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.
Strengthen your algebra skills by exploring factorials, exponents, and the unknown.
Learn to solve exponent problems quickly and efficiently.
Play with lines and build an understanding of the equations that define them.
What kind of algebraic errors lead to obviously wrong conclusions?
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.
A powerful language for the very large and the very small.
Learn how to use scientific notation to more skillfully talk about very large and very small measures.
Derive the rules for combining exponential terms by thinking about exponents as repeated multiplication.
Learn to spot patterns that will help you simplify an exponential expression.
Learn how to interpret exponents that have a negative value.
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.
Bang! Now it's huge!
Learn how to efficiently count cases when there are several sequential choices.
Explore and practice techniques for efficiently manipulating factorials.
The large values produced by factorials become easier to work with when simplified or reduced.
Permutations count the number of ways things can be put in order.
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!