Have the student write down her thinking when she works on practice questions. This will enable her to work on harder questions, and develop the study habits needed to answer those questions. After she masters the questions for her challenge level, have her work on the questions for the next level. This will make her comfortable answering harder questions, which can help when unexpected material is used in the challenge.
Contact the Math Challenge organizers for copies of past questions. This will help the student grow comfortable with the breadth of material likely to be used. Also, many organizations provide students with a list of the books that will be helpful to competitors. Form a study group with fellow students to learn the material in the books. By working as a group, students use their different strengths to conquer the material faster.
Have the student answer questions for which he has not prepared. Since many Math Challenges deduct points for wrong answers, this gives the student a chance to decide if he is confident enough in his answer. Have him assess each guessed answer to decide if it is worth the risk of losing points.