That's exactly what I feel like I do now. Sometimes I don't even spot the errors because I'll look back at questions and follow my working out going through it, but I won't analyse my working to see if I did something wrong. My most common mistake is having a negative somewhere when it's supposed to be positive which I won't spot in a quick glance. I'll quickly look like 3-5 times depending on the time allowed for the task and never spot the mistake.
How would you recommend slowing down in a task? and how do you know if you go too slowly?
a good way to "force" yourself to slow down and think things through is to write down every single step of working. example:
prove 2var AM-GM inequality (sorry for those not doing ext 2, but hopefully this is simple enough):
let a, b be real numbers.
notice (a-b)^2 >= 0 |
because every real number squared is non-negative, and the difference of two real numbers is a real number
a^2 +b^2 -2ab >= 0 |
by using the binomial expansion
a^2 + b^2 >= 2ab
(a^2 + b^2)/2 >= ab as required
this isn't necessarily the best example to use for this as it is difficult to make a mistake, but the small asides that i bolded help to explain why you have done things in the proof. obviously these are not necessary for the proof, but you can at least track line-by-line what happened. then when you check your answer, you can compare the working out line to the short aside. if they are the same, you know the line of working out is correct. even just writing "to make a common denominator" and writing what u times each fraction by when adding fractions can help, especially when u are dealing with various different symbols, potentially all raised to different powers, to ensure u multiplied by the correct thing and didn't miss something. you can ditch these asides in questions that you feel very comfortable with/maybe have seen before, but in a tough question these are quite useful.
not necessarily related to slowing down, but in some questions it is possible to use several methods to arrive at the same answer, particularly in subjects like physics - eg u can use newton's laws, or the law of conservation of energy, in many problems. obviously, u can always double check your answer with another method. if the answers match up, you can be more confident that you haven't made a mistake somewhere. of course this takes slightly more time, but in a way this acts as a guarantee that your answer is correct.
another way to slow down and digest a question is to always write/draw another representation of the problem. in math and physics especially, you will often be given a long slab of text that has a geometric equivalent, or vice versa. drawing the problem can help you to better visualise what the question is asking of you, and perhaps allows you to have some inkling of what the answer should look like - e.g. if you are swinging an object in a circle vertically, the tension will be larger at the bottom compared to the top (which is easily seen from the diagram due to force addition). say the question asked for you to find the tension at the top; then the diagram allows you to easily tell how the net force should look like, compared to just imagining the situation in your head. so here the diagram helped you by giving you the force directions, and also allowed you to better visualise the situation.
for some reason in physics it is drilled into your head to always draw a diagram, but not in math. however it is often equally as useful in math to draw a diagram, if not just to get some intuition on what the answer should look like. it might be somewhat more time consuming, but it at least gives you some indication that your answer might be wrong, as it might not match what your diagram looks like.
hopefully she lied