M2 Kinematics Question

Whenever I encounter a question asking to "consider energy" or use the "work-energy principle", I know that I have to use the following equation:
Final KE = Initial KE ± GPE (-friction force)

However, I find it difficult to figure out when I should subtract or add GPE. I initially thought that I should minus it if the particle is moving upwards because though it gains GPE, in the energy equation, it is going against the change in KE. However, I found that I got a few questions incorrect using this thought process.. Could anybody teach me when to ±GPE, please? Thank you!!

Easier if you post the question/your working on the things you got wrong, but as a general principle, you can imagine that both PE and KE are relative to their "starting position" and that the change in energy between the initial and final position is zero. So
0 = Change in Energy = Final Energy - Initial Energy
Then when you choose an origin to define your GPE height with respect to, you can get the heights of both the Iniital and Final GPE and the sign your talking about sorts itself out. Obviously, most people choose the initial position to be the "origin" so the Initial GPE is zero, but choosing that origin is a good thought process to go through. A sketch where you mark the origin and the height explicitly on is probably better than trying to remember +/-.

However, if you want to try and "remember" the sign,, remember that the change in GPE is work done by a constant force (mg) in moving an object a distance h. If gravity is pointing downwards, in moving the particle upwards, you're working against a force -mg a distance h, so the change in GPE over that distance is
- - mgh = mgh
the first - is because youre working against gravity, the second because gravity (g) is acting downwards and you're moving upwards. So if youre moving a particle against gravity, the change in GPE is positive, and energy has been stored from doing this work. If the particle moves in the direction of gravity, the change is GPE is negative.

Thank you for your explanation!
It was this question. Before reading your quote, I wrote -mgh. But seeing your explanation I think that since B is downwards from the initial starting point A, I am supposed to add mgh.. am I right..?

Youre "guessing the sign" and if you used the first part of the response, using the origin is base
final GPE = 30mg
initial GPE = 45mg
...

But how are you defining h? That is arguably where your problem is? Are you saying its 15 or -15?

I put 1/2 x m x 24.5^2 = 1/2 x m x u^2 -15mg, thinking by using your response that as initial GPE is 45mg and final GPE is 30mg, the difference in GPE is -15mg, given that the direction from A to B is positive.

Intuitively, the speed u must be less than 24.5 as A is higher than C so subtract the change in GPE from KE at C
(m/2)*24.5^2 - 15mg = (m/2)u^2

Being systematic and using the base as the origin
Final Energy = Initial Energy
(m/2)*24.5^2 + 30mg = (m/2)u^2 + 45mg

Or work done, the distance 15 is moved between the points in the direction of the force (gravity), so the work done against gravity is negative (change in GPE) so
(m/2)*24.5^2 - 15mg = (m/2)u^2
If the work done is in the opposite direction to/against gravity, then the change in GPE is positive. Here by definition of the height. the inital GPE is zero, so you're "adding" the (signed) change in GPE to the final energy.

Alternatively, define h as the displacement from the initial point, where positive is upwards (opposite to gravity which is downwards), then the change in GPE is
mgh
but note here that h has a sign to denote direction with upwards positive.
...

wow I finally understand why this equation is being formed. Before, I was just systematically forming equations by guessing, but thanks to your response I now understand. Thank you so much, you just saved my grades.