a lot of後幾時用單數定雙數名詞??

你的句子應該: There have been a lot of activities.

We use a lot of with both plural and uncountable nouns.

A lot of + uncountable noun
A lot of + countable noun (plural)

Use a singular verb if you are using a lot of before an uncountable noun, and a plural verb if you are using it before a plural noun:

A lot of money was spent on it.
money ~ uncountable noun
was ~ singular verb

A lot of soldiers were killed.
soldiers ~ plural noun
were ~ plural verb

應該看noun是不可數名詞或可數名詞(雙數), 決定 verb 用單數定雙數
Noun 如果是 countable (noun 要 plural), verb 一定是雙數
Noun 如果是 uncountable, verb 一定是單數

Verb 是跟noun, 不是 noun 跟 verb

Some more examples:
There is a lot of money to be made in advertising.
A lot of students come to our class.

2012-09-07 07:34:17 補充：
There has been a lot of activity. ("activity" is used as an uncountable noun ~ abstract noun of "active")

Know the difference:
Activity (countable noun) = (某一團體的)特殊活動; 帶消遣性的活動
Activity (uncountable noun) = 行動, 活動力, 活力,活躍

2012-09-07 07:50:29 補充：
改正:
你的句子應該: There have been a lot of activities.

I assume the "activity" here is used as a countable noun ~ in plural form 例如課外活動