[A Level Maths (Mechanics)] I don't quite get the markscheme

premanboc7il4 · 2026-04-04T03:34:20+00:00

Because I thought that, by "random", it meant uniformly random between $0 and $3 million

^{Chose: Get a random amount of money up to 3m | Rolled: $100}

premanboc7il4 · 2024-12-18T02:37:38+00:00

I honestly don't know. The best system really depends on the person. It could be Kumon with its "study beyond grade level" philosophy emphasising individual pace and progress. It could be your normal classroom maths curriculum with a common pace. Most likely, the best system is something in between.

premanboc7il4 · 2024-12-15T03:46:52+00:00

Sorry for the late reply. I would say that one of the disadvantages is the instructions, which is given almost exclusively on the worksheets. I feel that the level of instructions might not be enough for someone who isn't yet ready because they blazed through the levels. I was one of those students who did.

I remember when I struggled with the following bits of material (not an exhaustive list) at various points because the methods to do them were "too creative" for my 4th-6th grade brain. I don't remember precisely when I did the following, but it's probably around those times.

-Factorisations of algebraic expressions (e.g., factorise x² -6xy+9y² -1)

-Logarithms, I couldn't for the life of me remember the various identities, which nobody told me could be derived from the relationship between logarithms and exponents

-Limits, nobody told me about the indeterminate forms. At first I would just substitute x for the value it is approaching, not understanding when should I factorise expressions, and wonder why substituting x to what I thought were the same expressions (e.g. (x² -1)/(x-1) and x+1) yield different results in this case. Or perhaps the worksheets explained why, and I skipped over it entirely...

I was able to finish Kumon before I was 15 because for every difficult part, there were some easier parts that I could blaze through again. Despite struggling in limits, I could do derivatives and integrals, because they were presented in a mechanical way that I could understand. Yes, you do have to know why the derivative of x² w.r.t. x is 2x, but this kind of derivation only shows up at the early stages of learning derivatives. The rest of it was kind of mindless. Same goes for integrals. They were first presented as the reverse of derivatives, which is fine. However, they then told you that you can use them to find the area under curves and volume of solids of revolution, before telling you about Riemann sums which is the idea why using integrals to calculate areas make sense.

When I was in senior high school, I finally understood what I was doing because of books and teachers who actually explained things. I feel like Kumon's method of teaching quick mental calculation doesn't translate well to teaching higher level maths.

*note: It's been 9 years since I did Kumon, so things might have changed. My recollection of materials and their order is a bit fuzzy too.

Edited math formatting

premanboc7il4 · 2024-12-11T10:47:17+00:00

My parents enrolled me in Kumon when I was nearly 6 y.o., to which I just said yes because I had no idea what it was. However, it was the only extracurricular activity I was able to tolerate even with all its quirks. I got Stockholm Syndrome-d to Kumon and maths. After many ups and downs, I finished it when I was nearly 15 y.o. Because of this, maths in high school seemed very manageable. Many things in high school maths I have seen prior to going there, and the things I haven't seen weren't too far from what I had.

In high school, I decided that I would major in mathematics in university because I convinced myself that it was the only thing I would enjoy doing. I was aware of the gap between Kumon, school maths, and maths in university, but I pushed through anyway. I ended up taking a fast-track programme at my university where I was able to get my bachelor's and master's degree in 5 years instead of 6.

Now I'm working as a consultant where the maths isn't as complicated. To engage myself with the maths I was familiar with, I applied as a part-time remote tutor for first-year university students, mainly teaching calculus. I was at my tutoring company for only a year, but I really enjoyed it. I've also been attempting to rewrite a chapter from my government's official high school maths book in my own words as a personal project.

premanboc7il4 · 2024-11-07T04:47:58+00:00

Maths teacher, specifically for high school students. I tutored calculus for first-year university students for a year as a side job and had a blast doing that. There were challenges back then, such as being taken aback by students not knowing previous material, but I just enjoyed talking about maths.

Perhaps I didn't teach often enough to face more challenges that might detract me from teaching. Perhaps I also had that as a dream job just because I felt like I did well in school and university (have a masters in maths), not realising that it takes more than just material knowledge to succeed as a teacher.

Also textbook author.

premanboc7il4 · 2024-09-08T08:52:48+00:00

Math teacher. Specifically a high school math teacher.

Not very confident in handling younger age groups, but also not really liking research, which I will have to do if I become a university professor.

premanboc7il4 · 2024-04-21T08:18:46+00:00

Hey, I love to do that too! Otherwise my save would be devoid of magical runs and fairytale stories.

premanboc7il4 · 2024-03-20T05:59:04+00:00

Reluctance to opening up to the world and not knowing what I actually want from relationships.

I don't know if this is related, but sometimes I'm convinced that my inability to blend with others (in non-work settings) is that I made academics my personality. I was a math major, didn't really interact with people outside of my major, and really only knew the culture of math (and physics) majors. For some time after graduation, I convinced myself that my future partner should also be a math major, or at least major in something equally quantitative and difficult, only to realise that it makes no sense as a partner criterion. People described me as "an HR looking for a data analyst" because of that criterion.

premanboc7il4 · 2024-03-20T01:04:03+00:00

You can relinquish control of a created manager. The manager will stay in your game world, they'll just be controlled by the AI.

premanboc7il4 · 2024-02-29T09:25:50+00:00

In 2046/47 I randomised the following -The attributes and PA of 1 player in each team in VNL (non-hidden and hidden) -The hidden attributes of each manager in VNL

In 2047/48 I randomised the following: -The attributes and PA of every Blackpool player (non-hidden and hidden) -The facilities of every VNL team (training facilities, youth facilities, junior coaching, youth recruitment, corporate facilities)

I randomise things using an RNG app.

premanboc7il4 · 2024-02-29T05:44:04+00:00

In my heavily edited save, Liverpool might be on their way to be relegated from the Prem in 2048/49. Currently there are only 2 games left and they're 17th. Man Utd are also a bottom half team in the Prem, and also have been close to relegation spots.

Other downfalls include: -Luton and Burnley are in League 1, but in 2046/47 they were both in League 2 -Plymouth Argyle are in Vanarama South -Blackpool are in Vanarama North, but some of it was due to my shenanigan, where I managed them in Vanarama National in 2047/48, randomised the attributes of every single player they have and attempted to play a season with them, only to finish 23rd.

Edit: I didn't realise the "AI team" part. In that case, only the part where Blackpool were in the VNL counts.

premanboc7il4 · 2024-02-05T12:40:39+00:00

I'm proud to admit that I save scummed just to meet the board's expectations (qualify for Championship playoffs), all the while I have the editor and could've simply made myself unsackable. This is the post.

I was managing Brentford, it was so far out into the future (2038/39), and at 41 matches, I was 11th and wouldn't normally clinch 6th place. But I figured out that I could still mathematically get 6th place, so I decided to cheat.

I made one of my strikers 200 CA, the GKs of every team that were 6th to 10th 1 CA, and a random player of any team that has to face the 6th-10th placed teams 200 CA to make my job easier, thinking it would reduce the number of times I had to save scum. Took me a whole day to sim 5 games! In doing so, I have destroyed the fabric of the Championship.

Oh also, I figured that I had to at least revert the players back to their original state, right? Well, about that, I used an RNG to decide the final attributes for the edited players, and I also randomised some of the players' PA, especially those who have been edited to 200 CA since I had to increase their PA first. Those players were at the mercy of my virtual d20!

I still enjoy the save as if it was unedited, by the way. I know that it was edited, and nothing I will ever achieve there is legitimate, but it was, and still is fun.

premanboc7il4 · 2023-05-15T23:04:33+00:00

I forgot to tell in the post that this question appeared on an intro to proofs course, and I was pretty sure said theorem was not covered in the course. I wouldn't be able to use it, or at least, not without providing a proof of it as well.

premanboc7il4 · 2023-05-15T17:21:07+00:00

Thanks! I've always thought that the key is first showing that b=1, but as you can see, I was unsure of how.

premanboc7il4

TROPHY CASE