yes! i just finished algebra this past year and it was SO hard!
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You can take any math you want in High School that is at your level. Most of the available classes for most schools are Intro to Algebra I, Algebra I, Geometry, Algebra II, pre-Calculus, and Calculus (not always offered). As long as you take any of these maths (the amount in years varies from place to place), and pass, you can graduate from high school.
Depends. Most of us would not know what "Algebra Foundations 2" or "Algebra 1B" are, since the name of such a course is probably determined by the school or local district. Compare the curricula of both courses to see if they are the same.
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Most likely it is called BOOLEAN ALGEBRA I.