Introduction to algebra
Videos exploring why algebra was developed and how it helps us explain our world.
Exploring a world where both sides aren't equal anymore!
Graphing and analyzing linear functions
Use the power of algebra to understand and interpret points and lines (something we typically do in geometry). This will include slope and the equation of a line.
Systems of equations and inequalities
Solving a system of equations or inequalities in two variables by elimination, substitution, and graphing.
Multiplying and factoring expressions
This topic will add a ton of tools to your algebraic toolbox. You'll be able to multiply any expression and learn to factor a bunch a well. This will allow you to solve a broad array of problems in algebra.
In this topic, we'll analyze, graph and solve quadratic equations.
Exponent expressions and equations
Solving exponential and radical expressions and equations. Using scientific notation and significant figures.
Identifying, solving, and graphing various types of functions.
Ratios and proportions
What ratios and proportions are. Using them to solve problems in the real world.
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)!
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).
Identifying and graphing circles, ellipses, parabolas, and hyperbolas.
Understanding and solving matrices.
Imaginary and complex numbers
Understanding and solving equations with imaginary numbers.
Algebra seems mysterious to me. I really don't "get" what an equation represents. Why do we do the same thing to both sides? This tutorial is a conceptual journey through the basics of algebra. It is made for someone just beginning their algebra adventure. But even folks who feel pretty good that they know how to manipulate equations might pick up a new intuition or two.
- Why we do the same thing to both sides: Simple equations
- Representing a relationship with a simple equation
- One-step equation intuition
- One step equation intuition exercise intro
- One step equation intuition
- Adding and subtracting the same thing from both sides
- Intuition why we divide both sides
- Why we do the same thing to both sides: Two-step equations
- Why we do the same thing to both sides: Multi-step equations
- Why we do the same thing to both sides basic systems
This tutorial is a survey of the major themes in basic algebra in five videos! From basic equations to graphing to systems, it has it all. Great for someone looking for a gentle, but broad understanding of the use of algebra. Also great for anyone unsure of which gym plan they should pick!
- Super Yoga plans: Basic variables and equations
- Super Yoga plans: Solving one-step equations
- Constructing and solving equations in the real world 1
- Super Yoga plans: Plotting points
- Super Yoga plans: Solving systems by substitution
- Super Yoga plans: Solving systems by elimination
- Constructing and solving equations in the real world 1 exercise
Like the "Why of algebra" and "Super Yoga plans" tutorials, we'll introduce you to the most fundamental ideas of what equations mean and how to solve them. We'll then do a bunch of examples to make sure you're comfortable with things like 3x – 7 = 8. So relax, grab a cup of hot chocolate, and be on your way to becoming an algebra rockstar. And, by the way, in any of the "example" videos, try to solve the problem on your own before seeing how Sal does it. It makes the learning better!
- Simple equations of the form ax = b
- Example solving x/3 = 14
- One-step equations with multiplication
- Example solving x + 5 = 54
- Examples of one-step equations like ax = b and x + a = b
- One step equations
- Solving ax + b = c
- Two-step equations
- Example: Dimensions of a garden
- Example: Two-step equation with x/4 term
- 2-step equations
Now that we are reasonably familiar with what a linear equation is and how we can solve them, let's apply these skills to tackling real-world problems.
You've been through "Equation examples for beginners" and are feeling good. Well, this tutorial continues that journey by addressing equations that are just a bit more fancy. By the end of this tutorial, you really will have some of the core algebraic tools in your toolkit!
- Variables on both sides
- Example 1: Variables on both sides
- Example 2: Variables on both sides
- Equation special cases
- Equations with variables on both sides
- Number of solutions to linear equations
- Number of solutions to linear equations ex 2
- Number of solutions to linear equations ex 3
- Solutions to linear equations
You feel comfortable solving for an unknown. But life is all about stepping outside of your comfort zone--it's the only way you can grow! This tutorial takes solving equations to another level by making things a little more abstract. You will now solve for a variable, but it will be in terms of other variables. Don't worry, we think you'll find it quite therapeutic once you get the hang of it.
You know that converting a fraction into a decimal can sometimes result in a repeating decimal. For example: 2/3 = 0.666666..., and 1/7 = 0.142857142857... But how do you convert a repeating decimal into a fraction? As we'll see in this tutorial, a little bit of algebra magic can do the trick!
In 72 years, Sal will be 3 times as old as he is today (although he might not be... um... capable of doing much). How old is Sal today? These classic questions have plagued philosophers through the ages. Actually, they haven't. But they have plagued algebra students! Even though few people ask questions like this in the real-world, these are strangely enjoyable problems.
You are absolutely tired of not knowing how to deal with equations that have absolute values in them. Well, this tutorial might help.
- Absolute value equations
- Absolute value equations example 1
- Absolute value equation example 2
- Absolute value equations
- Absolute value equations 1
- Absolute value equation example
- Absolute value equation with no solution
- Absolute value equations
- Absolute value inequalities
- Absolute value inequalities example 1
- Absolute inequalities 2
- Absolute value inequalities example 3
You feel good about your rapidly developing equation-solving ability. Now you're ready to fully flex your brain. In this tutorial, we'll explore equations that don't look so simple at first, but that, with a bit of skill, we can turn into equations that don't cause any stress! Have fun!
When solving equations, there is a natural hunger to figure out what an unknown is equal to. This is especially the case if we want to evaluate an expression that the unknown is part of. This tutorial exposes us to a class of solvable problems that challenges this hunger and forces us to be the thinking human beings that we are! In case you're curious, these types of problems are known to show up on standardized exams to see if you are really a thinking human (as opposed to a robot possum).
This tutorial is for you if you already have the basics of solving equations and are looking to put your newfound powers to work in more examples.
- Mixture problems 2
- Basic rate problem
- Early train word problem
- Patterns in sequences 1
- Patterns in sequences 2
- Equations of sequence patterns
- Finding the 100th term in a sequence
- Sum of consecutive odd integers
- Challenge example: Sum of integers
- Integer sums
- 2003 AIME II problem 1
- Bunch of examples
- Mixture problems 3
Some of Sal's oldest (and roughest) videos on algebra. Great tutorial if you want to see what Khan Academy was like around 2006. You might also like it if you feel like Sal has lost his magic now that he doesn't use the cheapest possible equipment to make the videos.