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'?)

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.

In addition to Writeacher's comments:

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

1. "I made up my mind to go there," 2. "I decided to go there," and 3. "I determined to go there" all convey the same basic meaning: that the speaker has resolved or firmly decided to go to a particular place. However, there are slight differences in tone and formality between these phrases.

In #1, "to go there" is an infinitive phrase that functions as the object of "made up." It does not directly modify "mind" but rather describes what the speaker has made up their mind about.

Regarding #4 to #7, these sentences convey similar meanings but differ slightly in nuance:

4. "I caught a bad cold" suggests that the speaker contracted a cold, possibly from being exposed to a virus or a sick person.
5. "I took a bad cold" is less commonly used and may imply that the speaker intentionally acquired a cold, which is not a typical usage.
6. "I got a bad cold" is a more neutral statement, simply indicating that the speaker acquired a cold without implying intentionality.
7. "I had a bad cold" conveys the idea that the speaker experienced a cold at some point in the past. This tense may imply that the cold has since resolved or that the speaker no longer has it.

Regarding the use of the article 'a,' it is necessary in each sentence. "A" is a determiner that introduces a singular noun, emphasizing that the speaker acquired or experienced a specific cold. Without the article, the sentences would lack clarity.

The term "bad cold" generally refers to a common cold, which is a viral infection that affects the upper respiratory system. It differs from the flu (influenza) but can share similar symptoms, such as sneezing, coughing, congestion, and a sore throat.