I'm going to assume that "ecuasions" is a mispelling of equations. While typically not taught at the high school level, a few relevant equations related to the patched conic approximation (or rocketry in general) come to mind.

https://en.wikipedia.org/wiki/Sphere_of_influence_(astrodynamics)

https://en.wikipedia.org/wiki/Vis-viva_equation

https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation

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Universal gravitation.

Newton's laws of motion, of course.

The rocket equation.

The escape velocity formula.

Thank you

Come on man of course that’s what he meant

It's hard to tell with these questions. I actually was wondering if this was one of those word-salad sentences and they were asking about "explanations", or there was some untranslated word or something.

I recommend playing kerbal space program and trying to land on the moon! It’s a lot of fun and very educational (especially newtons laws of motion)

Most of these are taught in high school physics. There are additional equations and tricks that are specialized, but all of them are derived from those 4 basic equations.

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It seems like there should be an xkcd about this.

KSP is a fantastic introduction for those curious about—but not yet entirely familiar with—orbital mechanics. I bought and played KSP when it first released, and it holds an honorable mention in the list of reasons of why I became an aerospace engineer. The fascination of physics and space it instills in the everyday gamer is (at least in my case) wildly understated. I highly recommend that anyone at least remotely intrigued by space pick up a copy of KSP (with KSP 2 coming soon, it's pretty exciting).

With that being said, to answer this post specifically in light of the KSP comment, here's a few things that KSP would have taught (in one way or another) that would have been understood by Apollo trajectory engineers that has not already been mentioned.

1. KSP operates on the two-body gravitational model. Great for introductory understanding, yet not realistic (but close enough, and I don't blame the developers for not including an accurate gravity model that would likely light your computer on fire). This would have been considered by the team working on Apollo, and they would have found that any gravitational effects outside of the three-body Earth-SpaceCraft (SC)-Moon system and the respective perturbations would have been negligible (and easily corrected when present). They would have committed a lot of computational labor (at least at the time when modern computers weren't available) to the calculation of gravitational forces in the transition between orbiting around the Earth and Moon, which is something KSP does not reflect.
2. The Vis-Viva equation is very much present in KSP, and this would have been well understood by the trajectory engineers when predicting the trajectory around a dominant gravitational force. This equation is certainly worth learning (if you're interested, of course) and is not overly complicated.
3. Rotational momentum is decently well respected in KSP (but it doesn't account for gravitational rotation, again because you probably like not torturing your computer). If you keep your focus on one SC, it will maintain its rotational momentum and it won't stop unless the astronauts (Kerbals, those mighty adventurers) act against it. Specifically for landing and burns (acceleration using the thrusters), rotational momentum and direction would have been very important and considered by the Apollo team. Rotational momentum is a commonly taught lesson in introductory physics classes.
4. KSP does not account for atmospheric drag above a hypothetical Kármán line (again, this is so your computer does not jump itself off a cliff, so no shade at the developers). This is a consideration that is less important and not completely relevant to the Moon landing itself, but just to its build up in the early stages.

Just my two cents (and probably much more, sorry) about what KSP can teach and how that might differ from physical simulations and what the Apollo team would have considered. It is by no means exhaustive or infallible. There was a tremendous amount of work that went into the Apollo program, and I hope both KSP and a part of my explanation could help peak any interest in space :)

Besides the navigation, which others have mentioned, are equations for temperature and pressure used in the cabin gasses, propellant system and general thermal management. There are inverse square falloff equations for signal strength on the radio transmissions and radar returns. There are basic electrical equations for voltages, current, and resistances in the equipment.

Thanks for the info! So cool that ksp got you into aerospace engineering!