GCSE Maths Exam Challenge — Full Breakdown & Transcript

[00:05] read the question this is so embarrassing god my math teacher is gonna be so so ashamed of this hey guys welcome back in today's video we're doing something a bit different and that is the

[00:19] gcse exams for high level mathematics and i'm doing the 2018 past paper of australia's year 11 so it should hopefully not be too hard mathematics in high school but it has been like four or five years

[00:35] now so i might have forgotten everything but let's give it a shot and see how i go so let's get started this is the 2018 paper and let's go

[00:49] three to negative two over three over three okay not too odd so that's just three to the 7 minus 2 minus 3 which is three to the 7 minus 2 minus 3 which is 3 squared which equals to 9.

[01:09] all right question 2. so work out the value of v okay so just subbing in numbers once again v squared equals to again v squared equals to 12 squared plus two times negative three

[01:21] times eighteen which equals one four four four minus 6 times 18 equals to 48 108 144 minus 108 equals to 36

[01:37] okay i hope that i don't make any mistakes because i'm doing this live and anyways let's see how it goes i can make s the subject so

[01:50] squared s equals to v squared minus u squared on how many marks is that this is six marks already and i've spent just over a minute okay this doesn't seem very hard at all

[02:06] but it gets harder we'll see company 40 of the bonus is shared equally between

[02:19] three managers rest is shared between salesmen shed equally i'll get 25 percent more money they actually get so 2100 times 0.4 is the amount shared to

[02:35] the managers which is uh 2 1 so 880 because 21 times 4 is 880 and that is between

[02:50] 3 m so the rest is 3 m so the rest is 2 1 0 times 0.6 which equals to 2 1 0 times 0.6 which equals to 1 to 60.

[03:06] basic math but yeah that should add up to 2 100. yeah that should add up to 2 100. 2100 times 0.6 is 1260 divided by 7 four per person per salesman

[03:25] done division without a calculator okay so

[03:37] one there so 56 left over that's eight so 180 that's eight so 180 180 per salesman um now if it was just shared between two 10 people equally then

[03:51] 10 people equally then if 10 people equally he would get 210 pounds 30 over 180 is

[04:04] well it's clearly not 25 but that's one over six so it's over six so it's how much is that now 16.67 percent yeah that's right so they did not

[04:21] obviously get 25 percent more money so therefore therefore salesmen not correct

[04:33] only on four minutes minutes if only three tabs are used so

[04:47] if only three tabs are used so assuming five taps equally so

[05:03] filled that means it would have filled um one fifth of the pool so cool so um how do we get it to three like it's pretty obvious but like i'm just trying to see if i can explain it

[05:18] trying to see if i can explain it uh one fifth of the pool

[05:31] in one minute it would fill 1 over 120 times 5 which is 720 1 over seven twenty three taps would fill three over seven

[05:43] twenty which is one over uh to get that so that means it would

[05:56] uh to get that so that means it would take hundred so three over six hundred

[06:09] which is one over two hundred so that means it would be two hundred minutes means it would be two hundred minutes well i'm pretty rusty

[06:21] school saw this they'd be pretty ashamed of me right now your working out okay so that was just or taps fill at the same speed

[06:44] right now but like it's not an actual exam that's being marked so it doesn't a plane travels at a speed of 213 miles per hour just just use kilometers but i don't estimate the number of seconds it takes the plane to travel one mile

[06:58] it takes the plane to travel one mile okay so okay so how many okay so to 13 miles in 3 600 seconds right so

[07:13] in that one hour there's 60 minutes in one minute the 60 seconds so that would just be so we're dividing one mile okay

[07:34] divided by 213 for the number of seconds oh another long division i didn't see a point of the test like it just doing stuff we did in year so long okay so that's one there

[07:51] okay so that's one there two one three uh ten minus three is two one three uh ten minus three is seven two thirteen so that is we've got an estimate so that seems

[08:06] about 17 seconds right because two times seven is fourteen times seven one two seven nine fourteen ninety one okay so just under 17 seconds

[08:20] 17 seconds so but it is very close so uh i don't know how many decimal places is two

[08:37] that's understood overestimate uh so 17 seconds seconds and overestimate

[08:55] [Music] is 16 point something

[09:13] is less than 17. oh how do i explain this 213 times 17 is greater than 3600 but okay i'm not sure if that's what they're looking for but that's what i'm going to put okay way up

[09:28] question six solve the simultaneous equation okay yeah this is what we learned in year seven australia wow i really wish i did i did high school in the uk now

[09:41] so using the second equation we get x is equal to three y plus nine so five three y plus 9 plus y equals to 21. plus 9 plus y equals to 21. 15y plus 45 plus y equals 21.

[09:56] 16y equals to negative 24 y equals to negative 1.5 right okay and then that means x using that equation is equal to 4.5

[10:08] using that equation is equal to 4.5 so double check 4.5 minus so double check 4.5 minus minus 4.5 is 9 yep minus 4.5 is 9 yep 5 times four point five check

[10:21] point five equals to twenty two point five minus equals to twenty one yep okay so x equals to 4.5 y equals negative 1.5

[10:34] equals to 4.5 y equals negative 1.5 oh the time

[10:47] semicircle okay probably finding the area oh probably finding the area oh okay abs diameter ac is the arc okay

[11:03] square okay area of square is easy okay area of square is easy which is just

[11:17] 20 squared area of shaded region

[11:29] um so the r is pi r squared on four since we're taking a quarter only which is pi times 20 squared on four

[11:42] pi times 20 squared on four and then i forgot area so that's not the shade region that is the quarter circle area of uh small

[11:58] hemisphere the heaviest we have a semicircle semicircle series

[12:12] it is pi r squared on 2 which is pi times 10 squared on 2. pi times 10 squared on 2. so area of shaded region remember we're trying to look for that pi of 8

[12:25] pi of 8 area of shaded region is

[12:39] that one minus that one so pi 20 squared on 4 minus 10 squared on 2 20 squared on 4 minus 10 squared on 2 which is pi 20 squared on which is pi 20 squared on 4 minus 20 we doubled that times four

[12:52] and then times the bottom by four as well two times four so that is just pi 20 squared on it so

[13:12] shaded on area square is then just get this over 20 squared so that is pi

[13:26] over eight yep that next question

[13:39] write down the exact value of 10 45 okay so oh my god i actually forgot this tan is this over that so tan 45 is one

[13:57] 60 0.5 work out the value of x oh x oh okay so well four over x equals to

[14:18] 4 equals to 0.5 x x equals to 8. i might have to do the a levels next time um

[14:31] all right question nine how many questions are there questions are there so ten oh okay i think it will get so ten oh okay i think it will get harder

[14:55] of minutes the trains were delayed correct to the minute okay the shortest delay of zero the longest delay was 42.

[15:24] about the delays on monday huh so it's not linear so there were a lot here there were a lot lot short delays

[15:42] 42 so it was 42 is here i kind of forgot how to draw a box plot now um oh okay so now there's this uh okay

[15:54] at 12. so that is 12. so that is here at four minutes delayed so that matches to this and what about

[16:08] so that matches to this and what about 24 that is matching to 10-minute delay okay it looks kind of what we're looking for and then 36 so yeah because um each quarter right 0 12 24 36 48

[16:23] 0 12 24 36 48 36 is here at 20 minutes delayed okay so that is kind of the box plot i reckon i think that's how i do a box plot i kind of forgot

[16:37] kind of forgot okay yeah what's that for

[16:49] on monday with the distribution whoa uh whoa uh i don't know what can i say uh i don't know what can i say uh monday spread further apart

[17:04] this is one of those bs questions that we kind of have to do in some last tests we kind of have to do in some last tests um on average um on average it was longer

[17:34] max i mean roughly is still very similar question like this before mary says the longest delay on

[17:48] tuesday was 33 minutes yup this means there must have been some delays between 25 and 30 minutes uh no

[18:08] have been a lot of 33 minutes

[18:28] in between 25 and 30. so there were a lot like at um this point and a lot of this point but none zero here i guess

[18:42] it's just one over five x minus one one i don't know if it wants me to expand one over five x minus five yeah okay uh

[19:02] factorize fully 50 minus two oh okay so 2 25 minus y squared 2 5 minus y five plus y yeah this isn't

[19:14] as hard as i really expected it would be but question 11 now jack and say you work for coming out sauce boxes or breakfast cereal company idea switch over and do not change the price

[19:28] the amount of serial in each box so who wants to her idea to yet by what percentage price okay so assume

[19:42] price okay so assume 100 of cereal initially so now 125 for

[19:57] 125 for x is equivalent to x is equivalent to 100 for 100 for uh y dollars

[20:15] so in this case we reduce we divide by 1.25 percent to match what we're looking for and x divided by

[20:28] one point two five x okay so percentage okay divide by 5 over 4 so it is 0.8 which is

[20:44] 80 right so this is if we flip that up equals to 4 over 5x which equals to zero point eight x so um twenty percent reduction

[20:59] discount would be at 80 so it's a 20 reduction

[21:16] abc points on circumference circle o d a is tangent to circle a okay circle geometry let's go kind of forgot the formulas but angle b a e

[21:29] a e is 56 cbo is 35 cba cbo cbo okay cao what's ca okay so this

[21:42] cao what's ca okay so this is what we're looking for

[21:55] to opposite angle what's the formula what's the this angle is equal to that angle i remember remember so bca equals two

[22:09] 56 degrees uh tangent angle too strong that but that's 56 that's 35.

[22:27] uh okay crap now i was not right in thinking now i was not right in thinking ah okay okay so b-o-a equals to 2 times

[22:41] 56 equals to 1 1 2. equals to 1 1 2. angle at center

[23:02] those two angles okay i can't be bothered like writing up the theory first so that those two are 180 minus one one two on two since those two are equal because radii are equal

[23:15] like it's only three marks so uh 68 on two equals to 34 out okay i did so angle sum

[23:32] okay i did so angle sum b c bac is equal to 180 equals to 56 plus 35 plus 2 times 34 plus 2 times 34 plus cao

[23:53] oh i can't believe i'm not allowed to calculate it calculate it plus three times 35 approximately so plus three times 35 approximately so 103 plus cao

[24:17] because angle some of that and there you go transformation that maps triangle a to triangle oh

[24:33] i remember how to do this i mean it's just

[24:51] rotate 180 what was the single transformation though

[25:27] i don't know times one and rotate don't know how to what the other platform platform never done it before

[25:42] 81. so yeah this is not too hard 16 on 81 to the power 3 on 4 is equal to 2 to the power of 4 on 3 to the power of 4 to the power of 3 on 4 which equals to

[25:55] cancer 2 to the power 3 and 3 to the power 3 equals to 8 127 uh yeah that has working so work out the value of a plus b plus c

[26:08] value of a plus b plus c okay so plus c is equal to 10 times together which is

[26:26] times one on root three which equals two one so a plus b one so a plus b plus c equals two zero

[26:40] 15 three solid shapes a b and c are similar surface area is for surface areas b looks like a square ratio of volume oh

[26:52] looks like a square ratio of volume oh okay yeah okay yeah so it's a cube yeah that's a square proportion two and five

[27:04] and uh length ratio of shape b to volume machine c is 27 so it's three cubed c is 27 so it's three cubed and four cubed

[27:21] and four cubed is that right four times four yeah yeah of c okay so height

[27:41] height b to c is equal to 3 to 4 because 3 cubed and 4 cubed so that means a to c is equal to

[27:57] this is it would just make it easy 15 to twenty which equals two times three so six to fifteen is six to twenty which is equal to

[28:23] written as that okay so this is equal to zero two five six five six five six dollars

[28:35] five six five six five six dollars which equals to

[28:50] zero five six okay it's been a while since i did this

[29:11] so that is how does this work

[29:25] exon 100 okay okay so that is yeah so these two are equal equate these two now

[29:41] so just comparing these two equations to get this let's do x to get this let's do x 99x on 100

[30:18] 99 plus five times 5.6 on four nine five which should i'm going to bother calculating one twenty seven four nine five assuming what i've done

[30:36] right okay we're 30 minutes in there okay we're 30 minutes in there my throat is pretty dead though

[30:50] my throat is pretty dead though [Music] 21. uh oh is a triangle

[31:31] what oh oh p to p m looking for um all right

[32:23] o and and b how the heck do i do this i did by ariel i did by ariel now

[32:59] m is the midpoint of a b opm apn are straight lines if it has a and b in the result then i'm going to be very annoyed

[33:16] i'm going to draw another line through this ends up oh

[33:32] don't know this one i just put a big f here and we'll just skip it for now and move on to the last question which is question 22 and we're 45 minutes in so

[33:44] in a box there are three more blue pens and green pens in the box there are more than 12 pens in the box

[34:00] the same color as 27 on 55 work out the number of ring pens on the box okay this is very doable so let's say there's n pens in box you know n is greater than 12 and let's

[34:17] say there's b blue pens

[34:32] and we also know we can remove these from the equation we can we know that from the equation we can we know that um b equals to three plus g green so

[34:44] green so let's start with n minus b to b equals to n plus three b equals to n plus three on two uh g is equal to

[35:02] uh n minus n plus 3 on 2 which is n on 2 minus n minus 3 on 2 okay so

[35:17] n minus 3 on 2 okay so it takes two pens in the same color b and g so that would be our second simultaneous

[35:29] is uh blue and blue or green and green so uh blue and blue or green and green so let's say it's blue and blue first

[35:45] then we have uh so n plus three on two on n and the second one is green as well n minus one and there's one less so n

[35:57] plus one on two this is blue and this is blue and green is

[36:13] so this first one and second one so this gives us and this is all over two n n minus 1 plus

[36:30] n squared minus 8 n plus 15 equals 2 okay so that's good to n squared to [Music] minus four n plus 18

[37:10] okay so what are the 10 and 11 so that's only possibility n times n minus 1 is a number like 10 and 11

[37:25] equals to so that means which is yeah 110 so that means which is yeah 110 55 times 2 so you get 55 times 2 so you get n is 11. so 121

[37:40] n is 11. so 121 minus 22 plus 9 is

[38:04] huh i must have done some oh okay on four yeah yeah one yeah okay yeah on two yeah so that equals two

[38:21] the 2 is still there so 220 which is equal to 2755 n is equal to 11 wait what the heck

[38:36] than 12 pence in the box huh so what else 55

[38:48] times 3 is 165 uh 5 and 2. so 5 11. um what else could it be

[39:28] harder than the first few questions that's for sure

[39:50] so 55 let's see so it can be 11 10 unless the top is divisible by 11.

[40:12] eight so squared plus eight that's divisible by eleven divisible by eleven what could that be

[40:39] ah so there's more than 12 pins in the box so

[40:51] what okay so it has to be 11 and 12 but then there's a 5 there as well

[41:06] 20 so 44 and 9 oh sorry 44 and 45 oh sorry 44 and 45 could that be it that probably is it so

[41:33] and n minus 1 is 44. so 45 squared is equal to 4 times 5 plus 25 45 squared is equal to 4 times 5 plus 25 so 22 5 minus 2 that's why i have so much minus 2 times minus

[41:48] so much minus 2 times minus 90 plus 9 90 plus 9 okay over 45 times 44 so 9 times 220 times four at the bottom

[42:03] because i forgot that in the equation so

[42:16] so yeah the two's there so 1 so 1 18 1980 times two is that right

[42:36] 203 five one one nine three five plus nine nine one nine four on one nine four on 1980 is that

[43:02] it's just on the half that seems about right so does this equal to 27 on 55

[43:20] so what is the factor here 1944 divided by 36. ah this is four five five yeah 180 oh it does work one four is four of those yep 54. sweet so n is 45

[43:38] 54. sweet so n is 45 and that was found from it has to be a of 5 and 11 105 and 1 and 11 and the difference is one and it wasn't it was more than 12 so n is 45 that means

[43:51] means the number of green is the number of green is uh n minus 3 on 2 which is

[44:03] but that's 21. so that just leaves the last question which i didn't get which is question 21. ah

[44:25] that's a and that is b and i want the ratio

[45:03] i'm gonna guess two to three but it i mean so that's the last one last question i think i got most of the rest um when i didn't get um i did finish uh question 17

[45:20] which was just subbing these two numbers into the equation and finding solving for the two unknowns a and b so two equations two unknowns you can get that and 18 was some graphing so one of them

[45:32] i drew the graph and one of them i put a negative sign in there and 19 was yeah a function manipulation and

[45:44] another function manipulation and 20 was just uh factorizing and rationalizing the denominator done uh i'll just go and mark it now and

[45:59] double check the answers with my marking sheet that i have here and work marking sheet that i have here and work out what it is

[46:13] answer's right i'll like mark it correct because like um in terms want us to lay it out and i've never done it before but right then i'm just going to assume that i can do the working out for

[46:27] um if i actually did know how to do it so our answer is nine yep six or minus six holy f

[46:40] read the question this is so embarrassing oh my god my math teacher is going to be so

[46:53] so so ashamed of this

[47:14] yeah which is correct so in total out of eighteen lost five minus one minus one minus one is 72 out of 18.

[47:26] get back and quickly check what is that good or bad i actually do not know but i'm gonna see what like the average mark on it is and

[47:38] yeah let's get back to it okay so doing a little bit of digging um i later found out that the 72 out of 80 is 90 and that is roughly either a grade 8 or a grade 9

[47:51] mathematics the grade 8 is 85 plus and grade 9 is 90 plus plus demonstrates creative use of relevant mathematics to solve an or use of mathematics to provide an answer to an ambiguous problem

[48:07] the questions and i lost a few marks and silly mistakes don't know if this isn't like a formal grade or anything but i just based on a rough estimate and

[48:20] guide from like some teaching educated guesses by teaching experts it says but uh do let me know what you guys got similar gcses and like let me know if there was anything wrong with like

[48:33] the way i marked it or the way i gave myself a grade in the end you guys want to see more of this kind of format of videos later on in the definitely let me know in the comments if you want me to do some other exams

[48:45] i might have a girl at the a levels next time or some american sats and give that a try or maybe i'll just redo my uh hsc mathematics that might be in one of the later videos so yeah hopefully you enjoyed the video

[49:00] big thumbs up down below and i hope to see you guys up down below and i hope to see you guys in the next one