I found the following question on an Internet English forum.

Choose the correct answer.

We need someone with ____ knowledge of Chinese.

1. good 2. a good 3. the good

The answer is 2. (a good), but I think 1. (good) is also acceptable. I found the following phrase in Longman Contemporary English Dictionary: salesmen with good technical knowledge of what they are selling

What do you think?
I agree it's also acceptable without the article, but this particular expression is more common as "a good knowledge of . . . "

The adjective "technical" seems to make a difference in the Longman, perhaps making "good" an adverb?? Edit. No, that's not right.

Also, if you omit the "good" you would also omit the article, as it would clearly be uncountable: "Do you have [any] knowledge of her whereabouts?" Edit. I'm changing my mind on this one too. "Do you have a knowledge of chess?" is okay.
Students: Are you brave enough to let our tutors analyse your pronunciation?
(sorry - strange things are happening with the posting routine. )
Thank you. I think I got it. According to Heinle's Newbury House Dictionary of American English, "Knowledge" is used as a countable or uncountable noun depending on the context.

1 an area of learning: The study of English (math, history, etc.) is a field of knowledge. 2 an understanding of s.t. and the ability to use that understanding through study and experience: She has a knowledge of mechanical things and knows how to fix cars. 3 information about or familiarity with s.t.: He has knowledge of the accident and how it happened.

Therefore, "a good knowledge of ...." is the most suitable.
they have a deep distrust of the authorities....

Dom= )
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