Explore graphs of equations, exponents, counting problems, and more, emphasizing intuition and understanding over just finding an answer.
This course will deepen your knowledge of basic algebra and introduce you to some surprisingly useful applications of this powerful mathematical tool.
Describe the world with the language of algebra.
See the structure of algebraic relationships.
Coordinates give us the tools to describe locations with precision.
Reason about equations to uncover their properties and patterns.
Take a tour of the variety of shapes that equations can form.
Use graphs to solve problems that resist algebraic unpacking.
Sometimes x is unknown, and sometimes it's unknowable.
How much information is needed to pin down the exact combination?
How does the number of variables affect what can be known about the equations?
Practice solving multi-equation problems.
Explore the connections between lines and the equations that generate them.
Mostly, we just want to see the collisions!
Explore the algebra that describes motion and change.
Use these dangerous motion problems to practice and strengthen your skills!
Learn how to calculate the average of two speeds.
Speed becomes more complicated when what you're travelling in (a river) is also moving.
You'd be surprised how many contest these algebraic facts.
Identify and repair the mistakes in thinking that lead to these common errors.
The order in which you evaluate the parts of a calculation can have a huge impact on the outcome.
Understanding the ideas behind "cancelling" will keep you from making some common errors.
Test the limits of your understanding of addition, multiplication, and how they interact!