I would like to double check my work:
A. Invert the following:
Est-ce qu’elle veut boire un apéritif?
Answer:
Bois qu'elle un apéritif?
B. Make the following statement negative:
Nous allons au cinéma et au théâtre.
Answer:
Nous n'allons pas ni cinéma ni au théâtre.
A.
Your answer is very close, except that the qu' is part of the Est-ce que...., and should be eliminated. The question reads: Boit-elle un apéritif?
Note: (bois, bois, boit, buvez, buvez, boivent)
However, the auxiliary verb vouloir must be maintained, so the question would read:
Veut-elle boire un apéritif?
B.
Yes, the idea is sound, but "au" must be repeated in both au cinéma and au théâtre. Repetitions are required for à and au, and practically all prepositions of two letters or less. So it should read:
Nous n'allons pas au cinéma ni au théâtre.
(The verb ni is used here to replace "and" in a negated sentence).
For, A. wouldn't it be veut'elle because of the vowel beginning of elle?
The apostrophe would be used when some letter is dropped, and in some cases only.
For example,
il faut que elle... would be shortened to
il faut qu'elle... because phonetically it is difficult and unpleasant to read the two vowels one after another.
It is perfectly acceptable to have a vowel follow a consonant.
To double check your work, let's go over your answers and determine if they are correct.
A. Invert the sentence "Est-ce qu'elle veut boire un apéritif?"
Your answer:
Bois qu'elle un apéritif?
The correct inversion of the sentence "Est-ce qu'elle veut boire un apéritif?" would be: "Veut-elle boire un apéritif?" Inversion requires moving the verb (in this case, "veut") before the subject pronoun (in this case, "elle"). So, the correct answer would be "Veut-elle boire un apéritif?"
B. Make the statement "Nous allons au cinéma et au théâtre" negative.
Your answer:
Nous n'allons pas ni cinéma ni au théâtre.
The correct way to make the statement negative would be: "Nous n'allons ni au cinéma ni au théâtre." In this case, you need to add the negative particle "ne" before the verb "allons" and use the conjunction "ni" to join the two places ("cinéma" and "théâtre") where you are not going. So, the correct answer would be "Nous n'allons ni au cinéma ni au théâtre."
In conclusion, the correct answers are:
A. Veut-elle boire un apéritif?
B. Nous n'allons ni au cinéma ni au théâtre.