High Schoolmath
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Consider the following questions:
Calculus can be tough stuff. Calc AB was the first AP class I ever took in high school, and though I love the subject now, I certainly didn’t love it when I was first struggling with limits or with the chain rule for derivatives.
Taylor series can often seem a bit mysterious the first time that we learn about them. The formula for the Taylor series of a function f(x) around a point x=a is given by
One topic that seemed a bit mysterious and magic to me when I first learned calculus was implicit differentiation. In this post, we’ll start by reviewing some examples of implicit differentiation and then discuss why implicit differentiation works.
The symbol “dx” comes up everywhere in calculus. For example:
Suppose that we have many towns spread across the country and we are trying to connect them with a network of roads. If we would like to do so by laying as little road as possible, how do we do it? In this blog post, we will use Calculus to tackle a special case of this optimization problem.
There are many misconceptions when it comes to the subject of mathematics. One of the most common myths I encounter is related to the way one approaches learning math.
Complicated algebra is the last thing many students want to deal with on a high-stakes test like the SAT or ACT. Yet it seems like there is no way around it, with the alphabet soup of variables scattered throughout the exam. Thankfully, there is a strategy for those problems where your algebraic manipulations are leading nowhere. It’s called ...
SAT, ACT, SSAT, ISEE, GRE. What do these acronyms all have in common? Well, they’re all standardized tests, but more importantly, they all have multiple-choice math test sections. Despite whether or not they’re accurate indicators of student performance in the classroom, lab, or office, they are all essential for entry into some educational career ...
You’ve heard it before. Or you’ve said it. I’m not good at math. I hear it from seventh graders struggling with fractions, high school students preparing to take the SAT, friends at a restaurant when splitting a check, and even from parents assuring me that their child’s own difficulties are in fact genetic. And while I’ve heard it countless ...
Equations in math are useful but they’re also kind of inefficient – for each x value, you have to do a separate calculation to figure out what y is. Graphs take that equation and turn it into a visual, something you can look at and immediately see what happens at different values of x, how the function changes, and more!
Math has changed a lot over the years. When most people think of math, they likely think of someone sitting quietly at a desk with a book or some paper. It’s an unmoving image. When we think of people who are good at math, we conjure up people who blaze through problems quickly and alone. They follow the rules in math and in life. But this is a ...
If you’re the parent of a teenager, chances are good that a few years have passed since you had to graph a polynomial or find a derivative. Since high school math covers topics that people working outside of STEM don’t come across very often, many parents don’t feel like they can give much help to their teenage children with their math homework. ...
Have you ever wondered where the formulas for volumes that you studied way back in geometry come from?
Mathematical applications on the SAT The College Board emphasizes that the Mathematics section on the new SAT is intended to test especially the mathematical knowledge that will be relevant for a broad range of careers—not only the mathy professions like accounting, statistics, or chemistry—as well as for the needs of daily life. Mathematics for ...
Learning about logarithms is one of those times in math class where you wonder if this will ever be useful in any way. I see lots of students struggle with topics like logs, since they can seem abstract and they aren’t obviously useful. But I’m here to explain why they are actually incredibly important and describe so much of the world we live ...
If polar equations have you second-guessing your future as a nuclear physicist, fret not! Almost every pre-calculus student I have tutored has struggled here, and it isn’t surprising at all. Remember the first time you saw an equation and were introduced to these strange x and y variables? It may seem like second nature now, but you were ...
Trigonometry should be simple—you’re just using the given information to solve for only one answer, right? Well, with the Law of Sines, sometimes there is more than one right answer. This situation is also known as the Ambiguous Case. Before we dive into the Ambiguous Case, let’s review the Law of Sines and Congruence.
It’s a shame that so many people can go through college as math majors and minors without ever learning the history of mathematics. Who were Euler and Gauss? Newton and Leibnitz? Euclid? We all know their theorems and mathematical contributions, but rarely do most of us think of the people —with their messy lives, quirks, and stories— behind these ...