Question

1. I made up my mind to go there.
2. I decided to go there.
3. I determined to go there.

(They are all the same, right? By the way, in #1, does 'to go there' modify 'mind'?)

4. I caught a bad cold.
5. I took a bad cold.
6. I got a bad cold.
7. I had a bad cold.
(Are they the same? Can we omit 'a' in each sentence? Does bad cold mean 'influenza'?)

Answer 1

1 - 3 -- All three are OK, but 3 is rarely used. The phrase "to go there" is an infinitive phrase; the word "there" means "that place" and modifies the infinitive "to go." It's not easy to say what the infinitive phrase is doing in this sentence, although it's used correctly. I see it as a complement for "mind" but another teacher may have a different idea.
http://grammar.ccc.commnet.edu/grammar/phrases.htm#infinitive
http://www.chompchomp.com/terms/infinitivephrase.htm

4 - 7 -- A cold and influenza (flu) are different in several ways. Flu is worse; the symptoms are usually more severe and last longer than a cold does.

All four sentences are grammatically correct and mean approximately the same thing, but #5 is not often used. 4 and 6 could mean that the person still has the cold; 7 means the person is over the cold now.

Do not omit "a" in these expressions.

Answer 2

In addition to Writeacher's comments:

3 would be better as "I was determined to go there."