1)  Which describes the motion of a star across the sky over the
    course of one sidereal day?
    (a) Makes one complete circle around an axis through the
        North Star.
    (b) Makes slightly more than one complete circle around an
        axis through the North Star.
    (c) Makes an approximate circle around an axis through the
        North Star, but does not return to the original point.
    (d) Moves from west to east across the sky with occasional
        loops in the opposite direction.

(a) is correct. (b) is what a star does in one solar day, not one sidereal day. (c) is what a planet does in one sidereal day. (d) is what a planet does over the course of many days.