They Were Eleven

A 1975 Sci Fi Shoujo Manga originally written by Moto Hagio, with an anime adaptation released in 1986.

It is the future. Earth, now known as Terra, has made contact with various other planetary civilizations, and formulated one central school for the cream of the crop. Beings from around the known universe gather to take the entry examination; the test is hard, but it's said that admission guarantees an influential position after graduation, and the riches of the universe are theirs for the taking. Ten young space cadets are put onto a decommissioned spaceship in orbit around a small star as the final part of the test.Their orders are simply to survive as long as they can with what they have. There is an emergency beacon that they can activate to be rescued, but the implications for their score on the exam are obvious. However, once they arrive at the decommissioned ship, they find that their crew has mysteriously gained an eleventh member. And then things start going wrong...

As the days pass, the eleven cadets, each from different cultures, species, and walks of life, must deal with their suspicions of each other as well as the sudden knowledge that the orbit of the spaceship is gradually decaying, rising the on-board temperature as it gets closer and closer to the star. With this rise in temperature, a mysterious sickness begins to spread among the crew as they work to stabilize their orbit and determine who among them is the spy.

They Were Eleven shows examples of the following tropes:

 * Bokukko: Even though Frol considers himself a man, he generally comes across as one of these.
 * Crowning Moment of Funny: The cream pie fight in the anime.
 * David Hayter: "Fourth" in the dub.
 * Dropped a Bridget On Him: Frol
 * "Friend or Idol?" Decision:
 * Hermaphrodite: Frol -- his species is asexual until adulthood, when gender is determined; traditionally, only the firstborn of a family is made male, and the others female. However, someone who was admitted into the Cosmo Academy can pick their own gender, and that's why he's here. Knu delivers the exposition because his species is similar.
 * Samus Is a Girl: Played with. The other students react this way the first time they see Frol out of his spacesuit, until he corrects them. Later, when another student sees Frol in the shower and notices that he's missing something important, most of the other students conclude that Frol's pulling a Sweet Polly Oliver until Knu makes The Reveal.
 * Secret Test of Character:
 * Steven Jay Blum: "Rednose", "Amazon", and "King" in the English dub.
 * Ten Little Murder Victims:
 * Training Accident
 * Wendee Lee: As Frol in the English-language dub.
 * Whack a Mole: Obviously.
 * You Fail Physics Forever: Orbits about a single star (or other massive object) don't decay, except possibly unnoticeably slowly (as on the order of centimeters per million years -- except for binary neutron stars).
 * Those could be some really powerful Explosion Propulsion, Inertial Damping and construction materials.