All our knowledge begins with experience and it can be either:
— Analytic (e.g. “All bodies are extended”).
— Synthetic (e.g. “All bodies are heavy”)
Judgements based on experience (a posteriori judgements) are always synthetic.
However, there is such a thing as pure a priori knowledge. Even though it begins with experience, it does not come from it: these are ideas that our “faculty of knowledge provides out of itself, with sensible impressions merely prompting it to do this.”
There are analytic a priori judgements, but is it possible to have synthetic a priori judgements?
What [Kant] is suggesting is that we cannot know things, that they cannot be objects of knowledge for us, except in so far as they are subjected to certain a priori conditions of knowledge on the part of the subject. If we assume that the human mind is purely passive in knowledge, we cannot explain the a priori knowledge which we undoubtedly possess. Let us assume, therefore, that the mind is active. This activity does not mean creation of beings out of nothing. It means rather that the mind imposes, as it were, on the ultimate material of experience its own forms of cognition, determined by the structure of human sensibility and understanding, and that things cannot be known except through the medium of these forms. [Frederic Copleston, A History of Philosophy, Vol. VI]