category: ap
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ap calculus review: average value of functions
the average of a set of data is typically defined as the sum of the values divided by the number of data points. but what if you have infinitely many data points? what is the average value of a function? read on to find out! average value of functions suppose f is a continuous function…
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ap calculus review: differential equations
a differential equation is a relation that involves an unknown function and its derivative. there are many kinds of differential equations and tons of specialized techniques we may use to solve them. fortunately, on the ap calculus exams you will only encounter a handful of the most basic kinds. basic differential equations: integration you have…
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themes across apush: party politics
we know that getting all the details about what happened in u.s. history (let alone explaining the significance of those events) can be hard. our latest blog post on apush themes: party politics will help you practice the skill of identifying changes and continuities by looking at the development of political parties.
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ap calculus review: optimization
this review article is all about optimization. here, you’ll learn the tools and techniques for setting up and solving these often difficult problems. and along the way, we’ll work out a few examples! optimization the method of optimization uses derivatives to find maximum or minimum values. however, the functions that need to be optimized typically…
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themes across apush: expansion
the latest post in our series focuses on apush themes: expansion. you’ll be able to practice the skill of examining patterns of change and continuity over time by looking at one apush theme: territorial expansion throughout u.s. history.
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ap calculus review: applications of derivatives
calculus is primarily the study of rates of change. however, there are numerous applications of derivatives beyond just finding rates and velocities. in this review article, we will highlight the most important applications of derivatives for the ap calculus ab/bc exams. applications of derivatives here is a list of some of the essential derivative applications.…
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themes across apush: social movements
this next post in our series of change throughout history covers apush themes: social movements! read on for an overview of social movements in the united states, from the revolutionary war and beyond.
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ap calculus review: derivatives of inverse functions
one of the trickiest topics on the ap calculus ab/bc exam is the concept of inverse functions and their derivatives. in this review article, we’ll see how a powerful theorem can be used to find the derivatives of inverse functions. then we’ll talk about the more common inverses and their derivatives. what are inverse functions?…
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themes across apush: voting rights
welcome to our blog post on apush themes: voting rights! the focus this week will be for you to practice the skill of identifying changes and continuities throughout u.s. history, using voting rights as our example.
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ap calculus review: shell method
the shell method is a technique for finding the volume of a solid of revolution. just as in the disk/washer method (see ap calculus review: disk and washer methods), the exact answer results from a certain integral. in this article, we’ll review the shell method and show how it solves volume problems on the ap…