Algebra II

Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
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Manipulating functions

A great cook knows how to take basic ingredients and prepare a delicious meal. In this topic, you will become function-chefs! You will learn how to combine functions with arithmetic operations and how to compose functions. You will also learn how to transform functions in ways that shift, reflect, or stretch their graphs. Finally, you will learn about inverse functions and how to find them!

Introduction to complex numbers

Learn about complex numbers and how to add, subtract, and multiply them. This will come in useful when working with polynomials.

Arithmetic with polynomials

Learn how to add, subtract, multiply, and even divide polynomials.

Polynomial expressions, equations, and functions

Learn how to manipulate polynomials in order to prove identities and find the zeros of those polynomials. Use this knowledge to solve polynomial equations and graph polynomial functions. Learn about symmetry of functions.

Radical equations and functions

In this topic you will learn how to solve radical equations (which are equations with radical expressions in them) while avoiding extraneous solutions. You will also learn how to graph radical functions.

Rational expressions, equations, and functions

Rational expressions are like fractions, but instead of integers in the numerator and the denominator, you have variable expressions! Learn how to work with such expressions. Namely, simplify, add, subtract, multiply, and divide them (much like fractions!). Then, solve some equations with rational expressions in them, and analyze the behavior of rational functions.

Exponential growth and decay

Learn how to analyze and manipulate exponential functions and expressions in order to study their rate of change.

Exponential and logarithmic functions

Learn about logarithms, which are the inverses of exponents. Use logarithms to solve various equations. Then analyze both logarithmic and exponential functions and their graphs.

Advanced equations and inequalities

Learn how to approximate the solution to any kind of equation by graphing; Learn how to solve non-linear inequalities; Learn how to solve systems with more than two equations.

Advanced functions

Learn how to determine the domain, the range, and the graph of relatively advanced functions. Learn how to interpret advanced features of functions (like symmetry, end behavior, and periodicity) in terms of their context, and compare features of various types of functions. Learn about two-variable functions.

Modeling with algebra

Practice modeling problems with a variety of function types.

Conic sections

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



Old content

Content that is more basic and belongs in earlier missions than Algebra 2. This content will be removed from Algebra 2 soon.

Conic sections

A detailed look at shapes that are prevalent in science: conic sections
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All content in “Conic sections”

Conic section basics

What is a conic other than a jazz singer from New Orleans? Well, as you'll see in this tutorial, a conic section is formed when you intersect a plane with cones. You end up with some familiar shapes (like circles and ellipses) and some that are a bit unexpected (like hyperbolas). This tutorial gets you set up with the basics and is a good foundation for going deeper into the world of conic sections.


What would you call a circle that isn't a circle? One that is is is taller or fatter rather than being perfectly round? An ellipse. (All circles are special cases of ellipses.) In this tutorial we go deep into the equations and graphs of ellipses.


It is no hyperbole to say that hyperbolas are awesome. In this tutorial, we look closely at this wacky conic section. We pay special attention to its graph and equation.

Conics from equations

You're familiar with the graphs and equations of all of the conic sections. Now you want practice identifying them given only their equations. You, my friend, are about to click on exactly the right tutorial.

Conics in the IIT JEE

Do you think that the math exams that you have to take are hard? Well, if you have the stomach, try the problem(s) in this tutorial. They are not only conceptually difficult, but they are also hairy. Don't worry if you have trouble with this. Most of us would. The IIT JEE is an exam administered to 200,000 students every year in India to select which 2000 go to the competitive IITs. They need to make sure that most of the students can't do most of the problems so that they can really whittle the applicants down.