Hodgmaths Predicted Paper 1F for Edexcel

Added: 2026-05-15

[00:05:33]Testing. Testing.

[00:13:51]Evening all. Thanks for joining. Uh this evening I'll be going through a predicted paper that I've written based on what I think is most likely to come up uh on the exam tomorrow morning. Uh if you want me to clarify anything, go through it a bit slower. go to it again.

[00:14:08]Uh I'm on the teams page uh on a different screen. So I will see your message come up uh straight away. Uh and big shout out to all of my year eights and year nines who have logged on to the stream. Uh really appreciate you joining to get my numbers up.

[00:14:24]So if you're aiming for a grade four tomorrow, we're looking to get around about 48 to 50 marks per pay paper. So that's what we're aiming for today. um making sure that we've got uh at least 48 marks absolutely guaranteed in the bag and that will uh secure us our pass.

[00:14:46]As you're probably sick of me hearing in class, it is absolutely vital we get the first page perfect. Take your time on these uh questions on the first page. Uh they are not um one mark on page one is worth the same as one mark on page 30.

[00:15:02]Okay. So, we're going to take our time and make sure it's absolutely perfect, even though the questions might seem easy at the beginning.

[00:15:10]So, a little bit grammar you got to know for the first one is that 1 cm is 10 mm.

[00:15:20]Therefore, 30 cm multiplied up by 30 is 300 mm.

[00:15:29]And we're getting one mark for the um correct answer only.

[00:15:35]Next question asked for two factors of 15. Now I know many of you can often get your factors and multiples confused. So what I want you to do is memorize that a factor is a number that 15 can divide by. So we're looking for two numbers that 15 can divide by and not leave a decimal. So, we know that 15 can divide by one because every number can.

[00:16:01]It can't divide by two because it's not an even number.

[00:16:05]It can divide by three. So, it's in the 15 in the three times tables. It's not in the fours. It is in the fives because it ends in a five. And we've got 15 itself.

[00:16:17]And we just have to pick any two of those to get that mark.

[00:16:23]Right. We now uh look at this list of numbers 14 through 20 and we want to find a first of all a prime number.

[00:16:32]So what I notic is that a lot of you that are aiming for grade four, you're really good at the product of prime factors later on in the paper. And yet when I say identify a prime number, um that's when it gets a bit trickier. So, what I'm going to do is for each number, it might seem like I'm we're taking the long way round, but once you start to get the hang of it, it get a bit quicker, right? Can I do this?

[00:16:56]So, for 14, yes, I can. So, it's not a prime number. 15, yes, I can. So, it's not a prime number. And I'm going to repeat that process until I get to 17 where I find there's nothing else that goes into it other than one and 17. So 17 is a prime number.

[00:17:16]We could also have 19 in that as well.

[00:17:18]That would also be correct.

[00:17:20]A square number is again if you can't memorize these by tomorrow morning that's absolutely fine. We can uh list our square numbers. So one squared means 1* 1 which is one. So one's a square number. 2^ 2 means 2 * 2 which is 4. 3 squar 3 * 3 9. I'm going to repeat this process until we've got a little list of our square numbers there.

[00:17:45]Now I can see that 16 is in my list. So my square number is 16.

[00:17:54]A multiple of seven means which number is in the seven times tables. So factor the number goes into it. A multiple is in the times tables.

[00:18:04]So which of these numbers appears in seven times tables? It's only 14.

[00:18:14]Question four asks us to uh it's an average question this one. So we're looking at three different types of averages.

[00:18:21]First one is the median, which means a middle number. Now when I wrote this question, I put them in order for you. I don't think anyone's getting to tomorrow's exam without being able to order some positive integers. And what we're going to do is we're going to find the middle number. So I've got I'm going to cross them off till I get to the middle, but I find out that it's between 10 and 11.

[00:18:43]So I'm therefore going to find the number that's halfway between them, which is going to be 10.5.

[00:18:50]If you struggle to do that, what you can do is add the two numbers together. 10 add 11 is 21 and then half it for 10.5.

[00:18:59]The mode is the most common number. So, which number appears in that list uh most often? Eight is the most common number and the range is the biggest number subtract the smallest number. So, we're going to do 20 subtract seven which is 13.

[00:19:18]If you got four marks in that first page, that's six out of the 48. We need to secure it. So, we're well on our way.

[00:19:30]This is the question we're praying for.

[00:19:34]It says, "A color of a group of vehicles is recorded below. It's about cars and vans or whatever." And it says, "Draw a suitable graph." It doesn't tell you what type of graph to draw. This is where the examiner can be a little bit of a pain and they're not actually signposting you what graph to draw. So, yeah, you could do line graphs, you could do all sorts, but if you given the choice, you should be looking to do a bar graph. So, we're going to start off up the side is going to be our frequency, the number of each vehicle.

[00:20:02]And it's usually just going up in ones or twos. If you go up in twos, this on this it will be absolutely fine. If you go up in fives, you're not going to be able to see it.

[00:20:13]Go up in the smallest number you can you can get away with, which in our case, the biggest number there is seven. So, I know my scale needs to go up to a minimum of eight.

[00:20:23]So, taking our sweet time to put each of the numbers up to eight or further if you wish on that scale up the side.

[00:20:35]I know this might seem really obvious, but a frequent mistake that uh students make in this is forgetting a number like they just go straight from six to eight.

[00:20:43]It's really important that you get those numbers in order and label it as frequency.

[00:20:53]you can lose a m depending on how harsh a mark scheme is. You can lose a mark if you don't write the word frequency up the side there. So along the bottom we're going to do each color separately.

[00:21:03]So I'm going to uh do red first. No particular you could do it in any order you want. You won't lose a mark. And I'm going to choose to do the cars first and then the vans. It doesn't matter which one I choose to do first as long as I uh maintain that order throughout.

[00:21:20]I'm going to leave a gap to start at the beginning and then I'm going to do the cards which go up to seven.

[00:21:30]Obviously using a ruler for this tomorrow and that's my card up to seven.

[00:21:37]Attached to it the fans goes up to six. And that's my red ones done.

[00:21:49]I'm going to leave a gap before I do the one after that.

[00:21:54]So, the next one I'm going to do is a black one. So, I'm leave a gap of one.

[00:21:58]You can leave a gap of whatever you want as long as it's consistent. So, I'm choosing to leave a gap of one. If you have done two or whatever, that's fine.

[00:22:07]On a dual bar chart like this, you must leave a gap. Okay? It must have a gap between um this the different colors. So this time we're going four five and that we're going to label that black.

[00:22:29]We're going to silver is 33. Nice easy one. They're both the same.

[00:22:37]And white is just going to be that one there. Now notice we don't need to write anything for white vans that there weren't any. Now I we're just missing one thing. We have to state which ones are the uh cars and which ones are the vans. So what we're going to do is we're going to shade one of them in.

[00:22:59]So I'm going to say my shaded one is a car and my unshaded one is the van. Now if it did that I could do it other way around. So I could write the 76 as 67 if I preferred, but I as long as I do the car, then the van all the way, it's absolutely fine.

[00:23:15]So shade them in.

[00:23:21]And that's done. Form some of the easiest formats you're ever going to get.

[00:23:29]I've missed something out there. I've not labeled my last color.

[00:23:36]And I'm done. That is perfect.

[00:23:48]Okay, the next one we're ordering these decimal numbers.

[00:23:53]Now, what I've done here is that I've not put the same number a decimal points after each uh number that I've written.

[00:24:01]So, this one has two after decimal points, three, two, one, and so on.

[00:24:05]We're going to make them all have the same I'm going to make them all have three numbers after the decimal point by just chucking in some zeros there.

[00:24:15]So now what I can almost do is ignore that uh that decimal point and say right that's 67 that's 6700 670 607 and uh 670 and now it becomes much clearer what the order is clearly 67 is the lowest one I'm going to write what the original is the original was 0.067 067.

[00:24:44]I'm going to cross it out when I'm when I'm done with it so I don't duplicate it. My next most one is 607 0.607 then 670 which is uh 0.67.

[00:25:04]I've I if I wrote this zero here it would still be correct but this is no need to.

[00:25:12]Next is 670. The original was 6.07.

[00:25:16]And finally, the one at the end 6.7. We're going to grab two marks if it's perfect. We're going to grab one mark if three of them are in the correct order.

[00:25:33]Okay. Next one. Question seven is on some basic uh simplify algebraic questions.

[00:25:40]We're going to uh take a quick moment to look at the wording. So simplify means we don't know what x or y is. We don't care what they are. We're just going to we're not our answer is going to have an al some algebra in it. So 3 * 4 is 12.

[00:25:58]And I've got that x there. That's my final answer. I can't do anything else with that.

[00:26:04]12 y / 2. 12 / 2 is 6. And that doesn't affect the y.

[00:26:13]And f now we've got the most common one, collecting like terms. So this is where they like to put the negatives in there.

[00:26:19]So let's just look at the x's to start with. So I have 4x subtract 3x. That gets me 1 x. If you don't write the one, that's absolutely fine.

[00:26:30]Now I have 6 y subtract 11 y.

[00:26:38]So 6 subtract 11 is -5 y and that is our final answer. There's nothing else I can do with that.

[00:26:49]Obviously if you wrote it without the one that is absolutely fine as well.

[00:26:55]Just remember we can't um combine the x's and y's and the regular numbers. We leave them completely separate.

[00:27:08]Okay, next one. There is going to be a whole lot of money problem solving on there tomorrow. So, we expect to see between 15 and 20 marks on uh each of the papers. That's just pure um money problem solving.

[00:27:22]So, this one I've put in a little bit of um percentage of ratio in there just to pat it out because we no idea what topics it might come at us with. So, first of all, we read the question carefully. Ashton, Ch, Charlie, and Jamie each share 720 pound between them.

[00:27:36]Ashton gets 25%. So, we're going to do 25% um without a calculator. And there's a bunch of ways you can do it. So, if you know that 25% is divide by four, great.

[00:27:49]If you don't know that, we're going to do this method. So, we're doing 25% of 720.

[00:27:57]10% is 72.

[00:28:00]I'm going to need two of them to make 20%.

[00:28:03]And 5% is just going to be half of that, which is 36. Add them all together and we get 180. So Ashton's getting £180.

[00:28:16]We're going to label it really carefully to make sure I know that's the amount of money I'm dealing with. Right, Charlie and Jamie share the in the ratio 2 to 7.

[00:28:26]So our first step is going to add two and seven together to get nine.

[00:28:32]They share the remaining money. So we're going to do 720 subtract 180 to get me 540.

[00:28:40]And we're sharing 540 in the ratio 27.

[00:28:43]So we're going to do 540 divided by 9 is 60.

[00:28:49]So Charlie gets two of those which is going to be 120.

[00:28:55]and Jamie. So, Jamie gets uh 6 G time 7, which is 420.

[00:29:04]But we're interested in how much more Ashton gets than Charlie. So, Charlie's got uh 120.

[00:29:10]Ashton's got 180.

[00:29:14]Take him away and we get 60 in total.

[00:29:23]Okay, next one is an expand and simplify question. Now, notice there's not the word solve in that. We don't know what x is and we don't care what x is. So, I'm going to start by expanding the brackets. 4 * 2x is 8x.

[00:29:38]4 * 3 is 12. We're sticking a negative between that. You've already got one mark if you wrote that.

[00:29:46]Same with other side. 5 * x is 5 x 5 * 1 is 5.

[00:29:53]Now I've done that, I can gather together my x's. 8 x add 5x is 13x.

[00:30:02]-12 add 5 is -7.

[00:30:08]We can't combine those. So that is our final answer.

[00:30:24]Okay, the next one is a mean question.

[00:30:30]So, five number cards uh are shown below. The mean of seven numbers is uh mean of the five numbers is seven. Find the value of the blank card. So basically we know all of these added together divided by five is seven. Just going to go back uh for someone for question eight.

[00:30:54]So the answer to question eight was 60 at the end. I'll leave it up for a second.

[00:31:14]Okay, so I know all these added together divided by five is seven. We know we're dividing by five because there's five numbers including the blank one we're trying to figure out. So what I can do now is I can start making a an equation out of this. six add five add 1 add 9 gets me 21.

[00:31:37]So 21 add something divided by 5 = 7. So I'm going to solve this like a regular equation. The opposite of divide by 5 is times by five. 21 add something is 35. I got that 35 because 5 * 7 is 35.

[00:31:54]21 add something is 35. 21 add 14.

[00:31:59]is uh 35.

[00:32:13]Where did the five come from? Uh so the the 21 came came from adding these together. 6 add five is 11. 12 21.

[00:32:24]The five I divided by five because there were five numbers in total including the blank one. So one, two, three, four, five. That's where the five came from.

[00:32:41]Okay, moving on.

[00:32:50]So got a few questions.

[00:32:56]Um yes, I will be doing um additional live streams if there's uh appetite for it. If people uh want me to do them, I'm more than happy to do that.

[00:33:11]Uh right, next one. So next two terms of this sequence, I can see the sequence is going up in sevens. I'm adding seven each time. So this is going to make the next one 39 when I add seven to 32 and then 46.

[00:33:33]The 10th term is exactly the same skill. I'm just going to keep going. So I go up to the seventh term there because it's just, you know, four is the first term, 11 the second term and so on. So I'm just going to keep going. So the one after that would be 53 60 and then 67.

[00:33:54]So 67 67 is my answer.

[00:33:59][clears throat] The nth term of the sequence.

[00:34:03]Now it's going up in sevens. So I'm going to write 7 n the number that would appear below four. So what number go there? What number when it adds seven to it gets me four -3? So it's 7 n subtract three.

[00:34:26]Right. Olivia says that the number 130 does appear in this sequence. Is she correct? So what we're going to do, we're going to grab a mark straight away for writing 3 7 n subtract 3 equals 130.

[00:34:40]So that's one mark in the bag already.

[00:34:42]We're now going to solve that. If n is a whole number, then it is in a sequence.

[00:34:48]If n is not in um if n is a decimal, then it's not. So, let's solve it. Let's add three to both sides. 7 n = 133.

[00:35:02]Right, I'm just going to go back to the nth term because it's I can't um few people asking me about it. Right.

[00:35:10]The seven n is because it's the sequence is going up in sevens. If it was going up in fives, it would be uh 5n.

[00:35:19]What the -3 is the number that would if I carried the sequence on one space to the left, it would be it's just that number. So I'll be asking what number is uh do I when I add seven to it gets me four.

[00:35:39]I'll just do another example of that.

[00:35:41]So, let's say I had um 11 16 21.

[00:35:52]So, I get a few messages in the chat.

[00:35:54]Just give me a moment. I'll answer all of them. So, this n term of this one would be 5 n because it's going up in fives.

[00:36:03]And the number that would appear before the 11. So what number would I add five to it gets me 11? It would be six. And in this case it would be positive six, not negative. So that's how I do the n term.

[00:36:25]Um the person that's messaged me about the 64, could you be more specific, please? Which question are you looking at? Question 11 B.

[00:36:47]I'll come back to that one. I think might be a little bit of delay in the chat.

[00:36:55]So, back to this one at the end, the end turn one. Um no the nth term is it's 7 n cuz it's going up in sevens subtract three because -3 will be the number um before um the four. So I subtracted if four subtract seven that's where the neg3 will have come from. Now I can't actually figure anything out with that.

[00:37:25]That's just the se the term for the whole um uh the whole sequence. Right, moving on.

[00:37:36]So, going back to this one. So, all I do is set my nth term. Now, even if you got this one wrong and you set it equal to 130, you're still grabbing a mark there.

[00:37:45]We're going to solve it by adding three to both sides to that undo that um subtract three.

[00:37:52]And now I'm going to do 133 divided by 7.

[00:37:58]I'm hoping that we can do bus stop method.

[00:38:02]If you can't do bus stop method tomorrow morning, I want you to count up. We're going to keep counting in sevens. Yeah, it'll take a while. Yeah, it'll um be messy, but you are guaranteed to get the mark.

[00:38:16]Bus stop method obviously much more um efficient use your time. Seven goes into one zero times. Carry the one.

[00:38:28]Seven goes into 13 once with six left over. Seven goes into 63 nine times with none left over. So I've got 19 as my answer. So it's a uh 130 would be the 19th term. 19 is a whole number. So, is she correct? Massive conclusion. Yes, she is. Because 19 is a whole number.

[00:39:02]Right. This time we're on a solve question.

[00:39:08]When we do a solve question, we are expecting our answer to say at the end x equals and then have a number.

[00:39:19]We're dropping a line down the middle. I know some of you in my some of my colleagues class, you do a line down the side. Whatever is working for you, you stick with that. I like to get rid of my x's first. I want to get rid of this subtract 3x. I'm going to add 3x to both sides.

[00:39:36]That gives me 11x subtract 5 = 72.

[00:39:42]I'm going to add five to both sides.

[00:39:46]11x is 77.

[00:39:50]And finally, we're going to divide by 11.

[00:39:53]So, I get a final answer of x = 7.

[00:39:58]We grab one mark for any two of these done correctly. And our third mark for the correct answer, x= 7.

[00:40:10]Where's the 11 come from? So I added 3x to both sides because that's the opposite of subtract 3x.

[00:40:20]8x add 3x is 11x.

[00:40:25]It then didn't get touched when I did the opposite of subtract five, which is add five.

[00:40:32]So then I end up with 11x = 77. I divide by that 11 to get 1 x, which is what I want for my final answer, equals 7. And that's it.

[00:40:51]Okay, the next one, the probability one. Jeff spins a spinner bias forided spinner.

[00:40:59]Biased means unfair. So, we know we're not expecting to land on each one a quarter the time. So, on the mock we did, that was one that was done uh particularly poorly because a lot of you just wrote, "Yeah, it was a coin. It should be half and half." And it wasn't.

[00:41:10]It said biased. So, this is uh that means we're not expecting the same number in every box. We know these add to make one whole one. You are going to grab one mark by showing some sort of understanding that they should all add to make one.

[00:41:27]So, what I'm going to do is going to add together to that I know and that gets me 0.60.

[00:41:35]You won't lose a mark if you don't write that zero.

[00:41:40]I'm going to subtract that from one whole one.

[00:41:46]So I know these two add together to make 0.4 or 0.40.

[00:41:51]It tells me in the question that they're the same.

[00:41:57]So, I'm going to divide it by two to get me 0.2.

[00:42:04]If you uh when I saw a few of you uh doing this test um before a lot of uh yeah, I'll do another probability one in just a moment.

[00:42:16]So, um I'm in the gym before we go into the exam hall. Um, I can't actually go into the sports hall, so I'm not allowed in the actual room where you do the exam, but I can be in the room where you you get ready and find your numbers and that, I think.

[00:42:35]>> Okay. Um, I want to do another one of these in just a moment, so don't worry if you're struggling. The spawner is spun 60 times. How many times would you expect it to land on green? So, we're going to do 60 times by 0.25.

[00:42:51]And this gets me. So there's a couple ways I can do this one. I can either say I know that 0.25 is a quarter and I can do a quarter of 60 and get 15 or I can do 60 * 25 and uh that will get me 1,500 and then divide that by 100. So a bunch of different ways of doing that. Uh few comments in the chat. Uh yes, I'll be revising in my room from 8:00 a.m.

[00:43:20]tomorrow morning. Um and thank you for people that tell me they're watching the live stream. Really appreciate that.

[00:43:35]Right, I'm going to do another one of the probability questions.

[00:43:38]They are quite likely to come up.

[00:43:49]So, it will have most likely a table and um so it might say like like three different colors and it'll have a few of them filled in and one left for you to fill in yourself.

[00:44:13]Right. So basically we're grabbing a mark for understanding that they should all add to one. So that 0.3 add 0.2 add 0.1 add something is one whole one.

[00:44:34]So I'm going to simplify this bit to get 0.6.

[00:44:39]So 0.6 6 add something is one whole one and I can figure that out by doing 1 take away 0.6 is 0.4 and that would be my answer.

[00:44:54]I will do a few more of these tomorrow morning if you if that would be helpful for you.

[00:45:16]Okay, go on to adding fractions, which is I know it's a bug be there for a lot of you, but we're going to uh yes, I'm doing revision before the exam. So, be in uh my room uh from 8:00 a.m. in the morning and I'll be uh revising uh most likely um appearing um foundation topics.

[00:45:43]Right. So, we're going to grab one mark for multiplying the two denominators, the two bottom numbers. If I was marking this as an examiner and I see a fraction with 15 on the bottom, I'm grabbing a mark straight away.

[00:46:00]I got that 15 by doing five * 3 because I multiplied the five by three to get the 15 and multiplying the four by three to get 12.

[00:46:15]I multiplied the three by five to get 15. So multiply the two by five to get 10. Now I've got my two top numbers bottom numbers the same. I can add my top ones. This gives me 22 out of 15.

[00:46:33]It doesn't ask you to in this question, but we're going to do it anyway. We're going to convert it into a mixed number.

[00:46:40]You would get the full marks for that because it doesn't tell you to. But let's practice just in case. 15 goes into 22 once with seven left over.

[00:46:52]And that's our final answer.

[00:47:02]Right. Dividing fractions is easier but just with a bit more for you to remember.

[00:47:09]I keep the first fraction. I change the divide to a times and I flip the fraction on the right. I only flip the fraction on the right, not both of them. So, keep it, change it, flip it.

[00:47:26]I can now multiply my top two numbers to get me seven, multiply my bottom two numbers to get me 18. There's now else I can do with that.

[00:47:36]So, that one's finished.

[00:47:38]You're going to grab one mark for uh changing that to a times and flipping that and one mark for correct answer only.

[00:47:47]We're trying not to call it KFC anymore because it's kind of like that would be keep it, flip it, change it. But if you're getting that right, you know, you do you.

[00:48:07]Okay, little bit of algebraic simplification here.

[00:48:10]So, when we're multiplying, we add the top two.

[00:48:15]We're just going to add seven and five to get x ^ 12. Again, it says simplify, so we're expecting our answer to have an x in it.

[00:48:33]Divide. Now, I've made this question annoying because it looks like they should divide those two numbers, but we're not. We're going to subtract them.

[00:48:41]When I divide, I subtract the powers. So I should have a to the power of 64 as my final answer.

[00:48:55]And this one I'm going to multiply my powers.

[00:48:59]So I get B5 six. I get B to the power of 30.

[00:49:32]Right. The last one. I want you to put your brains in screenshot mode.

[00:49:35]Anything. Anything Anything to the power of zero is one. Any number to the power of zero is one.

[00:49:55]Okay. The next one is a angles and parallel lines. One, you can get all the marks by writing on your uh diagram. uh we're told as examiners that you are much much more likely to gain marks if you write on your diagram and we can grab two marks for doing a grade one skill on this grade four question. And I'm going to do that straight away by saying I know this one is 68 because there's 180 degrees on a straight line.

[00:50:28]That is two two marks. I know it looks way too easy. That's two. One correct angle, uh, one correct, um, reasoning to go with it.

[00:50:39]Now, there's a whole bunch of ways to tackle these questions.

[00:50:44]I'm going to start by saying that these two little lines here mean this is my absolute favorite type of triangle. This is an isosles triangle. That makes this one up here 68 as well.

[00:50:58]And we can write that in face angles in an isosles triangle are equal.

[00:51:19]So my next bit is I can fill in this angle here by saying that these two are alternate.

[00:51:34]So alternate angles are equal.

[00:51:39]Now still a whole bunch of ways of doing this. I can now say these two are alternate and equal.

[00:51:47]So my aunt X is 68.

[00:51:50]Now you don't have to write the same reason multiple times. Now the advice I always give is if you just fill in the entire diagram, you will not uh you are guaranteed to get the marks. You fill in the entire diagram, write a bunch of different reasoning down. Um obviously try and make sure it's um you know logically fits.

[00:52:11]Uh you are guaranteed to get you know the full marks. So, um, in this one, if I just wrote in that this one's 44 as well, fill in literally the entire diagram, every single angle, I'm guaranteed to get um those marks with the reasoning.

[00:52:33]Uh, just been asked for 13B. Give me two seconds.

[00:52:44]Okay, 13B. Let's go through that one more time. I keep the fraction on the left as it is.

[00:52:53]The divide changes to a times.

[00:52:57]The fraction on the right gets flipped upside down. So, it was 67. It's now 7 over six.

[00:53:07]And now I can multiply those top two and the bottom two. And that's just it.

[00:53:13]That's all you have to do.

[00:53:25]Uh yeah.

[00:53:27]Uh why would the other angle be 44? It's a great question. So uh what I did was I did 180 degrees in this triangle. also added 68 add 68 is 136 and then 180 take away 136 is 14 is 44.

[00:53:47]So that's where I got the 44 from.

[00:53:50]I'm just going to go to that question one more time a little bit slower will be a little bit smaller. I do apologize.

[00:53:59]So, I started off by saying that these two angles at the bottom must add up to 180 because they're on a straight line.

[00:54:14]From there, I know that this angle at the bottom is also 68 because it's an isosles triangle.

[00:54:24]Once I know that one's 68, I can then jump up to this one and say that these two angles are equal because they are alternate.

[00:54:34]And that is all the working out I need.

[00:54:36]There's a couple other ways I could do it. I could have said that one is at the top is co 68 because they are co- interior. So they add to 180.

[00:54:45]Uh and use that as a way to find out that was 68 and so on.

[00:54:50]on these ones. Your best bet is just try and fill in the entire diagram. The word corresponding comes up mo more often than any other one. Uh I will make sure I do one of those tomorrow morning before the exam.

[00:55:13]Okay, this one when I've seen people attempt it, it's I I want you to really take your time with this because this is a format question that's really worth um your time because as you can see there's just by reading it, there's no um deeper question in it. There's no um like there's no fractions, no algebra, there's nothing like that. So it is really worth your time even this far on in the paper.

[00:55:41]So there's a lot of information to try and organize. So we are going to organize it in a table.

[00:55:48]So what's the table about?

[00:55:52]I've got men and women and I'll put a total down the bottom.

[00:56:00]I've got coffee, tea, hot chocolate, and I've got a total.

[00:56:07]Now, I'm going to try and um get rid of as much of this information at the top as I can.

[00:56:15]So, overall, he sells 150 drinks. Let's get rid of that. Put 150 in that bottom left right hand corner. The grand total 150. 16 men bought tea.

[00:56:29]23 women bought hot chocolate.

[00:56:34]So notice I'm crossing out um each line of working as I've been through it. 43 people bought coffee in total. So my total coffee is 43 of which 17 were men.

[00:56:47]This last one where it's a little bit more complicated. Twice as many men bought drinks and women. So this number here, the total men is double the total women.

[00:57:00]So I need two numbers that add to make 150. But one number's double the other number.

[00:57:08]So you could either do it with algebra and say that's 2x, that's x, so it's 3x is 150. But talking to a few of you, it looked like most of you were happy to uh jump in and say, "Right, that's obviously 100 and 150." So, let's throw those numbers in.

[00:57:27]You're grabbing one mark for just starting to write the table.

[00:57:32]You're grabbing a second mark for this 100 and this this 50. So, now we can just go ahead and fill it all in. And the one we actually want from the question is, how many men bought hot chocolate?

[00:57:44]Now we can jump straight in and figure that out by doing 17 add 16 is 33 and 100 subtract 33 is 67.

[00:57:54]Now although I've got the answer, if I make sure that the rest of my uh table all adds up, then I know for certain that's correct. So let's fill in the rest of the blanks. 67 add 23 is 19.

[00:58:10]43 take 17 is 26.

[00:58:15]26 add 23 is 49. So 49 add 1 is 50 and 16 add 1 is 17. If I add this bottom line and it gets to 150. I know it's right.

[00:58:30]So our final thing we're going to write is our final answer. How many men bought hot chocolate? It was 67. So massive conclusion at the end exactly what we um need to get the format in the question.

[00:58:51]Okay, next one is a um ever interval question.

[00:59:03]So uh an average weight of a baby is 3.2 2 kilogram rounded to one decimal place.

[00:59:08]So basically 3.2 is the answer. What's the biggest number it could have been rounded up from and rounded down from?

[00:59:15]So I'm going to write 0.1 because it says one decimal place. I want to half it to get me 0.05.

[00:59:22]I add it on to the 3.2 to get the big one.

[00:59:27]I take it off from the lower one. You can cheat at this question. For this upper bound, write that with a five on the end. For the lower bound, same again. Second to last number, reduce by one, right? Standard form. So, we're really getting into the grade um you're well into grade four, possibly five in some of these questions. We're well past that 60, that 48 mark. Uh so, we know if we are um if you got everything right so far, you're well into a pass, right? 300 32,400 in standard form. So standard form is where we have to write it something times 10 to the power something else.

[01:00:10]So the number at the beginning must be between 1 and 10. So let's bounce a decimal point until it's between the first two numbers. We go one 2 3 4 3.24* 10 and we bounced it four times power four.

[01:00:28]We can cheat at this question as well.

[01:00:30]When it's a power negative and it's a make it into an ordinary number, we can write three zeros decimal point between the first two 54 at the end and we're done.

[01:00:45]Last one is a calculate in standard form. So evaluate means that work out.

[01:00:50]Can ignore these brackets completely. So let's get rid of them.

[01:00:56]Let's put our two regular numbers together. 3 * 7. We can do that. It's 21.

[01:01:03]And we are going to multiply our powers, sum up our powers of 10. And we do that by adding. So we get * 10 to the power of 11.

[01:01:14]Now that's not the answer because 21 is not between 1 and 10. So I'm going to make that 2.1 * 10. And I've still got that time 10^ the^ of 11. So that's another power of 10 that I can add on.

[01:01:27]So I got 2.1 * 10^ of 12.

[01:01:40]Right, I'm going to be honest. This next question I made a bit of a hash writing it. Okay, so it will not be these horrible numbers um when you do your test tomorrow if a question like this comes up. Okay. So, if you look at my numbers and you think, "What on earth are they chatting on about?" It will not be this hard tomorrow.

[01:01:55]Uh-oh.

[01:01:58]So, first of all, it is an estimate question. You see all these horrible numbers up here? There's no way you're going to be dividing or timesing 146 or 282 tomorrow, okay? On a non-calculate paper. So, what I'm going to do is 282 300. If you think it's too hard, make it easier. Round it like round it even further. 146. Let's make that 150.

[01:02:27]That is actually getting you one mark already. I know it seems that that's it.

[01:02:32]So, we're doing this at 45 miles per hour and this at 50.

[01:02:39]Now, we want the total time. So, that's our process here. If we find the total time it takes uh and then the total distance, we can do the total distance divided by the total time and that'll give us our answer. So, we're going to do on this one 150 divided by 50 and that gets us a nice answer of 3 hours.

[01:03:00]The other one, it's not as nice. This is where I've messed up a little bit. 300 divided by 45 is 6 and 2/3 or 6 hours 40 minutes.

[01:03:16]So our total distance is going to be 300 add 150 is 450. So he's driven a total of 450 miles. His total time is 9 hours 40 minutes.

[01:03:34]So to find the speed, we're just going to divide them. 450 divided by um 9 and 2/3.

[01:03:45]That looks awful, but we can round it a little bit or make it a little bit easier by saying 3 * 9 uh is 27 time add 2 is 29. So, we're dividing that by 29 over 3.

[01:04:00]Just like before, we can keep it, flip it, change it. 450 times by 3 over 29.

[01:04:09]And that 29 we can round that to 30. So we've got 1,350 divided by 30 which is approximately 45.

[01:04:21]It will not be that hard tomorrow.

[01:04:23]That's me writing this question um a bit poorly.

[01:04:28]But even if it does come off and it's that hard tomorrow, you're still grabbing a mark for doing a rounding bit at the beginning. Doing a mark get another mark for um speed, distance, time. So to find time, you do distance divided by speed and so on. So it's nice quite easy to grab those early couple of marks in that question.

[01:04:47]Right. The next one asks um is it answer these questions?

[01:05:01]Right. So is your answer to part A an overall underestimate? Now we rounded our 282 up to 300. So it's actually going to take him less time in the end. He's only got 282 miles to travel, not 300. same 146 up to 150. I rounded it up. So, it's actually going to take us less time in the end because I rounded everything up.

[01:05:27]So, because it's going to take us less time, my calculation is an underestimate because I rounded up the distances.

[01:05:57]Okay, properly into the grade five stuff. Only a couple of questions left.

[01:06:01]Make x the subject. That means at the end it should say x equals and we've got this equation.

[01:06:08]So, we're going to essentially pretend this y is a is a number and then solve it.

[01:06:15]We're going to do the opposite of divide by 3 first, which is times by 3. So, that gets me 3 y = 4x add 7.

[01:06:24]So, I want to get everything away from that x. Let's take seven from both sides. 3 y * 7 is 4x.

[01:06:33]And finally, I want to divide by four to get rid of that four in front of the x.

[01:06:38]I'm going to write it really lazily. 3 y subtract 7 all over four. I am done.

[01:06:50]Right. Brains in screenshot mode. This is the most likely one to come up. So, we're well into grade five temperature in this question. Write down the exact value of sin 30. It is 0.5 or a half.

[01:07:01]Memorize that. The exact value of sin 30 is 0.5.

[01:07:06]There's 14 that we should remember, but because it usually comes attached to a question like this one, cos 60 is 0.5 time 45 is one. They're the most likely to come up. Those three. So screenshot that in your brain.

[01:07:22]Right, we now got a trigonometry question. Now, we know it's trigonometry because, well, it says s up there. So, we can be pretty certain.

[01:07:31]Let's start by labeling the sides.

[01:07:33]Longest side is hypotenuse.

[01:07:35]One that's opposite to the angle is O. And the last last one is A.

[01:07:50]Um I was reading the question from the chat. Um basically if you haven't seen this before, don't worry about it. What I want you to do is memorize it. If it says sin 30, write 0.5. If it says co 60, write 0.5. Don't worry about it. It, you know, we're not going to be able to teach it to you in the next um, you know, uh, couple of hours. I want you to just memorize.

[01:08:16]Yeah. Right. So, guys, I want you to not worry too much about the trig. I want you to just memorize this. Basically, I'm doing a full pass papers worth because it, you know, makes sure we go up to grade five. Those of us that are looking to smash a grade four tomorrow, this is it. Three marks. It's it's not worth our time. But memorizing that sin 30 is 0.5 is worth your time. Right. So I'm going to start by labeling the sides. The longer sides on opposite the right angle is the h.

[01:08:47]Y is the opposite because it's opposite to that angle.

[01:08:51]and the remaining side is therefore a the adjacent.

[01:08:56]Now in the front of your you'll have a little uh attached sheet tomorrow with your formulas on it and it will have um your three formulas for sink cause and tam. Now but we're going to remember saw ca and toa.

[01:09:13]Now we have uh no you won't you won't get a mark for that. you will get a mark for this next part.

[01:09:23]Now, A doesn't have any writing on it, but H and O do.

[01:09:29]So, which one of these three has uh H and O? It's soft. You're you can grab a mark from literally writing from the formula booklet. Sin of our angle is opposite over hypotenuse.

[01:09:46]Now we know that sin 30 is our so 30 is our angle. We know our opposite is y.

[01:09:54]That's what we're after. And we know our h is 12. That goes in the bottom. So this bit here that grabs you a mark.

[01:10:03]Now we know synthetic is 0.5.

[01:10:10]So something divided by 12 is 0.5.

[01:10:16]So if I times by 12 on both sides I get 0.5 times by 12 is six as our final answer.

[01:10:29]This is what um many teachers might have um thought is this whole thing for uh for two marks might not be the best use of your time. If you're planning more of it tonight, in the morning, whatever. If this is something that you haven't seen for a long time, it might be not worth your time uh stressing over.

[01:10:54]This next one is a really easy mark to get at grade five. This one is definitely worth your time.

[01:11:01]Craig buys a phone for £640 after it was reduced by 20%. What was the original price?

[01:11:08]So, we're going to start with the number 100. So, on these questions, if you're not sure, always start with the number 100. It'll usually guide you in the right direction. Reducing by 20 is 80.

[01:11:19]So, we know that £640 is 80%, but we want to know what 100% is.

[01:11:29]So, what I'm going to do is I'm going to find out what 10% is. To get from 80 down to 10, I have to divide by eight.

[01:11:36]So let's divide this by 8. 640 divided by 8 is a bit difficult but 64 divided by 8 is all right. We can do that. It's eight. Sit the zero on the end. 10% is 80.

[01:11:50]Let's time by 10 and we get 800 as our final answer.

[01:12:02]Right. Last question.

[01:12:11]So, this is going to be the hardest element we ever do. So, if you again, you get to this part in the paper, you got your 48 marks, and you haven't got this one. Do not stress too much. I've made this one really, really nasty. We are going to make our y's the same. I'm going to do that by multiplying this one by two to get me 8x. Take 10 y = 34.

[01:12:35]I'm going to multiply this bottom one by five so that they both have a 10 y in them.

[01:12:43]35x take 10 y 9.5 * 5 is a little bit tough.

[01:12:50]9 time 9 * 5 is 40 45.

[01:12:58]Yeah, I'll go back to 22 in in a moment.

[01:13:04]I thought we read these questions.

[01:13:18]I see. Um, so that person just sent me an image. Um, so it's not 80% of 640. So just looking at uh 22 again, it isn't 20 80% of 640. is telling us that 80% equals 640.

[01:13:36]We expect to see this one on the the last page of the of the test on foundation. The most difficult one we expect to see is right at the very end.

[01:13:44]Um so if it was 80% of 640, we'll expect to see that question maybe uh six seven something like that. But it's this one um was right at the end. We're expecting to see a interest question or a reverse percentage question like this. So this question is really saying 80% equals 640. What's 100%. I hope that makes a little bit more clear. I'll make sure I go to one of them tomorrow morning.

[01:14:12]Um I'm not sure I can. A lot of people messaging about shout outs. I'm not sure I'm allowed to. Uh I will check that uh before I do uh I want paper two. um and see if if I'm allowed to see see if it's okay. But for today, uh there'll be no shout outs, I'm afraid.

[01:14:33]Right. Sorry, back to the um simultaneous equations one. Uh yes, I can I'll go through the reverse percentage one tomorrow morning again.

[01:14:40]Don't worry, we plenty more uh those questions tomorrow. Sorry, back to this one. Right. If you make or if you attempt to make your um y's the same, you can grab one mark straight away. So just doing that, even if you can't multiply, don't worry. You're grabbing one mark just for doing that.

[01:15:05]So what I'm going to do now is if I have the same signs, I take. If I have different signs, I add.

[01:15:15]So, I've got the same signs. So, I'm going to take them. I'm just writing that one again below. It's the same as that one. Just so I have the bigger number on top because I'm going to take them. If you try to take them away, you are grabbing your second mark.

[01:15:30]35x take away 8x is 27x.

[01:15:37]-10 y subtract -10 is nothing, which is what we want.

[01:15:42]We want to only have one letter.

[01:15:45]47.5 take away 34 is 13.5.

[01:15:50]So I now know that 27x is 13.5.

[01:15:56]If I divide by 27, I get x equals. Now this looks really awful, doesn't it? 13.5 over 27.

[01:16:06]It's actually going to simplify really nicely. Let's just multiply up by 10.

[01:16:11]135 over 270.

[01:16:14]I can simplify that down. I can divide them both by five and that will get me um 54. So 27 over 54 and divide by five.

[01:16:27]And I might notice they're both in the nines. That's going to be 3 over six.

[01:16:31]And eventually that's going to go all the way down to x=0.5.

[01:16:40]In the exam, yes, you would get a mark for doing that. It would make this next section really tough though. So if you you grabbing a mark third mark for that, it would make finishing it as you see in a minute really really tough. Um so I'm going to pick one of the equations to replace x with 0.5 in. I'm going to pick the top one because it doesn't have a decimal and x has a even number in front of it. So that means when I time it by 0.5 it's uh it's not it's going to give me a whole number. So four lots of 0.5 take 5 y = 17.

[01:17:22]4 * 0.5 or four halves is two.

[01:17:29]Just substituting that in grabs you a mark even if you can't do it. So even if you did write four lots of this take 5 y= 17 that would grab you as a third mark.

[01:17:40]And our last mark is hidden behind some pretty tough algebra. Let's take away two from both sides. -5 y = 15. Divide through by -5.

[01:17:53]Y is 15id 5 is 3. So 15 / 5 is -3. My final answer is 0.5 and negative -3.

[01:18:04]And that is us done. Slightly behind schedule. So I do apologize.

[01:18:11]I would strongly recommend you now go and get some sleep.

[01:18:16]I will be in my classroom from 8:00 a.m.

[01:18:19]tomorrow morning where I'll be going through um so I've been requested reverse percentages. this one. Um, you mentioned someone mentioned probability. Uh, so I'll do a probability table question. And if there's anything else uh that you want me to go through, uh, I should be able to wing it on on the morning. If there's anything really specific you want me to go through, uh, bring it with with you and I'll go through it then. Other than that, thank you very much for your time, guys, and I'll see you tomorrow morning.

[01:18:49]If I don't see you, best of luck in your exam.