I graduated high school never having had ONE history class.
In about 6th grade I asked my father how Lincoln could have been our President during the war if George Washington was our first President after the war. (I learned of those two men from stories in story books not in school.)
My father immediately told me to go to the library and look up books on the Civil War and the Revolutionary War. I did and read up on both wars.
That summer he took me to Gettysburg.....

I spent time learning new math and never had it easy with old math after that. I went to a different school in 7th grade and the teacher had to show me how when multiplying by 10 or multiples of 10 one could "cheat" and just add the same amount of zeroes to get the product.
I'd never been shown anything like that!

I never was taught grammar. To this day I struggle with it.
I got through college grammar classes by relying on grammar I had learned in French class -- I literally had to translate every sentence into French, figure out the parts of speech, noun, verb, adjective, etc., then I could write down what it was in the English sentence.

Shakespeare I had as a subject in high school. We did Hamlet and Midsummer Night's Dream. And the only thing other than attempt to read those two stories that we did was have to write out a famous soliloquy from each and translate it to modern English. Never even heard of most of his other works in that class.
I found out more about Shakespeare after seeing a Star Trek episode that featured a Shakespeare Troupe in it ("Conscience of the King" TOS) and then read more of his works and became, at least, familiar with them.

Other than Shakespeare, the only literature we had to read in high school was in Sophomore Lit class. We read Catcher in the Rye and Dandelion Wine.

Catechism class wasn't spent on religious matters, such as learning the sacraments (parochial schools...), but instead on social issues. Like the time they had us make placards and signs and took us protesting on a political issue in 6th grade....

I could tell you more, but I guess all that is to say, that the "bases" are more someone's agenda than knowledge necessary to the child.

Also, we cannot know it all -- we can only continue to study throughout out lives, and I'm not too concerned about what my child does or does not know by the time s/he is finished with "high school" as long as the child knows how to read well, and cipher and knows how to find the answers to questions or research s/he wants to do.

My emphasis is rather, that my child has a close relationship with the Heavenly Father -- He will definitely lead my child into the paths s/he should follow, even if I mess up in listening to His voice and leading. And that has to do not only with my child's education (not my main reason for homeschooling BTW) but with my child's eternal soul!