Seeing as Newton pioneered Calculus, or as he called it The Method of Fluxions, it’s no wonder that one of the first topics you’ll learn about in Calculus involves an application of physics: rates of change.

If these sorts of applications make your eyes cross, then this quick tutorial will hopefully ease the pain. We’re going to start with some very basic concepts and work our way, gently, up to the idea of the limit, which lies at the heart of Calculus.

Galileo’s Law

We’ll begin our exploration of Calculus by investigating a simple and classic concept: the rate of a falling…

Part One: Solving Triangles w/ Sine, Cosine, & Tangent

You might be surprised to find that the heart of Trigonometry lies in Geometry. Understanding the relationships used to solve right triangles geometrically is fundamental to pretty much everything you do Trigonometry. So whether you’re learning this for the first time or are here for a little refresher you’ll walk away from today’s tutorial with a good grasp at how to solve right triangles.

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Three Key Concepts

We’ll be using three key concepts in today’s lesson:

  • Trig Functions: Sine, Cosine, and Tangent (aka SOH CAH TOA)
  • The Pythagorean Theorem: a² + b² = c²
  • 180 degrees in…

A Beginner’s Guide

What are Algebraic Expressions?

The first question you might have is “What exactly are algebraic expressions?” As the name implies you have expressions involving algebra, but what does that mean?

An expression is a grouping that can include any combination of numbers, symbols, and operators (addition, subtraction, multiplication, division). The one thing that expressions don’t have are equal signs. The presence of an equal sign makes an equation, not an expression, although an expression can be part of an equation.

Since the expressions we’ll be dealing with are algebraic we know that they will include algebraic variables, making them a tad bit more abstract…

So you’ve graduated from two-variable systems of equations to the big leagues, three-variable, three equation systems! Gone are the days of simple Substitution and Elimination methods and welcome to the world of nearly page-long solutions.

In this guide, you’ll learn about two different techniques you can use to solve these complicated systems. Let’s jump in!

What is a Three-Variable System of Equations?

The first question you may have is what exactly is this three-variable system? You may remember from two-variable systems of equations, the equations each represent a line on an XY-coordinate plane, and the solution is the (x,y) intersection point for the two lines. …

You’ve heard it time and time again, “Rationalize the denominator. Make sure to rationalize the denominator!” But why??? Who decided that getting the root out of the denominator and into the numerator was the thing to do?

Here are three reasons why RTD became the standard from Algebra to Calculus.

The Commonsense Reason

The standard reason why you need to RTD is perfectly practical. As you’ve most likely discovered, in mathematics you can often write solutions in multiple different ways and forms. All of these variations are cool, but for practical purposes, they make life more difficult for those grading your papers.


Plus their reciprocals: Cosecant, Secant, Cotangent Graphs

In our modern world, it may seem like graphing functions by hand is...well…a bit archaic. When you can easily enter any function you wish into Desmos or Wolfram Alpha from the comfort of your phone, why should you learn to graph functions longhand? Especially the more complicated functions like the ones we encounter in trigonometry?

Well besides the obvious likelihood that you are reading this because in some Trigonometry, Precalculus, or Calculus course your instructor is requiring you to graph sans technology, I’d like to present the argument that true understanding can only be gained through *doing*. The fact remains…

Throughout Algebra 1 and 2, one of the key concepts you’ll learn is how to factor polynomials including but not limited to quadratics. Factoring is an important process that helps us understand more about our equations. Through factoring, we rewrite our polynomials in a simpler form, and when we apply the principles of factoring to equations, we yield a lot of useful information.

For example from the factored form, you can easily identify solutions. You get an idea of the quantity and type of solutions an equation has. You can find its roots/x-intercepts, which makes it easier to graph. You…

(as easy as pie 🥧)

Happy Pi Day friends 🎉 It’s finally the one day of the year where math gets some love instead of the shade it gets the other 364 days! Feeling all the warm fuzzies about math makes March 14th one of my most favorite days of the year!

In celebration of Pi Day, I’m going to teach you a little pi memory trick that, for me, made memorizing the first 100 digits of pi easier than baking my Pi Day Pie 😂 I wish I were kidding but it’s true. It took me just over a day to memorize 100 digits…

Taking the jump from algebra to the land of matrices 🎉

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Confession: I love linear algebra. Okay, maybe that’s not much of a confession, but I do love it! In a large part, because linear algebra doesn’t feel like the rest of mathematics, it feels like a puzzle.

Now that may sound crazy, but hear me out.

This new land of matrices and vectors may look and feel intimidating, and for good reason: new notation, new rules, new properties. It’s all a bit different. But maybe viewing it as a puzzle will help you jump over that new notation hurdle.

plus a simple explanation of why 0! = 1

If you’re studying advanced statistics or combinatorics, you will surely run across these, dare I say, exciting (!) factorials (yes, I’m a math nerd, and I’ll take any opportunity I get to make a pun however weak 😜).

But seriously, this mathematical notation can be confusing for beginners especially as we move from standard numeric problems to more difficult variable expressions. Don’t you worry though, this quick factorial tutorial (cheesy, I know 😊) will get you cruising in no time.

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What is a Factorial?!

A factorial, denoted by an exclamation point (!), is an operation…

Brett Berry

Check out my YouTube channel “Math Hacks” for hands-on math tutorials and lots of math love ♥️

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