here is an AQA GCSE maths Foundation paper 3 ready for your next GCSE exam so question one what is 6.219 to two decimal places we look at the third decimal place it is one so it doesn't affect the eight so it'll be six point two eight fifty percent of a number is 40 so that whole number must be 80 because 50 is half of it Circle the correct statement 0.7 is bigger than 0.07 shapes a b c d are on a square grid which two shapes are congruent so congruency would be a and C because they've just been rotated slightly here are three number cards use all three cards to make the answer to this calculation a multiple of ten that would have to be 38 times by five because 8 times 5 is 40 and that ends in a zero use all three cards to make the answer to this calculation a single digit number three times five because of bid Mash you would do that first and then take away eight is going to give you seven use all three cards to make this a correct calculation six plus five and then eight plus three eleven over eleven is going to be one Greg wants to buy a games console that costs 267.50 he already has 125 pounds he will save 7.50 each week in how many weeks will he have saved enough so 125 plus seven pound fifty Times by something to equal 267 pounds 50. so if we take away the 125 267.5 take away 125. is going to be 142.50 and then if we divide that by 750 we get 19 so 19 weeks match the algebra to the correct description one has been done for you if it's equal to that's often an equation and an expression is one that does not have an equals a team of two players is picked from these people the team must have one female and one male complete this to show all the possible teams so we can have a and E A and R A and T and then we can have L and e l and R and L and T So six teams in total 500 people started a race 281 men and the rest were women 80 of the men finished the race 30 of the women did not finish the race so there's 280 men that means there was 500 take away 280 is 220 women 80 of the men finished the race so if we do 280 times where 0.8 that gets us 224 which means that 56 did not finish the race and then 30 women did not finish the race so that must mean 190 did finish the race put these distances in order of size 1.8 kilometers is 1 800 meters that stays the same one and three quarters is going to be 1750. meters so the shortest is 1 600. the key part with these is make sure you write them in their original form and that one will be 1.8 kilometers a b is a straight line work out the size of angle X so 103 again make sure you write your workings I know it's tempting not to 103 add 49 is 152 and then 180 take away 152 is equal to 28 degrees some players will ask the shirt color of their football team each answer was either white blue red or green a pie chart is shown two of the sectors are shown we need to complete the pie chart so the pie chart has to add up to 360 degrees so 360 take away 75 add 165. so 75 165 is 240 so that means if we take that away it's going to be 120 and if red is three times the number of green this is almost like splitting it in the ratio of three to one so that's going to be 90 and that's going to be 30. so you would draw this accurately with a ruler of course and you would have your red hair and your green here in a little 30 degree angle that there were 600 players altogether how many players answered white so we know that 360 Degrees represents 600 players so white was 75 degrees so if we do 360 divided by 75 that means we've divided by 4.8 to get down to there so we need to do 600 divided by 4.8 which gets us 125 players Millie has an equal number of 20 coins on 50p coins the value of our 20p coins is 2 pounds 80. so 2 pounds 80 divided by 0.2 is going to be 14 coins so if we do 0.5 pounds technically Times by 14 that's going to get us 7 pounds so seven pounds plus two pound 80 is going to equal nine pounds and 80 Pence here are ticket prices for a theme park Freya buys tickets for three adults and four children she pays the cheapest possible total cost how much does she save compared to buying all single tickets so four months you'd have to show both even if you can spot it straight away so three adults so 48 times 3 and 26 for children so four times twenty six if we add both of those up we're going to get 104 and 144 which means if we add those together it's going to be 248 pounds but with the deal as you can see two adults and one adult is going to make three adults and in total four children so that is exactly what we need so 82 add 120 is going to equal 202 pounds so the special offer tickets is going to be the better deal how much does she save we have to do 248 take away 202 which is going to equal 46 Pounds Leroy buys five single adult tickets he uses a voucher that reduces the price of the tickets by a quarter in total how much does he pay so five single tickets that would be five times forty eight which is equal to 240 pounds and then if we want to take a quarter off we can just times it by 0.75 because that's like 75 and that gives us 180 pounds in total n is negative Circle the expression that is positive when we square a number no matter whether it's positive or negative it's always going to be positive as the outcome because a minus number times a minus number is always a positive number here is a Formula draw the graph of 3.6 x from 0 to 20. so you could hear sub in the values of X so if you had X and Y 0 5 10 20 for example so that's 3.6 times 0 is going to be 0. 3.6 times 5 is going to be 18. 3.6 times 10 36 and 72. so we can plot all of those so 0 0 it all works out nicely so in the formula y equals 3.6 x y is the speed in kilometers per hour and X is the speed in meters per second we want to convert 50 kilometers an hour to meters per second so if we just find 50 on here and then go down you can see that goes to roughly 14 or exactly 14. alternatively we could do 50 equals 3.6 x so X if we divide it underneath which gets approximately 14 to the nearest whole number anyway convert 30 meters per second to the miles per hour we know that Y is equal to 3.6 Times by 30 and that is 108 kilometers per hour so if we want one mile an hour is equal to 1.61 we know that 108 goes there and we want to work out that miles per hour there so what you would want to do here is if you divide 108 by 1.61 you can see what we've Times by to get from 1.61 to 108 which is 67 point something and then we times that by the one on the opposite side so it is just 67.08 for example so 67.1 miles an hour let's say a record was kept of the number of days that 25 students were absent one term the chart represents the results work out the mean number of days absent so what we actually want to do here is times them so five students had one day absence so that's five in total now six students had two days absent so that's 12 days in total eight students had three days absence so that's 24. that would be eight and that would be 20. if we add all those together that is going to come to 69 days in total and we want to divide that by the 25 students and that comes out to 2.76 days per student always double check with your means just make sure they mean makes sense because 2.76 comes roughly around here and as you can see most of the data is centered around that point anyway so that's really good one of the students is chosen at random work out the probability that the student was absent for less than four days so there was 25 students in total so our probability is going to be out of 25. and less than four days would be one two or three days in total as you can see five students were absent for one day six here and eight here so five add six add eight is equal to nineteen so 19 again just put the workings just to be safe but 19 out of 25 would be our answer there Bobby has these notes the total value of her notes is T pounds write a formula for T in terms of x so T is equal to three times five plus ten times x so we can write this as fifteen plus ten X and that is our final answer the side elevation and plan of a cuboid are shown on the centimeter grid draw the front elevation of the keyboard on this centimeter grid so from the side you can see it's three high and from the plan you can see it's too wide so we are literally just going to want to do a two by three rectangle exactly like that and it sometimes is worth just writing the scales down so you know exactly what you do to the nearest thousand there are eighteen thousand people at a festival the minimum that could be is seventeen thousand five hundred the maximum would be eighteen thousand four hundred and ninety nine Circle the equation of the line that is parallel to y equals five X plus two when you have a parallel or perpendicular question literally just look at the gradient now the gradient comes before the X so there which is the five which other one has an x value of five that one there so that's our answer ABCD represents the plan of a field there is a path across the field that starts at B and is the same distance from B A to BC so what we would want to do this is a loci question we'd want to get our compass and I apologize I don't have a compass digitally I can't really do it on here but we would set our Compass to a certain distance doesn't really matter what distance and we would do a Big Arc like this you only really need the middle points here though we would then take our point a bit of the compass and put it on these two arcs here and again as long as the length reaches far enough we want to do a mark there from the point and also put that here and do a point like that if that makes sense and then our line is going to go through there and that would be a perfect split between the ba and BC let me know in the comments if you want me to explain that a bit further because it's not the easiest of topics so that would be the position of the path a is two times B in these situations what I say to people is make up some numbers so if a equals 10 B must equal 5. so that means A to B would be ten to five which is the same as two to one which will be that far one there use Pythagoras Theorem to work out the value of x a squared plus b squared equals c squared and Azure where current year 11's you are given the equation for this so we are working out the long side so we can keep it as that we don't need to rearrange 32 squared add 60 squared and then we square root the whole thing is going to give us C so if we substitute this in 32 squared add 60 squared is going to give us 68 when we square root that before we move on to the next question I'm very happy to announce I've recently partnered with revised guys now if you feel like over the next year you could do a helping hand and a guide through to your GCSE exams then I highly recommend you check these guys out for the price of only a few private tutoring sessions you can get full access to over ten thousand exam style questions 250 unique past papers this alone will be enough to get you way above where you currently are and also really informative I did videos on every single topic you can imagine for your GCSE maths I've got the links to all of this in the description even if you just think it might be useful please go and check them out and if you use code brainstorm you can get 25 pounds off of their course for the entire year thank you for your time and let's get back to the next question 25 Chris visits a library he Cycles to the library in half an hour at a speed of 12 miles per hour so he goes for half an hour at 12 miles per hour he stays at the library for one hour as we can see at the bottom and then he then Cycles home work out the speed in miles per hour at which Chris Cycles home so to get the speed we're going to need the distance over the time we know the time is 0.75 hours because it's like 45 minutes but we still need to work out the distance so if Chris does half an hour at a speed of 12 that is going to be a total of six miles so that must mean that there is six so that also means that the distance he has to travel back home is also six so that's going to be six divided by three quarters and that must mean the speed is equal to eight miles per hour these two triangles are similar work out the value of a so straight away with any question like this is we just want to spot the scale factor so 20 divided by 16 gives us a scale factor of 1.25 so a would be 12 divided by 1.25 and that is going to equal 9.6 Circle the expression that is equivalent to x minus 1 all squared if we expand this out it's just going to be x minus 1 x minus 1 x squared minus two X plus one this one right there here are some information about 26 houses ABC are all different numbers the median number of bedrooms is 3.5 work out a possible set of values for a b and c so we know there are 26 houses in total so 7 plus 8 plus a plus b plus C must equal 26. now the median value Falls at 26 plus 1 divided by 2 which is going to be the 13.5 house now to get a median of 3.5 that must mean it must be exactly in between the three and the four if we do like a cumulative frequency on the right hand side that's seven if we add two to that that makes nine we want three to be at thirty so that must have to be at 4 making our total thirteen C has to be something else to make sure that by the end of it they all add up to 26 so this must have to be five that would make it 18 and that would be 26. so a we're saying is 2b is 4 and C is five and that should give you the right answer a rectangle has a length of 60 and a width of 40. the length decreases by 15 and the width decreases by 10 percent so first of all what do those decreases correlate to in terms of a length so 60 times by 0.85 would show a decrease of 15 percent that equals 51. and 40 times by 0.9 will be 36. so the perimeter now decreases supposedly by 25 percent let's just work out what the new perimeter is so we've got 51 there 36 there 36 also there I'm 51 there so two lots of 51 add two lots of 36. 174. now the perimeter before would have been just 200. now as you can see 25 of 200 is equal to 50. and 200 minus 174 does not equal 50 so they are wrong expand and simplify fully we just do our floor method here and also because there's a negative on the second one we have to include that in there so 8C plus 12 minus 5c plus one so 8C take away 5c is going to be 3C and then 12 add 1 is going to be 13. and the final question 4C so 4C is going to be four times the 4 and the nine so 16 and 36. plus 3D which is going to equal 6 and minus 15. so adding those together we're going to get 22 and 21 and that is the end of this paper thank you very much for watching I hope this helped and good luck with your GCSE paper 3 exam