Take another look at the sentence:
On Sunday Michael spent the afternoon waxing his new car. If he had knew about the two pop quizzes on Monday, he would have given his algebra problems and accounting spreadsheets more attention.
Know is an irregular verb; the chart below shows its forms.
|Verb||Simple Present||Simple Past||Past Participle|
Would have given, the verb you chose, is perfectly correct. Before you continue, review the rules for irregular verbs.