I. Latin to English:
1. Quintus was approaching the priest of Apollo with great reverence, lest the god become/so that the god might not become angry with him.
NB the reflexive pronoun in the purpose clause refers to the subject of the main verb, not of the subjunctive verb.
2. The young man drinks from the Castalian spring to become/so that he may become a poet.
3. The god uttered dark oracles so that those seeking easy answers might be turned away.
NB when the subject of a purpose clause is different from that of the main clause, it does not work to use an infinitive phrase to translate the purpose clause--you must use a "that" clause.
4. The priest says, "Let (people) unworthy of Apollo's wisdom not enter this shrine."
NB the subjunctive is the main verb in this sentence, and must therefore be a "hortatory" subjunctive.
5. Many of Theomnestus' pupils will depart from the Academy to fight/so that they may fight for the republic's freedom along with Brutus.
6. Brutus spoke to the young men in the Academy to inflame/so that he might inflame their passion.
NB suum refers to the plural subject of the main verb discedent, but agrees in gender, number, & case with the word it modifies, namely studium (accusative, neuter, singular).
7. The young men say to one another, "Let us join Brutus, lest the republic/so that the republic may not lack supporters."
NB Latin uses iungo reflexively to mean "join the cause of," "ally oneself to"
8. Brutus was besieging many cities in Asia to acquire/so that he might acquire money for his troops.
II. English to Latin:
1. dona ad Apollonem ut ei persuadeamus.
NB remember that the infinitive phrase in English must become a subordinate clause in Latin. You have to think carefully about what the subject of the subjunctive verb would be; if you rewrote this sentence, you'd get: "We shall bring gifts to Apollo so that we may persuade him." Remember, too, that persuadeo requires the dative!
2. Quintus aures (suas) texit ne oraculum terribile dei audiret.
3. Marcus epistolam ad Quintum scribit ut ille se in Asia iungat.
NB littera is a letter of the alphabet. You can remember the right Latin word by bearing in mind its English derivative "epistle." Ille is required in the subordinate clause to indicate the change of subject; se is needed (rather than eum) because it refers to the subject of the main clause.
4. omnes iunvens cum Antonio militent ut coniurationem deleant.
NB the hortatory subjunctive "let...campaign" is considered a future tense, requiring the present subjunctive in the purpose clause.