u/Mobile_Membership915

Does anyone know of any good websites which have practice questions which use undergraduate maths? I know there’s lots of textbooks but I’m looking for something free.

I know that the volume of a cone is 1/3 pi r^2 h, and the volume of a cylinder is pi r^2 h. Can we not break the cone down into an infinite number of triangles and then layer the same amount of triangles upside down on top to make a cylinder. I understand calculus and how to get to the 1/3 but I don’t understand why this approach is wrong. Can anyone explain my mistake?

I am in the UK and am in my final year of secondary school. I study Maths, FM, physics, and economics A-levels.
Next year (if I meet my offer) I will be studying maths at the University of Warwick. I really enjoy physics and want to self teach some undergraduate university physics to myself (just in spare time in the summer), but am unsure on where to do this. Does anyone know of good online resources to do this? Or even a list of things to study? I would greatly appreciate any help.

I am in the UK and am in my final year of secondary school. I study Maths, FM, physics, and economics A-levels.
Next year (if I meet my offer) I will be studying maths at the University of Warwick. I really enjoy physics and want to self teach some undergraduate university physics to myself (just in spare time in the summer), but am unsure on where to do this. Does anyone know of good online resources to do this? Or even a list of things to study? I would greatly appreciate any help.

I am in the UK and am in my final year of secondary school. I study Maths, FM, physics, and economics A-levels.
Next year (if I meet my offer) I will be studying maths at the University of Warwick. I really enjoy physics and want to self teach some undergraduate university physics to myself (just in spare time in the summer), but am unsure on where to do this. Does anyone know of good online resources to do this? Or even a list of things to study? I would greatly appreciate any help.

How many people a year get 100% in a level maths or further maths each year. It’s obviously incredibly difficult since you can’t even make a slight mistake, so does anyone have any idea of the number?

I’m considering taking a gap year to apply for maths, and I think that I would preform much better at interview and TMUA in my reapplication (they didn’t do TMUA last year but I think I’d do good enough to be interviewed). I am sitting STEP and I am only considering a gap year if I get SS (which I have been getting on past papers).

My main concern is the holistic way they treat applications. Since I have had a gap year to improve will they treat me way to harshly?

I’m quite confused about something and was wondering if someone smart could explain something to me.
The earth is moving through space at a fast speed, so why is it that when I throw a ball, it only needs the energy to increase its speed from 0 to say 10ms^-1 instead of from 1000 to 1010ms^-1 (which would be considerable more energy)?