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Algebra I

Strengthen your algebra skills by exploring factorials, exponents, and the unknown.

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.

Interactive
quizzes

39

Concepts and
exercises

375+
  1. 1

    Introduction

    Strengthen your algebra skills by exploring factorials, exponents, and the unknown.

    1. Exponent Shortcuts

      Learn to solve exponent problems quickly and efficiently.

    2. Line Exploration

      Play with lines and build an understanding of the equations that define them.

    3. When 1 = 2

      What kind of algebraic errors lead to obviously wrong conclusions?

  2. 2

    Equations and Unknowns

    Sometimes x is unknown, and sometimes it's unknowable.

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      Combination Locks

      How much information is needed to pin down the exact combination?

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      Equations and Variables

      How does the number of variables affect what can be known about the equations?

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      Scaling and Adding Equations

      Practice solving multi-equation problems.

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      Graphing Equations

      Explore the connections between lines and the equations that generate them.

  3. 3

    Manipulating Exponents

    A powerful language for the very large and the very small.

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      Orders of Magnitude

      Learn how to use scientific notation to more skillfully talk about very large and very small measures.

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      Same Bases 1

      Derive the rules for combining exponential terms by thinking about exponents as repeated multiplication.

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      Same Bases 2

      Learn to spot patterns that will help you simplify an exponential expression.

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      Negative Exponents

      Learn how to interpret exponents that have a negative value.

  4. 4

    Algebra in Motion

    Mostly, we just want to see the collisions!

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      Distance, Rate, and Time

      Explore the algebra that describes motion and change.

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      Stunt Driving and Collisions

      Use these dangerous motion problems to practice and strengthen your skills!

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      The Harmonic Average

      Learn how to calculate the average of two speeds.

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      Boats

      Speed becomes more complicated when what you're travelling in (a river) is also moving.

  5. 5

    Factorials

    Bang! Now it's huge!

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      Counting and Factorials

      Learn how to efficiently count cases when there are several sequential choices.

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      Factorials

      Explore and practice techniques for efficiently manipulating factorials.

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      Operations and Simplification

      The large values produced by factorials become easier to work with when simplified or reduced.

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      Permutations

      Permutations count the number of ways things can be put in order.

  6. 6

    Common Misconceptions

    You'd be surprised how many contest these algebraic facts.

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      The Basics

      Identify and repair the mistakes in thinking that lead to these common errors.

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      Ordering and Reordering

      The order in which you evaluate the parts of a calculation can have a huge impact on the outcome.

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      Two Kinds of Cancel

      Understanding the ideas behind "cancelling" will keep you from making some common errors.

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      The Distributive Property

      Test the limits of your understanding of addition, multiplication, and how they interact!