First time solving a GCSE maths paper!

[@bprpmathbasics]

Correction to the last question: kzbin.info/www/bejne/hJjUmIurn798iLs

[@fantasypvp]

Maybe try an A level further maths paper XD. We sit GCSEs at 16 so it's not really an equivalent to American highschool which ends at 18 rather than 16.

[@phuc6523]

These questions are in grade 9 exams in Vietnam, not in high schools.

[@uyangapuujee4508]

I sat this paper, the last question gives me flashbacks 💀

[@okenough2124]

Same. That LAST CIRCLE QUESTION

[@thecoolpanda1]

same 💀

[@nobored451]

Those are free

[@JJSbestmoments]

nothing compared to question 20 in june 2019 p2

[@nobored451]

@@JJSbestmoments that wasn't hard lmfao This was wayy harder

[@bprpmathbasics]

Don’t ask a calculus teacher to do a cumulative frequency graph 😆

[@72kyle]

Shocking! I really love your videos but as an English A-level teacher that teaches Calculus, Geometry, Algebra, Mechanics, Statistics... And so on. Do you specialise as teachers more I guess? I find it amazing that you don't know about cumulative frequency! Plot the CF at the end of the interval since you have reached that frequency only by the time you reach the end of that interval. Use the graph to estimate the quartiles by going across from the CF axis (vertical) to the line then down to the horizontal axis and the value of Q1 and Q3 etc. Props to you for putting yourself out there with this one!

[@anuragguptamr.i.i.t.2329]

Sir, in question 21 your answer was wrong. Area of a circle's sector is not r.Theta. Area of a circle's sector is 0.5 r^2 Theta.

[@zachansen8293]

@@72kyle Are you in the US? I've never heard of this type of table or how to solve weird questions about them.

[@charg1nmalaz0r51]

@@72kyle From what i have noticed they split their maths lessons up into topics with different teachers. Unlike over here where you have one teacher teaching the whole curriculum. So this guy has probably been doing one type of thing for a very long time lol

[@72kyle]

@@zachansen8293 Nah I'm in England. So our maths contains Algebra, Number, Proportion, Geometry, Statistics and Probability all in one subject at GCSE (16 year olds). So I learnt these diagrams when I was like 15. I guess there will be other things that everyone in the US learns that I probably have never heard of! 😄

[@harryslaughter9393]

As a maths teacher in the UK, I would recommend trying the A-Level Mathematics and/or A-Level Further Mathematics (for advanced students) papers. A-Level qualifications are for 18 year old students (pre-university) and therefore include calculus, complex numbers, linear algebra etc. GCSEs are for 16 year old students so are generally more basic and focus on fundamentals. Great video! :)

[@YouTubechannel-fb9yd]

Yeah but in America we do all that stuff at 14-16 yrs old? I did pre-calc (so complex numbers, unit circle etc) and calc 1 at 14/15. Is the UK rlly that behind in maths?

[@TheMightyHams]

@@KZbinchannel-fb9yd It's difficult to judge because your naming schemes are different to ours. UK schools tend to emphasise giving students a wide range of subjects up until 16, and then they specialise. So while you might be ahead at 16 years old, any UK students who progress with maths after 16 will be doing maths as one of only 3-5 total subjects that they will study for the next two years. I've had a look through the pre-calc page on Khan's Academy and I believe a few of the topics are covered at GCSE level. I don't believe limits, matrices or complex numbers are included in that. GCSE students also (I believe) have the option to do GCSE Further Maths which covers a lot of the pre-calc stuff. A-level Maths covers the rest of the pre-calc stuff and brings you up to a decent standard in the introductions of calc 1 but will also split that qualification evenly with statistics/mechanics. A-level students (16-18) also have the option of doing A-level Further Maths that will complete most of Calculus 1 and some Calculus 2 (I think), although that's only 1/3 of the syllabus as students are also expected to cover both mechanics and probability & statistics. Most UK STEM degrees will cover calc 1 and 2 (and 3) in the first year anyway to make sure everyone is up to speed depending on where they had their education. I'm a final year Mechanical Engineering student and I haven't done any maths modules since 2nd year of uni. They weren't called calculus 1-3 for me, just engineering maths 1 and 2, and covered up to fourier, laplace, taylor/mclauran, 2nd order ODEs, vector calc, volume & surface integrals, stokes, and partial diff 2 and some extra modelling/stats stuff that's only relevant for my course. Edit: There were reforms in 2017 that changed the syllabus so now there's a bunch of stuff with algorithms and modelling and I believe the calculus has been stepped up. Hopefully someone who's a current student can offer more.

[@PebbleSmall]

@@KZbinchannel-fb9yd No you don't lmao you're only required to take AP Calc 1 and 2 before college right really? Comparing a few students who will take college classes 4 years early and saying that it is representative of the US education system is delusional. A level FM contains elements of linear algebra (which there isn't an AP course for if I'm correct, meaning that it isn't taught in high schools usually?) as well as requiring two optional modules in either even more pure maths not in the core pure (includes taylor series and some other calculus, some basic group theory and modular arithmetic) or in statistics or mechanics. But then, A level FM doesn't include some parts of calc 1 such as epsilon-delta definition of a limit. As far as I can tell the A level FM is harder in some ways and easier in others than the AP courses which high school students are taking. Honesly just quit lying through your teeth and spreading misinformation. Students aren't consistently taking calc 1 at 14 in US high schools. I feel like you just wanted to mention you took calc 1 at 14 to flex in YT comments really, which is just sad.

[@YouTubechannel-fb9yd]

@@PebbleSmall can you relax? lololl. I was asking and no it’s very normal to take precalc at 14 - and move onto calc 1 at 15. And I don’t go to a private school or anything before you ask. I didn’t take calc 1 at 14, I took it at 15 - which again is very normal

[@notruuuuuth8186]

I think the only thing we have that’s comparable is GCSE further maths which covers the basics of calculus. Most students don’t do it though, majority only do GCSE maths

[@HenrikMyrhaug]

Full explanation of question 10: a) Cumulative means everything up to that point, so to find the cumulative frequency, you take the sums of the frequencies up to that point. If the frequencies are (2, 4, 5, 3, 2, 4), the cumulative frequencies are (2, 6, 11, 14, 16, 20) Conversely, the frequency values will be equal to the difference between each step in the cumulative frequency (with the first frequency being equal to the first cumulative frequency) b) The cumulative frequency graph is a line graph, where you draw the cumulative frequency values as points at the end of each range, and connect the dots (with a smooth curve). Because the first value range is 0

[@bprpmathbasics]

Thank you for the explanation. I wasn’t sure the rule to do the graph for the x is given in intervals. I will remake that one. Thank you!

[@harley_2305]

I actually sat this paper when doing my GCSE’s, by then I had been watching a lot of your videos and they helped me gain confidence in my abilities. I ended up getting a grade 8 (second highest grade and roughly equivalent to a high A/low A*) so thank you

[@mysticflame5456]

So r u doing ur alevels this yr

[@harley_2305]

@@mysticflame5456 I already did my maths a level last year, and my further maths this year along with physics (my college does maths in 1 year and further maths the next)

[@mysticflame5456]

@@harley_2305 did u get ur results back or do u get that in august

[@harley_2305]

@@mysticflame5456 I got a grade A in my maths a level from last year, this year I’m predicted an A* in further maths (not doing the stats module, that was my biggest downfall in a level maths) and a B or A for Physics. I haven’t sat the papers yet but I will next month and then get them back in August

[@mysticflame5456]

@@harley_2305 alr u planning to go uni or r u going straight to a job

[@Andromeda4482]

So glad I got to see you take this paper, I helped teach a class who would take this exam! It was the first paper out of COVID, so was an interesting time for teaching staff! That last question made it into national news, at it wasn't well received! You should consider looking at an Edexcel A-level Maths Paper 1 or Paper 2, these are pure papers (Stats and Mechanics are in Paper 3) and are the exams you would take in college to qualify for university. For context our curriculum goes GCSE>AS>A-Level>Uni! - If you do ever do an Alevel paper, do note there is a formula booklet that would be with it!

[@evanpoole7829]

that question 21 is probably the most notorious gcse maths problem ever made

[@ManiacalPenguin_]

I sat it

[@x6173]

I sat that paper, didn't think it was too bad especially looking back after the paper, imo i think the conditional probability question with the red and green marbles from 2019 (i think) is more notorious

[@legend_legend_legend]

@@x6173 the hexagon question is also quite bad, 2023 p1 q21 i think

[@x6173]

@@legend_legend_legend havent seen that one, after i sat my gcses i never wanted to look back😭 i didnt hear about any bad hexagon questions but I did hear about a difficult octagon looking question if that's what you meant but i do not know

[@filipeoliveira7001]

It was easy asf you just had to notice the equilateral triangle formed by the radii and subtract 4 60 degree sections from the area of one full circle

[@shipmate8008]

Thanks, this is like a fun way for revision.

[@mikejackson19828]

Petrol is what we call gasoline in the UK.

[@bprpmathbasics]

Ahh I see!

[@charg1nmalaz0r51]

@@bprpmathbasics petrol short for petroleum spirit, aka gasoline

[@TheAussieLeo]

@@bprpmathbasics Gasoline is a derivative of Petroleum, we just shortened the word :)

[@hendy643]

@@TheAussieLeo Gasoline IS petroleum. the term gasoline derived from the Brand Cazeline. Kinda like how a vacuum Cleaner get's called a Hoover in Britain.

[@TheAussieLeo]

@@hendy643 Forgive me if my sources are incorrect, however, the source info I have cite that Gasoline is a 'finished' product of Petroleum products, ie Oil -> Petroleum -> Petrol/Gasoline If I am wrong, I am happy to correct my understanding.

[@ievastrolyte1057]

I think the American system is taught way differently and in the uk we are trained for more of these type of questions because some of the questions were severely over complicated.

[@lyiosvf]

Fr, the ratio questions was over complicated

[@cigmorfil4101]

For the vectors length ratios, you can use simulator triangles as the vectors are multiples of each other. Thus you have DE : DF = 1 : (3.5-1)[1] = 1 : 2.5 = 2 : 5 [1] As EF is 3.5 times the length DE, and as FDE are on a straight line, DF must be 3.5 less the DE part, ie 3.5-1.

[@danielaltmann1308]

Amazing video - U should try and do a additional maths paper (used for gcse students who have done their GCSE early) since its more basic calc and stuff like that it would be quite interesting idk.

[@Vandel96]

When i did it, it had basic differentiation, mechanics (suvat equations) and combinations mostly , may have changed in the last 12 years though.

[@QuentinStephens]

I'm looking forward to seeing you do an A level paper. We also had AS levels in my day (40 years ago!) which were a step up again. I would also like to see you compare papers of the old O levels with today's GCSEs.

[@QuentinStephens]

@cjjk9142 I moved to Scotland and lost track. Here we haver Lowers (National 5s), Highers, and Advanced Highers.

[@dogwithwigwamz.7320]

I have a CSE / O Level Textbook in my possession from 1979. It contains chapters on Differential and Integral Calculus. Much more geared toward the O Level than CSE, but these days we only become reasonably well aquainted with Calculus mid way through C2 (AS ) A Level Mathematics.

[@QuentinStephens]

@@dogwithwigwamz.7320 FFS! I was first exposed to calculus when I was 13.

[@dogwithwigwamz.7320]

@@QuentinStephens I`m agreeing with you, ffs !

[@QuentinStephens]

@@dogwithwigwamz.7320 Middle-aged moment there; sorry.

[@jeffeloso]

For the last question it was easier to do the general case, using 6 equilateral triangles of side circle radius and the segment left over from subtracting the equilateral triangle from1/6th of the one of the circles. The result is that the required area is equal to the area of 4 equilateral triangles side Radius of circle , minus 2/3rd of the area of one of the circles.

[@bprpmathbasics]

Ah nice!!

[@adityangopalakrishnan9354]

also you wrote the answer wrong - 16pi/3 + 16root(3)

[@ingiford175]

For number 9, you can make it easier, by placing the top 'area' of the square into the hole and figure out the surface area of the bottom piece and add just the 4 x4 extra walls

[@bprpmathbasics]

I don’t know why I didn’t think of that 😆

[@ingiford175]

@@bprpmathbasics Easier to see other ways when your not under pressure :>

[@anuragguptamr.i.i.t.2329]

@@bprpmathbasics Sir, in question 21 your answer was wrong. Area of a circle's sector is not r.Theta. Area of a circle's sector is 0.5 r^2 Theta.

[@Oakeybloke]

​@@bprpmathbasicsalso, 42 - 16 = 26, not 28 😬 No judgement, I've been there too, tripping myself up on the simple part!

[@bprpmathbasics]

So far I got Q9, Q10, and Q21 wrong. How many marks did I get?

[@zachansen8293]

I don't count q10 (oops, originally mis-typed Q9) as that's obviously something you have to be specially taught how to interpret the language question. For calculating a percent, I say throw out that question entirely.

[@tsarpyotr3884]

Don't know how many marks but for 2022, you needed about 81% across the 3 papers for a grade 9. Even if you didn't reach that in this paper, I think you'd likely reach that if you aced the 2 remaining papers

[@rix_1723]

@@zachansen8293 no, in q9 his mental math calculation was wrong. He did the calculation for the surface area of the top of the cuboid wrong which is why his final asnwer is 280, not 278

[@zachansen8293]

@@rix_1723 oops, I meant the one about the chart. Was that q10?

[@dannymeshow]

I believe you would get 74/80 You lost one mark on each of 9 and 21 due to minor calculation errors, but your method was correct for both. You would get 2/6 for question 10 - one mark for the correct table, and one for a correct estimate for (c). A kind marker may give you another mark for the correctly plotted bar chart - the mark scheme is slightly ambiguous 😅

[@enterlessguy]

The x intercepts for question 6 are actually phi+1 and (-1/phi)+1, just for my fellow mathematicians !!! (Context: phi is the golden ratio which Is a constant in math, phi≈1.618... and phi is an element of Q')

[@lukecheung3599]

off topic: phi in physics is magnetic flux (Wb)

[@belsnickel9670]

it happened to be that way but how did you see it, did you recognise the polynomial?

[@trini-rt6xn]

Great exercise primarily because students can understand your thought process as you were thinking aloud instead of just solving problems. Most of the time teachers just solve, but never share each thought involved in the solution process. In other words, I think it's more important to first teach APPROACH to problems rather than solutions. Just as an example, an APPROACH to solving 100 problems might only take 20 minutes while solving 100 problems can take hours, but the benefit to the student is learning how to think and how to tackle a problem. After a while, students will see repetition in the APPROACH to solving similar problems, and that's more than half the job since it's just simple math after that. Anyhow, I enjoyed how you were THINKING 🤔 ABOUT THE PROBLEM since you never saw it before, and I believe there's more learning that way for the student who's weak in math. Great job!

[@TurquoizeGoldscraper]

For Q5, you can also extend the shared angle and calculate the exterior angles on each side. For a regular polygon, the exterior angle is 360 degrees/n. For a regular hexagon and pentagon, the exterior angles are 360/6 + 360/5 = 60 + 72 = 132 degrees.

[@ianfowler9340]

Q15. I think I heard you say that a and b are unit vectors. The arrows would have been appropriate. All vectors in R^2 and be represented by a single point if the initial point is the origin. (4,5) and are 2 popular notations to represent these "algebraic vectors". So the vector joining A(2,3) to B(6,5) can be represented by the SINGLE vector AB = (6-2,5-3) = (4,2). Where the initial point is now at the origin (0,0). So in R^2: 1) If 2 vectors are scalar multiples of each other, they are collinear and therefore any linear combination will still be collinear with the original 2. This pair forms a "linearly dependent" pair. -2(4,1) + 3(8,2) = (16,4) = 4(4,1). Any linear combination will always be stuck on this line. 2) If a and b are not collinear then they form an "independent pair" called a BASIS for R^2. This means that any other vector in R^2 can be expressed as a linear combination of the basis pair. If a and b are STANDARD unit basis vectors then a = (0,1) and b = (1,0). All Vectors in R^2 can now be expresses as a linear combination of the basis pair a and b. This still works for the non-standard basis pair, like (2,3) and (-1,4). But We usually express a basis pair as unit vectors on the co-ordinate axes. AB and AC clearly have linear combinations that are scalar multiples. Therefore AB and CD must also be scalar multiples of each other and point in the same direction. Since they share a common point(A), then A,B, and C must be collinear. Note: if vector CD = -3* vector EF, then they point in the opposite.directions and CD is 3 times longer than EF.. I used to reach all this stuff (also in R^3) in high school - for like 30+ years.Let me know if you want to know about non co-planar vectors and basis triplets in R^3.

[@kingpran4420]

I think how we learnt it at GCSE was: the 2 vectors are scalar multiple and so are parallel. They also share a common point (A) and so are collinear.

[@idontknow1630]

lmao this is the paper i sat for my actual gcses, i'll never forget about that last question

[@ubz05]

Same lol

[@tobp]

Fr that thing was memorable

[@benbeaton5410]

I gave up

[@idontknow1630]

@@benbeaton5410 same bro i just did pi x 4^2 and called it a day

[@abduking.]

same i got a 9 in maths but a fucked up the last question it was impossible bro. We all laugh at it tho beacause the rest of the paper was lightwork then randomly some high level question claps us

[@zhelyo_physics]

Excellent! Try the Further Maths A Level exam next! You will enjoy it! : ) Hope you are well!!

[@bprpmathbasics]

Hey!!!! Good to see you here!! Things are well for me and I hope the same for you! And yes, A-level is going to be next. We will see how that goes 😆

[@zhelyo_physics]

​@@bprpmathbasics absolutely! Fantastic to hear and lovely to see you producing great math content as always. : )

[@danielarnold9042]

Hi Z Physics! Your content is extremely helpful for A-Levels, pretty cool that you watch bprp too lol

[@tsarpyotr3884]

Be warned that A-level FURTHER maths will likely be quite difficult without prior studying or learning about the course, so good luck if you ever try one of those papers!

[@TheSourovAqib]

​@@bprpmathbasics please try 2023 paper when it is available.

[@gorilla452]

Try the further maths alevel paper, specifically core pure. Much more exciting than the normal maths paper, as a student I can guarantee it.

[@fantasypvp]

Further pure 1 is pretty interesting as well. Way more fun than core pure other than conic sections because honestly just no.

[@jonahansen]

This video is great! It shows the real process people go through when not only solving the problem, but also trying to interpret what the problem is. Like, what is petrol anyway, and what does "standard form" mean?

[@MahmoudSayed-hg8rb]

question 15 you can do inv_tan(4/3) & inv_tan(20/15) to prove that they have the same angle

[@iAzazelHD]

56:51 wouldnt it be proved by using linear algebra? determinant. Or actually, if u can write AC as a linear expression of AB, then AC and AB are colinear. Or considering them a basis of some subspace or something? Or maybe this is more advanced lol. I would go for the linear expression, i think

[@ethaniac61]

Can we all take a moment to appreciate the effort that BPRP puts into his videos!

[@gwfuad1801]

no we all cant a take a moment to appreciate 😊

[@Andrew-nk7nh]

Really enjoyed the video! Great job doing it on the spot!!

[@bprpmathbasics]

Thank you!

[@DarkKittens123]

Pls do the beautiful STEP paper

[@Dyrox2333]

PLZZZZZZ

[@zachansen8293]

40:00 I would have just said the lime probability is 9/21 since there are actually 9 limes that makes the probability the same as the actual fruits... so then it's just 21-4-9=8

[@bprpmathbasics]

Ah!!

[@philneal3750]

Sat this paper, was the only one to get full marks on that last question in my school. Looking back it was not a difficult paper but when you’re in the exam hall the nerves can really make you forget everything

[@nvapisces7011]

15a all you need to write left is that A is a common point, making A, B, C collinear

[@bprpmathbasics]

Ahhh, right!!!

[@bprpmathbasics]

Thanks!

[@ilicktrains8304]

You should do this for some of the other levels of maths exam in other countries and compare them in difficulty to each other. I think that would be really interesting and, especially if you break down what made said exam difficult like time pressure or question format; it would also finally help to confirm which exams are the hardest Off the top of my head, I think you could do the further maths GCSE from AQA and the admaths/fsmq paper from OCR which have different content, but are supposed to be equivalent in difficulty You could then do some harder papers too, like the A level maths and Further maths, and maybe even some of the university entrance exams here like the MAT, TMUA or STEP even These are only the UK exams as well, it would be even more interesting if you branched out to other countries exams, like the Singapore A level exam, the IB maths exams or the notoriously hard exams from India, China and Korea

[@fantasypvp]

I've got an A level further maths exam in like 3 weeks 💀 Also took TMUA which was literal hell but I somehow got 6.8

[@xArinzzay_]

You got everything in the very last question correct up until the very last line

[@RobertHorton1975]

Question 4.b was awkwardly phrased to say the least. They didn't say anything about significant figures, so I'm not sure if the trailing zeroes should be retained or not.

[@leonobilis1]

I solved the Question 21 using calculus by imagining an x-y-diagram, where the middle circle is centered at (0|0) and can therefore be described by x^2 +y^2 = 16. The shaded area is the area of this circle minus two times the ellipsoid area. A quarter of this ellipsoid are can be described as the integral of sqrt (16-x^2) from 2 to 4, which by trig sub (x = 4 sin (u)) corresponds to 16 times the integral of (cos(u))^2 from pi/6 to pi/2. Using integration by parts the integral can be evaluated as (8pi/3) - 2sqrt(3) (approx. 4,91). Now we just have to subtract 8 times this integral from the area of the circle and we get 16sqrt(3) -(16pi/3) (approx. 10,96 cm^2). I hope i am correct.🙂

[@RambleDan85]

No idea if that is right but GCSE students do not learn integrals in mathematics. That is taught at A-level

[@maximum_75]

Honestly a big overcomplication. The content you are using is taught in Year 2 Alevel maths (17/18 yr olds) and is not taught at GCSE meaning there is a much simpler method

[@ishmaelwadee]

this was the paper I sat 2 years ago weird to see it again 😅 I’m doing my A level maths in a couple of months so I hope you do one of those papers

[@sweettoy3824]

Couple of months? Isn't it like 44 days away?

[@Alistair1607]

for number 3 i think most people do it by "assuming" 3 and 7 have variables, like its unlikely there are just 3 and 7 of the cars and fence and add up to 160, so we know its a multiple of 3 and 7 that add up to 160, and since its the same multiple (so in the ratio they can be divided back to 3:7) its basically 3x : 7x, where 3x + 7x = 160, hence x = 16, going back, it means the cars are 3x = 3(16) = 48

[@marcusng6482]

Please try the Singapore Cambridge o levels Additional Maths paper 2 from 2020

[@Beesechurgersports]

Hey sir could you do an a level paper? You could do a further maths a level paper to make it more interesting for you

[@WTU208]

4:45 petrol is petroleum / gasoline.

[@sendoq]

Please do CAIE further maths paper 2, I think you'll enjoy it much more as the topics are more in line with your expertise

[@marcmarco1305]

At 21) isn’t the area of the sector r^2 times theta?

[@ianfowler9340]

Internal and External Division of a Line Segment: 1) If we say that C divides AB in the ratio 2:3 then C lies between A and B. The ratio is positive and the division point (C) in "internal" - between A and B. Start at A, 2 units right label C, 3 units right label B. 2) I we say that C divides AB in the ratio 2:-3 then the division point C lies outside the segment AB and we refer this as "external" division. To get the correct proportions you can do the following: Place the point A on the paper. Travel 2 units right and label point C. From C travel 3 units left to final point B. You can now see that from the picture that C lies to the left of A and |AB| is 1. If you switch the negative sign to the the 2, the picture gets flipped, but still in the correct proportions. Here's a typical question I would have asked my students in grade 11. Given the points A(3,4) and B(9,12), find the point C so that C divides AB in the ratio 2:-5. Great video material.

[@franciscook5819]

I used to teach year 7 through 13 (Oxbridge Entrance) maths here in the UK. We don't specialise but do it all from arithmetic through algebra, stats, geometry, calculus etc. I know in the USA teachers "specialise" by year and/or topic so it was interesting to see an obviously accomplished mathematician struggle with fairly simple questions (e.g.15, 16). Lack of practice, I guess. Q3. It is easier to see that C:V = 3:7 means C=3/(3+7) and V=7/(3+7) Giving C= 160*3/10= 48 (which you eventually got) Q5 an alternative is the exterior angle of a regular polygon =360/n (n=number of sides) so interior is 180-360/n; giving 120 and 108. Q9 It's nice to know you are human and make arithmetic mistakes, as I do. Q12 I think the examiners would want working (not following a rule) to get to 17/990. So multiply by 10 (because we want integers) and 1000 (integers with aligned recurring decimal) and subtract the smaller from the larger. Gives (1000-10)x=117.1717...- 1.1717...=116 => 116/990 = 58/495 Q15 I would show that the two lines have the same start point and the same slope so must lie on a line (which you effectively did by showing one is a multiple of another). Q16 Simpler to see P(T)=0.75, P(notT)=0.25; P(P)=x, P(notP)=1-x; P(1 only)= P(T)*P(notP) + P(notT)*P(P) 0.36=0.75(1-x) + 0.25x => 0.5x=0.39 or P(P)=x=0.78 Q21 The way into the problem is to realise that we create an inscribed regular hexagon made up of equilateral triangles using compasses stepping around a circle (the middle one, say). The top shaded region = 1 equilateral triangle (side 4) -2*segment (the two other circles) + segment (middle circle) = 1 triangle - 1 segment Area of triangle: I think of 30,60,90 triangles as 1,root 3, 2 triangles so area=4*root 3 (base=4, height=2*root 3) Area of segment: = area of sector - area of triangle = (1/6)pi*r^2 - 4*root3 = (8/3)pi - 4*root3 Area of shaded area = 2*area of top shaded area = 2*(triangle - segment)=2*(4*root3 -( (8/3)pi-4*root3) )=2*(8*root3 - (8/3)pi) =16*root3 -(16/3)pi

[@sampan04]

I remember doing my GCSEs 2 years ago, nice video

[@bprpmathbasics]

Thanks!!

[@Lil_electrician]

I have my GCSES so soon ! 😭 should be easy though I’ve been watching your videos for so long 💀😎

[@striker8380]

Qu 5 it's quicker and easier to work out the exterior angles and sum for x. 360/6 =60 and 360/5 =72 therefore x = 60+72=132

[@abiazkiron7]

tbf i would love to get taught by u for GCSEs u explain it better thn some of my teachers lmao.

[@mrreddoesart2112]

That circle question at the end is bringing back ptsd

[@johng.1703]

for Q21 the answer should be 16√3 - 16π/3 this is based on 4 arc's of 60 degree or 2 of 120 degree. area of segment = area of sector centre A - area of equilateral triangle Total shaded area = area of circle - 4 × area of sector - 4 × area of segment or area of circle - 4 × area of triangle - 8 × area of segment

[@anderslvolljohansen1556]

Area of circle - area of four 60° sectors = area of six 60° sectors - area of four 60° sectors = area of two 60° sectors = 2/6×pi×r² = 1/3×pi×r² Area of four areas outside sectors to be subtracted = area of four 60° sectors - area of four equilateral triangles = 4/6×pi×r² - 4×sqrt(3)/2×r×r/2 = 2/3×pi×r² - sqrt(3)×r² Area shaded: 1/3×pi×r² - (2/3×pi×r² - sqrt(3)×r²) = sqrt(3)×r² - 1/3×pi×r² = sqrt(3)×4² - 1/3×pi×4² = 16×sqrt(3) - 16/3×pi

[@johng.1703]

@@anderslvolljohansen1556 I have just checked the marking scheme for 1ma1-1h-rms-20220825 the answer they have is 16√3 - 16π over 3 you can find the marking scheme by searching for 1ma1-1h-rms-20220825.pdf on google. it has 3 methods to get the answer.

[@silver6054]

For the parabola question (6?) I think the last part, root of the equation, would require you to read a value from your graph, so 0.5/2.5 is probably not what they are looking for.

[@chillx656]

He did exactly that you silly boy

[@reminderIknows]

calculus teacher fails to solve 42-16

[@magic2186]

Every body do that mistakes

[@aazie8336]

bro shut up hes the goat

[@reminderIknows]

@@aazie8336 bro i aint making fun out of him im just remarking it..

[@unnevenn]

@@reminderIknowsissajokesondonchagetit

[@CxR14]

Hate it when I do that

[@VioTheCutie]

seeing the cf graph like that makes me cackle 😂 but i understand, doing something you dont know is basically asking us to create new stuffs 😂

[@arcticphoenixttv]

For anyone wondering, here in the UK you take standardised exams in Year 11 and 13, or in the US, 10th and 12th grade. These can heavily impact your job and higher education opportunities. There are two papers for GCSE Mathematics (Year 11 standardised exams) - Foundation, which caps at a mediocre score overall but is significantly easier, and Higher, which caps at the highest possible score (100%/grade 9). There is also a special subject only offered to students very gifted in mathematics known as 'Further Maths'. This also has an A-level (Year 13 exam). Having good Further Maths qualifications is highly regarded and is definitely something you would want if you aim to teach mathematics at higher education.

[@freezy8593]

US takes standard tests for multiple subjects… English 1 and 2, Biology, History, Algebra…

[@arcticphoenixttv]

​@@freezy8593 Thanks - I'm from England so I wasn't really aware of the standardised testing across the pond.

[@freezy8593]

@@arcticphoenixttv Granted I’m speaking from my own experience. These tests I took were primarily to see where your knowledge of a subject was rather than credit to advanced education. The US only has an SAT/ACT that has some impact on where you can/ could go.

[@arcticphoenixttv]

@@freezy8593 Yeah, GCSEs and A-levels are less of an aptitude test, and more 'which subjects are you good at and what jobs are you suited to'. For example, you aren't going to get into a medicine course at university with Cs in Chemistry and Biology.

[@YJYat1116]

you should try 2023 hong kong dse (diploma of secondary education) math exam

[@bprpmathbasics]

I would probably get destroyed even more 😆. Anyone tho, do you have a link to that? Thank you.

[@YJYat1116]

dse.life/static/pp/m0/eng/dse/2023/p1.pdf dse.life/static/pp/m0/eng/dse/2023/p2.pdf Here you go! There are two parts in the examination, paper 1 should be finished in 135 minutes while paper 1 should be finished in 75 minutes Good luck! Do you need the answer key as well?🤣🤣

[@YJYat1116]

I posted the link here but it got deleted😭

[@ghgv3059]

Please do a Higher level analysis and approaches IB paper :)

[@striker8380]

Qu 21 in the UK would be calculated in degrees not radians as radians isnt taught until the second year of A levels.

[@PushpendraSinghYadav-vg7gh]

I am from India ❤ and I love mathematics and I will become a mathematician of India

[@MVG7]

U have been awarded NPC comment of the day! Well done to u👍🏻😄

[@MulukenAndualem-ok3um]

Concerning the cumulative frequency 0 to 50 ~10 50 to 100 ~15 100 to 150~25 150 to 200~30 200 to 250 ~5 250 to 300~15 first arrange like this because what is given in the question is cumulative frequency so first please change it to individual frequency like I have done so far therefore now it is simple to calculate and draw the graph.

[@MarieAnne.]

No, what's given in the question is exactly what you typed in (you can see it at about 30:50 when he shows the paper). From this he needs to fill in cumulative frequency, which is the only part he showed on the whiteboard.

[@Afterburner440]

question 6c, you need to use quadratic formula to get exact values

[@MulukenAndualem-ok3um]

It is better to add both equations like line DE =3e+6f and line EF=10.5e - 21f then the question is the ratio of Line DF:DE therefore first find the equation of line DF =7.5e -15f ,it is found just by adding both equations D-------E---------F and hence the DF to DE becomes 2.5:1

[@MarieAnne.]

You forgot a few negative signs: DE = 3e + 6f EF = −10.5e − 21f EF = DE + EF = (3e + 6f) + (−10.5e − 21f) = −7.5e − 15e = −2.5 (3e + 6f) = −2.5 DE Now we can easily calculate ratio |DF| : |DE| = |−2.5 DE| : |DE| = |−2.5| : |1| = 2.5 : 1 = *5 : 2*

[@GollyGoshGale]

at 19:10 lil bro was struggling and so was my heart as i saw my grade 9 flash before my eyes

[@Smoakz]

very interesting to see the US methods compared to mine (british)

[@anuragguptamr.i.i.t.2329]

Sir, in question 21 your answer was wrong. Area of a circle's sector is not r.Theta. Area of a circle's sector is 0.5 r^2 Theta.

[@bprpmathbasics]

Thank you!!

[@xevira]

For #5, I would have just used the external angles (60 and 72) and just added them.... You went the long way around to get the same answer.

[@KekiOFFC]

which one is harder IGCSE or GCSE? because IGCSE contains 100 marks…

[@hihowrya6463]

I sat this paper in 2022. Apparently the last question was leaked in a discord server if i remember correctly.

[@radiumuppet]

I sat this exact paper for my GCSEs... that last question was brutal I spent all day working on it

[@sigmagamer111]

try singapore gce o level additional maths pleaseeee :)

[@shankho5478]

I actually solved the 21 question by integration but I got the area in negativee . If someone can help me

[@Joseph-mv3rz]

I beg you do an International Baccalaureate Higher Level analysis paper 2 or 3. That shit makes me cry

[@Or1gami_]

This was really helpful! Thank you!

[@luigicappetta348]

Petrol is the word used in the UK for gasoline I think

[@derbar7051]

Correct. We also use the word Diesel.

[@DrFuzzyaka-atomic]

@@derbar7051Diesel is a different though.

[@mista5796]

The area of a sector is the proportion of a circle multiplied by the area of a circle. You’ve quoted the arc length rather than area of the sector. Then right at the end there’s a separate mistake; 4 x 4pi/3 = 16pi/3

[@sampletext9426]

you can take a picture of the question and edit it at the side of the video. Of course, that is much more editing time so its understandable to not do it.

[@zachansen8293]

**ERROR** Q9 is wrong 27:55 I would have just not counted the top of the small cube. Then it's just the surface area of the large box plus four sides of the small cube and you're done -- less weird subtractions but all you've done is add then subtract the top area of the cube. So why do it at all? 29:00 edit: and then you did that exact math wrong. 42-16 is NOT 28, it's 26. So the answer is 278 not 280

[@bprpmathbasics]

Yea it was a horrible mistake of mine, lol!

[@drainage9219]

You need to do the Churchill Papers, they're are best papers with almost hardest GCSE questions.

[@colinknabe4577]

Great video, I sat these papers 2 years ago. Would be great if you did the A-Level Maths and Further Maths papers (Edexcel board)

[@Thalweg]

This is the paper I did for my GCSE maths. I don't remember the exact mark i got for the non calc but i know I got 227/240 in total across all the papers (I vaguely remember getting 73/80 on this paper but that's probably wrong). Funny thing is I had the right method for question 21 but I forgot to divide the area of the triangle by 2 because i'm an idiot. Sitting my Further Maths and single maths A level exam in a months time along with the STEP 2 exam (needed for imperial CS). Not looking forward to it.

[@ianmoseley9910]

Seems easier than the o-levels as I remember them, but that was nearly 60 years ago!

[@markymark7803]

This is crazy tough for 16 yr olds and what can it actually be applied to in real world jobs other than probably high end engineering and physics? Even in accounting I can't see these type of questions being applied.

[@falsebanned2899]

for 15 u mention they share point a and since they have the sae gradient its a straight line

[@KattarMuslim-Revert]

5:34 I would have solved this like this, C:v= 3:7 K be the common ratio multiplier C=3k, v=7k C+v=160 3k+7k=160 10k=160 K=16 C=k*3=16*3=48 1/8th= 1/8×48=6 1/4th = 1/4×48= 12 Number of car that use petrol is (48-6-12) =(48-18) =40

[@IOwnKazakhstan]

😬

[@gamerv0]

Is 30 not 40

[@olivercollard8767]

I sat this exact paper as a real exam!!

[@asdfgfgfhg]

Brave bastard

[@victuvaporub]

im actually so happy i can actually try to study and do it with you 😃😃😃

[@jmrs_]

That Q21 still gives me nightmares.

[@notreallydavid]

Non-UK people - GCSEs are the exams that UK kids take at 16. They take A levels at age 18, at which stage it's usual to be studying only three subjects. It follows that A level mathematics is reasonably tough.

[@mikefish8226]

GCSE are taken when children are 15 or 16, depending on when their birthday is.

[@benchapple1583]

A lot of comments on how difficult Q21 is. I don't agree, it seems straight forward to me. Your error with the area of the sector of a circle didn't get picked up due to using numbers rather than letters. Long, long ago in a galaxy far, far away my maths teacher warned me to solve everything algebraically and only then to substitute the numbers. He argued that it was easier to spot errors and I agree with him and follow his advice to this day. Well that's my penny's worth. Thanks for the video. It would be interesting to compare the 'O' level circa 1970 with the current GCSE.

[@polaarr]

you make maths fun to watch

[@d4rren09]

I sat this paper and I still remember the last question even now lmfao. I managed to get a grade 9 for it (highest you can get in this exam). It's weird looking back lol.

[@ZakariaDhan]

Is question 15b a matrix question?

[@johng.1703]

so total is 160 and you have a proportion of 3 : 7 so total of 10 portions 160 / 10 = 16 per portion 3 portions of 16 = 48 cars 1/8 = E (electric) 2/8 = D (diesel) 5/8 = P (petrol = gas) 48 cars / 8 = 6 5*6 = 30 petrol cars.

[@Blindeditss]

Sir can you solve jee advanced (mathematics section ) you will find amazing problems

[@DoodleNoodle129]

Pretty sure this was the GCSE paper that I sat 2 years ago. Now I’m about to sit my A levels 😅

[@MobscastBlackOut]

Please do Scottish advanced higher. It is also for high school students in the UK

[@yaz4659]

I would be nice to do A-level maths it is more challenging than the GCSE exams

[@jolt4404]

bprp can you please do an A level paper next

[@thesounddisciple9213]

Please do an a level or further maths a level paper! They are much more like you are used to, no more tables and some calc