AII.1.0: Students solve equations and inequalities involving absolute value.

Inequalities Involving Absolute Values
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

AII.2.0: Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices.

Modeling Linear Systems - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A
Systems of Linear Inequalities (Slope-intercept form) - Activity A

AII.3.0: Students are adept at operations on polynomials, including long division.

Dividing Polynomials Using Synthetic Division

AII.4.0: Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

AII.5.0: Students demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically. In particular, they can plot complex numbers as points in the plane.

Points in the Complex Plane - Activity A

AII.7.0: Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including those with negative exponents in the denominator.

Addition of Polynomials - Activity A
Dividing Exponential Expressions
Multiplying Exponential Expressions

AII.8.0: Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the complex number system.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Roots of a Quadratic

AII.9.0: Students demonstrate and explain the effect that changing a coefficient has on the graph of quadratic functions; that is, students can determine how the graph of a parabola changes as a, b, and c vary in the equation y = a(x - b)² + c.

Parabolas - Activity A
Quadratics in Factored Form
Roots of a Quadratic
Translating and Scaling Functions

AII.10.0: Students graph quadratic functions and determine the maxima, minima, and zeros of the function.

Cubic Function Activity
Function Machines 2 (Functions, Tables, and Graphs)
Parabolas - Activity A
Polynomials and Linear Factors
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

AII.11.2: Students judge the validity of an argument according to whether the properties of real numbers, exponents, and logarithms have been applied correctly at each step.

Dividing Exponential Expressions
Exponents and Power Rules

AII.12.0: Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Half-life
Simple and Compound Interest

AII.15.0: Students determine whether a specific algebraic statement involving rational expressions, radical expressions, or logarithmic or exponential functions is sometimes true, always true, or never true.

Exponential Functions - Activity A
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Simplifying Radicals - Activity A

AII.16.0: Students demonstrate and explain how the geometry of the graph of a conic section (e.g., asymptotes, foci, eccentricity) depends on the coefficients of the quadratic equation representing it.

Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A

AII.17.0: Given a quadratic equation of the form ax² + by² + cx + dy + e = 0, students can use the method for completing the square to put the equation into standard form and can recognize whether the graph of the equation is a circle, ellipse, parabola, or hyperbola. Students can then graph the equation.

Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A

AII.18.0: Students use fundamental counting principles to compute combinations and permutations.

Permutations
Permutations and Combinations

AII.19.0: Students use combinations and permutations to compute probabilities.

Binomial Probabilities
Permutations
Permutations and Combinations
Spin the Big Wheel! (Probability)

AII.22.0: Students find the general term and the sums of arithmetic series and of both finite and infinite geometric series.

Arithmetic Sequences

AII.24.0: Students solve problems involving functional concepts, such as composition, defining the inverse function and performing arithmetic operations on functions.

Addition and Subtraction of Polynomials

AII.25.0: Students use properties from number systems to justify steps in combining and simplifying functions.

Addition and Subtraction of Polynomials