for your gcses past papers are the best thing to practice however past papers take a long time so in this video I have summarized an entire Foundation past paper in under 20 minutes as I go through the questions I highly recommend you pause the video and give it a go for yourself just to make sure that you could maybe start the question but if not my mark scheme will be there and I will show all my workings and how to get to the right answer so thank you and I hope you enjoy here we have an AQA GCSE maths paper One Foundation paper it is a non-calculator exam so starting off with question one 0.02 times 100 is going to be two Circle the expression that is equal to X Plus X Plus X that's 3x minus X takes us back to 2x add X will be 3x so that'll be our answer 260 millimeters in centimeters 10 millimeters in a centimeter so 26. which shape can have sides with lengths that are all different that would be the trapezium all the others have to have similar ones minus eight times five is going to be minus 40. Luke buys four apples and five bananas the total cost is 3.70 each apple costs 35p 4 times 35p is going to be equal to one pound forty so we want to do three pound 70 take away one pound forty which is equal to two pound Thirty and so then we want to do 2 pound 30 divided by the five bananas is equal to 46p so our answer is going to be 46p Rashid counted the piece of homework that he's done in three subjects he draws a pictogram and this is important here so one Circle represents four pieces so if he's done five pieces of geography homework that would be one full circle and a little section like that Russia had spent 30 minutes on each piece of homework work out the total time he spent on homework for these three subjects give your answer in hours and minutes so looking at this we want to work out how many homeworks he had for maths so you can see there's five circles here so five times four is going to be 20. English is going to be 14 and we know geography is five so adding those up is going to be 39. so 39 homeworks multiplied by half an hour is going to equal 19.5 hours which is 19 hours and 30 minutes a travel company is taking some passengers on a trip they can use coaches on minibuses each coach carries this each minibus carries this the trip would fill exactly three coaches so 53 multiplied by 3 means they have 159 passengers in total so how many times does 12 go into 159 that's going to be one with three left over and three remained at six so they're going to need 14 in total because you can't hire 13 and a half mini buses so it's going to be 14. one side of a triangle is extended Circle the angle of X so we know in a triangle it adds up to 180 so 40 add 60 is 100 take that off 180 we get 80. so the straight line adds up to 180 so it has to be 100 Carvel uses this calculator to work out this circle the last digit now if it ends in a 208 multiplying two and eight together gets us 16 which ends in a six complete the diagram so that it has rotational symmetry of order 4 and center of rotation at a so rotational symmetry of order 4 means that you can spin it within 360 four times so that it looks the same each time so you'd basically have to have the same thing but just replicated four times around the point a so kind of like a windmill I suppose 10 of 2100 is 210 work out 43 so I have 10 equals 210 then 40 is equal to 840 by multiplying that by four we can also work out one percent is twenty one so three percent is equal to 63. so 840 add 63 leaves us with 903 Casey records the number of cars here is the data so we have a tally and a frequency chart we do not need to complete the chart write down some criticisms so straight away I've noticed in the groups there's a lot of overlapping so overlapping in the groups would be one criticism and criticism two if you have a look in our data you notice there are some points such as 53 and 57. that wouldn't fit in any of the groups so the groups don't account for all the data so that would be a big problem now because 57 and 53 we wouldn't know where to put it counters in a bag are red white or blue we know that the probabilities have to add up to one so 0.15 add 0.4 is equal to 0.55 one take away 0.55 is equal to 0.45 so that would be our answer here here is a calculation you can use the calculation to help answer the following questions so if this equals 2604 if we just do that backwards the answer is going to be 31 there 3.1 times 8.4 we know 31 times 84 is 2604 so 3.1 times 8.4 we've divided the whole thing by 100 basically so it's going to be 26 point o four there is a point in there and 31 times 85 so if we know that 31 times 84 is 2604 31 times 85 is going to be 2604 with an extra 31 here because we have 85 lots of 31. so our final answer is going to be 2 6 3 5. a password has 30 characters it's made up of five numbers 15 letters and some symbols so just to get four markings here I would say 5 out of 15 equals twenty Thirty minus 20 is equal to 10. so the ratio for that would be 5 to 15 to 10 and then because it's asking for the simplest form each of these numbers divide into five so it's going to be one to three to two next we're adding fractions straight away common denominator we can multiply this one by two making it 10 over 12. this one stays the same because we have that common denominator now we can write that as 17 over 12 which as a mixed number 12 goes into 17 once with 5 left over so that's going to be our answer the cost of making a phone call is a fixed charge plus a charge per minute write down the fixed charge now the fixed charge is always going to be before the calls even started how much does it cost you so at zero minutes you can see it's 20 so 20 pence will be our answer next we have to work out that charge per minute so going back to the graph you can see this straight line here ultimately we want to work out the gradient of that graph so for those of you that don't know the gradient of a line is going to be the change in the Y over the change in the X so you can see the change in the Y goes from 60 to 20 so that's going to be 40. and the change in the X goes from zero to five so that's going to just be five so if we go back over here 40 divided by 5 is equal to 8 Pence per minute work out the cost of a phone call lasting seven minutes so we don't actually need to go back to the graph here we know that 20 is the fixed charge and for every minute it's going to cost eight P so 8 multiplied by 7 is going to be 20 add 56 which is equal to 76 Pence a company sells bags of toffees and mints the company claims the average number of sweets per bag is at least 50. using medians okay so we need to work out the medians and then verify if that's more than 50. I'm actually going to start with the mints on this one because it's already in order so it's a little bit easier so the mints because it's 10 the median value is going to be the 5.5 because 10 doesn't have a middle number so one two three four five six in between those two we have 49 that is not bigger than 50. so it's going to be no because the median is 49. for the toffees the median value for 11 is going to be 6. so which one is our lowest we're starting off with 47 then we have 249s 250s so that's five so far so the sixth value is 51. so the medium for the toffees is 51 and yes that is bigger than 50. so we're happy with that Freddie tries to work this out his answer is this by rounding each number to the nearest ten show that his answer is incorrect so I'm going to rewrite this by estimating it so using the nearest tens 29.15 is going to be 30 83.47 is going to be 80 and 9.82 rounds up to 10. so that's going to be 110 over 10 which is equal to 11. a straight line passes through two parallel lines Circle the angle that is corresponding to angle X corresponding refers to the F lettered angles where these two angles are the same so if you were to imagine this upside down the X would be this bottom one here and the B is actually going to be the one corresponding to that so that's going to be our answer Lucy wants to simplify this her answer is this is she correct now very common mistake with this one and it's very difficult to Spot It so I'm just going to rewrite it first when we expand out this bracket we have to take the minus into consideration 6A minus 7B because it's a minus 2A as well these technically count as a double negative so it's going to be plus 2A so it's going to be actually 8A minus 7B so Lucy is not correct she also wants to simplify this she says we add three and five and then we add 2 and 7. so indices laws when we're multiplying we do add the powers so the two and seven part is correct however the normal numbers we still multiply so we would do 3 times 5 so she is not correct on that one our final answer should have been 15p to the 9 there things of a number 10 times the number equals 10 divided by the number the first answer that comes to mind is one because 10 times 1 is equal to 10 and 10 divided by 1 is equal to 10 as well if you think of any other answers please put them down in the comments I'd be intrigued to find out if there's any others Lily's age is two years and four months Hugo's ages one year and eight months right Lily's age in months as a fraction of Hugo's age in months so converting these both into months we're going to have 28 there because 2 times 12 add 4. and then one year is 12 months Abby is going to be 20 and because it's Lily's age as a fraction of Hugo's age is actually going to be 28 over 20. which dividing both of those by four gets us down to seven over five which will be our final answer working alone it takes Kevin four hours to paint an area of 12 meters squared Kevin and Steve are going to paint an area of 24 assuming they work at the same rate they're saying it will take them eight hours well if it takes Kevin four hours to do 12 meters squared it would take Kevin eight hours to do 24 meters squared because we're doubling the size of it so if there's two of them it's going to take half the time so it's actually going to take four hours to do 24 meter sweat so they are wrong solve this so solve an inequality people often get confused with this because it looks a bit different but treat it like an equation so straight away we're going to want to take away 3x from both sides leaving us with 2x plus 6 is greater than 15. from here we want to take away 6 from both sides because we want the x's on one side the numbers on the other side so that's going to leave us with nine so X is greater than 4.5 and that'll be our answer there write down the inequality represented by the number line so X is going to be our middle number when we have a Hollow Circle that's going to not be an equal to so that's just going to be 5 and a solid circle is going to be a less than or equal to 2. the diagram shows an octagon x equals 1 and y equals five are lines of symmetry so what that means is the 0.15 is actually the center of the octagon and it also means that the distance from P to the center is going to be the same as the center to Q so if we can work out what's going on to get from there to there we can work out what's going to go from the center to q and we can use that to work it out so if we know to get from minus two to one that's going to be 3 and to get from minus six to five that's going to be 11. so we have to do the same thing going across and up again so starting at one adding three is going to be four that's going to be our x coordinate and 5 add 11 is going to be 16 and that's going to be our y coordinate there work out two thousand times seventy thousand in standard form I'm going to convert these straight into standard form two times ten to the three multiplied by 7 times 10 to the 4. when we multiply standard form we want to multiply the two numbers 14 and we want to multiply the two Powers now when we multiply Powers we add the powers together so it's going to be 10 to the 7. now this isn't proper standard form so that has to be 1.4 because that's got smaller this one has to get bigger so 1.4 times 10 to the 8. work out 1.8 times 10 to the 2 and fraction just means divided by 3 times 10 to the minus 1. similar concept firstly when we're dividing we take away the powers so that's going to be 10 to the 2 so 2 minus minus 1 which is actually 3. and then 1.8 divided by 3 is going to be 0.6 again not proper standard form so we increase that one so we have to decrease this one and because they want our answer as an ordinary number it's going to be 600. rather than standard form a b c and d are Junctions on a Motorway we know that CD equals 3 times a b so if we call this a b x then C D is going to be 3 lots of X we also know that BC is 25 miles she drives for 30 minutes at an average speed of 62 miles an hour straight away we have a time and we have a speed we can the first equation that comes to mind is speed equals distance over time we want to eventually work out a distance so that's going to be speed multiplied by time half an hour is 0.5 hours and 62 miles an hour would be that one so subbing those into the equation we get 31 and that is the distance from a to c now a to c we know is 31 so X must equal 6 because 25 adds something to get to 31. now if x equals 6 we know that this whole thing's 31 so c d must be three lots of six which equals 18. so the distance a d is going to be the 31 that is a to c add this 18 which gets us to 49 miles and that will be our answer here is a sketch of a graph this is quite a tricky question to be honest you might recognize the graph more commonly drawn like this and that's it known as a reciprocal graph which is normally y equals 1 over X the one that looks most like that is going to be this one here write 200 as a product of prime factors 200 we do a factor tree for this 20 and 10. 5 and 4 5 is prime two and two and ten is just two and five writing our answer in index form would be 2 to the 3 multiplied by 5 squared so when we have those Powers also known as product of its prime factors here is a right angle Triangle used trigonometry to work out the value of x now this is a non-calculated paper so you need to know your exact trig values so straight away which sides do we have opposite the angle is going to be the O and the long side is the H so from our socatoa we know that we want soft here which is sin so sin of our angle which is 30 is going to be X over ten multiplying that up we're going to have 10 times sin 30. now from the exact trig values that's just something I've memorized at this point sin 30 is the same as a half so 10 times a half is going to be 5 meters and the final question on the paper factorize a quadratic now factorizing means put it back into brackets and a quadratic would have two brackets we need to find two numbers that multiply to make ten and add to make seven that's going to be five and two so that is going to be our final answer and that is the end of the paper