Are You Actually Ready for A-Level Maths?

A GCSE grade is useful but it doesn't tell the whole story. I have taught people in A-level maths that have grade 8s and 9s that struggle initially in A-level maths and soon as they have gone grade 6s and grade 7s who actually progress and perform very very well. So this test here it just has a small snapshot of the type of algebra that you need to be able to be very very good at in order to succeed at A-level maths but again this is just a snapshot so if you want the full diagnostic that's going to be a free link in the description and also in the pinned comment in case you want to take that and then you can book a 15-minute course with me just to see you know where you're at and what you're thinking about A-level maths for. So the way this is going to work is you're going to have 20 to 30 seconds per question. You're only going to get one mark per question because as I mentioned in other videos these types of questions you don't really get marked on them in A-level it's just kind of a step that you're expected to be able to do 100% of the time. There's no calculator at all and in this case we're looking at the method as well as speed and I'm going to link this all to the various different topics that appear in A-level maths. So first of all of course we have simplifying algebra fairly self-explanatory it appears in basically all of A-level maths simplifying and collecting like terms. So again have a go I'm sure we've had enough time and again once again if you want to have a go just pause the video and then we'll go through it. Okay so again expanding the bracket something that we should hopefully be okay with now again you want to be really careful with this negative sign on the outside personally I expand it with the negative because that way I don't have to do two steps the first step being like put it in brackets and second step kind of expanding it out. Then we have 6x minus 2x that's 24x we have minus 15 minus another 8 which is minus 23. Perfect so again one mark if you got that right. Once again you have just like 30 seconds so pause have a go and then check your solution. So here we're going to be solving this equation equaling zero and then hence state the two points where the graph crosses the x-axis. So here we have I mean the best thing for me to do is to just quickly sketch this out so I can tell this is a quadratic graph it's going to look like a u-shape like this now it says when it crosses the x-axis which would be these two points here so these two points at the bottom here now what is true when you have that graph and it crosses the x-axis well it means that y is equal to zero so basically I'm just solving this equation here and that will give me the two x coordinates because that's when y equals zero if I sum y equals zero there I get the exact same thing as this equation how do you solve a quadratic we've got completing the square you've got quadratic formula and you've got factorizing now when I look at this I can kind of see that factorizing might be very quick because numbers are times 14 for example 7 and 2 and then because it's a negative number it adds so we get x minus 7 and x plus 2 equals zero which means our two solutions are x equals 7 and x equals minus 2 because remember you have to swap the sign over here so this coordinate over here is minus 2 and that one there is sorry uh is minus 2 and that one here is 7 perfect move on to the next one so here we have indices now indices again a super super super important topic that you have to be really really fluent in because it comes up in differentiation integration exponentials and logarithms as well differentiation integration makes up like 30 to 40 percent of the marks in your overall a level maths so really really important so we have x cubed to the power of 4 all over x to the 5 so first things first when you have a bracket so a power to the power of something else you're multiplying the two indices so here we have x to the power of 12 x to the 5 and then lastly when you divide two bases so in this case two x's we subtract the powers so we have x to the power of 12 minus 5 which is 7 so hopefully not too bad so far rearranging formulas again I would say it's very hard to tell you how many marks this is worth because it comes up in almost every single question and I'm not even exaggerating when I say that it comes up in stats mechanics and pure as well so it comes across all three strands and there are so many questions that are show that question so show that this can be written as this which is just rearranging so again pause have a go give yourself one mark to get it right so making s the subject so first thing I would do is in my head I would just highlight the s and then I'd look at everything else that's with the s when we make s the subject it means s should be the only thing on that side of the equal sign so in this case we want to get rid of u squared and 2a now which one should we get rid of first well I like to get rid of the thing that's not attached can you see how the 2a s that it's all together right it's like attached together so I'm going to get rid of things not attached first which is the u squared how do you get rid of u squared well you take away u squared and we'll do that from both sides so we get b squared minus u squared equals 2a s and then we have the 2a with the s what is the 2a doing it's times in the s so we're going to divide both sides by 2a dividing both sides by 2a we get b squared minus u squared over 2a equals s for our final answer so again comes up all of the time so the next thing with functions functions is one of the trickier topics in year 13 math and we use a lot of the same skills for functions in year 12 and year 13 maths it also comes up in basically every single university admissions test because functions are a really fundamental part of mathematics so let's see how we're going to do this well again pause it and give yourself one mark for each of these so here if you notice this says x and what they've done is they've replaced x with a minus 2 so what we're going to do is in the equation we're going to replace x with a minus 2 so every time i see an x i'm going to put a bracket and then what we're going to do is instead of that bracket we're going to fill it in with a negative 2 cool now we can actually work this out now again i said no calculators so we're going to do minus 2 squared so it's minus 2 times minus 2 which is 4 which is why we put the bracket if you don't put the bracket you'll get minus 4 so we get 4 times 2 which is 8 then we get minus 3 times minus 2 which is positive 6 and then plus 1 so we basically have 8 plus 7 which is 15 perfect now b is a lot more interesting because if you look here they've replaced x with x plus 1 now the steps are exactly the same but this is where a lot of students get confused or they might write something like the graph shifts to the left by 1 which is correct but that's not what they're asking you for they're not asking you for what is the actual transformation taking place they're asking you to simplify to work out the equation so once again instead of x i'm going to replace it with a bracket and then we are going to shove in x plus 1 and now this is a super easy question we're literally just expanding brackets which i'm sure we can all do right so 2 x plus 1 squared to be really quick we have x times x x squared then we have 1 plus 1 which is 2 so 2x then we have 1 times 1 which is 1 then that's expanding this we get 2x squared plus 4x plus 2 minus 3x and then minus 3 plus 1 is minus 2 so those twos will cancel out we get 4x minus 3x which is just x so 2x squared plus x so you can kind of use those tricks to be a little bit faster as well and lastly but not least we have this which it can sharpen in a level maths in terms of differentiation they like to apply modelling but the key thing here is modelling modelling comes up it's basically all of stats and mechanics and it comes up a lot in purer as well because they don't want to just test if you know the maths they want to test if you know how to apply it what does the maths actually mean so here the rectangle has length blah blah so i'm going to just draw a rectangle so x minus 1 x plus 3 and it tells me the area on the inside is 32 centimeters squared and then it says find the dimensions of the rectangle so well now i can ask myself what would i do if i just had numbers instead of letters well i'll times them together right so okay these two sides times together should give me 32 and now we can kind of see what the question is asking us to do this is a quadratic which we can solve x times x is x squared then we'll have minus x plus 3x that's going to be plus 2x minus 1 times 3 is minus 3 equals 32 shove that over here we now have x squared plus 2x minus 35 equals 0 so two numbers at times 35 add 2 again if you can't think of any completing the square also works or quadratic formula although quadratic formula for that calculator is a little bit long completing the squares a lot faster but i'm thinking 7 and minus 5 works quite nicely and i'm going to go through the first mistake in a second which is thinking that this is the answer so i see a lot of students that finish there that's not the answer what does the question say the question says find the dimensions of the rectangle i found out what x is x isn't even one of the sides the sides are x minus 1 and x plus 3 the other problem is i shouldn't have two solutions right so here i have minus 7 and 5 well i can't have two solutions right it says the dimensions of the rectangle it's singular it's one lot of dimension well if we think about it could it be minus 7 well minus 7 minus 1 would mean this side is minus 8 and this side is minus 4 have you ever heard of a length being given as a negative number no lengths cannot be negative now i want this to be really clear just because x is negative doesn't mean that the answer's wrong it's if the sides are negative because i've seen questions and this happened in a level maths paper actually where the negative answer was actually the correct one because when you did the working out here you got positive numbers whereas with the positive number you got negative so be really careful with that so in this case x is 5 and so the dimensions are it's a 4 by 5 plus 3 8 rectangle so if you want you could even draw it out you could say it's a 4 by 8 rectangle like that anyways i hope you found that vaguely useful i'll give you an interpretation of this result so again if you're 6 out of 6 you have you have the secure starting of algebra i'm not saying this is as hard as it gets but in terms of starting in september good job you should be okay if you keep up the practice if you're 4 to 5 a level still realistic but anything that's missing i'd recommend going over it probably take you 30 minutes tops 2 to 3 um honestly you're at risk of falling behind without structured preparations remember i said grade 8 and 9 students can do all of this it doesn't mean that they succeed in a level maths okay and i've seen grade 6 students that do very well that struggle with this it's all about being structured so again both that meeting with me let's have a talk i can help you plan but it and if it's zero to one then genuinely you need to really focus on gcc maths before september now once again this was a snapshot this is not if you can do this you can definitely do a level maths however i do have a diagnostic which i've linked in the description of the pin coin you can go on there and you can have a much more detailed look at what skills you have and what skills you need to develop before september so again try your best