I disagree with Matt. Singular countable nouns need a determiner. Basic Grammar in Use (Murphy), lessons 66-75. - ... __ summer vacation in China (odd/wrong - in North American English) - ... a summer vacation in China (correct - the vacation in China is one their family summer vacations) - ... the summer vacation in China (odd, but correct given that there is one summer vacation per year) - ... their summer vacation in China (correct) Seasons are somewhat complicated. - I spent a summer in China. (good) - I spent last summer in China. (good) or - I spent [...] summer in China. (good - last summer is understood) - I spent a summer vacation in China. (good) - I spent my summer vacation in China. (good) or - I spent [...] summer vacation in China. (odd - my summer vacation is understood - I would mark this wrong in an essay)

You don't need "A" here. "A" is generally used for things that occur in general, or when you don't know which specific person, place, thing is being referenced. The inclusion of 'last year' specifies which 'summer vacation' you are talking about, so there is no longer need to use "A."

You only have one summer holiday so 'a' not only sounds strange but is not applicable. You would use 'their' or 'the' instead.