Velocity and Acceleration positive and negative

I understood that you assign either up or down as positive, and then i.e. if you've assigned upwards as positive, then you make acceleration due to gravity negative. My question is - do you assign velocity positive or not? In this question, the particle is thrown up and it falls down again. In the first part of the question to find the speed of projection, you use a positive value, but then to find the highest height it hits you use a negative value? And for another question, a ball is thrown up and hits the ground, we're told to find the height above ground it was thrown from but they use a negative acceleration and a positive velocity?

The questions are 7 & 8 of 9E in Y1 Stats and Mechanics for Edexcel, and the solutions are on physicsandmathstutor.com, for reference.

If positive is up (you can decide but it is normal to call up positive), and you throw the ball upwards it has a postive velocity. If the question asks for speed, as speed is scalar, has no direction, you can just take the positive of your velocity. Does that make sense? I am not really sure of the question tho tbh.

Reading that back my question was so unclear omg. Basically if you assign one direction (i.e. upwards) positive, does that apply for both acceleration and velocity?

And if yes - what if in a question your initial value for velocity is positive, but regarding a ball being thrown in the air and falling to the ground? Then for the second half would you use a negative velocity? How come you don't actually do that in SUVAT question?

You can choose any direction you want as positive, as long as you're consistent and apply it to displacement, velocity and acceleration in the same way. This can probably be proven by differentiating the SUVAT equations.

If you have a ball in the air and initial velocity is given as (e.g.) +5 m/s, then this means the question has kind of hinted at you that you should be taking upwards as positive, although you can choose not to do this if you think the working would be simpler. If you chose to reverse the directions, you'd take initial velocity as -5, and in the falling part of the motion, velocity would be positive. Gravity would also be +g in this case.

So would you do that the whole way through, if that makes sense? So like if the ball goes up, then down would the velocity also go positive then negative, like the acceleration?

velocity is simply the rate of change of the displacement. if you have something that is moving 1 unit displacement in your coordinate system per unit time then its velocity is 1, it's that simple. if you instead use use other coordinate system then it might be moving 3 per unit time or -0.2 per unit time
velocity is the rate of change of your displacement and acceleration is the rate of change of that.
also the acceleration of an object in free fall is constant. it does not change direction after it reaches the maximum height.

But surely when it's going up it's gonna be a different direction to when it's going down? And since like you said its the rate of change of your velocity, it also means your velocity is changing from positive to negative when it goes up then down?