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author: lucas fink

lucas fink
lucas is the teacher behind magoosh toefl. he’s been teaching toefl preparation and more general english since 2009, and the sat since 2008. between his time at bard college and teaching abroad, he has studied japanese, czech, and korean. none of them come in handy, nowadays.

  • ap calculus: the difference between a graph and a function?

    did you know that a graph of a function f is not the same as the function itself? it might seem like there is clearly a difference, but sometimes it’s hard to articulate into words. we have spoken about the definition of a function. simply put, it’s a rule that transforms one real number into…

  • ap calculus: computing the antiderivatives of functions and polynomials

    warm-up: keeping with the theme of volume of solids of revolution, try this multiple choice question, which should need only understanding of the geometric meaning of the definite integral as a measurement of volume. question: a solid is generated by revolving the region enclosed by the function , and the lines x =2, x =3, y…

  • ap environmental science exam

    ap environmental science is a buffet of an ap course. in this article, learn everything you need to know about how to do your best on exam day!