Maths Misconceptions

I will try to, thanks.
I usually get in the area of the low 90's but I am trying to get somewhere in the mid to high this time round.
If it were you trying to get full marks in a test, high marks in low time, how would you set about doing it?

Wbf, doing well is a good thing to aim for, but why aim for full marks / whats the test / ... If youre in the 90s (assuming its out of 100), it would be fairly boring to repeat the same stuff to gain a marginal improvement and usually its time to move on.
But several ways to catch/identify problems (for the small number that you have) have been suggested above. Do you do any? But if youre asking how to improve on a small number of questions, maybe upload one or two with the mistake(s) that you made to see how they might be caught.

Its mainly because I am trying to win an award for maths, whoever gets the highest score in this upcoming test will win it.
As for an example, I don't really have many to upload, they are really just the stupidest things imaginable for no reason at all, like I randomly just add instead of subtract and don't notice until it is already wrong.
The problem is, it only seems to happen in exams when I am actually looking for a decent mark, not when I am practising and I don't know if this is down to pressure or what.
I was mainly just looking for ways to either ensure I don't do this, which I know would be hard for you to suggest without an example, or ways to be able to spot these mistakes when under exam pressure.

What’s the one main thing you can’t get your head round with maths?

Theres been a few already suggested. Do you do these? But without knowing what the test is / the type of questions / what type of mistakes / ... its hard to give specific advice. If youre not going to upload any questions/solutions with mistakes/... Ill drop out here.
But a rule of thumb is that it takes the same amount of time to halve the errors so to go from 80=>90 takes the same time as to do 90=>95 and 95=>97.5 .... If youre grinding stuff until youre approaching 100, its going to be somewhat tedious.
But dfranklins advice in #11 is sensible for working through your solutions, similarly verifying answers where possible and guestimating solutions can help identify if your answer is incorrect in the first place. Check youve read the question carefully, sketch the info in the question which can help guestimate solutions in some cases .... Your add/subract "example" (assuming its solving a bit of algebra) should be caught by validating the solution and then its a case of working backwards to see where equation balance goes wrong. Similarly being systematic about variables on one side ... can help minimize them in the first place. But this advice could be way off as the +/- example you mention isnt in the context of a question.

Thanks for your help, I've not made it easy 😅
I'm taking Scottish higher maths right now which I'm pretty sure is around a-level in year 12.
A final question before you go- if a question comes up that I have absolutely no idea how to do, what should I do?

At the risk of repeating myself, if you cant post an example of a question you dont know how to do, its kinda hard to give advice about what your "problem" is.
But some very general advice is that if you know your stuff (scottish highers?), then you should know how to do it, so really its a bit of problem solving until you can spot whats important in the question and how to move forward. So things like
So really its a case of 1) understanding the question 2) evaluate potential ways forward 3) develop solution 4) validate. Too often school maths concentrates on (3) and youve been asking about (4) and now mention (1) and (2). Theyre all important for harder / unusual questions
I like
https://www.worldscientific.com/worldscibooks/10.1142/9478#t=aboutBook
and theres a couple of introductory sample chapters at the bottom to flick through. But you need to practice this stuff, like practicing how to stop making mistakes for it to become second nature in an exam. Whether thats worthwhile is your shout and whether it has any relation to your "unusual" questions is ???

3d trig for sure - really struggle to visualise stuff. At least not enough to draw a diagram. Thinking about imaginary lines is always tricky

An example for you, my friend, I'll admit I've never done this before 😅
Some of the questions I find hardest are usually optimisation I'll try and find an example:
I don't know if you can actually see this or not so in case you can't it is question 11 on paper 2, the one about the chocolate box, you can find both papers in this link https://www.highermathematics.co.uk/wp-content/uploads/2022/11/2019-P1-P2.pdf
I know this might seem simple but I just never seem to be able to get the first bit right, finding the formula for the area etc.
I can do part B fine, but part A always presents itself as a struggle.
Any advice on how to do part A easier would be helpful!

For interest, did you get the surface area stuff sorted / what do you think you werent doing correctly?

Yeah, hi, I tried it but I can't seem to upload it.
I am able to find the formula for h - but then I can't sub it back in to find the area formula they give. It was pretty late last night when I tried it though, so don't think I'm too dumb 🤣

Without the hole, youd have something like volume:
2000 = 9hx^2
and surface area
2 * 9x^2 + 12hx
Do you understad those and can you combine those to get a surface area expression in terms of x?
Then can you account for the hole in the two expressions.

Yeah, I've worked it out now, they just sometimes stump me in the exam because they seem so easy, but I just can't get them to work out.
My test is on Tuesday and there is about a 100% chance that that will come up so wish me luck 🥲
Thanks for all your help, good luck in whatever you go on to do!

Good youre sorted now. For this one, if the hole stumped you, just do it without the hole then redo it with the hole. But for a question like this, I think its less about problem solving and more simply about practice as dfranklin suggested. The a level stuff is the differentiation (b) which you seem happy with. The part (a) goes back to old babylonian-egyptian stuff so transforming a field perimeter/area problem into a quadratic. Here its just 1 dimension higher, so transforming an area/volume problem into a cubic.

Good youre sorted now. For this one, if the hole stumped you, just do it without the hole then redo it with the hole. But for a question like this, I think its less about problem solving and more simply about practice as dfranklin suggested. The a level stuff is the differentiation (b) which you seem happy with. The part (a) goes back to old babylonian-egyptian stuff so transforming a field perimeter/area problem into a quadratic. Here its just 1 dimension higher, so transforming an area/volume problem into a cubic.

Good youre sorted now. For this one, if the hole stumped you, just do it without the hole then redo it with the hole. But for a question like this, I think its less about problem solving and more simply about practice as dfranklin suggested. The a level stuff is the differentiation (b) which you seem happy with. The part (a) goes back to old babylonian-egyptian stuff so transforming a field perimeter/area problem into a quadratic. Here its just 1 dimension higher, so transforming an area/volume problem into a cubic.

What’s the one main thing you can’t get your head round with maths?

What I cannot understand the most is whether mathematics was discovered or invented?

What I cannot understand the most is whether mathematics was discovered or invented?