rex Aegypti duos liberos habebat. hi liberi erant Cleopatra et Ptolemaeus. per multos annos liberi vitam laetam cum patre habebant. deinde post mortem patris Cleopatra erat regina. [passage taken from sample paper, own questions below]

How many children did the king have and what were their names? We look at the first line, which translates to: The king of Egpyt had two children, Cleopatra and Ptolemaeus. The nominative is 'rex' (king), the verb is 'habebat' (he had) and the accusative is 'duos liberos' (two children). We can see the ending of 'habebat' is singular, so we know it refers to the king. From the next line 'hi liberi erant Cleopatra et Ptolemaeus' we get: These children were Cleopatra and Ptolemaeus. What kind of life did the children have with their father? Looking at the line 'per multos annos liberi vitam laetam cum patre habebant', we can pick out the key information to make sure we're looking at the correct line. 'cum patre' (with their father) and 'vitam' (life) are both present, meaning from inspection the sentence is the correct one to be looking at. The translation is: 'for many years, the children had a happy life with their father'. 'liberi' (children) is nominative and agrees with the plural "they" ending 'habebant', and the accusative is 'vitam' (life). 'laetam' (happy) has the same ending as 'vitam', so the two words agree. We can conclude the children had a happy life with their father.