in this video I'm going to be going through a higher AQA paper for you and we managed to get the whole thing done in under 25 minutes which is less than a third of the time you're normally given to do these papers so by watching the whole of this video you can almost save yourself an hour's worth of revision I would again recommend pausing the video before I attempt the questions just to make sure you can give them a go and good luck if you do so thank you for watching and I hope you enjoy today we're going to be looking at an AQA GCSE maths higher non-calculator paper question one Circle the fraction is equivalent to 4.75 now the best way I would do this I know that 5 is going to be equal to 20 over 4 and we want one quarter less than that so it's going to be 19 over 4 so this one here is a vector a circle the column Vector that represents a a goes three to the right and two down meaning it's going to be three minus 2. which of these is a square number and a cube number that is going to be a million because a thousand squared and a hundred cubed both equal a million Circle the reciprocal of five over six we just flip the fraction reciprocal means to flip use trigonometry to work out the size of angle X so straight away I can notice we have an A and A H so we're going to be using cos and we want to find out X so COS of X is going to be 9 over 18 and we have to use our exact trig values here because if we simplify that fraction cos x is equal to a half the way I like to do these is I set up this triangle here 90 here 30 there 60 there if this is one this one's two this becomes root 3 by Pythagoras I recommend you check that out so if we want to use the 1 over 2 as our A and H that would mean that the 60 has to be our angle so 60 degrees is our angle for that one or if a and b are scatter graphs what type of correlation is shown by each graph so graph a we have first of all a negative and now that is quite a strong negative so we've write that down for that answer and graph B is no correlation at all just to save the time I won't bother writing that down here are some information about 80 people who play in bands 12 singers but not guitar players 30 are neither a singer nor a guitar player and a quarter of the guitar players are also singers complete the Venn diagram to represent the information so we have to get 80 people in here we know that 12 people are singers but not guitar so we can put in there 30 are neither a singer nor a guitar player so 30 of 80 10 is going to be eight so thirty percent is going to be 24 so that can go in the box outside so now that we've put the 12 and the 24 in that adds up to 36 people leaving us still with 44. so if there's 44 left a quarter of the guitar players are also singers there must be 44 guitar players so that means 11 must go in there and 33 must go in there this space would be provided to write down workings such as this and all of this stuff here just to secure those four marks the shorter side of a parallelogram has length of 6.5 centimeters the length of the shorter side is 1 9 of the perimeter work out the length of the longer side so 6.5 equals 1 9 of the perimeter so if 6.5 accounts for 1 9 of the perimeter then the whole perimeter must be 6.5 Times by 9 which is going to be 58.5 Now using the perimeter we know that it's going to be 6.5 plus 6.5 plus X Plus X and that is going to be equal to 58.5 so if we simplify this down a little bit we're going to have 13 plus 2X equals 58.5 if we take away 13 from both sides we're going to have 45.5 and then half of that we're going to have 22.75 centimeters and that is going to be our final answer all the terms of a geometric progression are positive the second and fourth terms are shown geometric means we multiply or divide between each rule work out the first and third terms so straight away here I've noticed to get from here to here to here we've multiplied by 4 so that means this must be two this must be 2 which means this also must be two so we have two and eight as are our final answers you could do working such as four divided by two and then four times two to get the two values there the first two terms of an arithmetic progression are shown arithmetic we add or subtract between terms so the difference between the first and the second term is going to have to be the same between the second and the third term so 5p take away p is 4p which means that the next term must be 9p and then using this we know that P plus five P plus nine p is equal to 90. so adding those up we're going to get 15 P equals 90 so P equals six and that's our final answer there the cost of a holiday is 2400 Runner pays a deposit followed by monthly payments in the ratio of this she makes six equal monthly payments work out her monthly payment well straight away this ratio share that into the 2400. so 2400 divided by the sum of the ratio that's going to be 300 because 2400 divided by 8. now 900 pounds of that is the deposit and then if we multiply this by five that's going to be 1500 for the monthly payments we then want to do the 1500 divided by six work out how many times six goes into that so zero carry the one two with three left over so it's going to be 250 pounds as a decimal 11 over 40 equals 0.275 work out 33 over 400 as a decimal based off this well using this if we do 11 over 400 that's just going to make it 10 times smaller so it's going to be 0.0275 and then 33 over 400 is going to be three times that so 275 Times by three we have 15 we have 22 and we have 8. so it's going to be 0.0825 just like that two wire shapes make an earring the shapes are a circle with radius 21. I'll just label that on and a quarter Circle the radius of the circle to the radius of the quarter circle is seven to two show that the radius of the quarter circle is six millimeters well if we're sharing in the ratio of seven to two and the 7 is 21 then we have multiplied by three to get there so we have to multiply by three on this side which is going to leave us to 6. work out the total length of the wire in the earring give your answer in the form a pi plus b where A and B are integers so going back to this we have 21 and we have six so I'll split this up into one and two just keep it easy the total length is just going to be the circumference of the big circle first of all so one we're going to have pi times diameter now the diameter must be 42 so it's just going to be 42 Pi nice and easy for the second one what you have to be careful of here is these values here are going to be six because they won't be included in the circumference calculations so it's going to be 12 because 6 add 6 plus pi times the diameter divided by 4 because it's a quarter Circle so the pi times diameter is going to be 12 Pi divide that by 4 so it's going to be 12 plus 3 pi and then if we add these together we have 45 pi plus 12 and that's going to be our final answer s and t are positive integers this is expanded and simplified the answer is this where K is a positive integer work out the smallest possible value of K so I'm going to start off just by writing our double bracket out and we know that equals x squared plus KX minus 40. so by kind of using a method called comparing coefficients here we know that s multiplied by minus t is equal to minus 40. so from here s and t could be a whole range of values we want K to be a positive number so the difference between s and t has to be positive in which case we could have eight and a minus five alternatively we could have a 10 and a minus four this one has the smallest difference so K would have to be a positive three and that will be our answer tries to solve a quadratic here is his working give a reason why his answer is wrong now straight away here this value is correct X does equal seven but to make that bracket equal zero would need X to be minus 2 not positive two because if you were to sub positive 2 into there that makes four not zero here it looks like we have some indices laws we need to work out 18 c so straight away 18c is going to be 18 lots of 2 to the 10 times 3 times 5 to the sixth 18 we can write as 3 squared times two and then it's going to be multiplied by 2 to the 10 times 3 times 5 to the sixth and then just by using our indices laws we can collect up these respective terms and our final answer will be 2 to the 11 times 3 cubed times five to the sixth and that will be our final answer work out the cube root of this we can simplify with this so it's going to be the cube root of 2 to the sixth times 11 cubed and the cube root of that is basically going to be dividing those numbers by 3 ultimately because for those of you that do know this we could also write this as the power of a third which also means cube root and then we multiply those Powers across so it's going to be 2 to the 2 multiplied by 11 and that's 4 times 11 which is equal to 44 because they want our answer as an integer 3x equals half y Circle the ratio of x to Y if we just multiply this by two we're going to get 6X equals y so it's going to be in the ratio of six to one a bit of iteration here for those of you that haven't done it this is what it's going to look like work out the values of U2 and u3 well to get U2 we're going to have to do 4 over U1 minus 1 which is going to be eight which is a half u3 is going to be 4 over then we use this value and sub that in instead so it's going to be a half minus 1 which is minus a half so our value is going to be minus eight and that is going to be both our values a half and minus eight Jim buys a plant of height 20 centimeters the graph shows how the height of the plant changes during the next four days work out the formula for H in terms of n so whenever you see a question when we need to find a formula or an equation that's got a graph think of y equals MX plus c our C value is our y-intercept that's going to be 20. so I'm just going to write that first and then it's going to be plus whatever the gradient of that graph is multiplied by n so something and and we're going to find out what that number is creating a triangle because it's a straight line our change in y that looks like 32 there this is 20 so our value is 12. and across the bottom we have a difference of four so 12 divided by 4 is going to be a gradient of 3 and that's going to be 3n so that's going to be our answer solve the simultaneous equations so a lot of people look at this and it might be substitution but what you'll find is if we just rearrange something quickly then we don't actually have to do substitution so we have minus 4X add to y equals minus seven if we bring that across so we can ignore this one now and then you'll find if we multiply this one by two this is going to be minus eight X plus four y equals minus 14. if I rewrite the other one on top you'll notice the Y's are now the same so we can take them away to cancel out the Y's leaving us with 10x equals minus 9 minus minus 14 mean add 14 so 5. so x equals 0.5 and then substituting it back in to for example the top one two lots of 0.5 add 4y equals minus nine so that's one plus four y equals minus nine if we take away that one we have four y equals minus 10. so Y is going to be minus 2.5 so X is a half and Y is minus 2.5 Circle the expression that is equivalent to this now straight away I've noticed we can make a common denominator here if we multiply that whole thing by two we're left with this which is going to be 3x over 10 and as you can see that's one of our options anything to the power zero is equal to one and work out the value of 32 to the minus 3 over 5. now whenever we have a negative indices we want to reciprocate the number so 1 over 32 to the power of three over five the fifth root of 32 is going to be 2 so it's 1 over 2 to the power of three which is one over eight write this number in order of size start with the smallest I think it might be best if we use approximations and try and get them all into a decimal like the first one for this one here at the end it's going to be 15.6 recurring now think about it 48 divided by 3 is 16 and a third is 0.3 recurring so if you minus them from each other you're going to get that that's how I've worked that one out 2.1 to the 4 well 2 to the 4 is 16. so 2.1 to the four is going to be just bigger than 16 but not massively bigger 3 root 23 now root 23 we can approximate this because we know root 16 equals four we know root 25 equals five so root 23 my guess would be around about 4.8 if we do three times by 4.8 that's going to be just shy of 15. so 14 points something Now using this it makes it quite clear because we know that the smallest one is the 14 one so 3 root 23 the next one is going to be 15.6 15.6 recurring is slightly bigger than that and then finally 2.1 to the 4 is going to be the biggest Y is directly proportional to X cubed so straight away setting this up make it an equation by introducing a scale factor when Y is 17x equals 4 we can use that to work out the scale factor 4 cubed is going to be 64. so k equals 17 over 64. work out an equation connecting Y and X so we then use that substitute it back into here and that will be our final answer y equals 17 over 64 X cubed that is our equation linking Y and X m is inversely proportional to the root of R so K Over the square root of r we're going to have two scenarios here let's let r equal four and R equals 16 when it's been multiplied by 4. if we substitute that in m equals K Over root 4 which is 2. if we try it when R is 16 it's going to be m equals K Over the square root of 16 which is 4. so as you can see what's actually happened here is M has been divided by two as R has been multiplied by four so it will be this answer here ABCD is a quadrilateral proof that a b c d is not a cyclic quadrilateral now cyclic quadrilateral means that the opposite angles add up to 180. so if we use this scenario here in theory 180 minus 92 should equal 4X now 180 minus 92 is equal to 88 so X is 22 in that case so if it works when X is 22 here then it should be a cyclic quadrilateral so we're going to use kind of like a counter example to prove that this doesn't work so 5 lots of 22 plus 30 is going to be equal to 110 add 30 which equals 140. so in theory 180 minus that should equal 40. so does X Plus 36 equal 40. well we know X is 22 adding 36 to that equals 58 which does not equal 40. so therefore not a cyclic quadrilateral again at the start it might be worth making a note that cyclic quadrilaterals the opposite angles add up to 180. I know I didn't put that but that's just to save time but I would recommend putting that if you want to in the exam as well Y is an obtuse angle which statement is true this is a pretty difficult question to be honest it's talking about sin and cause graphs so if we just draw this in and the cosgraphs the sin one starts at the middle one goes up and the cause one starts at the top and goes down now why is obtuse that means it's between 90 and 180. 90 on this graph is between here and here and 90 is here and 180 is here on the COS graph so as you can see when it's obtuse it is bigger than zero and for the COS graph it is less than zero because all of this is negative so we need to find the one where it's greater than zero for sin which is any of these two but it is less than zero so it's going to be this one here so we take that box there a histogram is drawn to represent the height of a sample of women three of the four bars are shown the bar for 170 to 180 is missing there are 74 women in the sample complete the histogram so we're missing a little bar at the end now the area of each of the bars is the frequency or the the number of people in the sample basically so I'm going to label these one two and three for number one we have five multiplied by two which equals ten so ten people are in that category for two we have 10 as the class width multiplied by three which is 30. and for three we have five multiplied by four which is equal to twenty adding all those up we have 60 and 74 minus 60 leaves 14 people we want the bar of 170 to 180 which has a class width of 10 which means the height must be 1.4 so we would draw that in line with their and it would look like that and let's just shade it in to make it nice and clear so there is our answer show that this can be written in the form a root B so rationalizing the denominator when we have this what we want to do is just multiply by the root at the bottom and we're going to get 14 root 7 over 7 that is simply our answer work out this and give your answer as an integer now straight away I've noticed most of those can be simplified so 2 root 10 multiplied by root 80 we need to find the biggest square number that goes into it I think the biggest square number there is going to be 16 so we can write that as root 16 root 5 and we're going to simplify that in a minute and root 18 can have 9 into it so root nine and root 2. so 2 root 10 multiplied by root 16 is 4 root 5 and root nine is three root two multiplying all that together the numbers first of all 2 times 4 times 3 is 24 and the roots are going to be root 100 and from there we know the square root of 100 is 10 so it's going to be 240 as our final answer A and B are solid similar cylinders the ratio of the area of a to the area of B is 9 to 25 complete these ratios the curved surface area is going to have the same ratio because we're still on about the area scale factor but the height is going to be three to five because we want to square root it to work out the normal scale factor and factorize this fully whenever you see a difference between two square values we do the difference of two squares this is probably the most common Mist Mark I ever see on papers because people just don't think of it simple answer we just square root both of them ones positive one's negative that is our answer the graph of y equals X cubed plus six is translated four units to the right the translated graph has equation y equals f of x and we need to work out what f of x is now if it's a translation of 4 to the right that's going to be f of x minus four so what we would do is we substitute that in so it's going to be x minus 4 cubed add six so for those of you that haven't seen a cubic before being expanded it's the same as a quadratic we just have four brackets so the best way to deal with it is we just do two of them first so x squared minus eight X Plus 16. but then we have to multiply all that by an extra bracket so Y equals X cubed minus four x squared minus eight x squared so all I'm doing is kind of the claw method but three times with all the different numbers just like that plus 32x add 16x minus 64. add 6 at the end because this one follows through so Y equals X cubed minus 12x squared add 48x and then minus 64 add 6 is going to be minus 58. and that's going to be our answer there and that is the end of the higher paper