Both sentences are accepted in Spanish. if you say "¿Tenéis que contestar las preguntas de la profesora?" or "¿Tenéis que contestar a las preguntas de la profesora?", the meaning of the sentence is the same. The difference between the first and the second, in Spanish, is the object which it refers to. In the first sentence, the meaning is that you have to answer the questions, in general, and in the second you say that you have to answer teacher´s questions. The preposition "a" is only a reinforcement, in this case, of the meaning, but it doesn´t change anyway. I hope this information will be useful for you.