of as a break. We'll We'll go through in a bit of a chill way um before you get back into your English revision. Alizain is in there with the W. Maths 2026 UK W. Portion Enthusiast W. Joe Gaming W. Zain W. Mary lightning bolts. Carmel W and lightning bolts.

[00:04:35]Emily lightning bolts.

[00:04:37]Alizain says, "I've got this on in the background." Fantastic, guys. Let's get going then. In general, we're going to focus on some of the questions in the middle of the paper, but we will also just do this first little page as a warm-up. So, question number one is our first one. Simplify x to the power of 3 to the power of 5. Answers in the chat for me, please. Anitak says, "Is this useful for those doing um IGCSE and Edexcel maths?" Absolutely, Alizain. There's only a couple of differences between them.

[00:05:09]Um IGCSE has I think differentiation and maybe some series. That's not in regular GCSE, but everything we go through today is also in IGCSE.

[00:05:19]Ah, fantastic, Perry Paradox. Fan of the channel since 5K.

[00:05:24]Yeah, I can see Oh, wow, a few different answers going in the chat. Some people saying x to the power of 8. Some people saying x to the power of 15. Guys, this one is a real classic and it's really good to know. Simplify x to the power of 3 to the power of 5. When we have something to a power and we raise it to another power, we have to multiply those powers together. So, we do x to the power of 3 x by 5, that would be 15. So x to the power of 15 is our first one.

[00:05:53]1b, I'll go through this one now as well. Expand and simplify 4 (x + 3) + 7 (4 - 2x). What are we going to do?

[00:06:04]We're going to expand firstly our brackets, then collect our like terms.

[00:06:09]In order to expand our brackets, actually guys, I'm not going to do it yet. Get your answers in the chat for me.

[00:06:22]Very important question, guys, as well.

[00:06:25]Um, can you hear my music playing in the background? I would really appreciate it if you could turn the volume up to max and just let me know if you hear anything. You shouldn't be able to hear it.

[00:06:34]Um, if you can hear it, I'll have to turn it down a click.

[00:06:49]Fantastic. You guys are saying that you can't hear it mostly.

[00:06:53]Nice. Thanks, Alizain. Thanks, Porsha.

[00:06:56]Thanks, Anu.

[00:06:58]Yeah, fantastic, guys. Okay, 1b then.

[00:07:01]Expand and simplify. So like we said, we're going to expand first of all. So we're going to do the number on the outside times each of the terms on the inside. So 4 x by x is 4x. And then 4 x by 3 is 12. And then we have 7 x by 4, so plus 28. And then we have 7 x by -2x, so -14x.

[00:07:24]Now we can collect our like terms. 12 + 28 is 40.

[00:07:29]And 4x - 14x, 4 - 14 is -10. So we have 40 10x.

[00:07:38]1c, factorize fully 15x cubed. Oh, guys.

[00:07:46]Somehow my mouse has just disconnected.

[00:07:50]Oh, that is not good.

[00:07:55]Let's see if this comes back on. Okay, yeah, we're back on. Fantastic. Wow, that was a bit scary. Um So, factorize fully. Now, the fact that it says factorize fully is kind of a hint that we're going to have to pull out multiple things. So, if we look at the numbers, we have a 15 and a 3.

[00:08:13]So, we have a common factor of 3 for both of them, so we can write 3 on the outside. But, it does say fully. So, can we pull an x out or a y out? Well, we have an x cubed here. We have an x squared here. We need something which goes into both of them. Now, x squared times by 1 is x squared, and x squared times by x is x cubed, so we can actually put an x squared on the outside.

[00:08:36]And then, because there's a y in the second term, but there isn't a y in the first term, we can't put a y on the outside.

[00:08:44]So, now we can write our brackets in.

[00:08:45]What do we times by 3x squared to get 15x cubed? Well, 3 times by 5 is 15, and x squared times by x is x cubed, so we get 5x plus what do we times by 3x squared to get 3x squared y? Well, they're exactly the same, but this just has a y, so we just have to times it by y.

[00:09:04]And then, we have our answer uh 3x squared times by 5x plus y.

[00:09:11]Good work, Amalie.

[00:09:13]Yeah, fantastic, guys. Good work, Soft.

[00:09:15]Good work, Junior Aura. Brilliant work, guys.

[00:09:18]The next one we will go through is Let's go through question 4 now. This one's a four-marker.

[00:09:27]As I said, we want to prioritize some of the more challenging questions, and we only have a limited amount of time in this Monday live stream, so I want to make sure that we get through the most impactful questions possible.

[00:09:40]Hey Bacon, my pleasure.

[00:09:42]That sounds so funny me saying that.

[00:09:46]Somebody called Bacon just said thank you, for the for the record.

[00:09:50]>> [laughter] >> I can see a couple of questions going in the chat saying, "Is it AQA?" All of the questions we do today will be beneficial for Edexcel and AQA, but it is an Edexcel paper. So, it will help for both.

[00:10:23]But, it's a Edexcel paper that we're going through.

[00:10:35]Yeah, guys, for some reason um the TikTok stream got blocked again by TikTok. I have no idea why. So, we're back to just the YouTube.

[00:10:53]Are we all smooth on the YouTube still just since I ended the TikTok live?

[00:11:01]Ah, fantastic Perry Paradox. Says, "I'll be leaving since I completed my GCSE O level in 2025 and I passed maths due to the channel. I came back to say hi. Best of luck with the channel and continue it and keep that happy face."

[00:11:15]>> [laughter] >> Love it.

[00:11:18]Anita UK said, "Should we join the masterclasses if we're not Edexcel?"

[00:11:22]Great question, Anita. So, you guys can see my night before exam masterclasses.

[00:11:25]Um so I will be going through Edexcel past paper questions, but it will still be very beneficial for AQA. I will only go through questions which are Edexcel and AQA, and I'll base it a little bit on the paper one of Edexcel and AQA as well. So, if you're doing AQA, it's still going to be beneficial. There are some small differences, you know, the fonts are different, and also um some of the questions can be worded a bit different, but it's still going to be extremely beneficial.

[00:11:53]So, it's kind of your call, to be honest. It's still very beneficial.

[00:11:59]Okay. I can see some answers going in the chat. Some people saying it's too hard.

[00:12:03]Let's have a look at this one together, guys. I'm going to go through this one quite slowly just to make sure that you um yeah, just to make sure that you understand each stage of the working.

[00:12:13]So, it says festival A will be in a rectangular field with an area of 80,000 m². The greatest number of people allowed to attend is 425.

[00:12:22]Festival B will be in a rectangular field 700 m by 2,000 m. Now, what we notice is for the first one, we've been told the area. For the second one, we've not been told the area. We've just been told the measurements, but we also know it's rectangular. I've not even read the question, but I know already that I'm going to have to work out what the area is. So, before I even do the rest of the question, I'm going to work out the area.

[00:12:48]We know that the area of a rectangle is the two lengths multiplied by each other, so we can say area equals 700 times by 2,000, which you could do on the calculator if you wanted to. It's going to be 14 and then five zeros.

[00:13:06]Five.

[00:13:08]And that is 1.4 million m². Huge number.

[00:13:12]Okay. Um next step, what are we going to do?

[00:13:17]Um it says the area per per and the number of people allowed to attend is 6,750.

[00:13:23]The area per person allowed for festival B is greater than the area per person allowed for festival A, how much greater? You must show your working.

[00:13:33]Give your answer correct to the nearest whole number. So, how do we do this? We need to work out for festival A and for festival B the area per person.

[00:13:45]Now, how do we work out area per person?

[00:13:47]Well, area per person will just be the area divided by the number of people.

[00:13:54]And that's it. Whenever you hear per, you can think of it as divided by. So, for the first festival, festival A, we're going to do the area of 80,000 80 thousand divided by the max number of people 425 and we can literally pick our calculator up and type it in. We can do 80,000 divided by 425 and we get 188.

[00:14:23]188.2 and then it goes on a bit. What about for B? Well, we have an area of 1.4 million. So, we have 1.4 and then 1 2 3 4 5 and we have how many people? 6,750.

[00:14:40]So, we can do our division. 1.4 1 2 3 4 5 zeros divided by 6750 and we get 207.

[00:14:50]207.4 and that carries on.

[00:14:54]How much greater is the area per person? Well, now we need to find the difference. Because it asks us to give our answer to the nearest whole number, as long as these are accurate to 1 DP, then the answer will give us the correct um value or the yeah. So, we can do 207.4 188.2 207.4 - 188.2 and that is going to be 19.2.

[00:15:27]Giving our answer correct to the nearest whole number, we're going to round this to the nearest whole number, so the two makes it round down.

[00:15:34]Um so yeah, we look at the first decimal place, it's a two. Because it's less than five, we round down. So we get 19 to the nearest nearest whole number. 19 to the nearest whole number.

[00:15:53]Hopefully that one makes sense, guys.

[00:15:54]Any questions, let me know.

[00:15:58]Ah, thank you, Adam. I'll have a look for that, mate.

[00:16:01]Um Part B, Callum says 300 cm squared.

[00:16:06]Yeah, all guys, this is a classic. This is a classic. What do you think for this, guys?

[00:16:11]300 cm squared is the same as 3 m squared because there are 100 cm in 1 m, so you divide by 100. Callum's method is wrong, explain why.

[00:16:27]Moon says, "Matt, my mom saw your live and she said thanks for doing the live."

[00:16:30]Hey Moon's mom, my pleasure. My absolute pleasure.

[00:16:36]Thank you.

[00:16:39]Ah, there you go, Carmel. OMG, my bad.

[00:16:42]Didn't notice the first one was in meters.

[00:16:48]Yeah.

[00:16:52]Hey Kev the dev.

[00:16:56]What do we think, guys?

[00:16:59]300 cm squared is the same as 3 m squared.

[00:17:08]Emily says he should divide by 10,000.

[00:17:11]Yep, you're absolutely right. So guys, what is the logic for this one?

[00:17:15]Well, the problem is that when we convert from centimeters squared to meters squared, it's not the same thing as going from centimeters to meters.

[00:17:28]So, this is correct. There are 100 cm in 1 m.

[00:17:32]But, 1 m squared is not 100 cm squared.

[00:17:38]1 m squared 1 m squared is Well, it's going to be 100 cm times 100 cm or 100 cm by 100 cm, which believe it or not is 10,000 cm squared.

[00:17:56]So, if Callum wanted to go from 300 cm squared to meters squared, he would actually have to divide by 100 twice.

[00:18:07]So, he should divide by 10,000, not by 100.

[00:18:12]He should divide by 10,000, not by 100. He should divide by 10,000, not 100. Why? Because there are 10,000 cm squared in 1 m squared, which is kind of hard to believe. But, remember guys, regular length conversions are not the same as area and they're not the same as volume conversions. With an area conversion, you have to do it twice.

[00:18:44]With the volume conversion, you actually have to do it three times, which is crazy, but it's what you have to do.

[00:18:52]Okay.

[00:18:53]Let's keep it moving, guys. Question six is the next one we're going to do.

[00:18:57]I'm not going to give you too long for this, because it doesn't take too long, but it's very important for paper two.

[00:19:17]>> A little reminder guys for anybody who's looking for a bit of extra support over the next couple of weeks. I do have my night before classes, which are £20 each or £30 for both of them, but I also have my group tutoring.

[00:19:31]So, I can put the link in the chat if anybody wants it, but basically I do three 1-hour lives every week. Tuesday, Wednesday, Thursday 5:30 to 6:30. The Tuesday is grade 4 5, Wednesday is grade 6 7, Thursday is grade 8 9, and that one's £20 a week for access to all of the classes, and you can just find it on my website mygcsemaths.com.

[00:19:57]Nice portrait enthusiast, fantastic work.

[00:20:02]Hey hey.

[00:20:04]Good work, Zane. Good work, Amalie.

[00:20:14]What do we reckon, team? Are we ready?

[00:20:27]Calum Mells ready.

[00:20:29]Alizain says, "Sorry, I'm having to go and have dinner now." No worries, Alizain. Hopefully you got something nice.

[00:20:35]Yeah. Okay, guys, how do we do this one?

[00:20:37]Question number six.

[00:20:40]Classic compound decay. Let's have a look. It says a new phone costs £679.

[00:20:49]The value of the phone decreases at a rate of 4% per year.

[00:20:53]Work out the value of the phone at the end of 3 years. So, this is a compound growth compound decay, kind of the same as the compound interest topic.

[00:21:04]Basically, what we have to do is we have to decrease this number by 4% three times.

[00:21:11]And how do we do that? Well, we start off with our amount, our our starting amount, and then we times it by 1 plus Oh, not plus. 1 plus our amount that we're increasing or decreasing by as a decimal, and we raise it to the number of time periods.

[00:21:35]Now, in this case, because the phone is decreasing, we're actually going to end up having a negative here.

[00:21:41]So, we're going to do our start amount, 679 pounds, 679 pounds, times by then we're going to have 1 minus, and then we're going to write 4% as a decimal. How do you go from a percentage to a decimal? You divide it by 100.

[00:21:58]So, we could do 4 / 100, it's 0.04.

[00:22:03]So, we can write that in, 1 - 0.04, and we're going to raise that to the number of time periods, it's for 3 years, so we're going to raise it to the power of three.

[00:22:14]If you were going to do this in shorthand, you could have written it as 679 times by 0.96 to the power of three. That's exactly the same thing.

[00:22:26]So, we're going to do 679 * 0.96 to the power of three.

[00:22:32]And that on the calculator is going to give us 600 600.

[00:22:38]74 to two decimal places. 600.74 to two decimal places.

[00:22:45]So, that is our answer.

[00:22:52]Okay, let's have a look, Carmel.

[00:22:55]Great question. Absolutely brilliant question. Says, "Quick question. Why is it different when you subtract 4% three times versus when you subtract 12% once. Now, this is really interesting. So, this question is about the difference between compound interest and compound growth and simple interest and simple growth.

[00:23:17]So, here what essentially happens is the value decreases by 4% every year.

[00:23:26]>> [clears throat] >> So, we start off with 679 lbs.

[00:23:31]And then we decrease it by 4%.

[00:23:34]So, we times it by 0.96.

[00:23:37]And I Oh, I did not mean to write 6,000, just 679.

[00:23:46]And then we get 679 * 0.96.

[00:23:50]And that would be 651.84.

[00:23:55]And then with compound decay or growth, we then take the new value and we decrease that value by 4%. So, 651.84 times by 0.96.

[00:24:11]And then we do whatever that would be.

[00:24:13]It would be 625.

[00:24:18]7664.

[00:24:23]And then we do it with this value again.

[00:24:26]So, basically, we're always taking away 4% of the new value. Now, this is like the long way to do compound growth or decay. The short way is with the power, but ultimately, these two are going to work out the same thing.

[00:24:41]The difference with simple interest or simple um growth or decay is that we are always increasing or decreasing by the percentage of the original.

[00:24:54]So, that 4% would always be of the original amount rather than of each of the new amounts that we're changing by.

[00:25:02]So, that's the difference. It's the difference between simple interest and compound interest. Okay.

[00:25:08]Next up, question number Let's do question number 11. This is a good one.

[00:25:20]Mr. Loyens says, "Mr. Everly, by the way, are you still in Germany?" I'm actually back from Germany.

[00:25:26]I'm in the beautiful old UK.

[00:25:33]Hopefully, that description helped, Carmel. Did that answer the question?

[00:25:55]And also, guys, did that um help anybody else that description of the difference?

[00:26:04]Uh guys, did a question like this come up on paper one?

[00:26:07]Because if it did, then we can skip it.

[00:26:11]I've actually still not seen the papers.

[00:26:14]That's on my to-do list for tomorrow, actually, to have a look over them properly.

[00:26:21]Did this come up on paper one, guys?

[00:26:30]Okay.

[00:26:31]Yep. Yep. People are saying it did.

[00:26:32]Okay. Question 12, then.

[00:26:34]Let's go through this one.

[00:26:41]Or some of you are saying it didn't.

[00:26:47]Okay. Well, we're going to do question 12 um as our next one, and then maybe we'll loop back to question 11.

[00:27:00]Yeah, I know it says it's on TikTok.

[00:27:02]Yeah, I have actually seen I have seen the papers, but I haven't seen them enough to have memorized every topic. So, like I quickly had a look at the AQA's, I quickly had a look at the Edexcel's higher foundation, but I've not yet memorized all of the questions.

[00:27:18]Ah, unlucky Emily. Unlucky. This happens though. At the end of the day this happens.

[00:27:23]Um sometimes you come out of an exam and it can be very stressful, especially if you're aiming for a high grade or whatever grade you're aiming for. If you think back to questions that you didn't read properly or that you misread or, you know, maybe you didn't read about the fact that you had to round it or something like that. This happens all the time, guys. It's very natural.

[00:27:41]Um so, don't let it panic you if you if you did do that.

[00:27:50]Okay, question number 12. It's a show that question.

[00:27:54]Let's have a look, guys. I've given you a bit of time to think about it. And it's only a two marker. Question 12 it says the equation of the line L1 is Y = 2X + 3. The equation of the line L2 is 5Y - 10X + 4 = 0. Show that the two lines are parallel. What do we know about parallel lines, guys? Parallel lines have the same gradient, right? The same gradient.

[00:28:20]So, what we can do is we can show that both of these lines have the same gradient. Now, how do we work out the gradient? Well, we know that the general equation of a straight line is Y = MX + C where M is our gradient.

[00:28:37]So, we need to show that M is the same for both of them. Now, L1, we can see has a gradient of two. Because it's already in the form Y = and there's a two next to the X.

[00:28:47]But for the second equation L2, we don't currently have it in the form Y equals, so we can't see the gradient. What we need to do is rearrange it so that it says Y equals, and then we can read the gradient. So 5Y - 10X + 4 = 0. We're going to move all of the terms other than the 5Y over to the other side. So I'm going to add 10X to both sides and I'm going to minus four.

[00:29:13]I'm going to get 5Y equals 10X - 4.

[00:29:19]Now to get the Y on its own, I'm going to divide both sides by five. I'm going to get Y equals 10 / 5 is two, so 2X minus and I'm just going to write it as 4/5.

[00:29:30]Now we can see that the gradient of both of the lines is two.

[00:29:34]So the gradient of both lines is two.

[00:29:42]So they are parallel. So they are parallel.

[00:29:51]Hopefully that one makes sense, guys.

[00:29:53]Good work, Soft.

[00:29:55]Good work, Demolade.

[00:29:59]Yeah, good work, guys. We're actually going to loop back now to question number five. Question number five.

[00:30:07]Um five, yeah, five. This has just got the writing from the next question. The reason we're looping back to this is because it's actually a really tough question or it's a very tricky question and problem-solving questions like this have been coming up a lot in recent years, so I think it's a great opportunity to practice. Um I didn't go through it in order cuz I just wanted to warm you guys up a bit first.

[00:30:31]Uh nice, Portion Enthusiast.

[00:30:33]Says, "Oh yeah, I wanted to do this one." Absolutely.

[00:30:37]I knew a lot of you guys would have wanted to do this one.

[00:30:50]>> So, question number five.

[00:30:57]Let's have a look.

[00:31:02]>> [snorts] >> Can you guys tell that I'm suffering with a little bit of hay fever at the moment? I don't know if you can tell that my voice is a bit flatter than normal. I have a bit of a sore throat.

[00:31:17]So, hopefully it doesn't affect the stream. You probably couldn't even tell until I said that.

[00:31:21]But, it's a little bit annoying.

[00:31:24]More power and more blessings to anybody who has hay fever because I know how annoying it is.

[00:31:31]Camel said, "Nope, can't tell at all."

[00:31:33]That's good.

[00:31:39]Uh thank you guys.

[00:31:41]Some of you saying you can tell, some of you saying you can't tell.

[00:31:46]Oh, it's so annoying, Emily.

[00:31:51]52 VV says it's obvious.

[00:31:53]>> [laughter] >> This question's hard, eh?

[00:32:01]Yeah, exactly, be right. It's so annoying, isn't it?

[00:32:11]Yeah, Tanta F, exactly.

[00:32:15]I don't know why hay fever is so common.

[00:32:17]Like, I don't know why evolution decided to just leave it in as a feature. Like, surely you'd evolve that out, but anyway.

[00:32:28]Guys, I know this one's tough. If you just put ready in the chat for me when you're ready, we can have a look at it.

[00:32:45]>> Emily's ready, Zane's ready.

[00:32:47]Porsche enthusiast is ready.

[00:32:49]Carmel says not ready. Okay, guys, I'm just going to give a little hint then.

[00:32:53]So, it says L, M, and N L, M, and N are such that they are on a straight line.

[00:33:04]The coordinates of L of this, M is this, given that L to M to M to N is 2 to 3, find the coordinates of N. Guys, if you don't know how to do this now, but understand it after I go through it, please let me know in the chat. So, the first thing we're going to do for this question is we're going to recognize A that it's quite difficult, and therefore we're going to plot the points roughly on the page. So, L, M, N is a straight line.

[00:33:29]So, we could put L down here, -3, 1. So, L can be the point -3, 1.

[00:33:36]M can be the point 4, 9. Now, because 4 is greater than -3 and 9 is greater than 1, we're going to put it above it. So, we have M.

[00:33:45]This is 4, 9.

[00:33:48]And then L to M to M to N is 2 to 3. So, in other words, M is in the middle, roughly, of L and N. So, I'm going to put N up here, just roughly, and the question asks us to work out N. So, the goal then is to work out this, X and Y.

[00:34:06]Now, we've been told that the ratio of L to M to M to N Yeah, okay, more people are ready. Um is 2 to 3.

[00:34:17]So, what that means is that if we think of this as a ratio, this would be two parts. This distance would be two parts of the ratio, and this distance would be three parts of the ratio.

[00:34:33]Now, what we can do is we can find this distance here and we can find this distance here.

[00:34:39]That can be two parts of the ratio.

[00:34:41]Then we can divide it by two to find one part, times it by three to find three parts, and that's going to give us this distance here and this distance here, which we can add to this coordinate to work out this point here.

[00:34:54]So, the first thing that we're going to do is we're going to find this distance.

[00:34:57]We go from -3 to 4 in the X direction.

[00:35:01]So, that's an increase of 7 and 1 to 9 in the Y direction. So, that's an increase of 8. So, we know that two parts in the ratio two parts in the ratio is a movement of 7 to the right and 8 up. Now, I'm going to put it actually in a column vector, but you could just write seven right and eight up.

[00:35:21]One part of the ratio therefore, we divide both of these by two, it's going to be 3.5 and 4.

[00:35:30]And then three parts in the ratio three parts in the ratio is going to be three times by 3.5, which is 10.5. You can do that on the calculator. And four times by three, which is 12.

[00:35:43]Now, by doing this, we've worked out this distance here as 10.5 and this distance here as 12.

[00:35:50]And all that we need to do is we need to add 10.5 to our X coordinate here.

[00:35:56]So, the new X coordinate is going to be 14.5, which is 4 plus the 10.5.

[00:36:02]And then we add 12 to our Y coordinate of 9, which is going to be 21. So, we get 14.5 and 21. 14.5 and 21.

[00:36:18]Okay.

[00:36:20]>> [clears throat] >> Some Some people asking if I'm real or if I'm AI. Wow.

[00:36:27]>> [clears throat] >> Talk to me guys.

[00:36:40]Did we get it? Did it make sense? Mr. Lauren said I was so close. I got three marks. Carmel said I understand it now.

[00:36:46]Guys, let me know if you if it makes sense now for you.

[00:36:58]Fantastic.

[00:37:01]What guys? Sofas I understand the first part. Yeah, it's a tough one guys. It's a tough one.

[00:37:07]Okay, let's keep moving.

[00:37:10]Next up we're going to go to what's the time? 10 past.

[00:37:15]Um we're going to do We're going to do this one guys.

[00:37:25]Question 18.

[00:37:27]Question 18 is a four mark question.

[00:37:30]It's a tough one grade seven I would say.

[00:37:33]Grade six grade seven.

[00:37:41]A classic an absolute classic question.

[00:37:48]And now guys whilst you are all here I'm going to make a nice little announcement. All right? Oh no, no, I'm saving it for the end actually. I'm saving it for the end. Don't don't let me make it before the end.

[00:38:02]>> [laughter] >> Carmel says, "Yes, save the best for last." Absolutely. I almost got carried away and I almost said it too soon.

[00:38:36]Some of you will have seen on my stories, either on Instagram or Tik Tok, that I'm making an announcement on the socials on Friday. So, that's when it's going to hit everybody, but I'm going to tell you guys in advance cuz I have a question for you.

[00:38:52]Emily says, "Is this the cosine rule? It looks complicated." Okay, guys, let me come in with a little hint for this one, question 18, cuz we have jumped towards the end of the paper.

[00:39:00]So, understandably, and then Emily says, "And the sine rule as well."

[00:39:09]Yeah, exactly. So, how do we do this?

[00:39:11]So, what's my hint going to be?

[00:39:13]Calculate the length of QS.

[00:39:16]As soon as you see two triangles like this combined, you know that you're probably going to have to start with the triangle which is furthest away from the side length. So, we know we're going to start with this triangle.

[00:39:29]But, if we look at this second triangle, we need to work out QS. So, let me call that X first of all. Just so we can think about what we're working with.

[00:39:36]Now, we have a non-right angle triangle and we have a side length to work out. Straight away, I'm thinking cosine rule or sine rule. Then I need to decide which one.

[00:39:49]Well, I look at this and I think if I have all three of the angles, I can work out the side, but I don't have the third angle. I could work it out. Um Oh, sorry. Ignore that last little bit.

[00:40:03]Didn't mean that. Um but, basically, if we work out this side length, then we can use two pairs of opposites and use the sine rule. So, we need to work out this side length first, which we can do using this triangle, and then with two pairs of opposites, we can work out this one.

[00:40:25]Okay, I can see a couple of answers going in the chat.

[00:40:29]But yeah, guys, basically, we need to work out this side length.

[00:40:33]And I'll give another hint, actually, it's going to be the cosine rule up here.

[00:40:37]Which is then going to allow us to use the sine rule down here.

[00:40:43]If anybody needs the formula for the cosine rule or the sine rule, the formula for the cosine rule is a squared equals b squared plus c squared minus 2 b c cos a.

[00:41:10]That's our cosine rule.

[00:41:12]Then there's actually a couple of different versions of the sine rule.

[00:41:16]We're going to go for the one with the sides on the top, so a over sine a equals b over sine b.

[00:41:35]Oh, good question. No worries, Demolade.

[00:41:37]Great, great question. Um so, why do we not use half a b sine c, please? I'm forgetting the basics. Hey, but absolutely don't panic, it's a great question. The reason, as um Yep, 52 VV just said, is that half a b sine c is for the area. Half a b sine c is for the area.

[00:41:58]So, area equals half a b sine c is another formula which involves sine, but that one is only for area questions.

[00:42:08]Or questions that involve the area.

[00:42:17]>> Do we have any other questions in the chat, guys?

[00:42:31]>> [snorts] >> Ah, great question, Emily. Emily says, "Is when the little A above it, the side length for the length?"

[00:42:43]Yeah, so you know when I mentioned, guys, that there were two versions of the sine rule?

[00:42:48]Basically, in the sine rule, and also in the cosine rule, and in any triangle, the lowercase letters are the side lengths, and the uppercase letters are the angles. So, this is angle A, and opposite is side A. And this is angle B, and this is side B.

[00:43:06]Now, we can also, um, flip both sides of the fraction, if we want to, and we can get sine A over A equals sine B over B. Now, this is exactly the same formula. Exactly the same formula. The only difference is that this one makes it easier to find the angles because the angles are on the top. So, if you think about it, to find the angle here, all you have to do is move the A over to the other side, and then you have sine A, and you can do sine minus one of both sides. If the angle is on the bottom, you have to do a bit more rearranging to work out what you're trying to work out.

[00:43:50]So, two versions of the formula do the same thing.

[00:43:52]We just use them, we can use either of them in either situation, but it's just easier to use the one which has what you're looking for on the top.

[00:44:08]Yeah, no worries Emily. Great question.

[00:44:11]Are you ready for me to go through this one, guys?

[00:44:14]Let's get a quick ready in the chat for me, please. Also, if you want more time, just say more time in the chat.

[00:44:23]Mr. Loynes says, "Is it 4. or 7.63?"

[00:44:29]Misread that. 7.63 is an answer.

[00:44:36]Soft is ready.

[00:44:38]Mr. Loynes is ready.

[00:44:44]Okay, guys. Let's have a look then.

[00:44:46]Even though that wasn't many people saying ready considering there's 50 of us on.

[00:45:01]Anu is ready.

[00:45:07]Okay, guys. Let's have a look then.

[00:45:09]Question number 18. Now, this one is an absolute classic for papers two and three are calculator papers. Let's have a look. PQR and QRS are triangles.

[00:45:20]Calculate the length of QS. Give your answer correct to three significant figures. You must show all of your working. Now, we already said that in order to work out QS, we're going to firstly work out QR. Now, how can we work out QR in this case? We're looking for a side length and we're given two side lengths and the angle in between them. This is a classic cosine rule question.

[00:45:44]In the cosine rule, the angle that we have is A and small A is the side length opposite it.

[00:45:51]So, we can say that this is big A.

[00:45:53]This side length is small A and then the other two side lengths are B and C.

[00:45:57]Doesn't matter which one is which. Next, we can substitute all of our values in.

[00:46:00]So, we have a squared equals 9.4 squared plus 11 squared minus 2 * 11 * 9.4 * cos 27.

[00:46:18]Now, we can type all of this into the calculator on the right-hand side to make our lives a little bit easier.

[00:46:24]So, I can type in 9.4 squared plus 11 squared minus 2 * 9.4 * 11 * cos 27 and we get 25.

[00:46:38]25.

[00:46:40]00 99 Not 00, sorry. 0999 0999 and that is to 4 d.p. Now, why have I given this to so much accuracy? Well, it wants the final answer to three significant figures.

[00:46:56]So, I'm going to make sure that as I'm doing my working out, I do it to a large degree of accuracy.

[00:47:02]Next step to work out the value of a, we can do the square root of this. So, a is equal to the square root of 25.0999.

[00:47:14]I'm just going to do the square root of answer on the calculator and that is going to give us 5.

[00:47:20]0099 etc. And I'm going to round this one to 5.00 1.

[00:47:31]Now, the reason I've done this to one is because the 99 makes it very close to 5.001.

[00:47:37]Now that we have Sorry, not 001.

[00:47:42]That was a little silly mistake. I meant 5.01.

[00:47:46]Little silly mistake. So, um the nine causes the nine to round up, but the 99 makes it very close to this.

[00:47:52]So, a then is 5.001 5.01.

[00:47:59]5.01 And now I can have a look at what I can do. And we already said when we were planning this question out that we could use the sine rule. Now, in the sine rule, we have two pairs of opposites.

[00:48:11]So, we have an opposite angle and side and an opposite angle and side.

[00:48:16]And we said that we want to use the one where the lowercase letters are on the top. So, the next thing that I'm going to do is I'm going to relabel all of my side lengths as A, B, and C. So, I'm going to forget about these ones for now.

[00:48:27]And just to make it clear, I'm going to switch to a different color. So, I'm going to label this one angle A.

[00:48:33]And the side length opposite it as small A.

[00:48:36]And then this angle as angle B and the side length opposite it as lowercase B.

[00:48:43]Next step, we can substitute all of our values into our sine rule. So, we're going to have X over sin 88 sin 88 equals um 5.01 5.01 over sin 41.

[00:49:03]Now, how do I work out the value of X then? Well, the value of X simply is going to be what we get when we move this sin 88 to the other side so that the X is on its own.

[00:49:15]How do we move the sin 88? Well, at the moment, we're dividing by sin 88. So, I'm going to times both sides by sin 88 * sin 88 * sin 88.

[00:49:26]On the left-hand side, we're going to have X. On the right-hand side, 5.01 over sin 41 times by sin 88.

[00:49:38]And now I'm going to plug this into my calculator.

[00:49:41]So, fraction 5.01 over sin 41 times sin 88.

[00:49:51]And make sure you close your brackets, guys, if you have them on your calculator.

[00:49:59]And we get 7.63.

[00:50:03]7.631 8 etc. Giving it to three significant figures.

[00:50:12]Remember guys, our first significant figure is our first number which is not a zero. So, this is the first significant figure.

[00:50:19]That means this is the second, this is the third. To round it to three significant figures, we need to look at our fourth one.

[00:50:26]And that decides whether we round it down or round it up. We have a one as our fourth significant figure, so we round down.

[00:50:33]And we get 7.63 as our answer to three significant figures. Guys, how did we find it? Did it make sense?

[00:50:45]I know that one was long.

[00:50:47]But if you stuck with me, maybe it made sense.

[00:50:50]What do you think?

[00:50:54]Guys, I'm just going to quickly close the window because it started raining.

[00:50:57]Just give me a sec.

[00:51:01]I'm expecting lots of people's feedback in the chat when I come back.

[00:51:13]Anu says it makes more sense now. Emily said, "I got it." Emily, you can tell you've been in the group tutoring, eh?

[00:51:19]>> [laughter] >> Good work. Zain got it. Nice. Alicia Malik said it makes sense. Fantastic, Alicia.

[00:51:25]Um okay. Where should we Okay.

[00:51:32]Would you guys like to do one more question? Or shall I make the announcement now and ask you guys about it? Let's see.

[00:51:39]One more question? I know some of you are going to want to finish.

[00:51:47]And I know you want to do some English revision because I know you want to do some English revision.

[00:51:55]But you also don't want to miss out on the live stream. So, we're going to go with a poll and I am going to go with the majority.

[00:52:06]Okay, it's okay. It was very clear. 16 people have voted. 18 people have voted.

[00:52:11]Most people are saying one more. Guys, let's do one more question. I'm not going to do a long one.

[00:52:18]>> [clears throat] >> Let's do Let's do Let's do Let's do Let's do question 14. Question 14 is going to be our final question of the day.

[00:52:33]And then it is announcement time.

[00:52:56]A and J says, "Hi, could you please tell me what paper and year this is?" This is June 2022 paper two higher tier.

[00:53:07]I can see a couple of answers in there already.

[00:53:11]Take your time with it though, guys.

[00:53:13]Alicia says, "Is this the product rule?"

[00:53:16]It's not the product rule. I can see why you thought it was the product rule, but it's not the product rule. This one, guys, is actually capture-recapture.

[00:53:27]Capture-recapture.

[00:53:53]>> Anu says, "What is that?"

[00:53:55]Don't worry, Anu. We're going to talk about it.

[00:54:01]Oh, guys, an absolute bop of a tune just came on.

[00:54:05]I've not heard this in a long time. You guys know Hold You by Gyptian?

[00:54:11]It's a little bit of like a >> [laughter] >> That's an old song.

[00:54:20]Absolute bop, though. This is such a throwback. Such a throwback.

[00:54:27]That is not my normal type of music that I listen to while I'm live, but it just came on out of nowhere, and it got me.

[00:54:38]Hey, Aiden Shaji.

[00:54:42]>> [laughter] >> Very old-school tune.

[00:54:52]So, Saffron, Saffron, Saffron.

[00:55:07]Let's have a look together then, guys.

[00:55:09]So, the question, our last one of the day, says, "Saffron wants to work out an estimate for the total number of fish in a lake.

[00:55:19]On Friday, she catches 180 fish from the lake. As soon as you hear catches, probably capture-recapture. She puts a tag on them. Now, it's definitely capture-recapture.

[00:55:29]Um and then puts them back into the lake. On Saturday, Saffron catches 305 of the fish from the lake. 45 of them are tagged.

[00:55:38]Um work out an estimate for the total number of fish in the lake. Now, the way that capture recapture works is it looks at what fraction of the total fish we think we have tagged. Now, you know when she recatches the fish, 45 of the 305 of them are tagged.

[00:55:57]So, we would expect that the fraction, if this sample represents all of the fish in the um lake, we would expect that the fraction that are tagged is probably 45 over 305.

[00:56:10]So, 45 305ths of them are tagged.

[00:56:16]Now, what fraction did we tag?

[00:56:19]Well, we tagged 180 out of the total, which I'm going to call T.

[00:56:28]So, in order to work out an estimate for the total, we need to just rearrange this equation to work out T. This is the fraction that we think we've tagged.

[00:56:38]This is the fraction that we actually have tagged. So, we think the fraction that we've tagged is 45 over 305, but we don't have T, so we need to rearrange to work out T.

[00:56:50]So, how do we rearrange to work out T?

[00:56:52]Well, at the moment, T is on the bottom of a fraction, which we don't like. So, I'm going to times both sides by T, and I'm going to get T times by 45 over 305 equals 180. Now, to get T on its own, I'm going to divide both sides by 45 over 305. So, T equals 180 divided by 45 over 305.

[00:57:21]And I can type this into the calculator, and let's see what we get. 180 divided by fraction 45 over 305.

[00:57:32]Not 3.5 3.05 and we get 1,220 as our total. 1,220 as our total.

[00:57:47]Guys, that is our final question of the day. Let me know, did it make sense when I went through it? If anybody didn't get it, but understands it now, please let me know in the chat and just say makes sense now.

[00:58:11]Nice Carmel, good work.

[00:58:19]Nice Aisha.

[00:58:30]Guys, is it announcement time?

[00:58:34]Yeah, fantastic. Mr. Loynd says it makes sense now.

[00:58:41]Guys, let's get a little drum roll in the chat. Let's build some excitement.

[00:58:45]Let's get a little drum drum roll in the chat for me.

[00:58:49]If anybody can find the drum roll emoji, or you can get a lightning bolt emoji or whatever your favorite emoji is.

[00:58:56]I want to build up a little bit for this.

[00:58:58]>> [laughter] >> Emily's in there with the drum roll, Carmel with the drum roll, Porsche with the drum roll, Loynd with the drum roll.

[00:59:19]Hey hyperfocus, you were late, buddy.

[00:59:25]Anu with the drum roll, Emily with the drum roll.

[00:59:29]Okay.

[00:59:30]Guys, I am going to be doing a completely free boot camp over half term.

[00:59:38]I'm going to be doing a completely free boot camp over half term.

[00:59:42]Right here on YouTube.

[00:59:44]What it's going to involve is I'm going to go live five days in a row.

[00:59:49]From Tuesday until Saturday.

[00:59:57]Doing live GCSE maths revision. Getting you guys ready for paper two.

[01:00:11]Serenity says yay. Alicia says OMG yay yay.

[01:00:15]>> [laughter] >> My pleasure.

[01:00:18]Aiden celebrating. Serenity's going to Germany this half term. Hyperfocus is celebrating with the lightning bolt emojis.

[01:00:26]Alizein says thank you. Zane in there with the bolts.

[01:00:32]And I guys have a question for you.

[01:00:37]And that question is what is the best time?

[01:00:43]What is the best time? So we're going to be doing five sessions.

[01:00:48]Satur- Tuesday until Saturday.

[01:00:51]But I need to decide what time of the day is best to do the sessions.

[01:00:55]Now it's definitely going to be before 5:00.

[01:01:03]We need to decide whether we're going to do the morning.

[01:01:07]So 11:00 till 12:00.

[01:01:09]Whether we're going to do a bit later in the day. So 3:00 till 4:00. Or whether we're going to do lunch time.

[01:01:17]So it's definitely going to be in the afternoon or the morning.

[01:01:21]And I'm going to set up a quick poll and I'm going to see what you guys think.

[01:01:29]But guys, don't tell anyone because the announcement for this is being made on social media on Friday.

[01:01:36]So, are we looking at um let me set up this poll.

[01:01:47]Just so I have a sense of what you guys think.

[01:01:57]We have 11 till 12. We have 3 till 4.

[01:02:01]Both close in the poll. 3 till 4 is winning.

[01:02:08]And this is going to be from Tuesday till Saturday even.

[01:02:25]Oh, Emily says I won't be home for the later ones.

[01:02:29]Emily, you're in the group tutoring though. So, don't worry Emily, you still have group tutoring. So, that's that's even better than the even better than the boot camp.

[01:02:38]Cuz it's a smaller group. Um so, don't worry about it. Don't worry about it.

[01:02:44]But yeah, 3 till 4 is winning. And honestly, 3 till 4 is the best time for me.

[01:02:48]Um portion enthusiast says, will they be uploaded to your YouTube? Yes, they will.

[01:02:56]Yes, they will.

[01:02:58]All of the live sessions guys are recorded and uploaded straight to the YouTube channel.

[01:03:06]No, Emily, don't stress, please.

[01:03:09]>> [laughter] >> You But you can come to the evening ones, right? The group tutoring from 1/2 5 till 1/2 6.

[01:03:28]>> [snorts] >> Aleshin says, is it the same as these questions? Yes, in general the format is going to be that we're going to be working on past paper questions, the most important ones for paper two and three.

[01:03:59]Emily says, yeah, but on Friday and Saturday, I'm out till later.

[01:04:09]Okay, we're going to find a way to make it work. Don't worry. We're going to find a way to make it work.

[01:04:15]So, 3:00 p.m. to 4:00 p.m. it is, guys.

[01:04:18]3:00 p.m. to 4:00 p.m.

[01:04:20]the boot camp will be running over half term, which I'm very excited about. I've never done this before, and I think it could make a huge difference to your grades.

[01:04:30]Now, if you want more support, we also have the small group tutoring. So, if you go to my website mygcsemaths.com, £20 a week for the Tuesday, Wednesday, and Thursday evening sessions. They're still going to be running this week. So, tomorrow, um yeah, tomorrow, Wednesday, and Thursday.

[01:04:51]Um and we also have the night before classes. So, the spaces are filling up quite quickly, um and I am capping the number of spaces so we can make it really good. If you were studying with me for um paper one, it's the same format, 4 hours together the night before the exam, so you can sign up using the QR code there if you want. Or if you have any questions, you can send me an email [email protected], and I can uh can answer those for you.

[01:05:17]Alicia says, "I can't wait." And guys, I'm going to be promoting it a lot over the coming week, but you guys are the only people who know.

[01:05:26]Carmel says, "It's next week exactly."

[01:05:33]Ali Zine says, "Matt, thanks a lot. I have a math tuition teacher, and I guess this is going to help even more. You really helped me with paper one by going through these questions. Wish me good luck for tomorrow." Hey, good luck for tomorrow.

[01:05:45]Good luck to everybody for English tomorrow, if you're sitting English tomorrow. And honestly, Ali Zine, um hopefully you have a brilliant tutor.

[01:05:53]You said that this might be helping more. I do have the group tutoring, which is like my alternative to private tuition. Um so, you can sign up to that one if you want to on the website. It's also half the price.

[01:06:33]Banana Split says, "I feel like the grade boundaries are going to be high."

[01:06:35]Nobody knows yet. Nobody knows yet.

[01:06:40]Especially until paper two and three. We don't know whether we're going to get easier papers, more difficult papers, and it will all depend on that.

[01:06:55]Ah, fantastic, Emily. Fantastic.

[01:07:01]>> [laughter] >> Yeah, we're definitely we're definitely shifting the grade boundaries somewhat.

[01:07:05]But bear in mind, guys, that it's still 800,000 people who do GCSEs every year, and we don't have 800,000 people on the live, that's for sure.

[01:07:15]Um So, we're not moving the grade boundaries that much.

[01:07:19]Okay, guys. I know you want to go and revise English.

[01:07:23]So, I would I will say goodbye for this evening. Um if you're in the group tutoring, I'll see you tomorrow evening.

[01:07:30]Otherwise, I might do a cheeky live on Friday when I announce to the boot camp when I start marketing it. Um otherwise, I'll probably do a live on Saturday or Sunday or something. Um just to uh Yeah, just to announce everything and get everybody ready for next week.

[01:07:51]Thank you, Emily. Goodbye.

[01:07:53]And good luck for tomorrow. Thank you, Anu.

[01:07:57]Goodbye, Yaseen.

[01:07:58]Goodbye, Alicia.

[01:08:02]Goodbye, banana split.

[01:08:04]Goodbye, Mr. Aloyan.

[01:08:10]Goodbye, everybody. Good luck for tomorrow, and I'll see you in the next one.

[01:08:15]That's all from me tonight. Ciao for now.