Exactly, I was asking about those rules. They aren't explained in this lesson. The lesson only explains attributive adjectives and nothing about predicative. However, the exercises are full of predicative adjectives. What are the rules for those?
So why is it "det trötta barnet" but "barnet är trött"?
Oh, sorry. After googling a bit Strong and Weak forms seems to be the terms.
"Strong adjectives are used after the indefinite article and the words någon (a, some, any), ingen (no), en annan (another), vilken (what a), and all (all); as well as after the verbs to be and to become (vara and bli). Weak adjectives are used with the definite article, demonstratives, possessive adjectives or a possessive noun."
http://ielanguages.com/swedish3.html, scroll down to Adjectives.
Wikipedia has a little info too: http://en.wikipedia.org/wiki/Swedish_grammar#Adjectives