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Math

Algebra II

Conceptual videos and worked examples from basic algebra through algebra 2. Includes videos from the former algebra worked examples playlists.
Community Questions
A thumbnail for: Systems of equations and inequalities
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Systems of equations and inequalities

What happens when we have many variables but also many constraints.
A thumbnail for: Functions and their graphs
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Functions and their graphs

Revisiting what a function is and how we can define and visualize one.
A thumbnail for: Polynomial and rational functions
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Polynomial and rational functions

Exploring quadratics and higher degree polynomials. Also in-depth look at rational functions.
A thumbnail for: Rational expressions
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Rational expressions

You have probably been wondering whether our powers of algebraic problem solving break down if we divide by the variable or we have entire expressions in denominator of a fraction. Well, they don't! In this topic, you'll learn how to interpret and manipulate rational expressions (when you have one algebraic expression divided by another)!
A thumbnail for: Exponential and logarithmic functions
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Exponential and logarithmic functions

An look at exponential and logarithmic functions including many of their properties and graphs.
A thumbnail for: Logarithms
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Logarithms

Log-a-what? No, this tutorial is about neither chopped wood nor music (actually logarithms do have applications in music), but it is fascinating nonetheless. You know how to take an exponent. Now you can think about what exponent you have to raise a number to to get another number. Yes, I agree--unstoppable fun for the whole family. No, seriously, logarithms are used everywhere (including to measure earthquakes and sound).
A thumbnail for: Imaginary and complex numbers
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Imaginary and complex numbers

Understanding and solving equations with imaginary numbers.
A thumbnail for: Conic sections
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Conic sections

A detailed look at shapes that are prevalent in science: conic sections
A thumbnail for: Matrices
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Matrices

Understanding and solving matrices.
Functions and their graphs
Revisiting what a function is and how we can define and visualize one.

Function introduction

Relationships can be any association between sets of numbers while functions have only one output for a given input. This tutorial works through a bunch of examples of testing whether something is a valid function. As always, we really encourage you to pause the videos and try the problems before Sal does!

Domain and range

What values can you and can you not input into a function? What values can the function output? The domain is the set of values that the function is defined for (i.e., the values that you can input into a function). The range is the set of values that the function output can take on. This tutorial covers the ideas of domain and range through multiple worked examples. These are really important ideas as you study higher mathematics.

Function inverses

Functions associate a set of inputs with a set of outputs (in fancy language, they "map" one set to another). But can we go the other way around? Are there functions that can start with the outputs as inputs and produce the original inputs as outputs? Yes, there are! They are called function inverses! This tutorial works through a bunch of examples to get you familiar with the world of function inverses.

Properties and features of functions

You know a function when you see one, but are curious to start looking deeper at their properties. Some functions seem to be mirror images around the y-axis while others seems to be flipped mirror images while others are neither. How can we shift and reflect them? This tutorial addresses these questions by covering even and odd functions. It also covers how we can shift and reflect them. Enjoy!

Undefined and indeterminate answers

In second grade you may have raised your hand in class and asked what you get when you divide by zero. The answer was probably "it's not defined." In this tutorial we'll explore what that (and "indeterminate") means and why the math world has left this gap in arithmetic. (They could define something divided by 0 as 7 or 9 or 119.57 but have decided not to.)

More mathy functions

In this tutorial, we'll start to use and define functions in more "mathy" or formal ways.