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.

Thank you, Cristian and Mila for your answers and explanation.

Hi Fengying, In my opinion both sentences are correct. 1- ¿Tenéis que contestar a las preguntas de la profesora? "a" - always goes with the direct object (las preguntas). 2- ¿Tenéis que contestar a la profesora? "a" always goes with the indirect object (profesora)

¿Tenéis que contestar a las preguntas de la profesora? ¿Tenéis que contestar las preguntas de la profesora? En el primer caso esta de mas o sirve para reforzar la frase. En ambos casos esta correcto, por lo menos para un hablante nativo.