Revise Maths - Higher - Paper 2 (Calculator) with Tute | GCSE Revision Live | 2 June 2026

Ajouté : 2026-06-03

[00:00:54]Hey. Hey. Hey.

[00:01:11]Hey, hey, hey.

[00:01:42]Heat. Heat.

[00:02:27]Heat. Heat.

[00:03:03]Hi and good evening everybody. Welcome to our live revision paper two uh session here with me Ivan. I'll be your teacher for this evening. I hope you're ready for tomorrow's exam. Well, as I said, this is a revision of paper two and we're going to show you a few questions that might turn up and a few tricks and tips of how to get going.

[00:03:27]Okay. Uh so, this is how we're going to do it for the next uh for for the session. We're going to revise our basics exam skills. So, we're looking at the questions that will give you one, two, maybe even three marks, the simple ones. Then, we're going to go on to practice more core skills and uh go over some misconceptions. Then, we're going to analyze multimark questions to maximize how many marks we can get. So, let's get to it, shall we?

[00:03:55]Make sure that you have a calculator with you, right? A scientific calculator is best. There are many out there but I will be showing you a few things on a scientific calculator uh during this session. So other calculators are fine but there are shortcuts that you can use with scientific calculators. Okay. Make sure that you give a go to every single question. Um if you're struggling with pi use 3.142.

[00:04:26]Okay. Unless of course the question specifically tells you to do otherwise.

[00:04:30]Read each question carefully and check your answers. One thing that people tend not to do is check your answers at the end. Right then let's get to it. These are the type of questions that you will get in the first part of your paper.

[00:04:47]Okay, very simple. This first one is a two marker. Use your calculator to work out the value of that. All right. Now, simply put, the only way of getting the right answer getting the mark marks here is getting the right answer. And what we're what I'm going to do with you is show you how to use your calculator.

[00:05:08]Okay, I have the Casio one, but that doesn't mean that that is the only type of calculator out there. There are sharps and others out there. Make sure that you do know how to use your calculator, though. Okay. So, I've got one here 3.8.

[00:05:27]Now, this is a number in standard index form, which is great for a scientific calculator because you've got that button there. Plump, right? And you know that you're using standard index form there. It's usually at the bottom of your calculators. Some calculators may vary. So all I need to do now is put -4 in there because that was the question and then divide by 9.5 and again standard index form button time 10^ the 2. So all I need to do there is put a little two in there and then press the answer button and I get 4 * 10 ^ of -7. It is a little bit hard to see on this calculator but that does say07.

[00:06:14]It will be easier on some calculators.

[00:06:16]Okay. So, all you need to do there is 4 * 10 -7. You don't have to put the zero in front of it. -7 is just fine. Right?

[00:06:31]Then expand and simplify. Now, in maths, right? Maybe in other topics. I'm not I'm not an expert in any other topics, but in maths you can do things step by step. You don't have to do everything all in one go. And this is the first question that shows that really because you've got two sections to it. The first section is these pair of uh two pairs of brackets right there. Right? You can expand those first. Right? And that would give you well it depends on which method you're using. You could use foil. You can use the table. Uh smile method is the same as foil. Uh but what you do, you know, 4x * 2x, which is 8 x^2. Remember, you're multiplying by the x's as well. And then you've got 4 x * 5, which gives you an answer of 20 x. Remember the x with the four. So you need it there. And then you've got seven. Oh, actually it's -7.

[00:07:37]So it's going to be negative something.

[00:07:39]So -7 * 2x is -4x.

[00:07:44]And then you've got -7 * 5. So -35, right? And you can simplify that then.

[00:07:53]Right? So it would be 8x take away 6 x sorry add 6x not even. All right little things that could happen there. Right?

[00:08:07]So always check your answer. All right.

[00:08:10]I was lucky I did actually check my answer very very quickly with my eye there and I found out what mistake I made. Right. So it becomes 8x squared.

[00:08:20]Another mistake I did there. So checking once again, 8x^2 + 6x take away 35.

[00:08:29]Now I can deal with this one right here.

[00:08:32]I'm going to put the subtract in here and a bracket. Now because it's squared, I'm multiplying it by itself, right? So you're starting with x squ, right?

[00:08:44]Then you've got -6 x and then you've got positive 9. Be careful on that one. Okay, remember that when you're squaring a negative number, you do get a positive answer. Then you've got 8x^ 2 + 6 x takeway 35. Now everything within this bracket here, you are now multiplying out by -1, right? So take away x^2 + 6 x take away 9.

[00:09:24]That would give you I'm going down here 7 x^2 take away 12x take away 44.

[00:09:38]Therein is your answer.

[00:09:40]Question three. three marks I wouldn't sometimes this is two marks they vary from year to year to be honest with you okay so the max is maybe to three marking maybe two but this one is a very simple one right error interval well if you know that m is 0 4.08 08 to do decimal places. You need to go to that extra decimal place to see what they are. They aren't really asking you about the range where the numbers round to Z uh 4.08 so to two decimal places.

[00:10:20]So this one would be 4 075 and it must include that one. And then 4.08 085 and you can't include that number because if you round that to two decimal places you go to 4.09 09 two mark solving equations depends on what you want to do here. Uh which method you want to show. I would always show your method every single time even though you may only get your mark for showing the right answer. Always show your method. It is a time for you to show off to show your understanding to these examiners. All right? So please make sure to do it. So here I am using the inverse method.

[00:11:07]So basically I'm inversing until I've got x on one side and a number on the other. So I've inversed and take away 5 overx because it's a negative and I don't like dealing with negatives. Then I'm inversing the two.

[00:11:21]So the inverse of positive2 is -2. So 10 takeway 2 is 8.

[00:11:28]5 /x.

[00:11:30]Right? I would advise you to put one on top of each other here, but I'm running out of space. So I'm probably going to have to move to over here. Then you've got 8x because I'm multiplying through by the x is equal to 5. And then I'm dividing through by 8 and I've got an answer of 5 over 8.

[00:11:50]And you can check now you can slap that into your original equation. Okay. 5 over 5 over 8 take away 10 take away 5 over 5 over 8 and it will give you two. So you know you are correct. Okay. Some little things that will make you feel a bit better especially with these first questions. Make sure that you are checking them. Right. Make sure that you're checking them so that you build up a little bit of confidence. Right.

[00:12:20]Right. Then so here's your chance to do a bit more by yourself. Okay. Shop increases the price by 12% to £392.

[00:12:29]What was the original price? Pause the video. choose the correct answer. Well, hopefully you'll choose the correct answer and then I'll show you the correct answer.

[00:12:41]Here we go.

[00:12:43]It is 350. So, what you've done there is 350 multiplied by 1.12 because that's my multiplier for an increase and it should give you 392.

[00:12:59]Now, how did I do the other way? Well, I didn't know what 350 was to begin with, but I did know that I multiplied it by 1.12 to get an answer of 392.

[00:13:13]So, other way around, inverse operation just as we did with solving that equation, right?

[00:13:23]And of course, that would give you 350, right?

[00:13:28]So those are our basic exam skills, right? To practice core skills and cover misconceptions, right? Then first thing algebra I'm prophesizing I'm hypothesizing hypothesis that there will be a lot of algebraic manipulation in your exam tomorrow. So a lot of it will go to that. Okay. making sure that you understand the algebraic manipulation.

[00:13:59]So here we've got factorizing a quadratic equation.

[00:14:04]Now I can see quadratic equations we know well I hope we all know are all shaped like this.

[00:14:17]Not always is equal to zero but ax 22 + bx plus c. And what I'm realizing here is that a is greater than one.

[00:14:26]So my method slightly changes. So what I do is I go a * c.

[00:14:36]So a is 3 and c is -10.

[00:14:41]So I now know it's -30.

[00:14:45]And then of course b. Oh, there's no number in front of the x, but there is a negative, so it has to be negative one.

[00:14:53]What I want now is to find two numbers.

[00:14:56]Okay, I want the two numbers to add up to make one and I want the two numbers to multiply to give me a negative number. Now I'm looking at this and if I've got a ne negative product, I know that one of the numbers has to be positive and one of the numbers has to be negative.

[00:15:22]I'm seeing a negative sum.

[00:15:26]That tells me that one number the the biggest number has to be the negative one. So, I'm thinking of two numbers that multiply to give me 30, but there's a gap of one between them. And the number I'm thinking of is five and six.

[00:15:46]Now, one of them has to be negative. And the biggest one has to be negative because the sum has to be negative 1.

[00:15:52]So, I'm going to go for 5 -6.

[00:16:00]Little tricks there, right? What we do then is we partition or split that part of the equation. So I've got three x squared. Now I know my next step is going to be factorizing.

[00:16:15]I'm definitely not going to put the five beside the three. Why not?

[00:16:22]I can't I can only think of one as the highest common factor between them. So, it's going to be 3x^2 take away 6x. That's handy because 3 goes into 6 + 5x take away 10. Oh, another handy one. 5 10. Okay? And I have to put it as equal to zero. Right? Again, as I said earlier on, split it. So, what I'm going to do is I'm going to factoriize this bit here.

[00:16:55]Right? On the outside, I'm going to go 3x² and 3x, sorry. And on the inside, it's going to be x takeway 2.

[00:17:04]And then I can factoriize this bit here.

[00:17:09]So five is going to go on the outside. x takeway 2. Great. I know I'm on the right track because these two are exactly the same.

[00:17:21]Exactly the same.

[00:17:23]So what I can do here is I can factoriize again. Well, I'm going to factoriize the 3x and the five into one bracket and in the other bracket I'm going to factoriize and there's always going to be equal to zero. Now, because when you have two pairs of brackets stuck to each other, it means that you're multiplying. And the only way of getting zero when you multiply is by multiplying one of the numbers has to be zero. Okay, that means that either 6 3x + 5 is equal to zero or x takeway 2 is equal to zero. Okay, that means that 3x is = -5.

[00:18:29]x is = -5 over 3 or x = 2. Okay, factoriize and solve. Well, these are your two answers and you can check, right? You don't have to put you don't have to think whether you're right or you're wrong. You slap this into your original equation and if you get zero out, you know you're right. Okay? Always do that when you're solving equations, right? Or solving quadratics or what have you. Always put those numbers that you find at the end back in to see if they work.

[00:19:10]Right? Then simultaneous equations.

[00:19:13]Right? Three marker. Um going back to this one, right, this was as a three marker as well. Uh what you would get here probably is one mark for this, right? One mark for the factorization and one mark for your answers. Right?

[00:19:31]Sometimes they give four marks for that because there's a four step, but that's where you're looking at your marks. So if you make a mistake somewhere, don't worry. But definitely just don't put the solutions in there. just the solutions. Oh, we show you working out.

[00:19:46]As I said, you are trying to show off here. That's what the point of an exam is to show off what you understand. We all make mistakes. I've I've made a few here today, right? I have. But if we show our working out and it showed in that question that I did earlier on, right, I made an error in there, but because I did the working out, I was able to correct the error. So, it's vital that you check as well and it's vital that you show you're working out because if you do make a mistake and you don't spot it, you're still going to get most of the marks because you're showing you know what you're doing.

[00:20:26]Right? Then, simultaneous equations.

[00:20:29]What I'm noticing here is that we don't have the same coefficient of x. We don't have the same coefficient of y. So, let me call one one and the other one two. What I'm going to do is I'm going to multiply equation one by three and I'm going to multiply equation two by two. What that does is it gives me the same y coefficient. So I'm going to end up with 6 y and six - 6 y. Not exactly the same coefficient but we can use. So uh 5x becomes 15x and this one then becomes 2x.

[00:21:28]So 15x + 6 y is equal to 12 and 2x takeway 6 y is equal to -46.

[00:21:38]I'm going to call this one 3. I'm going to call this one four. What I'm going to do then is add them together. If I add six and -6 together, I get zero. So three add four.

[00:21:54]I'm talking about the equations here. uh what I get is 17x = to 3034.

[00:22:08]Then of course I'm solving the equation divide through by 17 and I get an answer of -2.

[00:22:17]That's my first answer. When we're solving simultaneous equations, you need an x value and a y value.

[00:22:25]So what do I do? So if x is equal to -2 then now I choose one of these.

[00:22:38]I'm going to choose equation two and equation two is -2 takeway 3 y is equal to -23 and then I solve adding two to both sides I get -3 y is equal to -21 now you're thinking to yourself oh you've got a negative value here doesn't matter because you're going to divide through if you're dividing two negatives by each other, you're going to get a positive answer.

[00:23:12]Then you need to check. How do I check?

[00:23:16]Well, because I used equation two to find y. What I'm going to do now is use equation one to check.

[00:23:26]So 5 * -2 + 2 * 7. Now that would give me -10 + 14 and that would give me four which is the answer I was looking for.

[00:23:50]Right? Then we're going into bit more difficult ones now which is functions of functions. All right. So the function f ofx is equal to 3x take 4 and the function g ofx is equal to 1 /x + 2.

[00:24:03]find f of g ofx. So what you have to do here is make sure that you input this into this.

[00:24:14]So f of g ofx would be well f ofx is 3 x takeway 4 but instead of x you're inputting 1 / x + 2 which would give you 3 over x + 2 takeway 4. Now you can simplify that even further but because this is a two marker I wouldn't expect you to do it.

[00:24:44]Now the final answer would be -4x take away 5 all over x + 2.

[00:24:55]What you would have to do is make sure that you have a common denominator. The common denominator would be x+2. So we would put 4 x + 2 all over x +2 and then deal with it from there.

[00:25:11]Right? Then find the inverse function of f ofx. Now the inverse function now ways of doing it what I do is I pretend and it has to be pretend that f ofx is equal to y.

[00:25:29]So y is equal to 3x takeway 4.

[00:25:37]Now 3x take away 4. If I want the inverse of it, what I'm going to do is rearrange until x is the subject of this formula. So, what that means is I'm going to start by y + 4 = 3x and then y + 4 all over 3 is equal to x.

[00:26:03]So, the inverse function f of x would be and instead of y I'm going to call it x.

[00:26:15]So it would be that one.

[00:26:22]Okay. Solve now g of f ofx. So we know we're going to have to put f ofx instead of g, right?

[00:26:38]Or not instead of g into g. So g of f ofx would be 1 / 3x takeway 4 + 2.

[00:26:58]Move that up there.

[00:27:00]What you have then is 1 3x takeway 4 + 2 gives you 3x takeway 2.

[00:27:12]And now it's telling you f of g of x g of f ofx is 1 7. So what you do is 1 / 7 equals 1 / 3x takeway 2. And what we're seeing here, you you could use your balance method, your your inverse method, but really what it's saying is that 7 is equal to 3x. take away two and then you solve this and you find that x has a value of three and that's a one marker according to the information that we gathered here I would have called it a two marker but if it works it works okay but always show every single step of your calculation Right? Every single step. Right? Then let's go on to finding the line gradient when here.

[00:28:24]That's the shape we've got there. That's not the shape that we're used to. So we want to find the gradient of the line perpendicular to it. Now perpendicular is that right angle. Okay. The first thing I need to do is find the gradient of this line. But I need it to be in this format here.

[00:28:45]I need it that shape because we know that m is the gradient. So I rearrange the formula. All right. And I rearrange it until I get to y is equal to 4 takeway 2 over 3x.

[00:29:06]Right? I know now that m and I'm going to call this m1 has a value of -2 over3. Now what you should remember about perpendicular gradients is that if you've got one gradient and you multiply by the other, so the product of two gradients, they have to be negative one if they are perpendicular to each other. So what we've got here is -2 over3 * m2 is equal to -1. And of course what we're going to do is we're going to divide.

[00:29:44]So it would be the second gradient would have to be -1 all over -2 over3. Now you can do that on your calculator. Okay.

[00:29:54]straight in plain plank pong and you would get an answer of 1.5 or 32 and again I'm showing every step of my way here. Right? Then find the equation of the line that goes through uh 6 -2 with a gradient of -4. That means that y is equal to -4 over 3x + c. Now, looks good, doesn't it? We don't have the C. Unless we have the value of C, the Y intercept, we don't have a complete equation. So, what we're going to do is we're going to find it by inputting Y as -2 and X as 6.

[00:30:49]This is a nice one because 6 / 3 is two.

[00:30:55]So what you get here is -2 is equal to -8 + c. And what you get there is that c has a value of six. Now you haven't finished. Find the equation.

[00:31:13]What you found is the value of c. you haven't found the equation yet. To found find the equation, what you're going to have to do is you're going to have to put the information into the equation. So, y is equal to -4 over 3 x + 6. And there's your marks. Okay.

[00:31:37]Right. Then estimating the mean for the information given to us here. Right. So day works for a weather station. The table shows the information for the temperature of midday for the last 30 days. There they are. Check that 2 + 8 10 + 1323 + 730.

[00:31:59]The data is correct. Okay. Work out the estimate the mean for the temperatures.

[00:32:02]Right. Then that's the information that you're given. My advice is create new columns.

[00:32:13]This is estimating the mean. You're going to have to find the midpoint. Now the midpoint is your range divide by two. So 0 + 5 / 2 is equal to 2.5.

[00:32:30]The midpoint of this group is 2.5. Now most people will see now oh okay yeah right. So, this has to be 7.5 and this has to be 12.5 and this has to be 17.5. Ooh, major boooo there, people. Major boo. This is one of the mistakes that tend to happen here. The range of this one is different.

[00:32:56]Okay, the range of that one is different. So, you have to make sure that you're getting it right. as it happens. It's not an it's not a hard one. What you got there is 20 because that is the midpoint between 15 and 25.

[00:33:12]Okay? You don't have to worry about the in uh the inequality symbols there.

[00:33:19]Right? I call this one f ofx because what I'm doing is my frequency multiplied by my midpoint.

[00:33:29]Right? Mid frequency multiplied by midpoint. Frequency multiplied by midpoint and frequency multiplied by midpoint which would give you well you don't really need the grand total there. Okay?

[00:33:48]Because what you're going to do is you are going to find the mean or you're going to estimate the mean. Okay? And to estimate the mean, you find your total of this column right here. So the column is called f ofx. So you're going to have the total column of f ofx. And then you're going to find the total. This is what this symbol means, right? There is a Greek letter for it. But the real thing that you have to remember is when you see that symbol, it means total, right? So, what you've got there is 5 + 60 + 162.5 + 140 all over 30. And pling plank plong into your calculator it goes.

[00:34:37]And Bob's your uncle. Mary would be your auntie if she ever married Uncle Bob.

[00:34:41]You've got 12.25 Celsius.

[00:34:48]Now you can round that but always show your original answer first. Always show your original answer first. Right.

[00:34:56]Histograms.

[00:34:58]We are quite certain that histograms will come up. If it doesn't come up in paper paper two, it'll definitely come up in paper three. But we are quite certain that will come up in paper three paper two to be honest with you. So a group of runners complete a 10k race. The the table shows information about their finishing times. There we go. Draw histograms. Worth three marks. Right.

[00:35:21]Remember a histogram is not a bar chart.

[00:35:25]A histogram. It is the area of your bar that tells you the amount the frequency.

[00:35:32]So if you want to find out and they will give you this information most of the time they will give you the x- axis. So I've given you the x axis here 0 20 40 60 80. But I don't have any numbers on my y axis. So what you have to do is you have to find the frequency density right you have to find the frequency density here. So when you're doing this add another column doesn't have to be pretty right as it happens because I'm doing this on computer this can be done pretty but it doesn't have to be right now to find your frequency density you are going to divide your frequency by your range.

[00:36:16]So this group has a range of 10. This group has a range of 10. This group has a range of 20. This group has a range of 20. different range sizes.

[00:36:28]There we go. So, we know that these are the numbers that we want to look at in our y axis. Now, the biggest number I've got here is 2.8. So, I'm not going to call this 10.

[00:36:42]The biggest number probably is going to be three. Right?

[00:36:47]I'm going to have to split this. One, two, three, four, five, six.

[00:36:52]Six, right? Probably three is going to be there. If I had one more, I probably do it as three, but three, two, one.

[00:37:08]There you go. A bit tidier than my chicken scratching writing. Okay, so I know that now these are my heights.

[00:37:16]So I know that this is going to be so between 10 or 10 is going to be about here. I need 1.2.

[00:37:26]It's going to be about here.

[00:37:32]You I would expect you to use pencil and paper. Okay.

[00:37:37]So there you are.

[00:37:40]Now there will be a second part to that.

[00:37:42]That's a three mark question. That's what they're looking for, right? There will be a second part to this. Estimate the number of people who took more than an hour. Okay, more than an hour would be over here. So 60 minutes, right? So you want to estimate the number of people here. Now the number of people your frequency is going to be the area of that part. So when you're finding the area and it's a rectangle, it's going to be the width, right? which is 10 minutes times your length which is 0.5.

[00:38:18]So 10 * 0.5 is 5.

[00:38:23]That is our second part of today's learning which is to practice core skills and cover misconceptions. Be careful when drawing a graph. Make sure that your x-axis and y axis have a good scale to them. Uh estimating the mean.

[00:38:39]Make sure that your midpoints are in the right places, things like that. And break your numbers down. Okay? Break your problems down into manageable chunks. Right? And for example, this one. Okay? What we've got here is a cylinder. Right?

[00:39:00]And it's got two different measurements.

[00:39:03]One's in centimeters, one's in meters.

[00:39:05]Now, a cylindrical tank has radius of 18 cm and 1.6 mters. Now, the first thing I notice is that and what I'm going to do is I'm going to convert one to the other. The water flows in that uh at a rate of 0.52 L per minute. Okay, we're dealing with liters. What do I know? Well, I know that one liter is equal to 100,000 sorry cm.

[00:39:36]Okay, that means that I'm going to change this to centimeters. So, the first thing I'm going to do is 1.6 m is equal to 160 cm.

[00:39:49]How long does it take the tank to fill?

[00:39:52]So, I need to know the size of the tank.

[00:39:56]That gives me volume.

[00:40:00]Our volume of a cylinder is pi r squar which is the area of the cross-section multiplied by its height or length or depth whichever you'd like to say there.

[00:40:12]Right? I'm going to call it height.

[00:40:16]Right? Then slap that into your calculators. So it's pi ultiplied by 18^ 2 * 160. And it is going to be a big number. It is going to be 162,860316.

[00:40:41]Try to put your answer uh as much as you can what you see on your calculator. Okay. Now, because I know this, right, what I'm going to try and do is find out how many liters can we fit into that. Okay.

[00:40:58]So how many liters is going to be that number 162.1636 divided through by a th00and.

[00:41:25]Now, even though it tells me to the nearest minute, I'm trying not to round until my final answer. Okay, so 162.

[00:41:38]I've forgotten something here.

[00:41:41]Got the 86.

[00:41:43]Oh, so 860 that is not a comma anymore. That becomes a decimal point and it is liters. Now I'm not going to I have rounded here.

[00:42:10]What you have to do is on your calculator try to keep that answer going. Okay, try to keep that answer going. Right then, so my flow rate just going to call it FR here is equal to 0.52 uh lers per min.

[00:42:30]So your time taken is going to be 162.860 860 divided through by 0.52.

[00:42:44]Now that gives you an answer of 113.192, but you wanted to round that to one decimal or to the nearest minute. So it's going to be 113.

[00:43:06]Right then we're coming to algebraic expressions now. All right. And I'm this one I'd really like to show how you deal with this one as a calculator. So the first thing show that the equation can be rearranged into that. Right? That's my first part to call. So the first thing I'm going to do is rearrange this.

[00:43:26]How you do that? Well, you write it out.

[00:43:34]And then you're showing the steps. This is what they're asking you to do. And this would be worth about one mark.

[00:43:41]Yeah, only one mark. But it's showing what you need to do here. Okay. So x is equal to 4x take x cubed sorry takeway 1 and then x would be equal to the cub root of 4 x takeway.

[00:44:04]So you've done the first part and you've gained a mark. Easy mark. Now use then use integration to x0 = 1.2 and find your solution to three decimal places.

[00:44:16]Right? Then what I would do is create a little table x0 then you've got for x0 takeway one the cube root of that and so x1 would be then you've got this this is where I need to get me calculator out again. Okay, but hopefully you'll remember that.

[00:44:47]Right then, so as you can see, we've still got the calculation from earlier on on my calculator, but what we want now is the next one.

[00:44:59]Right then, so what I do, find my cubic root. Well, I haven't got a cubic root, but I've got an empty space, so I do that. It will be here somewhere. Okay, every calculator is different, but it will be there. And then I've got four times 1.2 was my first number. So, I'm going to slap that in. Make sure that it's in brackets because of bid mass.

[00:45:21]You want to well want to make sure that you're not it's not taking away the one first. Take away one and you're getting an answer.

[00:45:33]Got to put the one in there. You see, there we go. You've got an answer in there. Now, instead of you having to write that all in again, all you need to do is put this in again. Yes, you're going to have to put it in once more.

[00:45:49]And I promise you, it's going to be once more. Now, if you press shift and look for the acronym NS answer, right, you can use that. Now, I forgot to press the multiplication, so I'm going to have to redo it. There we go. Close the bracket. Take away the one. I remember to take away the one this time. And then enter again. Now that's all you have to do.

[00:46:12]Now just keep pressing enter and it does it for you automatically.

[00:46:21]That's why it's handy to have a scientific calculator. So as you can see it's rounded to one decimal place. It would be 1.9 probably. Um, but what we're seeing is a pattern emerging and you can do this again and again, but once it's locked in to that fourth decimal place, you can stop. As you can see, I've had two answers that to four decimal places, 1.8608.

[00:46:51]Why to four decimal places when the question asks you for two? Well, you need it, don't you? So, put the answers in here. a couple of them, right? But in the end, what you want is x is equal to 1.86.

[00:47:09]Now, it says 860, but because the next number is 8, it's going to be 861.

[00:47:37]and you're back with me. All right, during this part, I'll be sharing some exam specific tips and advice on the screen. I'm also be responding to some last minute questions uh that we've had through the sessions via the chat box.

[00:47:52]Uh please post your questions using that link that I uh I informed you of at the beginning of our time. You'll find it in the chat box there. So let us get to it. Now one of the things that you gave me was was um what I've got was a bit of iteration here. Okay.

[00:48:16]Um knowing how to do this. It's a four mark question and you're thinking it's going to take me a long time to do that.

[00:48:26]Let me try and show you a bit of a shortcut. Okay? Because this is a calculator question. Now, show that that is equivalent to that. Okay? There's no problem there. What you need to do is you just go through the steps. All right?

[00:48:42]Go through the steps bit by bit. So, adding one. So x cubed take away 4x is equal to take -1 add 4x to both sides. So x cubed now because it's a positive I'm going to put it in the front there take away one and then your cubic rooting 4x take 1 cubed. Right.

[00:49:16]So what you've done there is you've got your first mark by showing how it's done. Now use iteration when x0 is 1.2.

[00:49:27]Right? This is where me is going to come into play.

[00:49:32]Here it is. I'll get me calculator up for you so that you can see what I'm doing.

[00:49:44]Right. Then so it is x is equal to 1.2.

[00:49:50]So the first thing that I'm going to do is just write 1.2 there. Press enter.

[00:49:54]Okay.

[00:49:56]That gives me that as an answer. Right thing I'm going to do is put the cubic root in there. So, it's four and I'm going to put the four times 1.2 in brackets just to make sure. But what I'm going to do here instead of writing 1.2, I'm going to use the answer function on my calculator. Clunk. Just like that and then it's take away one. So, I put all that into my scientific calculator.

[00:50:29]If you don't have a scientific calculator, you're going to have to do this again and again and again.

[00:50:35]Iteration is taking your answer and slapping it back into the original equation. So instead of 1.2 in the next one, you would give me the answer of 1.56. And it's 1.560490751.

[00:50:50]And it's a bit awkward. It is a bit awkward, but if you don't have a scientific calculator, that's what you're going to have to do. You're going to have to put all that number in. Or you can use the answer. Well, if if the button is not there, you can't use it.

[00:51:02]So what you have to do is you have to just continue doing it step at a time. But if you have got one of these calculators, it's brilliant. It remembers what you need to do. You just press enter again. So that first one is X1.

[00:51:17]X2 is 1.737125986.

[00:51:24]X3, X4, X5, X6, X7, X8, X9, X10. And what you see now is that 1.860 is coming up again and again and again and again and again.

[00:51:44]And if we continue just clicking that, what you see is that it's 1.860 eight. That's very important that you get to that because the question actually asked you to do it to if I'm right three decimal places. So that would give you an answer of x to the power of x 10 is equal to 1 86 and because it's 08 there's a one after it. Now, what I would do here to show that you know what you're doing is write the answer to X1 in, write the answer to X2 in, and then just get the answer to X and count. So, I know that that answer to X10 is that. So, I put it in there.

[00:52:39]Okay, that's a bit of a tip for you right there. So, that was one. And it's a bit of a shortcut that one. Okay. It is a bit of a shortcut for you. Right.

[00:52:51]Another the one that's come in is rewriting something by using um completing the square.

[00:53:03]So you remember that thing I told you early run that x takeway 3 that that that's going to come into play here. So what we want is to change this and to put it into this shape right here. So what I'm going to do is I'm going to do a bit of a cheat. I'm going to say that y is equal to 0. So 0 is equal to 2x^ 2 takeway 12 x + 5. It's not what you're looking for because you want it to that shape, but I'm just going to pretend.

[00:53:36]All right. Now I'm going to play about with this. I am going to get rid of that five. I don't like it. Right.

[00:53:46]Why? Because I can't divide through by two. I don't like this. It's a bit awkward. I can't divide through by two nicely there. I'm going to get rid of it by moving it to the other side. Doing the inverse. What I'm going to do now is I am going to divide through by two. So 5 over two. 5 over2 there. x take away 6x x squ. Sorry. Oh, that's a nice one, isn't it? That's a nice one.

[00:54:15]What do we do at nine?

[00:54:20]So, I have to add nine to one side, I have to add nine to the other, right? To keep it balanced. And what I've got there is a perfect square. So, you're trying to play about with the algebra until you get a perfect square.

[00:54:36]Okay. So what you've got there now now this becomes 13 / two right positive because you're adding nine. Uh and this becomes x takeway 3 squ.

[00:54:55]Now we don't have it that shape yet.

[00:55:00]How do I get it to that shape? Well I need a number outside of my bracket.

[00:55:04]That's easy. There's a two over here.

[00:55:06]So, let's do it. Right. So, 13 would be equal to 2 x takeway 3 all squared. And I need the number at the end here. Well, that's easy as well. Take away 13 and I've got a number.

[00:55:25]Now it's not exactly what I got but if I put but if I remember I stated that y was equal to zero and they have got zero here again. So y would be equal to 2 x takeway 3 all^ 2 takeway 13. Now hence state the coordinate of the turning point. Now the coordinate of the turning point would be a b well a is the negative of -3 which is 3 and b is3.

[00:56:09]Right then, I think I've just got just about got enough time for one more question to go through. And I think the one that I'm going to go with is this one right here. A lot of you have asked for a bit of trig. What I'm noticing is that this is not a right angle triangle, but I do have an angle and two sides.

[00:56:32]So, the first thing that I think of straight away is cosine.

[00:56:36]Now the cosine rule will also be in your the front of your papers. Look for it.

[00:56:43]Now what it's telling me here is that I want to find BC. So bc 2 would be equal to a b^ 2 plus c a 2 take away 2 * a * ca * cos of the angle.

[00:57:10]And of course what I can do now is slap in the information 11^ 2 + 8 2. And again I am writing these in. You can probably do these uh all in one go on your calculator. But the thing that when I was doing my homework for this, the thing I found, I had to ask a colleague, is that the right answer? Because my calculator was in radians, which is another way of measuring angles. Right?

[00:57:43]So, you've got to make sure that you are in degrees. It's very important, okay, that you are in degrees because if you're not in degrees, you're going to get a different answer to me.

[00:57:56]and it's going to sound reasonable.

[00:57:59]Right? Now, what I found there is that BC^ 2 is equal to 130.61 blah blah blah blah blah blah. Leave that into your calculator. Right? Because what you want to do now is you want to square root it.

[00:58:13]So, you press the square root button and you press answer.

[00:58:18]Don't round.

[00:58:20]Never round until you're right at the end. So it was going to be 11.4 something and then you put the answer of 11.4 to three significant figures.

[00:58:35]Okay.

[00:58:37]Well, we have come to the end of the time that we do have together. Thank you all for joining us this evening. It's been a pleasure. It really has. We hope you're walking away feeling a little more confident, a lot more confidence.

[00:58:50]hopefully is a lot more confident and prepared for your exam tomorrow. Before you go, make sure to check in for in the time table that we've sent in the chat so that you can join in with our next live uh revision session. Uh there's one in maths in a week's time, right? So, your feedback helps us improve as well.

[00:59:10]So, please take a moment to complete the pinned form in the chat. Don't forget to hit that subscribe button and turn on notifications so you never miss a session. And a huge thank you once again for being part of this evening. Really enjoyable. Remember, you've got this.

[00:59:26]You can do it. Break your problems down into smaller chunks. Best of luck in your exams. We are rooting for you. Keep focused, stay motivated, and believe in what you've learned. See you next time.

[01:00:57]Hey, hey, hey.

[01:01:15]Hello.

[01:01:56]Oh. Heat. Heat.

[01:02:18]Heat.

[01:02:31]Heat.