📗Algebra II

Treating polynomials as numbers you can add, multiply, and divide, and reading what a leftover remainder actually means.

Adding and Subtracting Polynomials · Multiplying Polynomials · Special Product Patterns · Dividing a Polynomial by a Monomial · +3 more

Cracking degree-three-and-up polynomials into their pieces, and reading what each piece says about the graph's roots.

Factoring by Grouping · Sum and Difference of Cubes · Factoring Higher-Degree Polynomials · The Rational Root Theorem · +3 more

The number that squares to negative one, what it does to the number line, and why multiplying by it is really a rotation.

The Imaginary Unit i · Powers of i · Adding and Subtracting Complex Numbers · Multiplying Complex Numbers · +4 more

Reading a polynomial's degree and leading coefficient like a weather forecast for what its graph does at the far edges.

End Behavior and the Leading Term · x-Intercepts and the Shape of a Polynomial Graph · Turning Points and Local Extrema · Graphing a Polynomial from Its Factors · +2 more

Fractions built out of polynomials, from simplifying and combining them to solving with them and catching the fakes.

Simplifying Rational Expressions · Multiplying and Dividing Rational Expressions · Adding and Subtracting Rational Expressions with Unlike Denominators · Simplifying Complex Fractions · +4 more

Roots and rational exponents as the same idea in two notations, and the equation-solving step that manufactures fake answers.

Rational Exponents · Simplifying Radical Expressions · Adding, Subtracting, and Multiplying Radicals · Rationalizing the Denominator · +2 more

Functions that grow by repeated multiplying, the inverse operation that undoes them, and the laws that turn products into sums.

Exponential Functions and Their Graphs · Transformations of Exponential Functions · Defining Logarithms as the Inverse of Exponentials · Graphing Logarithmic Functions · +7 more

Turning growth, decay, and compounding money into exponential equations you can actually solve for time or amount.

Exponential Growth and Decay Models · Half-Life and Radioactive Decay · Compound Interest · Continuous Compounding and the Number e · +1 more

Every parent function's family tree, stretched, shifted, reflected, chained together, and run in reverse.

Parent Functions and Their Graphs · Vertical and Horizontal Shifts · Vertical and Horizontal Stretches and Compressions · Reflecting Functions Across the Axes · +4 more

Lists of numbers built by a fixed rule, and what happens when you start adding every term in the list together.

Arithmetic Sequences · Arithmetic Series · Geometric Sequences · Finite Geometric Series · +3 more

Angles wrapped around a circle of radius one, and the wave that comes out when you unroll that circle into a line.

Angles in Standard Position and Radian Measure · The Unit Circle Definition of Sine and Cosine · Special Angles on the Unit Circle · The Unit Circle Unrolling into a Sine Wave · +4 more

Circles, parabolas, ellipses, and hyperbolas as literal slices through a cone, each with its own defining equation.

Conic Sections as Slices of a Cone · Circles in Center-Radius Form · Completing the Square to Find a Circle's Center and Radius · Parabolas Defined by a Focus and Directrix · +2 more

Where a line, a parabola, or a circle actually cross each other, and how many times they're allowed to.

Solving a System of a Line and a Parabola · Solving a System with a Circle and a Line · Solving a System of Two Conics · Counting the Solutions of a Nonlinear System Graphically · +1 more

Grids of numbers that add, multiply, and invert by their own peculiar rules, and how they solve a system in one shot.

Matrix Dimensions, Addition, and Subtraction · Scalar Multiplication of Matrices · Multiplying Two Matrices · The Identity Matrix · +4 more

Counting outcomes, weighing chance events, and describing how a whole batch of data spreads out around its center.

The Fundamental Counting Principle · Permutations · Combinations · Probability of Compound Events · +5 more