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!
Content

08. Exponential and logarithmic functions
09. Trigonometric functions 10. Advanced equations and inequalities 11. Advanced functions 12. Sequences and series 13. Modeling with algebra 14. Introduction to conic sections 
1. Manipulating functions
Combining functionsLearn how to take two basic functions and combine them into a new function which is their sum, difference, product, or quotient.
Composing functionsLearn what function composition is, how to to work with composite functions, and how to find the formulas of the composition of two functions.

Shifting functionsLearn how to transform functions so their graph is shifted horizontally or vertically. Learn how to find the equation of a function that is a shift of another function.
Stretching functionsLearn how to transform functions so their graph is stretched horizontally or vertically. Learn how to find the equation of a function that is a stretch of another function.

Modeling situations by combining and composing functionsMake use of knowledge in combining and composing functions, by modeling complex realworld situations.
Introduction to inverses of functionsLearn what inverses of functions are, and gain some experience with them by finding the outputs of the inverse of a function given that function.

Finding inverse functionsLearn how to find the inverses of polynomials functions, radical functions, and rational functions.
Verifying that functions are inversesLearn how to check whether a pair of functions are the inverses of one another.
Determining whether a function is invertibleLearn about the conditions for a function to be invertible, and learn how to manipulate functions to make them invertible.

2. Introduction to complex numbers
What are the imaginary numbers?Learn about the imaginary unit i (which is the square root of 1) and about imaginary numbers like 3i (which is the square root of 9).
What are the complex numbers?Learn about complex numbers (spoiler: they are numbers that consist of both real and imaginary parts).

The complex planeLearn how we can visualize complex numbers in a plane. This can be seen as an expansion of the 1dimensional real number line into a 2dimensional plane!
Adding and subtracting complex numbersLearn how to add or subtract complex numbers. For example, write (2+3i)(1+2i) as (1+i).
Multiplying complex numbersLearn how to multiply complex numbers using the fact that i^2=1 and the distributive property. For example, multiply (1+i) by (2+3i).

3. Arithmetic with polynomials
Adding and subtracting polynomialsLearn how to add and subtract two polynomials to obtain another polynomial. For instance, express (3x^3+2x1)+(2x^4x^3+7x) as a polynomial in standard form.
Multiplying polynomialsLearn how to multiply two polynomials to obtain another polynomial. For instance, express (2x^2+5)*(x^32x+6) as a polynomial in standard form.
Long division of polynomialsLearn how to divide two polynomials using long division.

Synthetic division of polynomialsLearn how to divide polynomials using long division.
Practice dividing polynomials with remaindersAfter learning about the different methods in which we can find the quotient and the remainder of two polynomials, gain some practice with actually performing polynomial division yourself.
Polynomial Remainder TheoremThe polynomial remainder theorem allows us to easily determine whether a linear expression is a factor of a given polynomial. Learn exactly what the theorem means, practice using it, and learn about its proof.

4. Polynomial expressions, equations, and functions
The binomial theoremLearn how to expand powers of binomial expressions (which are polynomial expressions with exactly two terms). This is done using the binomial theorem!
Understanding the binomial theoremNow that you know how to use the binomial theorem in order to expand powers of binomial expressions, let's gain further insight into why this actually works!
Factoring polynomials  Quadratic formsLearn how to factor quadratic polynomials of the form ax^2+bx+c as the product of two linear binomials. Learn how to identify these forms in more elaborate polynomials that aren't necessarily quadratic.

Factoring polynomials  Special product formsLearn how to factor quadratics that have the "perfect square" form and the "difference of squares" form. Learn how to identify these forms in more elaborate polynomials that aren't necessarily quadratic.
Advanced polynomial factorization methodsLearn more ways to factor polynomials with degree higher than 2.

Proving polynomial identitiesPractice proving polynomial identities, using all the factorization and expansion methods you know.
Polynomial identities with complex numbersProve more polynomial identities, this time including complex numbers!
Quadratic equations with complex numbersRemember all these quadratic equations with "no real solution"? Well, it turns out those equations do have a solution, it's just a complex number! Solve a bunch of those here.

The Fundamental Theorem of AlgebraYou may already have noticed that quadratic equations always have a solution when including complex number solutions. It turns out this is true for any polynomial equation, of any degree! Learn about this and more, right here.
Finding zeros of polynomialsUse all the knowledge you have about polynomials to find their zeros (which are the input values that make the polynomial equal to zero).
Zeros of polynomials and their graphsLearn how to use the zeros of polynomials to draw a pretty good sketch of their graphs.

End behavior of polynomial functionsLearn about the end behavior of polynomial functions. End behavior is the way the function behaves as the input values grow infinitely positive or infinitely negative.
Graphs of polynomialsCombine your knowledge about the zeros and the end behavior of a polynomial in order to sketch its graph.
Introduction to symmetry of functionsYou may already be familiar with types of symmetries of geometrical shapes. Learn how functions can be symmetrical too!
Symmetry of polynomial functionsLearn how to determine the symmetry of a polynomial function.

5. Radical equations and functions
Solving squareroot equationsLearn how to solve equations with squareroot expressions in them. For example, solve √(2x5)=√(73x).
Extraneous solutions of radical equationsLearn how to solve equations with cuberoot expressions in them. For example, solve ∛(26x)=x+3.

Solving cuberoot equationsLearn how to solve equations with cuberoot expressions in them. For example, solve ∛(26x)=x+3.
Domain of radical functionsLearn how the domain of radical functions is determined.
Graphs of radical functionsLearn how the graphs of radical functions look, and how we can reason about them using function transformations (i.e. shifts, stretches, etc.).

6. Rational expressions, equations, and functions
Learn what rational expressions are and about the values for which they are undefined.
Intro to rational expressionsSimplifying rational expressionsLearn how to simplify rational expressions by canceling factors that are shared by the numerator and the denominator. Sometimes this calls for factoring the numerator and the denominator in various ways.
Multiplying & dividing rational expressionsLearn how to multiply and divide rational expressions. You will be surprised to see how similar it is to multiplying and dividing fractions!

Adding & subtracting rational expressionsLearn how to add and subtract rational expressions. Like multiplication and division, this skill has a remarkable affinity to adding and subtracting fractions!
Nested fractionsLearn how to simplify rational expressions that contain further rational expressions within their numerators or denominators.
Solving rational equationsLearn how to solve equations that have a rational expression, or a few of those.

Direct and inverse variationLearn about direct and inverse variation, which are two types of relationships between two quantities. Direct variation is simply a proportional relationship, but inverse variation is more complicated and interesting. Gain some experience with it before we dive deeper into the world of rational functions.
End behavior of rational functionsLearn about the ways in which rational functions behave as x approaches positive or negative infinity. This gets interesting Learn how to determine this behavior for any kind of rational function.

Discontinuities of rational functionsLearn about the ways in which rational functions behave when their denominator is equal to zero. This gets interesting when vertical asymptotes are involved! Learn how to determine this behavior for any kind of rational function.
Graphs of rational functionsCombine your knowledge of intercepts, horizontal asymptotes, vertical asymptotes, and removable discontinuities, in order to analyze entire graphs of rational functions!
Modeling with rational functionsSee some examples of how rational functions and equations can come in handy when solving realworld word problems.

7. Exponential growth and decay
Equivalent forms of exponential expressionsLearn how to manipulate exponential expressions in different ways. For example, rewrite 8^x as 2^(3x).
Solving exponential equations using properties of exponentsLearn how to solve advanced exponential equations by manipulating the expressions in the equations using the properties of exponents. For example, solve 2^(x+1)=8^x by rewriting 8^x as 2^(3x) and then equating x+1=3x.

Introduction to rate of exponential growth and decayLearn about different ways of describing the rate of change of exponential functions.
Interpreting the rate of change of exponential modelsLearn how to analyze exponential modeling functions in order to find their rate of change.

Constructing exponential models according to rate of changeLearn how to find the modeling function of an exponential real world context, according to the description of its rate of change.
Advanced interpretation of exponential modelsLearn how to interpret an exponential modeling function by first manipulating it according to your needs. For example, rewrite 5^(2x+1) as 5*25^x to find that the unit growth factor is 25.
Distinguishing between linear and exponential growthLearn how to analyze realworld quantitative relationships given as tables of values to determine whether they represent linear growth or exponential growth.

8. Exponential and logarithmic functions
Introduction to logarithmsLearn how we define logarithms and use this definition in order to evaluate various logarithms. For example, evaluate log_2(8) as 3 by realizing that 2^3=8.
The constant e and the natural logarithmLearn about a very special constant in math that has a pivotal role in the world of exponential and logarithmic function, the constant e.
Properties of logarithmsLearn about special properties of logarithms that help us rewrite logarithmic expressions in different equivalent (much like we use properties of exponents to rewrite exponential expressions!).

The change of base formula for logarithmsThis is very helpful for evaluating logarithms with a calculator, which only evaluates base10 and basee logarithms.
Logarithmic equationsLearn how to solve equations that contain logarithmic expressions. For example, solve log(x)+log(3)=log(7).
Solving exponential equations with logarithmsLearn how to solve any exponential equation by using logarithms. For example, solve 2^x=3 by calculating log_2(3).

Solving exponential modelsLearn how to solve word problems that require exponential equations.
Graphs of exponential functionsLearn about the graphs of advanced exponential functions of the form y=a*b^(x+c)+d.
Graphs of logarithmic functionsLearn about the graphs of logarithmic functions, and how they relate to graphs of exponential functions.
Logarithmic scaleEnrich your knowledge with some videos about logarithmic scales and how useful they are.

9. Trigonometric functions
Introduction to radiansLearn about radians, which are the official unit of measurement for angles in algebra (in contrast to degrees, which are used in geometry).
The unit circle definition of sine, cosine, and tangentLearn how the trigonometric ratios are extended to all real numbers using algebra. Start solving simple problems that involve this new definition of the trigonometric functions.
The graphs of sine, cosine, and tangentLearn how the graphs of y=sin(θ), y=cos(θ), and y=tan(θ) look, using the unit circle definition of the functions.

Basic trigonometric identitiesLearn about very useful trigonometric identities that arise by considering different properties of the unit circle definition.
Trigonometric values of special anglesLearn how to find the trigonometric values of some special angles without the use of a calculator.
The Pythagorean identityProve the Pythagorean trigonometric identity for all real numbers and use it in order to solve problems.
Introduction to amplitude, midline, and extrema of sinusoidal functionsLearn about very important features of sinusoidal functions: the amplitude and the midline. Learn how they relate to the extremum points of the function.

Finding amplitude and midline of sinusoidal functions from their formulasLearn how to find the amplitude and the midline of the graph of a sinusoidal function from its formula. For example, find the amplitude and the midline of f(x)=3*sin(2x1)+5.
Period of sinusoidal functionsLearn about the period of sinusoidal functions: how it relates to extremum points and the midline, and how to find it from the formula of the function. For example, find the period of f(x)=3*sin(2x1)+5.
Graphing sinusoidal functionsLearn how to draw the graph of sinusoidal functions. For example, draw the graph of f(x)=2*cos(πx)7.
Constructing sinusoidal functionsLearn how to find the formula of a sinusoidal function from its graph or a few selected features. Model realworld situations with sinusoidal functions.

10. Advanced equations and inequalities
Solving equations by graphingLearn how to approximate the solution to any equation by using the power of graphs.
Quadratic inequalitiesLearn how to solve inequalities that contain quadratic expressions. For instance, solve x^2+3x+2>0.
Rational inequalitiesLearn how to solve inequalities that contain rational expressions. For instance, solve (x3)/(x+4)≥2..
Systems with three variablesLearn how to make the most out of the familiar algebraic techniques in order to solve systems of three equations with three variables.

11. Advanced functions
Determining the domain of advanced functionsLearn how to determine the domain of piecewise functions with different function rules.
Determining the range of a functionLearn how to find the range of a function, which is the set of all of the function's possible outputs.
Graphing nonlinear piecewise functionsLearn how to graph piecewise functions whose assignment rules are not linear.
Interpreting the symmetry of algebraic modelsLearn how to interpret graphs of modeling functions in terms of their context by considering their symmetry.

Interpreting the end behavior of algebraic modelsLearn how to interpret graphs of modeling functions in terms of their context by considering their end behavior.
Interpreting the periodicity of algebraic modelsLearn how to interpret graphs of modeling functions in terms of their context by considering their periodicity.
Comparing features of functionsLearn how to compare various features between two functions, each represented in a different way.
Twovariable functionsLearn about functions that take *two* inputs in order to output a single value.

12. Sequences and series
Arithmetic sequencesReview arithmetic sequences before you dive into arithmetic series.
Basic sigma notationLearn how to use and interpret sigma notation. Hint: It means take the sum!
Finite arithmetic seriesLearn how to evaluate and work with finite arithmetic series.

Geometric sequencesReview geometric sequences before you dive into geometric series.
Finite geometric seriesWhether you are computing mortgage payments or calculating how many users your website will have after a few years, geometric series show up in life far more than you imagine. This tutorial will review all the important concepts and more!
Finite geometric series applicationsApply what you've learned about geometric series to model situations in some fun word problems.

13. Modeling with algebra
Modeling with onevariable equations and inequalitiesLearn how to determine the appropriate *type* of modeling equation (or inequality) according to the description of a realworld context.
Manipulating formulasLearn how to solve problems that involve multivariable formulas.

14. Introduction to conic sections
Introduction to conic sectionsConic sections are formed when you intersect a plane with a cone. In this tutorial, you will learn more about what makes conic sections special.
The features of a circleLearn about the graphs of circles, and how their center and radius are represented algebraically.
Standard equation of a circleLearn about the standard form to represent a circle with an equation. For example, the equation (x1)^2+(y+2)^2=9 is a circle whose center is (1,2) and radius is 3.

Expanded equation of a circleLearn how to analyze an equation of a circle that is not given in the standard form. For example, find the center of the circle whose equation is x^2+y^2+4x5=0.
Focus and directrix of a parabolaA parabola is the set of all points equidistant from a point (called the focus) and a line (called the directrix). In this tutorial you will learn about the focus and the directrix, and how to find the equation of a parabola given its focus and directrix.
