A Starfleet Academy entrance exam had to be taken before someone could enter Starfleet Academy.
Federation citizens could apply for this test and after they completed the preliminary test, they might be chosen to do the actual entrance exam. For non-Federation citizens it was also possible to do the entrance exam only their request needed to be backed by a letter of reference from a command level Starfleet Officer. (This is how Nog became a Starfleet cadet) (DS9:"Heart of Stone")
The exam itself had the purpose to look for certain qualities a person had like, integrity, intelligence, courage, imagination and the quality of that what made someone a leader. Candidates were told to expect the unexpected during this exam.
An entrance exam could be made up of the following tests:
- Dynamic Relationship Test - a spinning 3D cube consisting of a grid of blue dots in a 6x6x6 configuration, totaling 216 individual points. Surrounding the cube are 216 red dots flying around in a seemingly random pattern. To complete this test you must match up each of the red dots with a blue dot, which requires discovering the appropriate rotation factor and vector coordinates.
- Hyperspace Physics Test - among others, it features a trick question: "If the matter and antimatter tanks on a galaxy class starship are nine-tenths depleted, calculate the intermix ratio necessary to reach a starbase one hundred light years away at warp factor 8." It is a trick question because there is only one matter/antimatter intermix ratio, that being one to one.
- Psych Test This test had the purpose to let the candidate face his or hers deepest fears. (Wesley Crusher feared this test the most) The test itself was tuned to the experiences of the candidate.
- Other Cultures & Species Test Not always announced in advance. It had the purpose to test the candidate how he or she reacted when a member of another species was encountered. The reaction of the candidate was important.
- Carlundrum I.Q Test Here the candidate had to predict the variable patterns of Platonic Solids. The response time was important.
The flux coordinating sensor was part of the apparatus on which the candidates performed some of the tests. (TNG: "Coming of Age")
One of the exam facilities was on Relva VII