Questions about French prepositions
Q: Why is it je vais à Paris and not je vais au Paris?
Unlike English, French uses à, au and en, depending on whether the speaker is referring to a city versus a country, state or province, even though these may all be translated into English by "to" (or "in", depending on the meaning). The form à is found with cities, e.g.: Je suis allé à Paris, the form au is used before masculine countries, provinces and states, e.g.: Je suis allé au Texas, while the form en is found before feminine countries, provinces and states, e.g.: Je suis allé en France. Note that en is also used before masculine countries, provinces and states that begin with a vowel, e.g.: Je suis allé en Ontario.
Q: Why is it Paula le donne à mon frère and NOT Paula le donne a mon frère?
Without an accent, a is a form of the verb avoir. If you mean "to", write à with an accent.
Q: Why is it J'ai cherché le livre and NOT J'ai cherché pour le livre?
Unlike English, the verb chercher ("look for"/"seek") is not followed by a preposition in French. The noun comes directly after it.
Q: Why is it J'aide ma mère and NOT J'aide à ma mère?
The verb aider is followed directly be a noun in French (there is no intervening preposition).
Q: Why is it ma soeur joue du piano and NOT ma soeur joue le piano?
When you mean "play an instrument", use jouer de; when you mean "play a game/sport", use jouer à.
Q: Why is it Nous l'avons terminé en une heure and NOT Nous l'avons terminé dans une heure?
When referring to time, use en to mean "within". The word dans means "from now" (and, as such, only refers to future events).
Q: Why is it Elle l'a fait pendant deux heures and NOT Elle l'a fait pour deux heures?
Use pendant when describing how long a past event lasted (pour is only used to describe future events).